D60's ( APS-C )sensor is too small to stop down below f/11?

[zilch0md]

Consider this before purchasing a Canon EOS D60: If your goal is to achieve a resolution of 5 lp/mm in an 8x10 print, you will not be able to stop down further than f/11, thanks to the visible diffraction that will be magnified from the D60's tiny CMOS. Quite simply, this camera has too many pixels for its sensor size.

The rules that govern diffraction apply to digital photography just as they do when using film. Diffraction's Airy disks become visible in the final print and thus, spoil the apparent sharpness, when their diameter reaches whatever goal you've set for overall resolution.

Many people say that we should strive to achieve an on-print resolution of 8 lp/mm, but for this discussion, let's shoot for a more relaxed goal of only 5 lp/mm in the final print.

The diameter of diffraction's Airy disk, at the sensor (or at the film plane), before magnification is easy to calculate:

For all lenses and all formats it is simply:

Diameter Airy Disk = N * 0.00135383mm

(This assumes a frequency of 555nm - yellow-green light, at the center of the visible spectrum.)

So at f/11, for example, on any lens, any format size, film or digital, the Airy disks will have a diameter of:

11 * 0.00135383 = 0.0149mm

To convert the diameter of a spread function to its equivalent in lp/mm, just take the reciprocal:

f/11 Airy disk at sensor = 1 / 0.0149mm
= 67.1 lp/mm

That's at the sensor or film plane, not in the print.

Now, what will the Airy Disk diameter be after magnification to our final print size?

That portion of the D60's CMOS sensor which delivers the maximum file size of 3072 x 2048 pixels measures only 22.7mm by 15.1mm (0.8937in. by 0.5945in.)

Let's assume we will create the largest print we can at a data density of 300 dpi, without resampling. The EOS D60's 3200 x 2048 file will therefore print to a

300 dpi print size = 10.67in. x 8.27in.

How about that? We can actually get an 8x10 print out of this camera, but...

What's the enlargement factor necessary to get from our sensor size of 0.8937in. by 0.5945in. all the way to our print size of 10.67in. x 8.27in.?

The enlargement factor is 11.94x

So, if the f/11 Airy disk diameter at the sensor is 0.0149mm, after 11.94x magnfication it will be

f/11 Airy disk on-print = 0.0149mm * 11.94
= 0.1779mm
the reciprocal of which is:
= 1 / 0.1779mm
= 5.62 lp/mm

Ahhh.... we're safe at f/11 - diffraction's Airy disk diameters will be SMALLER than the reciprocal of our target on-print resolution of 5 lp/mm. Diffraction will not be visible in this print as long as the viewer is far enough away to resolve no more than 5 lp/mm (a viewing distance of roughly ten inches).

Let me do the same math as above for f/16 - skipping right to the bad news:

f/16 Airy disk on print = 0.2586mm
the reciprocal of which is: 3.87 lp/mm Oops!

At f/16, thanks to the D60's small sensor vulnerability to diffraction, it will be impossible to resolve 5 lp/mm. We'll only manage to deliver 3.87 lp/mm to a 300 dpi print from the 3200 x 2048 file. The pixels are there, sure enough, but the sensor is too small to exploit them at apertures smaller than that had at f/11. The enlargement factor is too great.

That's the truth.

The really incredile story here is that Canon actually makes their own CMOS sensors. They should know better to than to squeeze so many pixels on so small a sensor. Quite simply, if the sensor were larger, the enlargement factor necessary to make the 300 dpi print would be smaller -AND- if as the enlargement factor were smaller, pixel count remaining the same, diffraction's Airy disk diameters would shrink proportionately and we could stop down further than f/11 without inducing visible diffraction in our prints.

Throwing more salt into this gaping wound, I'll add that at f/22, the Canon EOS D60 will only be able to resolve 2.81 lp/mm in a 300 dpi print made from its 3200 x 2048 pixel files.

It gets worse: If you consider some people believe 8 lp/mm to be the the limit of human resolving power instead of 5 lp/mm (see: Michael Reichmann's "Understanding Sharpness page at http://luminous-landscape.com/sharpness.htm) and decide to set that as your goal resolution in the final print, you'll have to first increase your data density from 300 dpi to 406 dpi. The good news is that this will shrink your enlargement factor because your final print will now be:

406 dpi print size = 7.88in. by 5.04in.

Well, it was nice thinking about 8x10's for a little while...
Now we're down to 8x5, but these will be sharp enough to tolerate the most critical scrutiny (at 8 lp/mm.)

Our enlargement factor is now only 8.82x instead of 11.94x (which is a good thing in regards to avoiding diffraction!)

So, can we use f/22 if we intend to make 406 dpi prints from our 3200 x 2048 files coming from the EOS D60's 22.7mm by 15.1mm sensor?

Nope! Even at this smaller enlargement factor, diffraction will prevent us from getting more than 3.81 lp/mm at f/22. That's not only less than 8 lp/mm, it's less than 5 lp/mm. Oh well.... stay away from f/22.

How about f/16?

Nope! f/16 will allow us to resolve 5.24 lp/mm, but nothing larger, definitely not the 8 lp/mm we're aiming for. So, we can't use f/16 when making 300 dpi 5 lp/mm prints, but we can use it when making the smaller, sharper, 406 dpi 8 lp/mm prints. Is that good news?

How about f/11?

Almost! f/11 will yield Airy disks, after magnification to our 406 dpi 8x5in prints, that are small enough to allow us to resolve 7.61 lp/mm. That's nearly 8 lp/mm.

In a nutshell, the EOS D60's sensor is too small to allow us to exploit the DoF we could enjoy were we not diffraction-limited to using apertures no smaller than f/11.

I've done the math. Wake me up when someone is making $1,000 digital cameras with 60.7 Megapixels on 61x77.5mm (MF) sensors, for 7 lp/mm resolution, 20x25-inch prints that will have no visible diffraction at f/16. Until then, I'll stick with 6x7cm Provia 100F and Mamiya 7II's.

Mike Davis

[D60wannabe]

WOW!

Wake me up when any of this makes sense! Just a thought....When "science" tries to explain why a Bumblebee flies, it says it can't......;)

Paul

[sudaplatov]

But he is right.
Couple months ago I decided to buy D30 instead
of D60 (I knew it would be available soon) because
of described reason.
I prefer to use D30 now and wait till good digital
Canon SLR with big enough sensor.
Actually big sensor will solve to problems - one
described above and focal multiplier problem, I mean
full size sensor of course.

[Vipermike]

http://www.luminous-landscape.com/d60.htm

[zilch0md]

Hi Paul!

D60wannabe wrote:
WOW!

Wake me up when any of this makes sense! Just a thought....When "science" tries to explain why a Bumblebee flies, it says it can't......;)

Paul

The EOS D60 bumblebee crashes and burns at stops smaller than f/11. It is truly incapable of resolving even 5 lp/mm in a 300 dpi print if you make the mistake of using f/16 or f/22 with the 3200x2048 mode. It's more like a bummer-bee than a bumblebee.

Mike Davis

[zilch0md]

Hi!

sudaplatov wrote:
But he is right.
Couple months ago I decided to buy D30 instead
of D60 (I knew it would be available soon) because
of described reason.
-snip-


Thanks! I'm glad it made sense to someone. Yes, the D30's pixel density is perfectly matched to its sensor size - I once calculated that its sensor is just large enough to permit use of f/22 without causing Airy disks to be larger than 5 lp/mm in a 300 dpi print for the file sizes it generates. I remember writing a friend about it, saying how impressed I was that Canon had made the D30's sensor exactly the right size relative to its resolution to avoid visible diffractiona at f/22. Now they've gone and blown it with the D60. I guess the D30's design was a fortuitous accident in this regard - either that or they figured nobody would catch the diffraction problem when they decided to save bucks by avoiding a larger sensor as they increased the pixel density.

But we're wide awake out here... Back to the drawing board guys!

Mike Davis

[zilch0md]

Vipermike wrote:
http://www.luminous-landscape.com/d60.htm

Yeah, he makes no mention of the diffraction problem. Zzzzzzz....

Mike Davis

[edhofler]

I think you're supposed to use the numerical aperture not the fstop in Diameter Airy Disk = N * 0.00135383mm.

To solve for the radius (r) of the central disk in the Airy pattern you would use the following:

r=(1.22 x wavelength)/(2 x n.a.)

and n.a. = 1/2 x fstop

Try your formula with the numerical aperture and the results are very different.

[D60wannabe]

zilch0md wrote:
Hi Paul!

D60wannabe wrote:
WOW!

Wake me up when any of this makes sense! Just a thought....When "science" tries to explain why a Bumblebee flies, it says it can't......;)

Paul

The EOS D60 bumblebee crashes and burns at stops smaller than f/11. It is truly incapable of resolving even 5 lp/mm in a 300 dpi print if you make the mistake of using f/16 or f/22 with the 3200x2048 mode. It's more like a bummer-bee than a bumblebee.

Mike Davis


Mike,

Now you got me thinking........

I did some checking and found this web-page with a home made computer program on it that I believe addresses this "problem". It is here:

http://home.t-online.de/home/mrimkus/diffmain.htm

I didn't have time to really look it over and/or download it but maybe this will help with the calculation questions. Let me know what you think!

Paul

[edhofler]

Paul

Looks interesting, I'm gonna play with it later today.

My equation for n.a. should have been:
n.a.=1/(2 x f/stop)

Ed

[fastlane65]

it shure do make pertty piktures, dont it

[zilch0md]

Hi!

edhofler wrote:
I think you're supposed to use the numerical aperture not the fstop in Diameter Airy Disk = N * 0.00135383mm.

To solve for the radius (r) of the central disk in the Airy pattern you would use the following:

r=(1.22 x wavelength)/(2 x n.a.)

and n.a. = 1/2 x fstop

Try your formula with the numerical aperture and the results are very different.

David Jacobson's Lens Tutorial (http://www.photo.net/learn/optics/lensTutorial ) shows the formula used as I am using it - with N being the stop (5.6, 8, 11, 22, etc.)

Another reference that supports this formula is my favorite text on photography: "Basic Photographic Materials and Processes" by Stroebel, Compton, Current and Zakia; (c)1990 Focal Press. See the section on Diffraction (pp 168 to 170).

I'm confident my math is correct.

Thanks,

Mike Davis

[zilch0md]

Paul,

D60wannabe wrote:
-snip-
Mike,

Now you got me thinking........

I did some checking and found this web-page with a home made computer program on it that I believe addresses this "problem". It is here:

http://home.t-online.de/home/mrimkus/diffmain.htm

I didn't have time to really look it over and/or download it but maybe this will help with the calculation questions. Let me know what you think!

Paul

That's a neat page - haven't seen it before. It will take me awhile to digest it, but at first glance, I'm not sure if it can either prove or disprove my contention that we must avoid stopping down below f/11 with the EOS D60 to avoid visible diffraction.

In any case, I'm very comfortable with the math. I'm not the only person on the planet that is aware of this problem with digicam sensors being too small. Diffraction is a very real phenomenon, which cannot be engineered out of the optics. It's always there - it only becomes visible when it's Airy disk diameters exceed a size that we can resolve with our naked eyes, when scrutinizing the final print. We WILL see it's degrading effects on image clarity whenever the Airy disk diameters become large enough to be resolved by the human eye in the final print, after magnification, at a given viewing distance. If we set as our goal to keep diffractions's Airy disks smaller than the reciprocal of 5 lp/mm (a very generous figure - some would say our eyes can resolve 8 lp/mm) in a final print that's intended for viewing at a distance of 10 inches, the Canon EOS D60 will fail to meet that goal if we stop down below f/11, with any lens, any subject. That's a fact.

Mike Davis

[edhofler]

Mike

Thanks, it's going to take a little time to digest the info on your link.

My source is http://micro.magnet.fsu.edu/primer/java/imageformation/rayleighdisks/

Ed

[raymo960]

Hmm, I am not sure I understand any of this but I just went ahead a took a picture with my D60 at f22 and 1/30 second. I've loaded the image on my computer and have blown it up to see actual pixels. The image looks great to me!

I don't see any problems at all.
//Ray

[oops]

My Lord! I love you guys!

Thanks for all the research, hard work, and links displayed here. I appreciate the work and hours @ 56k. I can't even keep up with the links/sub-links!

Just a simple "thanks" from one who doesn't have the time or background to analyze this topic.

Keep bang'in away!

[zilch0md]

Hi Ray!

raymo960 wrote:
Hmm, I am not sure I understand any of this but I just went ahead a took a picture with my D60 at f22 and 1/30 second. I've loaded the image on my computer and have blown it up to see actual pixels. The image looks great to me!

I don't see any problems at all.
//Ray

It's difficult to notice diffraction without doing a careful side-by-side comparison of a print where the Airy disk diameters exceeded the reciprocal of 5 lp/mm vs. one where they did not. Try comparing a 300 dpi print made from the D60 at f/22 to the same image taken at f/11. Be careful to choose a subject where f/11 provides plenty of depth of field for the near and far distances. We're not trying to compare DoF at f/22 vs. f/11. Shooting something like a tapestry hanging on a wall at 90-degrees to the lens axis would be an ideal target for this comparison.

Many people who shoot 35mm know to stay away from f/22 - others ignore the warning and have no problem with the results they get. It is somewhat subjective, but the fact is, the Canon EOS D30 (predecessor to the D60) is an improvement over the 35mm format in this regard - you can actually use f/22 without concern for visible diffraction in a 300 dpi print (vs. what the proportionately larger print from 35mm). The Canon EOS D60, however, doesn't even equal the performance of 35mm in this regard, much less the D30. At just beyond f/11, the D60 will suffer the same diffraction had with 35mm format at f/16. If you shoot the D60 at f/16 or f/22 and don't have a problem with less than 5 lp/mm resolution, you just aren't as discrimanating as some people.

Mike Davis

[rootcausefound]

Here's an interesting article about PowerShot G1 that uses much smaller 3.34 megapixel CCD.

http://www.canon.com/camera-museum/tech/report/200101/report.html#t5

Here you can find the following sentence.
"The reason that the minimum aperture is restricted at f/8 is to prevent the degradation of the image reproduction capability due to diffraction.?h

This supports Mike's speculation is correct and even Canon has already been aware of that problem.

So we'd better choose the correct stop value when using D60.

(Well, I haven't got D60 yet....)

[edhofler]

Mike

Have you considered how the Bayer algorithm fits into this?

The camera is effectively taking the results of at lease 3 pixels and combining them to get color. This would increase the effective pixel size by a factor of 3 (in some respects).

I still come up with different results then you. It’s bugging me enough to spend the time to figure out who is correct. I’ll get back to you when time permits (a day or two).

Haven’t had this much fun since physics class.

Ed

[zilch0md]

Hi!

rootcausefound wrote:
Here's an interesting article about PowerShot G1 that uses much smaller 3.34 megapixel CCD.

http://www.canon.com/camera-museum/tech/report/200101/report.html#t5

Here you can find the following sentence.
"The reason that the minimum aperture is restricted at f/8 is to prevent the degradation of the image reproduction capability due to diffraction.?h

This supports Mike's speculation is correct and even Canon has already been aware of that problem.

So we'd better choose the correct stop value when using D60.

(Well, I haven't got D60 yet....)


Yes, several of Sony's cameras can not stop down below f/8 and I've always assumed it was because they acknowledged the diffraction issue. I appreciate you providing this reference as evidence this is a real problem. I've been using these formulae for years and recognize that I have to spell everything out for people who both enjoy photography and even produce wonderful results without understanding the bits and the bytes. Still, it's often frustrating to know that the sky is blue and try to prove it in a world where everyone is color blind.

Again, with appreciation for your intent, I have to respond to your use of the word "speculation." The math I have used is sound and long understood by people much more knowledgable about optics than I am. Everything I've said about the limitations of the EOS D60 are facts, evidenced by well-documented formulas which can be applied to the specifications Canon has provided for the camera. I haven't made any speculations.

Their Powershot G1 does not accept lenses designed for Canon's 35mm bodies. Canon engineers were able to design in an f/8 restriction when they built the lens for the G1, because they designed it purposely for that sensor. I will specualate that Canon knew exactly what they were doing when they put too many pixels on their D60 sensor - so many that visible diffraction is unavoidable at f/16 and f/22. Once Canon made the decision to limit production costs by keeping the sensor size at basically the same size as it was in the D30, while simultaneously offering more pixels, they had two choices: Tell the consumer to avoid stopping down below f/11 or don't tell them. I suspect most people will be content with the results they get at f/16 and f/22. They won't know what they're missing.

Mike Davis

[zilch0md]

Ed,

edhofler wrote:
Mike

Have you considered how the Bayer algorithm fits into this?

The camera is effectively taking the results of at lease 3 pixels and combining them to get color. This would increase the effective pixel size by a factor of 3 (in some respects).

I still come up with different results then you. It’s bugging me enough to spend the time to figure out who is correct. I’ll get back to you when time permits (a day or two).

Haven’t had this much fun since physics class.

Ed


Here's an analogy that might help. Imagine a "projected" Airy disk intersecting the film or sensor plane to be like a wedding band tossed onto a bed covered with a finely patterned quilt (except that there are actually gezillions of rings, overlapping each other, covering the entire surface.) Now, let's push the bed outdoors and hover directly above it in a helicopter. From 1000 feet overhead, we probably won't be able to detect the ring's presence on the bed, but as we descend closer to the bed, an adult with healthy vision, hanging out of the helicopter, looking straight down, will eventually be able to detect the ring's presence at some distance over the bed. Now, tell the pilot to hold that altitude and consider this analagous to our viewing distance to the print (I've chosen 10-inches throughout this discussion as the closest distance at which someone is likely to scrutinize a print - most adults with healthy vision can't focus any closer than that.) OK, stay with me... imagine we replace the bed with a wire-mesh screen stretched taught in a frame. The bed and it's quilt were the subject matter of our picture, but the wire-mesh screen is the combined resolving power of our image-making system and it supports everything that can be seen.

Now our wedding band is a very special ring in that it changes diameter as we turn the f/stop dial on our camera lens. As we stop down, it gets larger. As we open up, it gets smaller. The goal is to make the ring disappear from the view of the guy in the helicopter because it (and its many siblings) interfere with our ability to see the quilt's pattern with clarity. One way to get rid of the ring would be to increase the coarseness of the wire mesh (reduce our resolving power) until the mesh is so coarse, the ring drops through, out of view. Another way to make the ring disappear from view is to simply shrink the ring (by opening up a stop or two) until the guy in the helicopter says he can't resolve it from his viewing position. But get this: Once we've made it small enough for him not to see at his viewing distance, it can still be lying there, supported by a wire mesh that's fine enough to hold it. It's just too small to be seen from the helicopter - but that's just fine. That's what they did with the Powershot GS1 when they designed the lens with an f/8 limit. The Airy disks are there, but they just aren't large enough to be resolved in the final print after magnification. (By limiting the lens to f/8, they made it impossible to increase the diameter of diffraction's Airy disks to a size large enough be seen in prints produced by that camera.)

So, no matter how fine our mesh is, the ring will be resolvable IF it's large enough to be seen by the viewer hovering in the helicopter. And: Making the mesh coarse enough to allow the ring to fall through becomes foolish at the point that you can no longer resolve the pattern of the quilt you're trying to photograph. Clearly, it's smarter to shrink the ring than it is to limit the number of pixels you have on your sensor for the sake of avoiding diffraction.

Punchline: With any mesh fine enough to deliver adequate resolution of the quilt's pattern, the issue is reduced to only one question: Is the ring so large it can be seen by the viewer at the anticipated viewing distance?

Dropping the analogy, I'll say it this way: Once an Airy disk has been enlarged to a final print size that's great enough for us to see, it will degrade image clarity. At a viewing distance of 10 inches, that size is said to be 0.2mm (equivalent to 5 lp/mm) - the limits of resolution of the human eye (Some say it's as high as 8 lp/mm). So, whatever the resolving power of the system is at the print, if it's enough to deliver a really sharp image of our intended subject matter (the D60's 2000 pixels for an 8-inch print will deliver 5 lp/mm), it will be fine enough to deliver undesirably large airy disks, too. Shrink the Airy disk diameters to less than 0.2mm in the final print and you'll have no visible softening of the image due to diffraction. You can do that by opening up more stops -or- by increasing the size of the sensor so that the Airy disks aren't magnified as much when making the same sized print.

Going back to the analogy briefly, instead of shrinking the ring, we could enlarge the bed and then ask the pilot to ascend to whatever height makes the bed occupy the same angle of view as it did before. Voila - the ring becomes invisible without having to open up to wider apertures, but we get the same sized print.

Again: In going from the D30 to the D60, Canon should have increased the sensor size in proportion to the increase in number of pixels.

Mike Davis

[edhofler]

Mike

Would you have the same problem going from a course-grained film to a fine-grained film?

If the overall resolving power of the digital recording system (not including the lens) is less then film wouldn't the Airy disk problem still be less of an issue with the D60 then, lets say, a good slide film?

That is to say that if the Airy disk problem becomes an issue with sharpness as you move from the pixel density of the D30 to the D60 wouldn't it be even more of a problem with film, which has an even higher "pixel density"?

What you’re saying in your analogy is that you are looking to keep the diameter of the Airy disk smaller then one pixel.

Ed

[sudaplatov]

Mike!
It looks like your arguments could be very
interesting for quite a big number of people.
Moreover, they may change general attitude to D60.
Could you make them more public?
Ivan

[Geert]

Mike wrote:
``I will specualate that Canon knew exactly what they were doing when they put too many pixels on their D60 sensor - so many that visible diffraction is unavoidable at f/16 and f/22. Once Canon made the decision to limit production costs by keeping the sensor size at basically the same size as it was in the D30, while simultaneously offering more pixels, they had two choices: Tell the consumer to avoid stopping down below f/11 or don't tell them. I suspect most people will be content with the results they get at f/16 and f/22. They won't know what they're missing.''

This is of course not a very useful statement, and even misleading. It is well-known that on all cameras diffraction limits resolution. A rule of thumb is that you get the best resolution when stopping down 2 or 3 stops from wide open aperture. You make it sound as if resolution at say f/16 would be worse on a D60 than on a D30. That is not true.

It may just be the case at f/16 or f/22 that you will not be able to get as high a resolution as you would theoretically be able to get with the D60. This is not any different however in resolution limitations introduced by camera shake, subject movement, focusing error and lens error, and is no different between using film or digital cameras.

The only thing you could say is with the 1.6x crop of the D60, you have the same diffraction effect as at an approximately 1.5 stop more closed aperture on regular 35mm film.

Even if it is the case that resolution is diffraction-limited, you still have an advantage in using a higher resolution CCD. The diffraction functions as an ideal low-pass filter, which helps prevent aliasing errors in the Bayer mosaic.

-Geert

[zilch0md]

Hi Ivan,

sudaplatov wrote:
Mike!
It looks like your arguments could be very
interesting for quite a big number of people.
Moreover, they may change general attitude to D60.
Could you make them more public?
Ivan

I wouldn't know how, other than by sharing my findings here and on the USENET, but really, Canon isn't the only manufacturer running into this problem of having lenses that will stop down into ranges that produce visible difrfraction. The Nikon D100 is nearly as bad - diffraction's Airy disks become large enough to be resolved in a 5 lp/mm print at about f/13 as calculated with their combination of sensor size and pixel count.

Here's a convenient rule of thumb:

If the ratio of pixel height to effective sensor height in mm (or pixel width to effective sensor width in mm) exceeds 100 (actually 97.7, but 100 is easier to remember), you will not be able to use f/22 without inducing Airy disks large enough to be resolved in a 5 lp/mm print.

This holds true, and is useful, for any digital camera equipped with a lens that has stops going down to f/22 - like many of the made-for-35mm lenses being used on the Canon and Nikon digitial cameras (and others?).

Let's compare the D60 to the D30 using this formula:

D30's pixel height to sensor height ratio: 1440 pixels / 14.9mm = 96.6 pixels/mm

We'll be able to use f/22 without concern for visible diffraction because the ratio is less than 100 pixels/mm.

(If you want to see how this was derived, you'll have to work through the math in my original article - at the top of this thread.)

D60's pixel height to sensor heigt ratio: 2048 pixels / 15.1 = 135.6 pixels/mm

This exceeds 100. We won't be able to use f/22 without inducing visible diffraction because the ratio exceeds 100 pixels/mm.

I've only picked on the Canon EOS D60 because their EOS D30 didn't suffer visible diffraction at f/22 (or f/16).

They took a step backward in the area of diffraction to give us bigger prints without increasing the sensor size. It's not the end of the world and I would still like to own a D60, but I would avoid stopping down below f/11, just as I avoid stopping down below f/16 with a 35mm camera.

Mike Davis

[zilch0md]

Hi Geert,

Geert wrote:
Mike wrote:
``I will specualate that Canon knew exactly what they were doing when they put too many pixels on their D60 sensor - so many that visible diffraction is unavoidable at f/16 and f/22. Once Canon made the decision to limit production costs by keeping the sensor size at basically the same size as it was in the D30, while simultaneously offering more pixels, they had two choices: Tell the consumer to avoid stopping down below f/11 or don't tell them. I suspect most people will be content with the results they get at f/16 and f/22. They won't know what they're missing.''

This is of course not a very useful statement, and even misleading. It is well-known that on all cameras diffraction limits resolution. A rule of thumb is that you get the best resolution when stopping down 2 or 3 stops from wide open aperture. You make it sound as if resolution at say f/16 would be worse on a D60 than on a D30. That is not true.

It may just be the case at f/16 or f/22 that you will not be able to get as high a resolution as you would theoretically be able to get with the D60. This is not any different however in resolution limitations introduced by camera shake, subject movement, focusing error and lens error, and is no different between using film or digital cameras.

The only thing you could say is with the 1.6x crop of the D60, you have the same diffraction effect as at an approximately 1.5 stop more closed aperture on regular 35mm film.

Even if it is the case that resolution is diffraction-limited, you still have an advantage in using a higher resolution CCD. The diffraction functions as an ideal low-pass filter, which helps prevent aliasing errors in the Bayer mosaic.

-Geert

Earlier in this thread, I posted two sources where you can find the formulae I used to determine precisely how large diffraction's Airy disks will be at any f-stop, for any format size enlarged to any final print size. This stuff goes way back. It's not theory, it's fact. Take my math apart - have at it. It will survive your scrutiny. But don't put spins on what I said.

Above, you wrote: "You make it sound as if resolution at say f/16 would be worse on a D60 than on a D30. That is not true. "

You are patently incorrect Geert. I have not said that D30 resolution exceeds D60 resoltion - at any f-stop. Find it Geert. Where did you read that? Search this entire thread.

What I have said, repeatedly, is that the D60, when used at stops smaller than f/11, will produce Airy disks with diameters that exceed the reciprocal of 5 lp/mm in a 300 dpi non-resampled print. I have also said that the D30 does NOT suffer this weakness. The Airy disks produced by the D30 in its 300 dpi non-resampled prints will not be large enough to be resolved at 5 lp/mm.

Speaking of what I have said and have not said...

I have not said that one should purchase a D30 instead of a D60.

I have said that Canon forfeited unresolvable Airy disks to give us larger prints in going from the D30 to the D60.

I have not said that this is an unacceptable trade-off.

I have not said that the larger Airy disks produced by the D60 are cause for avoiding the D60 altogether.

I have not said that the resolution of the D60 is worse than the D30 at any aperture.

I have said that just as I and many others practice avoiding f/22 with 35mm cameras, the math has proven that diffraction-aware users, who are so inclined, should also avoid using f/16 and f/22 on the Canon D60 -and- they can go all the way down to f/22 on the Canon EOS D30 with no concern for visible diffraction. The numbers are verifiable and reproducible. It's not my opinion. It's not a theory. It's not anything but a factual observation that a few sensible people might consider employing.

Please don't put spins on what I've written. It's much more challenging to take on what I actually did write.

Mike Davis

[Geert]

zilch0md wrote:
Earlier in this thread, I posted two sources where you can find the formulae I used to determine precisely how large diffraction's Airy disks will be at any f-stop, for any format size enlarged to any final print size. This stuff goes way back. It's not theory, it's fact. Take my math apart - have at it. It will survive your scrutiny. But don't put spins on what I said.

Above, you wrote: "You make it sound as if resolution at say f/16 would be worse on a D60 than on a D30. That is not true. "

You are patently incorrect Geert. I have not said that D30 resolution exceeds D60 resoltion - at any f-stop. Find it Geert. Where did you read that? Search this entire thread.

Right, read the text you quoted. I have not said you said that. I said that you make it sound that way. Are you saying my opinion is "patently incorrect"?


I have said that just as I and many others practice avoiding f/22 with 35mm cameras, the math has proven that diffraction-aware users, who are so inclined, should also avoid using f/16 and f/22 on the Canon D60 -and- they can go all the way down to f/22 on the Canon EOS D30 with no concern for visible diffraction. The numbers are verifiable and reproducible. It's not my opinion. It's not a theory. It's not anything but a factual observation that a few sensible people might consider employing.


Notice that the the excellent sample image Canon produced to show off the D60 in fact uses f/22. See http://www.canon.co.jp/Imaging/D60/SAMP/D60_sample-e.html, or just the image at http://www.canon.co.jp/Imaging/D60/SAMP/CRW_8929.tif. It is not theory that one can shoot beautiful tack-sharp photographs with the D60 at f/22, but a factual observation.

The issue is not whether diffraction does change the picture at all, but whether it negatively influences a certain picture, which is a subjective issue. Shooting a picture where the resolution is slightly diffraction-limited may in fact improve the final quality, as the anti-aliasing effect prevents artifacts resulting from sampling and Bayer interpolation.

-Geert

[Foreside PhotoGraphics]

Hi-

Being a photographer (and not a scientist), I always thought (back in the film-only days), when using a curved field lens (in other words, a non-macro lens), that diffraction would occur at the smallest apertures due to the extreme angle of the light passing through the lens diaphram.

However, assuming that your statement is in fact sound, how would a flat-field optic (such as a true macro lens- which is corrected for diffraction at the smallect apertures) play out in this scenario?

Would not the curved field of conventional lenses contribute to this problem, whereas the flat field characteristics of a macro lens reduce the degradation?

Once again let me stress that I am not a scientist; however, before digital cameras there was still diffraction in film based photography; and it was always caused by the lens, was it not?

Thanks for the responses...

Gary Shepard
Foreside PhotoGraphics
Maine, USA

[edhofler]

Mike

I’ve spent way too much time on this, I gotta get a life…

I’m not trying to be obtuse, just want to get to the meat of what you are saying.

Basically your contention is that the pixel density of the D60 exceeds the capability of the optics to deliver a higher resolution (sharper not more pixels) image.

If this is what you are saying, then again I ask, what about film? If the maximum resolution (sharpness) of the image recording system (including lens) is somewhere between the D30 and the D60 why bother with fine-grained film?

If Airy disks are a problem on the D60 why aren’t they a huge problem on a 35mm transparency?

Thanks

Ed

[soumya63]

Diffraction is not refraction, and so it is not related with lens at all. It is a phenomenon happening because of the wave nature of light and it becomes apparent with very small aperture or when light travels beside a knife edge. Optically it manifests as dark ripples or rings beside any sharp knife edge or pin hole.

[zilch0md]

Ed,

edhofler wrote:
Mike

I’ve spent way too much time on this, I gotta get a life…

I’m not trying to be obtuse, just want to get to the meat of what you are saying.

Basically your contention is that the pixel density of the D60 exceeds the capability of the optics to deliver a higher resolution (sharper not more pixels) image.

If this is what you are saying, then again I ask, what about film? If the maximum resolution (sharpness) of the image recording system (including lens) is somewhere between the D30 and the D60 why bother with fine-grained film?

If Airy disks are a problem on the D60 why aren’t they a huge problem on a 35mm transparency?

Thanks

Ed


The pixel density of the D60 is too high relative to the sensor size to make use of stops below f/11 without inducing visible diffraction in a 300 dpi print made from its 3200 x 2048 pixel file. To calculate the diameter of an Airy disk for any camera, at the film plane or at the sensor plane, using any lens or pinhole is:

Diameter Airy Disk = N * 0.00135383mm

So, looking only at f/22 for the moment we get:

22 * 0.00135383 = 0.03mm

So, whether we're talking about a Canon EOS D60, a 35mm film camera, a Minox (8x11mm format), or an 8x10 Toyo view camera, at f/22, all of these cameras using any lens which can be mounted, will record Airy disks at the image plane which are 0.03mm in diameter.

The effects of diffraction will not be visible to the naked eye in the final print, viewed at a distance of 10 inches, until the Airy disks have been enlarged to a diameter equal to the reciprocal of 5 lp/mm.

1 / 5 = 0.2mm

So, if an Airy disk has been enlarged past 0.2mm in diameter in the final print, it will visibly degrade the image. Our eyes can't detect the presence of Airy disks that are smaller than 0.2mm in the final print. (Some would say that we can resolve as much as 8 lp/mm, the reciprocal of which is 0.0125mm, but let's run with 5 lp/mm for the moment.)

OK, if we know the size of Airy disks at the film or sensor plane had with any lens or pinhole at f/22 (0.03mm), and we know how large they can be in the final print before they will cause visible degradation of the image (0.2mm), then this whole issue becomes dependant on: Enlargement Factor.

The question is: By how much can we enlarge a 0.03mm Airy disk recorded at the film/sensor plane before it will become visible in the final print?

Answer: 0.2mm at print / 0.03mm at image plane = a 6.67x enlargement factor

Thus, if you intend to make enlargements greater than 6.67x, you had better stay away from f/22 - using any film, any sensor, any camera, any lens or pinhole, unless you are seeking the diffuse softness diffraction causes. See Geert's reference to an f/22 sample image made with the EOS D60 - http://www.canon.co.jp/Imaging/D60/SAMP/CRW_8929.tif) The greater the enlargement factor beyond 6.67x, the worse the diffraction will be as seen the final print of an image taken at f/22. Had that same image been taken at f/11, it wouldn't have that softness (assuming f/11 would provide sufficient DoF for the near and far subject distances to be imaged with circles of confusion smaller than 0.2mm.) The softness I'm talking about is a lack of acutance (or edge sharpness).

An 8x10-inch print made from the 24x30mm crop of a fullframe 35mm transparency has an enlargement factor of 8.47x. At 8.47x, our 0.03mm Airy disks at the image plane will be enlarged to a diameter exceeding what we can resolve with the naked eye in the final print:

0.03mm * 8.47x enlargement factor = 0.254mm

0.254mm is 25% larger than the 0.2mm diameter we can resolve. Ooops.

How about using f/16 with a 35mm camera when we intend to make an 8.47x enlargement (an 8x10 print)?

Again, we use this formula:

Diameter Airy Disk = N * 0.00135383mm

So at f/16 we get:

16 * 0.00135383 = 0.02mm

This is the size of diffraction's Airy disks at the image plane, with any lens or pinhole on any camera, at f/16.

So let's multiply the f/16 Airy disk diameter by our 8.47x enlargement factor:

0.02mm * 8.47 = 0.169mm

Hmmm... 0.169mm is smaller than what our eyes can resolve in the final print (0.2mm).

That's why it's best to avoid f/22 with a 35mm camera. Increase your enlargements further still, by going to a larger print or cropping from a smaller portion of the full 35mm frame, and you'll need to open up further than f/16 to avoid visible diffraction.

OK. It's time for a quick look at the EOS D60 (again.................)

With digital cameras enlargement factor goes hand-in-hand with our desire to print at 240, 300, or maybe 360 dpi, non-resampled. Let's assume that we print at 300 dpi.

Question: What's the enlargement factor for a 300 dpi print made from the largest files the EOS D60 can produce?

The D60's 3200 x 2048 file size will deliver a 300 dpi print that is 10.67in. x 6.83in.

The D60's effective sensor size is: 22.7mm by 15.1mm (0.8937in. by 0.5945in.)

So, at 300 dpi, the enlargement factor is The enlargement factor is 11.94x

The f/11 Airy disk diameter at the sensor is 0.015mm, but after 11.94x magnfication it will be 0.179mm
The f/16 Airy disk diameter at the sensor is 0.02mm, but after 11.94x magnfication it will be 0.239mm
The f/22 Airy disk diameter at the sensor is 0.03mm, but after 11.94x magnfication it will be 0.358mm

Notice that at f/11, the 300 dpi final print diameter for Airy disks from the EOS D60 will be LESS than 0.2mm (they'll be invisible). But at f/16 and f/22, they will be GREATER than 0.2mm (they'll be visible).

Let's look at the D30.

Question: What's the enlargement factor for a 300 dpi print made from the largest files the EOS D30 can produce?

The D30's 2160 x 1440 file size will deliver a 300 dpi print that is 7.2in. x 4.8in.

The D30's effective sensor size is: 22.0mm by 14.9mm (0.8661in. by 0.5866in.)

So, at 300 dpi, the enlargement factor is The enlargement factor is 8.31x (not 11.94x like the higher density D60).

The f/11 Airy disk diameter at the sensor is 0.015mm (same as D60 or any other camera), but after 8.31x magnfication it will be 0.125mm (not 0.179 like the D60 at f/11).

The f/16 Airy disk diameter at the sensor is 0.02mm (same as D60), but after 8.31x magnfication it will be only 0.166mm, (not 0.239mm like the D60 at f/16)

The f/22 Airy disk diameter at the sensor is 0.03mm, (again, same as D60 or any other camera) but after 8.31x magnfication it will be 0.249mm (not 0.358mm like the D60 at f/22).

Notice that with the reduced enlargement factor inherent to the reduced pixel density on a sensor that is essentially the same size as that in the D60, at f/11 and at f/16, the 300 dpi final print diameters for Airy disks from the EOS D30 will be LESS than 0.2mm (they'll be invisible). But at f/22 they will be GREATER than 0.2mm (they'll be visible).

So, my memory failed me in an earlier posting when I said the D30 can be used at f/22 without concern for visible diffraction at f/22. It actually kicks in at f/17.8, just before f/22. With the D60, it happens at about f/12.4.

Is this a "huge problem"? It's as huge as you are keen on seeking the very best possible results. Again, if you have practiced avoiding f/22 with 35mm film cameras, then you should practice avoiding f/16 and f/22 with the Canon EOS D60. If you don't mind the results had with 35mm cameras at f/22, you probably won't mind the results had with the EOS D60 at f/16 and maybe even at f/22.

Mike Davis

[Foreside PhotoGraphics]

"dif·frac·tion Pronunciation Key (d-frkshn) noun.
Change in the directions and intensities of a group of waves after passing by an obstacle or through an aperture whose size is approximately the same as the wavelength of the waves." (Source - Dictionary.com)

Hmmm.... "through an aperture" (as in lens aperture). sure sounds like what I was talking about with regards to lenses in my previous post.

As I recall, diffraction is what causes any specular light source (such as the sun), to appear as a multi-pointed star when the lens aperture is stopped down to (f/22) for example.

"refraction
n 1: the change in direction of a propagating wave (light or sound) when passing from one medium to another 2: the amount by which a propagating wave is bent [syn: deflection, deflexion]
Source: WordNet ® 1.6, © 1997 Princeton University"

The above definition was not what I was referring to.

Incidentally, you might be interested in what Ansel Adam's has to say on page 74 of his book "The Camera" on diffraction: "Light passing a sharp edge (such as the aperture blades in a lens) has the property of "bending" slightly around the edge, an effect known as diffraction (not to be confused with refraction). in practical photography, this effect is significant only at the smallest apertures; the light passing the aperture blades is slightly spread and diffused, causing a reduction in image sharpness."

So, based on the above, I believe that I was correct in my previous post in stating that DIFFRACTION has been a factor long before digital photography was invented; which returns me to my original question- would a flat-field macro lens specifically designed to minimize DIFFRACTION at its smallest apertures, have any bearing on the original post regarding the alleged degradation of the image at any aperture above f/11, based on the number of pixels, vrs the physical size of the D60's CMOS?

Cheers-

Gary Shepard
Foreside PhotoGraphics
Maine, USA

[edhofler]

Mike

Thank you...

Ed

[rootcausefound]

Hi Mike,

I am sorry about that word. That?fs because of my poor vocabulary and my poor brain.
Yeah, my brain refuses to understand the formulas. :) Sorry?c.

Well, here?fs another data. I got it from Photo shop owner?fs home page. He?fs already been aware of these stop limitation and made a wonderful chart for all major digital cameras. Unfortunately, he resides in Japan and his homepage written in Japanese (you also recognize some of them are/were not sold in US), but I got permission from him to copy a part of his table here. Also kindly enough he added a latest D60 data for us


Name Size Pixels Pitch f-stop limit
(mm * mm) (mega) (micrometer)
Contax N digital 36.9*24.6 6.12 12.18 32
Nikon D1H 23.7*15.6 2.62 11.87 32
EOS 1D 28.7*19.1 4.14 11.50 32
FinePixS1 Pro 23.3*15.6 3.06 10.89 32

Nikon D1x 23.7*15.6 5.33 8.33 22
EOS D30 22.7*15.1 3.11 10.50 22
SIGUMA 20.7*13.8 3.42 9.13 22
Nikon D100 23.7*15.6 6.01 7.84 22
FinePixS2 Pro 23.0*15.5 6.17 7.60 22
SONY 25.1*17.64 6.31 8.38 22
SANYO DSC-V1 4.8* 3.6 0.30 7.50 22

EOS D60 22.7*15.1 6.29 7.38 16
OLYM SLR 17.8*13.4 5.10 6.84 16
FUJI DS-300 8.8*6.6 1.28 6.74 16
RICO DC-3 3.69*2.77 0.30 5.77 16

DiMAGE7 8.8*6.6 4.91 3.44 8
Nikon CP 5000 8.8*6.6 4.91 3.44 8
SONY S85 7.1*5.3 3.87 3.12 8
PowerShot G2 7.1*5.3 3.87 3.12 8



In case of D60, he suggests f/16 is its limit. That seems to be different from Mike?fs calculation but I don?ft care because D60 sits between f/11 and f/16.

Remember those f-stop limit values are theoretical values and don?ft guarantee anything. Those values don't mean you cannot force to stop down bellow, either. You can still take a photo using larger f-stop as far as lenses allow. Those values are just guide values that indicate possibly your image starts degradation if you use the larger f-stop from those values. Of course, when you use flash, you should not hesitate to use larger f-stop because the aperture is the only way you can change the exposure under flash light. These values mean if you used larger f-stop values than ones on this list, possibly you could not get the full benefit of the rich pixel resolution. Also those values never suggest good or bad camera.

If you can display Japanese Font and can read Japanese, please visit the following URL.
http://homepage2.nifty.com/-kami-/digital/Aperture2.htm

[ruuskan]

I rather trust real-life results than 'scientific' agruments in this case. http://www.dpreview.com/reviews/canoneosd60/page23.asp has D60 resolution charts measured with differents lenses, aperture values up to f/16. Resolution power seem to be OK (better than D30) using all apertures. Explain that!

[Rich Andreoli]

Hi,

This is my first post on this forum and this is a very interesting topic. I am not an optics expert, but I am a very experienced professional photographer (24 years and a degree in photojournalism). The diffraction effect may be exactly as you say, however, you are forgetting one thing.

As we are dealing with a smaller sensor size than the image circle of the lenses being used we have a greater depth of field at any given aperture than we would normally have using these lenses on a 35mm camera.

This basic negates the necessity or even usefullness of the smaller apertures you speak of. I am not sure what the exact factor is (once again, I am not an optics expert), but this may make your argument somewhat null as far as the average photographer is concerned.

I don't mean that we should not be aware of this effect if it is true. What I mean is that we would be better aware of what the actual effect of this depth of field increase is at each aperture as well as the diffraction effects. This would allow us to know better what the photographic effect would be when we make an aperture choice.

I have heard many people complain that this depth of field increase is a terrible problem for people who wish to create blown out of focus backgrounds and other shallow depth of field effects. This could also be countered by the fact that the angle of view is so much narrower because of the "fov" crop and therefore is it possible that we are also getting a decreased depth of field at a similar focal length because of this.

It is also interesting that many people complain about the multiplier factor because it reduces the usability of the wide angle lenses. Just as many are happy because of the great enhancement of longer focal length lenses by the same effect.

I wonder if we have considered that some people may be more interested in having greater depth of field than their 35mm optics currently give them with film and so they may greatly appreciate any extended depth of field for their uses.

Just my 2 cents worth. I hope this spurs a little more debate.

Rich Andreoli

[karlg]

Interesting discussion of the math. I have a few questions/issues.

1. I read through the posts a few times and I did not see were the size of the pixel factored in. The overall size of the D30 and D60 sensors are the same size, just the pixels are smaller on the D60 to give more of them. Thus I would have expected the diffraction limit to be the same. I assume I am missing something.

2. These formulas, I believe, all assume "optical equivalent scaling." In digital we can "cheat" with non-linear scaling. It cannot creat true detail that is not there, but can preserve the apparent sharpness of edges and thus make the image appear sharper than a simply enlarging formula would suggest.

3. Then we have all the issues associated with digital sampling. There is the Nyquist rate, antialiasing filters and Bayer color filter patterns that factor in. The resolving power of a bayer sensor seems to be somewhere about 1.4X to 1.8X smaller than the pixel size. How this factors in with respect to the diffraction limit is pretty complicated I would think.

I'm an electrical engineer and used to dealing with formulas, but in this case things are going to be very complicated by the time everything gets factored in. I wonder if anyone has done a comparison of a D30 and D60 on a resolution chart shot at F11, F16, F22, and F32?

[Larry H. Smith]

soumya63 wrote:
Diffraction is not refraction, and so it is not related with lens at all. It is a phenomenon happening because of the wave nature of light and it becomes apparent with very small aperture or when light travels beside a knife edge. Optically it manifests as dark ripples or rings beside any sharp knife edge or pin hole.

Got a problem with "...not related with lens at all".

If we use "lens" in the common way (the thing you stick on the front of your camera-body), then we have something more than refractive elements (glass). The "lens" also has an aperture (a hole).

And that hole has an edge (which goes all-the-way-around ;-), ...and that edge causes diffraction, which IS thus"related with lens". (...at least "at all", no?)

Larry

[photoArne]

The smaller the negative or CMOS sensor gets the less one can stop down before diffraction becomes a problem, but the less one needs to stop down to achieve the same depth of field.
Suggesting that Canon should have put the increased number of pixels on a larger chip to avoid diffraction problems with the D-60 is questionable. Increasing the size of the sensor would mean using a longer focal length to get the same angle of view, thus reducing the DOF and therefore making a smaller f-stop necessary, and then you have the problem of diffraction again..
The most interesting point (for me) with Mikes post is his calculation of a number (f-11) where we should start beeing careful if optimum quality is required. Fortunately with the shorter focal lengths of the smaller "negative" of the D-60 going past f-11 can frequently be avoided.

Arne Hvaring

[zilch0md]

Well said Arne.

If you take diffraction into consideration and make it your goal to prevent Airy disks from being resolvable in the final print, you will find that the smaller formats have absolutely no DoF advantage over the larger formats using equivalent focal lengths at whatever aperture will yield Airy disk diameters equal to your largest circles of confusion, at the Near and Far sharps.

As you mentioned, when we increase format diagonal, depth of field decreases and diffraction increases, but at that aperture where the two are optimized for each format, setting the Airy Disk diameter equal to our chosen maximum permissible diameter for circles of confusion, we get the same near sharps - the same depth of field - across all formats.

If the intention is to prevent diffraction's Airy disk diameters from exceeding the maximum permissible circle of confusion diameter of 1/175-in. (chosen arbitrarily) after magnification to a 10-inch diagonal print (equivalent to CoC diameters of 0.02363mm on-film with the 35mm format (more agressive than the oft' used value of 0.03mm)), here are the smallest acceptable whole apertures for each format, when cropping to a 4:5 aspect ratio. These figures are true for any focal length within a given format:

Minox: f/ 4
APS: f/ 8
35mm: f/ 11 (f/16 for fullframe 35mm - all these values are for 4:5 aspect ratio crops)
6x4.5cm: f/ 22
6x6cm: f/ 22
6x7cm: f/ 32
6x9cm: f/ 32
4x5in: f/ 45
5x7in: f/ 64
8x10in: f/ 90
11x14in: f/128

It should be readily apparent that although the smaller formats really do have more depth of field, they can't exploit it without inducing diffraction that's worse than the near and far sharp defocus they had at the aperture where DoF and diffraction are optimized. Don't confuse what I have written here as a wholesale instruction to shoot only at the apertures given above. The aperture of best resolution and contrast for a given lens might very well be wider than these apertures where diffraction and depth of field are optimized. You can go wider than the apertures given, but stopping down below the apertures shown, in an attempt to improve depth of field, will only invite the more destructive effects of visible diffraction.

Also note that these apertures optimize circle of confusion diameters against Airy disk diameters only when one has chosen to limit both to a diameter of 1/175-inch in the final print. (That's a diameter of 0.145mm on-print, the reciprocal of which is 6.89 lp/mm. If we backed that off to a desired resolution of only 5 lp/mm, all the apertures in the table above could stop down a bit further. 35mm's diffraction-limit would go from f/11 to f/16, for example.)

This is why so many people stay away from using f/22 with 35mm cameras, why Mamiya doesn't offer f/32 on its MF lenses, and why the Canon Powershot GS1's smallest stop is f/8. The math proves that Canon's EOS D60 will, at f/16, give you the diffraction of a 35mm camera at f/22. You just can't stop down below f/11 (actually it's f/11 and about 1/3 stop) with the EOS D60 without inducing Airy disks larger than 5 lp/mm in the final print. In the pursuit of smaller CoC's at the near and far sharps, the uninformed will be softening the entire image with visible diffraction. The fact is, whether people actually need the extra DoF or not, f/16 and f/22 will be available on most of the lenses used with the EOS D60. Additional DoF isn't the only lure to using one of these stops - slower shutter speeds might be attractive, but will be had at the expense of acutance. Any increase in diffraction had when stopping down to stops wider than the threshold of visible diffraction isn't an issue. It's only when the Airy disks exceed a diameter that we can resolve when viewing the final print that we have need for concern.

It's interesting to note that if we mounted equivalent focal length lenses on each of the formats shown in the table above and shot the same scene with all of these formats, each using the aperture shown in the table, we would end up with identical depth of field in the final 10-inch diagonal 4:5 aspect ratio print. Needless to say, large format cameras compensate for their relatively poor depth of field by using tilt and/or swing movements to reposition the plane of sharpest focus.

Assuming everyone was "diffraction-aware", with zeroed movements, the real impact on photographers using large format cameras is much longer exposure times. Given that a Minox at f/4 yields the same depth of field as an 11x14 at f/128, we have a 10-stop difference in shutter speeds when using the same speed film at the respective diffraction optimized stops. 10-stops means a Minox photographer can shoot at 1/60th of a second at f/4 to get the same depth of field and diffraction as an 11x14 user does with a 17-second exposure at f/128 (with zeroed movements and before compensation for reciprocity failure, if any.) Often, a large format user will find there is sufficient depth of field for a given subject, without employing tilt or swing movements, but will use them anyway - for the express purpose of decreasing the exposure time.

Mike Davis

[soumya63]

Larry H. Smith wrote:
If we use "lens" in the common way (the thing you stick on the front of your camera-body), then we have something more than refractive elements (glass). The "lens" also has an aperture (a hole).

And that hole has an edge (which goes all-the-way-around ;-), ...and that edge causes diffraction, which IS thus"related with lens". (...at least "at all", no?)

Larry


Larry, you are absolutely right, diffraction always plays a role in any optics design but it is not a function of the glass itself. But a camera lens is a collection of lens elements as well as an aperture, so the resultant product also suffers from diffraction.

I just send an e-mail to Gary regarding this. I was trying to explain diffraction in plain simple english. I was a student of Pure Physics and later on Applied Physics. I can still recall some of the experiments in our Laser Lab, and it was fasinating to see diffraction pattern using diffraction grating and realise ligh does not travel in straight line!

The best light source to observe diffraction is a coherent monochromatic light from a single light source. Laser is one of the appropriate light else sodium vapor lamp also performs well for diffraction experiments. With white light, diffraction effect becomes less prominent as other optical phenomenon like refraction of various color rays influences the result.

In simple language, diffraction happens when two waves from the same light source get mixed with each other with a little phase difference. This produces a periodic ripple effect causing light and dark bands. Smaller the aperture and sharper the knife edge, more pronounced is the effect. This is analogous to the beat effect we hear when we play two very similar frequencies together. If you play guitar or piano, you should have heard it while tuning one string with the same tone of the other string or with the tuning fork. The dark bands are very close to each other and kind of indistinguishable by naked eye. So you need high magnification to see them. Now if the pixel density of the sensor approaches the spacing dimension if the bands, you will be able to see them in your digital photographs. Right now I do not know how major issue it is and how far it affects the picture quality as I have only D30 in my disposal, but Zilch0md definitely has a point. I also mentioned earlier in one of the post that I will wait till I get a 1:1 sensor with lower pixel density than to buy something with smaller sensor with higher pixel density as it magnifies lens abberations.

To me, high ISO noise is much bigger annoyance than diffraction degradation of image. I think that even if you can see the airy discs at very high magnification, a bit of Gaussian blur or despeckle may remove it, but no such luck with high ISO noise. You have to filter lot lot of fine details to reduce some of it. By the way, this thread is not a thread on High ISO, so I should not have mentioned this.

Lastly, in classical photography books, they used to teach all about hyper focal length, critical aperture etc. If we keep those old wisdoms in mind, we will never use aperture as small as 22 and in many case do without auto focus in action photography (with non telephoto lens)!

:)

Soumya Mitra (http://gfoto.tripod.com)

[zilch0md]

Hi Soumya!

soumya63 wrote:

-snip-

In simple language, diffraction happens when two waves from the same light source get mixed with each other with a little phase difference. This produces a periodic ripple effect causing light and dark bands. Smaller the aperture and sharper the knife edge, more pronounced is the effect. This is analogous to the beat effect we hear when we play two very similar frequencies together. If you play guitar or piano, you should have heard it while tuning one string with the same tone of the other string or with the tuning fork. The dark bands are very close to each other and kind of indistinguishable by naked eye. So you need high magnification to see them.

-snip-



I have never read a better description of diffraction. Truly! You left out the cause, but you've done a wonderful job of describing the effect.

Thank you!

Mike Davis

[soumya63]

Thanks Mike. Thanks for the issue you brought up. Very few of us really thought that deep and took the initiative to dig out the facts. Such vigil will keep Tool makers on their toes.

[soumya63]

zilch0md wrote:
You left out the cause ....

I was not sure if I was just interfering in this very interesting thread. Well let me try to explain the cause in plain English

Light has dual properly, one hand it has corpuscular property, which makes it appear as very tiny particle. In science lab we can demonstrate that it has enough kinetic energy to move a very light wheel in vacuum. Moreover very strong gravity also attracts the light. We all know black holes from science fiction movies, but these astro bodies are there for real. They are highly condensed mass having tremendous gravitational force and sucks in every thing including light!

On the other hand, light also exhibits wave property. We now know light is an electromagnetic wave. With the change in frequency, electromagnetic wave also changes its nature. In the lower frequency range, the AC mains 50 or 60Hz hum, Radio, TV or CB signals all are EM waves. As the frequency gets higher, it changes its property from Radio wave to invisible infrared, which we can feel as heat radiation. If the frequency gets a bit higher, we can able to see it as dull red light. The kind of light you see if you heat up a iron rod just enough to make it glow (From this the concept of color temperature arose). Keep on increasing the frequency, the color of the light changes from red, orange, yellow, green .. to violet and then again it becomes invisible ultra violet. If you keep on increasing frequency even more, it becomes XRay and ultimately becomes Gamma Ray, the deadly radiation from nuclear reaction.

Now as light has a wave property, it display all the attribute of a wave like Doppler effect, the phenomenon used by Police to give you speeding ticket and Astonomers use it to detect the speed of movement of Galaxies! Reflection and Refraction are other wave properties, so is Polariasation, interference and Diffraction.

A famous Scientist Huygens proved that every point on a wave front acts as a source of tiny wavelets that move forward with the same speed as the wave. If we extract a single wavelet by restricting the flow of light through a very narrow slit or pinhole, then we can see the crest and trough of that wavelet appearing a light and dark bands. click here (http://www.physics.otago.ac.nz/Physics100/simulations/Gamelan/java/slitdiffr/index.html) to see a cool java applet of diffraction pattern.

Now if multiple wavelets from the single source get mixed with each other, it produces interference, which also manifests as a dark and light band. This happens because the crest of one wavelet if get mixed with trough of other wavelet cancels each other and produces dark band. Where crest of two waves meet, they augment each other producing light band. This happens if you place two or more pinholes or slits close to each other.

By the way, it is diffraction from the microscopic pits on the CD or DVD, which causes the rainbow effect and it is the interference phenomenon, utilized by scientist to create Holograms on you Visa or Master Card!

Cheers

Soumya

http://gfoto.tripod.com

[thompsonkirk]

The Photodo website, which rates lens sharpness using the Hasselblad factory measuring equipment, offers data only down to f/8. They explain that after that point, diffraction becomes the limiting factor in lens resolution, and they add a firm statement that all lenses should be expected to resolve poorly at their smaller apertures. From this standpoint, the D60 sensor doesn't seem such a disturbing limitation. Consider that the D60 with a 35mm lens at f/11 offers as much depth of field as the f/64 Group could achieve with their 8x10 view cameras.

[zilch0md]

Thanks Soumya! I really appreciate the details you've provided.

Mike Davis

[Alan H]

Mike,

Thanks for doing the math! I was comparing notes recently with another D60 user and we did a test comparing two D60s with the Canon 50mm or 55mm macro @ F32. Both cameras performed poorly with the same lens and we weren't sure why... now that I've read your notes, I have a better understanding although it is over my head. We thought it might have been the lens because I was getting better results with my "L" lenses in field tests not thinking of issues like diffraction being a problem.

Anyway, I have some questions for you and I sure hope I didn't overlook answers to these questions that may have already been posted, if so, oops, sorry. I just want to make the most of the D60 and try to learn to use it knowing it isn't as you said , "a M7II with Provia F." After all, I bought it for web use and anything more is just gravy.

#1 If I put a high quality ND filter on so I don't need stop down beyond f11, will that solve the diffraction problem? (I have strobes that are so powerful that f22 is usually necessary for table top shots even on the lowest power setting @100 ISO)

#2 Will Contax's new full-frame 35mm chip have any diffraction problems due to their pixel size, if so at what aperture? (My 645 Zeiss lenses will fit on it with an adapter.)

#3 Is the Kodak 16MP chip that is now available for 645 cameras subject to the same diffraction dillema? Again what aperture is the threshold?



Thanks,

Alan

[mfulton]

Mike,

I think your math and conclusions are based on incorrect assumptions.

With regards to your math, I think Ed Hofler was right. When you talk about f/11, you cannot simply use "11" in an equation and expect the result to be an absolute value. In this context, "11" is a variable representing a particular fraction of the lens focal length, not an absolute value. If you use "11" you'll get a variable as a result.

You've cited a website with information about optics from David Jacobson, but I think you're misinterpretting some of the information. When he refers to a specific lens aperture value of f/22 in his discussion of diffraction, the result of the equation is a VARIABLE relative to the lens focal length, not an absolute value.

Lens diffraction is related to the absolute size of the aperture, not the size relative to the focal length. Aperture values are relative to the focal length, so the idea that you'd get the same amount diffraction with a 100mm lens at f/22 that you would with a 24mm lens at f/22 simply doesn't make sense.

The reason one sees more diffraction with smaller formats is simply because the lens focal lengths are shorter, and the apertures correspondingly smaller. When you get down to the 5 & 6mm focal lengths used by some of the digital cameras with 1/4" and 1/3" sensors, the lens apertures are practically pinholes even when they're wide open. So of course you see diffraction effects with these lenses even with relatively wider apertures.

The idea that lens diffraction is dependent in any way on what type of imaging media is located at the focal plane simply doesn't make sense. It may be that some digital image sensors don't have enough resolution to demonstrate the effects, while others do, but that's it. But the actual AMOUNT of diffraction always remains the same for a given lens at a particular aperture, regardless of whatever is at the focal plane.

And in the end, frankly, if a lens is producing diffraction effects, then I damn well want my image sensor to have enough resolution to record it. The results certainly aren't going to be any worse than using a lower image resolution sensor.

I've sent an EMAIL to David Jacobson mentioning this message thread and asking him to come take a look. So maybe we'll get his 2 cents worth.


Mike Fulton

[tagger]

Hey Mike,

Guess I'd like your opinion here since I have (3) D60s on order. I am getting them to produce posters. I want portrait quality of my subjects. Given the problem you have spelled out.....Do you know if there is any type of fractal software or interpolation methods that can take the RAW file and blow it up to a 24"X36" print and make it a high quality production on the finish print?
Thanks,
TAGGS

[zilch0md]

Hi Alan!

Alan H wrote:
Mike,

-snip-

Anyway, I have some questions for you and I sure hope I didn't overlook answers to these questions that may have already been posted, if so, oops, sorry. I just want to make the most of the D60 and try to learn to use it knowing it isn't as you said , "a M7II with Provia F." After all, I bought it for web use and anything more is just gravy.

#1 If I put a high quality ND filter on so I don't need stop down beyond f11, will that solve the diffraction problem? (I have strobes that are so powerful that f22 is usually necessary for table top shots even on the lowest power setting @100 ISO)

#2 Will Contax's new full-frame 35mm chip have any diffraction problems due to their pixel size, if so at what aperture? (My 645 Zeiss lenses will fit on it with an adapter.)

#3 Is the Kodak 16MP chip that is now available for 645 cameras subject to the same diffraction dillema? Again what aperture is the threshold?

Thanks,

Alan

#1: If your purpose for mounting an ND filter is to force longer exposures (to record the motion of a waterfall, for example) then yes, you can avoid visible diffraction in a 300 dpi print from the D60's largest files by not stopping down below f/11. (The cutoff is actually f/12.9 by the way - about f/11 + 1/3 stop.) If there's any possiblity of glare caused by sunlight falling directly on the attached filter, I would prefer the slight diffraction caused by f/16 or even that at f/22 to the reduced contrast of filter glare (with the exception perhaps of using very well cleaned B+H or Heliopan brand multi-coated ND filters.) With a clean and well-shaded ND filter, I'd stay away from f/16 and f/22.

#2: The Contax N's 24x36mm sensor will not generate Airy disks larger than 0.2mm (5 lp/mm) in a 300dpi print from its largest files until you stop down below f/20.7 (about f/16 + 3/4 stops). This is close enough to f/22 to use that stop without concern.

#3: I don't have the specs for the Kodak chip, but you can try this: If you divide the number of pixels in the height of an image it produces by the number of millimeters tall the sensor itself is and get a number larger than 77, you won't be able to use f/22 with that sensor without causing visible diffraction (5 lp/mm Airy disks) in a 300dpi print made from its largest files (viewed at a distance of 10 inches). It's best to divide the image diagonal in pixels by the sensor diagonal in millimeters (for accuracy's sake), but using height of both or width of both is close enough.

For any combination of sensor height and pixel height (or diagonals or widths), the following apertures will be the diffraction limit at various quotients (pixels divided by millimeters):

Pixels/Millimeter vs. Aperture at which Airy Disks will reach 0.2mm diameter (5 lp/mm) in a 300dpi print

77.2 pixels/mm - f/22 (which is actually f/22.6)
115.8 pixels/mm - f/16
154.4 pixels/mm - f/11 (which is actually f/11.3)
231.6 pixels/mm - f/8
308.4 pixels/mm - f/5.6

This shortcut will help you figure out where visible diffraction will kick in with any digital sensor.

Mike Davis

[zilch0md]

Hi Mike!

mfulton wrote:
Mike,

I think your math and conclusions are based on incorrect assumptions.

With regards to your math, I think Ed Hofler was right. When you talk about f/11, you cannot simply use "11" in an equation and expect the result to be an absolute value. In this context, "11" is a variable representing a particular fraction of the lens focal length, not an absolute value. If you use "11" you'll get a variable as a result.

You've cited a website with information about optics from David Jacobson, but I think you're misinterpretting some of the information. When he refers to a specific lens aperture value of f/22 in his discussion of diffraction, the result of the equation is a VARIABLE relative to the lens focal length, not an absolute value.

Lens diffraction is related to the absolute size of the aperture, not the size relative to the focal length. Aperture values are relative to the focal length, so the idea that you'd get the same amount diffraction with a 100mm lens at f/22 that you would with a 24mm lens at f/22 simply doesn't make sense.

The reason one sees more diffraction with smaller formats is simply because the lens focal lengths are shorter, and the apertures correspondingly smaller. When you get down to the 5 & 6mm focal lengths used by some of the digital cameras with 1/4" and 1/3" sensors, the lens apertures are practically pinholes even when they're wide open. So of course you see diffraction effects with these lenses even with relatively wider apertures.

The idea that lens diffraction is dependent in any way on what type of imaging media is located at the focal plane simply doesn't make sense. It may be that some digital image sensors don't have enough resolution to demonstrate the effects, while others do, but that's it. But the actual AMOUNT of diffraction always remains the same for a given lens at a particular aperture, regardless of whatever is at the focal plane.

And in the end, frankly, if a lens is producing diffraction effects, then I damn well want my image sensor to have enough resolution to record it. The results certainly aren't going to be any worse than using a lower image resolution sensor.

I've sent an EMAIL to David Jacobson mentioning this message thread and asking him to come take a look. So maybe we'll get his 2 cents worth.


Mike Fulton




I welcome David Jacobson's input. I see where you've gone astray in your thinking.

Quoting from above:

"Lens diffraction is related to the absolute size of the aperture, not the size relative to the focal length."

That's incorrect.

Earlier in this thread, I invited readers to reference Jacobson's Lens Tutorial and the book "Basic Photographic Materials and Processes" by Strobel, Compton, Current and Zakia. Here's another source that reinforces those two:

John B. Williams' book called "Image Clarity, High-Resolution Photography" has a discussion of diffraction. He gives the following formula for calculating the radius (r) of an Airy disk. (G.B. Airy is the astronomer who discovered diffraction in 1890 and diffraction's disks are named after him, Airy, not the word 'airy'.) I can't type a lambda, so I have substituted a "w" in the formula below, for wavelength. "f" is for focal length and "a" is for diameter of the aperture - what you have called 'the absolute size of the aperture.' Now follow this:

r = 1.22w(f/a)

OK, here's where you've gone astray: "f/a" can be replaced with "N" where "N" is the familiar f-number (or stop) that describes the ratio of focal length to aperture size. John B. Williams does this without difficulty. David Jacobson does this. Strobel, Compton, Current and Zakia do this. And so does Mike Davis. Join the club!

The fact is that we can substitute "N" for "f/a" in this formula and the new formula (below) will be appropriate for any combination of focal length and aperture diameter that has the specified ratio "N". The new formula will handle any focal length because we are no longer talking about "a", the 'absolute size of the aperture', we're now talking about "N", the ratio of focal length to aperture size. That gives us this formula from the above formula:

r = 1.22wN

Please note that Williams' formula at this point makes no reference to focal length. It only has two variables: lambda and N (a.k.a. wavelength of the light being diffracted -and- the f-stop.) I don't see focal length anywhere in this formula.

In his book, Williams selects 0.0005 mm as an average wavelength of light, but I prefer 0.000555 mm, or 555 nanometers as being the wavelength that is dead center in the spectrum of visible light. It happens to be a nice yellow-green, not far from William's choice anyway, and that's the wavelength Jacobson uses, too (or, at least, the wavelength that his source used.)

OK, moving on, that gives us this formula, using 555 nanometers as lambda for all future calculations.

r = 1.22 * 0.000555 * N

r = 0.0006771 N

To convert this formula to diameter (d) instead of radius (r), we just double the constant:

2 * r = 2 * 0.0006771 N

d = 0.0013542 N

This is the diameter of the Airy disk, in millimeters. It only has one variable, "N" and thus it works for ALL focal lengths.

When I first examined William's text, I didn't like the fact that William's formula has so few significant digits in the constant 1.22, so I went searching and found a longer, more accurate version of it and here it is -- infinitely accurate:
__
1.21966 (66 repeating)

Not much different from 1.22, but it does change my formula for diameter of an Airy disk to:

d = 0.00135383 N (The constant used here can also be found on Jacobsen's Lens Tuturial page.)


You wrote: "Aperture values are relative to the focal length so the idea that you'd get the same amount diffraction with a 100mm lens at f/22 that you would with a 24mm lens at f/22 simply doesn't make sense."

Your premise is not correct so your conclusion is false also.

A 100mm lens at f/22 will produce the SAME size Airy disks on-film as a 24mm lens at f/22.

You also wrote: "The idea that lens diffraction is dependent in any way on what type of imaging media is located at the focal plane simply doesn't make sense."

Search my previous posts - I've never said anything to the contrary.

You wrote: "It may be that some digital image sensors don't have enough resolution to demonstrate the effects, while others do, but that's it. But the actual AMOUNT of diffraction always remains the same for a given lens at a particular aperture, regardless of whatever is at the focal plane."

This is basically correct as written and again, I've written nothing that would contradict this. I would like to add that it is the enlargement factor suffered when we print a sensor's largest files at 300dpi, that distinguishes one sensor from another at a particular f-stop. At a given f-stop, the diameter of Airy disks at the sensor plane (or at the film plane) will be IDENTICAL for all cameras - even comparing a 4x5 view camera with a 90mm lens (wide angle) to a 35mm with a 500mm lens (telephoto). But when comparing digital cameras, the question becomes 'By how much are we going to be enlarging those Airy disks when we make a 300dpi print that might be viewed as close as 10-inches?' If the on-print Airy disk diameters exceed 0.2mm (the equivalent of 5 lp/mm) after enlargement, the average adult with healthy vision WILL be able to detect their presence. So, given two sensors with the same file size, say 1500x1200, if one is physically larger than the other, the enlargement factor necessary to make a 300dpi print (5-inch by 4-inch) will be less than the enlargement factor necessary for the smaller sensor. Same number of pixels, same sized print, same pixel density at the print, but the smaller sensor will deliver larger Airy disks after enlargment. If those Airy disks are larger than 0.2mm, at a given aperture, you'll have to avoid that aperture when shooting (unless you like the softness of visible diffraction.)

The moral of the story for manufacturers is this: Don't increase the pixel density without also increasing the sensor size. Otherwise, the physically larger 300 dpi prints that come from the higher pixel count will have a greater enlargement factor and therefore larger Airy disks in the final print. It's not a problem as long as you can use every stop available on the lenses that ship with the camera without inducing Airy disks larger than 0.2mm in the final print. The EOS D60 and the Nikon D100 sensors (and many others, I'm sure) simply have too small a sensor for the pixel count to make use of all the stops that come with their lenses without fear of visible diffraction. The EOS D30 can almost use f/22 and the Contax N Digital is better still.

Does that mean that we should stay way from the EOS D60 or Nikon's D100 altogether? I've never come close to saying that. If you want the very best performance your digital camera has to offer (or film camera for that matter) you should know where the diffraction becomes visible and stay away from those apertures if at all possible.

I hope that helps and apologize if you find this too pedantic.

Thanks,

Mike Davis

[zilch0md]

Hi!

tagger wrote:
Hey Mike,

Guess I'd like your opinion here since I have (3) D60s on order. I am getting them to produce posters. I want portrait quality of my subjects. Given the problem you have spelled out.....Do you know if there is any type of fractal software or interpolation methods that can take the RAW file and blow it up to a 24"X36" print and make it a high quality production on the finish print?
Thanks,
TAGGS

If you want to make 24"x36" prints from a camera which produces 5 lp/mm prints that are only 6.8"x10.2" you're going to end up with an additional enlargement factor of 3.53x - which means that everything will look absolutely as sharp as most people could want it AS LONG AS you view the posters no closer than 35.3 inches (instead of at 10 inches.)

Use of software like "Genuine Fractals" would improve the appaerance with some subjects - I've never seen how well it works with portraits. It works pretty well with stuff like pebbles and leaves and other such objects that can be reproduced in smaller versions and still look natural - literally creating tinier versions of already small elements that were present in the original data. I don't know of anyone claiming they are happy with pushing enlargement factors more than about 1.5x using "Genuine Fractals" (that's like going to 11x14 from the D60's original 6.8x10.2-inch 300 dpi limit.) Certainly at only 1.2x enlargement it should look pretty good.

So, I think it's safe to say that using "Genuine Fractals" you could reduce your viewing distance for 24"x36" EOS D60 posters from 35.3 inches to 29.4 inches (a 1.2x reduction), assuming the fractals look OK with portraiture. You'd still have the look of a 5 lp/mm print viewed at 10-inches. If you went the full 1.5x that some people do with "Genuine Fractals", and it turns out to look natural with portraits, you could reduce your viewing distance from 35.3 to 23.5 inches (from the original three feet to only two feet).

Overall, I think that's a reasonable minimum viewing distance for images you intend to sell as "posters." It's reasonable to assume a poster might be viewed at no less than three feet, but I'd get what I could out of "Genuine Fractals" just the same.

Mike Davis

[zilch0md]

One last comment for Mike Fulton.

I was just trying to put myself in your shoes and it occurred to me that the formula describing the diameter of Airy disks at the film plane (sensor plane) might haunt you forever if I don't throw in one further bit of explanation.

The reason f/22 for a 100mm lens throws the same size Airy disk on the film plane as f/22 for a 24mm lens is this: The 24mm lens is a lot closer to the film - by exactly the same factor as its aperture is smaller than that of the 100mm lens!

The 24mm lens has an aperture at f/22 that's 4 times smaller than than that of the 100mm lens at f/22, but that doesn't cause Airy disks at the film to be 4 times as large because the 24mm lens is four times closer to the film. The closer you move a slide projector to its screen, the smaller the image gets.

Any two focal lengths end up projecting the SAME size Airy disks onto the film plane at a given f-stop, even though the shorter focal length, which has a proportionately smaller physical aperture at f/22 than the longer focal length, has larger Airy disks than the longer lens at any fixed distance behind the lenses.

Mike Davis

[edhofler]

Mike Fulton

Whether your math is correct or Mike Davis is correct (I’m leaning towards MDs math at this point) your closing statement says what I was trying to say in my last posts.

“And in the end, frankly, if a lens is producing diffraction effects, then I damn well want my image sensor to have enough resolution to record it. The results certainly aren't going to be any worse than using a lower image resolution sensor.”

I don’t understand why this thread has had negative connotations about the D60. What Mike Davis has proven is that we finally have a digital camera where the camera itself is not the limiting factor regarding resolution…this is a good thing!

This puts cameras like the D60 (Nikon’s D100, which for all practical purposes, has the same size sensor and pixel density) in the same league as film cameras.

I do thank Mike (Davis) for increasing my understanding of the diffraction issue as it relates to photography as a whole.

Ed Hofler

[zilch0md]

Hi Ed!

edhofler wrote:
Mike Fulton

Whether your math is correct or Mike Davis is correct (I’m leaning towards MDs math at this point) your closing statement says what I was trying to say in my last posts.

“And in the end, frankly, if a lens is producing diffraction effects, then I damn well want my image sensor to have enough resolution to record it. The results certainly aren't going to be any worse than using a lower image resolution sensor.”

I don’t understand why this thread has had negative connotations about the D60. What Mike Davis has proven is that we finally have a digital camera where the camera itself is not the limiting factor regarding resolution…this is a good thing!

This puts cameras like the D60 (Nikon’s D100, which for all practical purposes, has the same size sensor and pixel density) in the same league as film cameras.

I do thank Mike (Davis) for increasing my understanding of the diffraction issue as it relates to photography as a whole.

Ed Hofler


I appreciate your appreciation of my efforts, which makes me especially reluctant to beat you guys up like this, but here goes...

You simply can not conclude that because a camera "has enough resolution to record" visible diffraction, we should celebrate its capabilities.

All pinhole cameras of just about any size have none of the aberrancies associated with lenses, but manage to record LOTS of visible diffraction.

A Minox camera with its 8x11mm format size can record visible diffraction at just about every aperture smaller than f/4.5.

Many of the early 640x480 pixel digitial cameras had sensors so small that EVERY image they produced had visible diffraction. (I used to call them 'digital pinholes'.)

So the added resolution of the Canon's D60 or Nikon's D100 is not at all necessary to record diffraction. There's only one trait they share that makes it possible for them to record diffraction at f/16 and f/22: Their sensors are too small for the number of pixels they carry. The good news is that we can get quite a bit of depth of field out of these small sensors even at f/11, so stopping down to f/16 or f/22 might not be necessary in most situations, but hear this: It's pointless to try to make your circles of confusion smaller at the near and far sharps of your DoF if doing so is going to make diffraction's Airy disks larger than the CoC's across the entire image. Thus, if someone who is uninformed does try to use f/16 or f/22 with these cameras, purposely to get more DoF, they'll be softening the whole image. That's not something to celebrate, unfortunately. It's just something to be aware of.

Lastly, the only thing that comes close to putting the EOS D60 and the D100 "in the same league as film cameras" is their 300dpi print size - which still can't compete with 35mm, but does leave APS in the dust.

Here are the 5 lp/mm, 2:3 aspect ratio print sizes (in inches) from various formats, sorted by print size. (For digital cameras this assumes we're making 300dpi prints. For film formats this assumes we have at least 45 lp/mm resolution at the film plane to give us a 5 lp/mm print resolution with a 9x enlargement factor.):

Minox: 2.6 x 3.9
Canon EOS D30: 4.8 x 7.2
APS: 5.9 x 8.9
Nikon D100: 6.7 x 10.0
Contax N Digital: 6.8 x 10.1
Canon EOS D60: 6.8 x 10.2
35mm: 8.5 x 12.8
6x4.5cm: 13.2 x 19.8
6x6cm: 13.2 x 19.8
6x7cm: 16.5 x 24.8
6x9cm: 19.8 x 29.8
4x5in: 28.4 x 42.5
5x7in: 40.2 x 60.2
8x10in: 57.9 x 86.8
11x14in: 83.3 x 124.9
16x20in: 120.0 x 180.0

The Minox and APS film formats have been eclipsed by the Canon EOS D60 and Nikon D100. 35mm will fall soon, but we've got a long way to go before digital cameras can outperform all the rollfilm formats in resolving power.

Mike Davis

[edhofler]

Mike

That wasn't so bad...I'm still standing.

Thanks

Ed

[zilch0md]

Addendum to my last post...

It's intersting to note that even though the Contax N Digital has a 24x36mm sensor - same size as 35mm film, it can't produce the 8x12-inch 5 lp/mm prints that we enjoy from 35mm. Why? It has too FEW pixels for its sensor size. They are in a good position to upgrade the pixel density on that sensor and beat everyone else to the 35mm peformance level.

Also: If you are into fine art prints, consider that most galleries will not accept prints smaller than 20x24. To get a resolution of 5 lp/mm in a print this size requires at least a 6x9cm film camera or a 6000x7200 pixel digital camera (43.2 Megapixels). And if they put all those pixels on a sensor any smaller than 77.7 x 93.3mm, we won't be able to use f/22 without inducing visible diffraction.

Mike Davis

[zilch0md]

edhofler wrote:
Mike

That wasn't so bad...I'm still standing.

Thanks

Ed

You're a good sport, Ed! If only we could all be as gracious as you...

:-)

Mike

[tagger]

Thanks again for the input. I appreciate everyones time in explaining some of the things going on in the background of digital photography.
Taggs

zilch0md wrote:
Hi!

tagger wrote:
Hey Mike,

Guess I'd like your opinion here since I have (3) D60s on order. I am getting them to produce posters. I want portrait quality of my subjects. Given the problem you have spelled out.....Do you know if there is any type of fractal software or interpolation methods that can take the RAW file and blow it up to a 24"X36" print and make it a high quality production on the finish print?
Thanks,
TAGGS

If you want to make 24"x36" prints from a camera which produces 5 lp/mm prints that are only 6.8"x10.2" you're going to end up with an additional enlargement factor of 3.53x - which means that everything will look absolutely as sharp as most people could want it AS LONG AS you view the posters no closer than 35.3 inches (instead of at 10 inches.)

Use of software like "Genuine Fractals" would improve the appaerance with some subjects - I've never seen how well it works with portraits. It works pretty well with stuff like pebbles and leaves and other such objects that can be reproduced in smaller versions and still look natural - literally creating tinier versions of already small elements that were present in the original data. I don't know of anyone claiming they are happy with pushing enlargement factors more than about 1.5x using "Genuine Fractals" (that's like going to 11x14 from the D60's original 6.8x10.2-inch 300 dpi limit.) Certainly at only 1.2x enlargement it should look pretty good.

So, I think it's safe to say that using "Genuine Fractals" you could reduce your viewing distance for 24"x36" EOS D60 posters from 35.3 inches to 29.4 inches (a 1.2x reduction), assuming the fractals look OK with portraiture. You'd still have the look of a 5 lp/mm print viewed at 10-inches. If you went the full 1.5x that some people do with "Genuine Fractals", and it turns out to look natural with portraits, you could reduce your viewing distance from 35.3 to 23.5 inches (from the original three feet to only two feet).

Overall, I think that's a reasonable minimum viewing distance for images you intend to sell as "posters." It's reasonable to assume a poster might be viewed at no less than three feet, but I'd get what I could out of "Genuine Fractals" just the same.

Mike Davis

[mfulton]

Mike Davis,

At some point you said:

"The reason f/22 for a 100mm lens throws the same size Airy disk on the film plane as f/22 for a 24mm lens is this: The 24mm lens is a lot closer to the film - by exactly the same factor as its aperture is smaller than that of the 100mm lens!"

Uh, no. At least, not in this context.

With 35mm-style lenses, the distance between the aperture and focal plane is generally NOT equivalent to the focal length. The aperture for a 100mm lens is usually NOT 4x farther from the focal plane than a 24mm lens.

The idea that the lens is "focal length" away from the focal plane when focused on infinity is only true for a "simple" lens design as used by something like a view camera, where you focus by moving the entire lens back and forth.

However, most SLR-style cameras use a different type of lens design where most of the focusing is done internally, and the distance between rear of the lens (or more importantly in this discussion, the aperture itself) and the focal plane is fixed, or at least, is not strictly dependent on the focal length.

So, if the basis for thinking that the diffraction would remain the same for a given aperture is because the distance between the focal plane and the lens would be increasing at the same rate as the focal length, that may be where the problem lies.


Mike Fulton



PS: One more thing... in your original message you said:

"If your goal is to achieve a resolution of 5 lp/mm in an 8x10 print, you will not be able to stop down further than f/11..."

I appreciate a sharp image as much as the next guy, but I have to say that I've never met a photographer whose goal in taking a picture was to achieve a resolution of 5 lp/mm in an 8x10 print.

[zilch0md]

Hi Mike!

mfulton wrote:
Mike Davis,

At some point you said:

"The reason f/22 for a 100mm lens throws the same size Airy disk on the film plane as f/22 for a 24mm lens is this: The 24mm lens is a lot closer to the film - by exactly the same factor as its aperture is smaller than that of the 100mm lens!"

Uh, no. At least, not in this context.

With 35mm-style lenses, the distance between the aperture and focal plane is generally NOT equivalent to the focal length. The aperture for a 100mm lens is usually NOT 4x farther from the focal plane than a 24mm lens.

The idea that the lens is "focal length" away from the focal plane when focused on infinity is only true for a "simple" lens design as used by something like a view camera, where you focus by moving the entire lens back and forth.

However, most SLR-style cameras use a different type of lens design where most of the focusing is done internally, and the distance between rear of the lens (or more importantly in this discussion, the aperture itself) and the focal plane is fixed, or at least, is not strictly dependent on the focal length.

So, if the basis for thinking that the diffraction would remain the same for a given aperture is because the distance between the focal plane and the lens would be increasing at the same rate as the focal length, that may be where the problem lies.

Mike Fulton



Yes, SLR's must use retrofocus designs for their shorter focal lengths because the mirror's movement prevents the rear of a lens from getting as close to the film as it would normally be for those focal lengths. Rangefinders, on the other hand, have short lenses that are not retrofocus in design - they actually sit closer to the film than SLR lenses with the same focal length.

That was a good effort to explain how I might be wrong, but what you have missed is that just as subject magnification is not proportional to these lenses' position relative to the film, NEITHER IS the magnification of the Airy disks they produce. In other words, the retrofocus designs are not as long in focal length functionally as they are physically and thus, as they compensate for the fact that they are sitting well forward of where a short lens would normally sit (by not producing the greater magnification that would normally come with a longer focal length), they are ALSO not producing the larger Airy disks on film that one would expect with a lens that sits farther away from the film. The effects of diffraction are magnified just as much, no more, than the subject itself with retrofocus designs.

mfulton wrote:

PS: One more thing... in your original message you said:

"If your goal is to achieve a resolution of 5 lp/mm in an 8x10 print, you will not be able to stop down further than f/11..."

I appreciate a sharp image as much as the next guy, but I have to say that I've never met a photographer whose goal in taking a picture was to achieve a resolution of 5 lp/mm in an 8x10 print.



I can offer only one explanation - you've not met anyone who pursues image clarity with the discipline and dilligence of several people I know and have known. 5 lp/mm is at the low end of what many knowledgeable people shoot for. I routinely limit all spread functions to the reciprocal of 7.5 lp/mm. (See Michael Reichmann's not very technical page about sharpness at http://www.luminous-landscape.com/sharpness.htm) In fact, since larger prints tend to be viewed at greater distances, the need for resolutions exceeding, or at least matching, what the eye can resolve is greatest with small prints, like an 8x10.

The oft' used circle of confusion diameter for depth of field calculations with the 35mm format is 0.03mm. Many people handle this as a constant, as if it's carved in stone somewhere and can't be changed. The reciprocal of this is 33.33 lp/mm on-film. If we enlarge the cropped 24x30mm portion of a 35mm negative to an 8x10 print, the enlargement factor is 8.467x. So, dividing 33.3 lp/mm on-film by the enlargement factor 8.467, we get an on-print resolution of only 3.94 lp/mm. (20% less than 5 lp/mm.) This explains why so many people are dissappointed with the results they've had when adhering to depth of field calculators, tables and lens engravings that are based on a maximum acceptable circle of confusion diameter of 0.03 mm. They can SEE the difference in sharpness between subjects in the foreground and those in the midground and they're not happy with the results. All they have to do is get their hands on a depth of field calculator, spreadsheet, java script, whatever, that allows the user to specify the maximum acceptable circle of confusion diameter and then make it SMALLER than 0.03mm on-film diameter so many people employ in ignorance.

For example, if you want to achieve 7.5 lp/mm on-film, just take the reciprocal,

1 / 7.5 = 0.1333 mm

then divide by the enlargement factor you anticipate to get the circle of confusion diameter you'll need on-film:

0.1333 mm / 8.467 = 0.0158 mm

Use THIS value as your maximum circle of confusion diameter for the 35mm format, in your choice of depth of field calculators, INSTEAD OF the anemic 0.03 mm value and you'll get circles of confusion on-print that are smaller than most people can resolve at a viewing distance of 10 inches. There's a price to pay, of course - your Nears are going to be a lot farther away from the camera than they were before - your depth of field will decrease as image sharpness increases.

I'm not the only photographer who practices this kind of thinking on a regular basis.

Mike Davis

[Alan H]

Mike D:

Wow! I'm amazed at how diligent you are about your image sharpness. Your info on DOF does explain an experience I had a number of years ago. I was shooting at Monticello with my DOF scale on a Hassy 150CF @ f32. I was sure I had infinity well within the scale and yet the pillars were unacceptably soft. I thought it was loss of quality due to the fact that it was shot at f32 but I wondered if the DOF scale was etched on the lens by someone a bit too optimistic. After some study maybe I'll be able to use your formulas! Wish I was a little brainier!

Do you think all the film plane flatness issues that the "Contax Camera Designers" have attempted to solve with their vacuum backs has any real value or is just hype? I have a 645 but haven't sprung for the $400. vacuum insert for the film magazine. See http://www.contaxcameras.com/index2.html
view the 645 film backs...

By the way there is a really nice 10x glass Peak loupe that is a real nice gift for folks who are so discriminating. I opted to buy my client's those big 4x Pentax loupes cause they're a bit more forgiving!

Thanks,

Alan

[zilch0md]

Hi Alan!

We're getting off-topic for both the thread and the forum, but I would say the vacuum back is only marginally useful for a 645 camera. I'd be a lot more excited to see it offered for a 6x17, 6x12 or even a 6x9cm camera, where the unsupported area of film is much larger than that of 6x4.5cm. There is a great disparity in performance between various rollfilm cameras and rollfilm holders made for 4x5 and larger view cameras when it comes to film flatness. The fact is that some products have managed to achieve exceptional flatness without resorting to vacuum backs with formats larger than 645 - take the Mamiya 6 and Mamiya 7 family of cameras (rangefinders) or the Sinar multi-format rollfilm holder, for example.

It may be overkill, but if you want to make absolutely sure your film is flat, the vacuum insert would be the way to go with the Contax 645 - I just think it's a shame they have to offer it for so small a format.

Regarding the use of formulas for calculating DoF: I have no problem with the idea of just offsetting your engraved DoF scales to get the results you want - no math required. For example, I "reverse-calculated" my Mamiya 7 lenses to have been engraved with DoF scales that were based on 0.062 mm diameter circles of confusion. This results in DoF that's about the same as that delivered by 35mm cameras with lenses engraved for 0.03mm diameter circles of confusion - too soft for my tastes!

Doing the math I gave in my last post for determining a CoC diameter on-film, in this case, one that will deliver 7.5 lp/mm in a 16x20 print from my 6x7cm negatives (instead of an 8x10 print from the 35mm format), I found that
I have to do all my DoF calculations with a maximum permissible on-film CoC diameter of 0.01834 mm, not the 0.062 mm that Mamiya's engineers chose for the lens engraved DoF scales.

0.062 mm is 3.38 times larger than 0.01834mm. Let's call it four times just to make things easy. Guess what? All I have to do is stop down two stops further than my engraved DoF scales suggest for a given situation and I'll get the circles of confusion that are 4 times smaller! No math required!

And really, by simply paying careful attention to the results had when using engraved DoF scales, as you did, you can decide for yourself how many stops you have to offset the scales to consistently achieve the sharpness you want - and the nice thing about this approach, is that it will automatically build in compensation for poor film flatness, if that's an issue with your camera.

Mike Davis

[sandyn]

OK--I accept the argument that you shouldn't stop down to f22 on the D60, but what does it all mean ?? what will I see if I have two prints from my Epson bubblejet---both taken at the same time, same settings, one with the D30 and one with the D60?? What difference would I see??? and can someone post a couple of samples. Show me!!!

[zilch0md]

Hi Sandy!

sandyn wrote:
OK--I accept the argument that you shouldn't stop down to f22 on the D60, but what does it all mean ?? what will I see if I have two prints from my Epson bubblejet---both taken at the same time, same settings, one with the D30 and one with the D60?? What difference would I see??? and can someone post a couple of samples. Show me!!!

On page one of this thread, Geert wrote:

"Notice that the the excellent sample image Canon produced to show off the D60 in fact uses f/22. See http://www.canon.co.jp/Imaging/D60/SAMP/D60_sample-e.html or just the image at http://www.canon.co.jp/Imaging/D60/SAMP/CRW_8929.tif. It is not theory that one can shoot beautiful tack-sharp photographs with the D60 at f/22, but a factual observation."

When I look at this image, I can see the effects of diffraction - it's a lack of accutance (edge sharpness), that's most readily evident in areas of the subject with high local contrast (where a dark color is against a light color, for example.)

Visible diffraction is only a problem if you personally (or your clients?) find the softness objectionable. A little bit of PhotoShop's unsharp mask can help, but that same application of USM would go further still with a crisper original.
Most people don't notice diffraction when it's this subtle because first, it is uniform across the entire image (unlike insufficient depth of field where one might easily notice some softness in the foreground or background compared to where the plane of sharpest focus was placed in the subject space) and second, they don't have anything to compare it to, lying alongside. The diffraction is visible just the same.

The subject shown in this shot probably required all the depth of field provided by f/22, given how close we are and how much Z-axis depth it has. I would love to find two images taken of some finely textured subject, using the same EOS D60 camera, same lens, same focus distance, same lighting, same everything for both shots except with one shot taken at f/11 and the other at f/22. It would be imperative to shoot a somewhat flat subject so there can be no question that f/11 provides more than enough DoF - otherwise, the f/11 image might appear softer than that done at f/22, due to insufficient DoF. We wouldn't want DoF to be an issue in this comparison.

Until then, the single example above should suffice to show you that the D60's diffraction at f/22 is far from horrible, but it can be seen.

Mike Davis

[edhofler]

I know this thread has D60 in the title and I know Mike will correct me if I’m wrong, but…

A better title would have been “Many of today’s digital cameras as well as 35mm film based cameras should not be stopped down below f/11” instead of “D60’s sensor is too small to stop down below f/11”, and a big part of the equation is how big your prints are going to be.

The degradation of print quality can be seen or proven with film. You would probably be able to find a film-based example on the net someplace.

As to whether or not you could see the difference on two prints made from your Epson, probably yes IF a whole bunch of other factors are in place i.e. lens choice, enlargement factor, paper being used, printer settings etc.

The bottom line is, knowing the physical limitations of the tools you use (optics, printer and recording device, be it a D30, D60, D100 or a piece of 35mm film) can only help you to be a better photographer.

Ed

[sandyn]

I had a look at the image and I'm not a good enough observer to notice. I accept that it's there--when you know what to look for, but I can't 'see' it.
I was concerned that it might be more noticable. For the type of photography I do, it shouldn't make much difference to my enjoyment of the camera and pictures.

I am about to get a D60--when i can find one for sale---at the righ price. I was concerned that it was a far more observable problem.

I'm already wondering if I should wait and see if Canon will bring out a Foveon sensor equipped camera. Of course that will happen the week after I buy my D60. The diffraction problem may have been a deciding factor if it had been more noticable.

thanks

[Yves C.]

Hello Mike; let me point out a mistake in your reasoning, and add a few comments.

zilch0md wrote:

David Jacobson's Lens Tutorial http://www.photo.net/learn/optics/lensTutorial shows the formula used as I am using it - with N being the stop (5.6, 8, 11, 22, etc.)


* You use his (correct) formula for the radius of the Airy disk.
But you also should use his formula for the resolution limit (due to diffraction). He uses 0.823 /(lambda*N) lp/mm [where lambda is expressed in mm] which corresponds to a MTF of 8.7%, whereas you use 0.410 /(lambda*N) lp/mm (derived from your first message). This assumes a cutoff frequency corresponding to a MTF of 49.3%. That is far too high to define a cutoff frequency. 10% or a bit less is more reasonable.
One can also choose 0% modulation, which leads to a cutoff frequency of 1 /(lambda*N) lp/mm - but this is often claimed to be too optimistic.
In any case, there is no serious reason to define the cutoff frequency as the inverse of the diameter of the Airy disc. By doing that, you find a quite pessimistic "stopping-down limit".

zilch0md wrote:

When I first examined William's text, I didn't like the fact that William's formula has so few significant digits in the constant 1.22, so I went searching and found a longer, more accurate version of it and here it is -- infinitely accurate:
1.21966 (66 repeating)


* Not exactly :). Just for fun, here are the first 50 decimals (true) :

1.219669891266504454926538847465255177879359330775 1

* Of course you are right when you explain that the Airy disc only depends on the relative aperture (may the lens be retrofocus, telephoto, or not - provided it is focused on infinity).

These were remarks on the "theoretical" side - of course real-world tests are of first importance, because no area array sensor is a perfect device.

Yves

[zilch0md]

Hi Yves,

Yves C. wrote:
Hello Mike; let me point out a mistake in your reasoning, and add a few comments.

zilch0md wrote:

David Jacobson's Lens Tutorial http://www.photo.net/learn/optics/lensTutorial shows the formula used as I am using it - with N being the stop (5.6, 8, 11, 22, etc.)


* You use his (correct) formula for the radius of the Airy disk.
But you also should use his formula for the resolution limit (due to diffraction). He uses 0.823 /(lambda*N) lp/mm [where lambda is expressed in mm] which corresponds to a MTF of 8.7%, whereas you use 0.410 /(lambda*N) lp/mm (derived from your first message). This assumes a cutoff frequency corresponding to a MTF of 49.3%. That is far too high to define a cutoff frequency. 10% or a bit less is more reasonable.
One can also choose 0% modulation, which leads to a cutoff frequency of 1 /(lambda*N) lp/mm - but this is often claimed to be too optimistic.
In any case, there is no serious reason to define the cutoff frequency as the inverse of the diameter of the Airy disc. By doing that, you find a quite pessimistic "stopping-down limit".



My calcuations aren't pursuing the resolution limit due to diffraction. I'm after the aperture at which diffraction's Airy disks will reach the same diameter as my chosen maximum acceptable diameter for circles of confusion. That ends up being only as pessimistic a stopping-down limit as my choice of circle of confusion diameter. I'm not interested in stopping down for addtional depth of field if doing so will cause Airy disks (across the entire image) to be larger than the largest circles of confusion I'm willing to allow (at the Near and Far Sharps.)


Yves C. wrote:

zilch0md wrote:

When I first examined William's text, I didn't like the fact that William's formula has so few significant digits in the constant 1.22, so I went searching and found a longer, more accurate version of it and here it is -- infinitely accurate:
1.21966 (66 repeating)


* Not exactly :). Just for fun, here are the first 50 decimals (true) :

1.219669891266504454926538847465255177879359330775 1



Thank you! That's significant! :-)

Yves C. wrote:

* Of course you are right when you explain that the Airy disc only depends on the relative aperture (may the lens be retrofocus, telephoto, or not - provided it is focused on infinity).

These were remarks on the "theoretical" side - of course real-world tests are of first importance, because no area array sensor is a perfect device.

Yves

Thanks for confirming my statements regarding retrofocus wide angle lenses.

Mike Davis

[Yves C.]

Hello Mike!

I was replying to your first message, where you were (I think) talking about achievable resolution ("If your goal is to achieve a resolution of 5 lp/mm in an 8x10 print") and your conclusion was very pessimistic, I explained why.


zilch0md wrote:

My calcuations aren't pursuing the resolution limit due to diffraction. I'm after the aperture at which diffraction's Airy disks will reach the same diameter as my chosen maximum acceptable diameter for circles of confusion. That ends up being only as pessimistic a stopping-down limit as my choice of circle of confusion diameter.


Well, OK, but I think that's no good choice... Here is why.

It is generally accepted that 5 lp/mm viewed at 10 inches is the "resolving power" of the eye. Of course that is a bit quick because one can go a little further if the contrast is good, etc. But let's stick to that. This leads (a bit quickly too) to a "circle of confusion" of 0.2mm. An important thing is that this circle of confusion is primarily defined to be used for depth of field calculation. We'll see why this has some importance. When you photograph something that is out of focus, any point of the subject will be convoluted with the projected aperture shape (let's say a disk), hence the image of a luminous dot will be a uniform disk. Now, consider a subject that is in-focus, but blurred by diffraction : any point of the subject will be convoluted with the Airy disk corresponding to the relative aperture (and the wavelength you consider). You can't compare directly these two kinds of "disks", because the Airy disk is more "dotted" than a blur circle. Other example : some aberrations (some kind of SA for example) can produce a well-defined image surrounded by a weak halo. If you consider the diameter of the halo in a "circle of confusion" reasoning, you will also be very pessimistic with regard to the sharpness of your lens...

Let's switch to a "resolution" point of view.
* The first zero of the MTF of a defocusing that produces blur disks of diameter D will be at 1.22/D.
* The (unique) zero of the MTF of diffraction that produces Airy disks of "diameter" D will be at 2.44/D. That's higher. We could go into the details of the MTF shapes, but that gives an idea.

I hope you will agree with that. I think one should use MTF concepts when possible, as I did in my previous post (then you will find a much lower "stopping-down limit"). Furthermore, the frequency domain is particularly suitable when dealing with discrete sampling devices like area arrays.

Greetings
Yves Colombe (from Paris)

[zilch0md]

Yves C. wrote:
Hello Mike!

[snip]


zilch0md wrote:

My calcuations aren't pursuing the resolution limit due to diffraction. I'm after the aperture at which diffraction's Airy disks will reach the same diameter as my chosen maximum acceptable diameter for circles of confusion. That ends up being only as pessimistic a stopping-down limit as my choice of circle of confusion diameter.


Well, OK, but I think that's no good choice... Here is why.

[snip]

You can't compare directly these two kinds of "disks", because the Airy disk is more "dotted" than a blur circle. Other example : some aberrations (some kind of SA for example) can produce a well-defined image surrounded by a weak halo. If you consider the diameter of the halo in a "circle of confusion" reasoning, you will also be very pessimistic with regard to the sharpness of your lens...

Let's switch to a "resolution" point of view.
* The first zero of the MTF of a defocusing that produces blur disks of diameter D will be at 1.22/D.
* The (unique) zero of the MTF of diffraction that produces Airy disks of "diameter" D will be at 2.44/D. That's higher. We could go into the details of the MTF shapes, but that gives an idea.

I hope you will agree with that. I think one should use MTF concepts when possible, as I did in my previous post (then you will find a much lower "stopping-down limit"). Furthermore, the frequency domain is particularly suitable when dealing with discrete sampling devices like area arrays.

Greetings
Yves Colombe (from Paris)

Yves, I am intrigued and, without question, acknowledge your expertise with this subject. I very much like the idea of employing MTF when possible because it offers a hope of providing "real-world" metrics. Unfortunately, in my experience, it doesn't seem to hold true for this application. Several years ago, I had considered exactly what you are proposing and abandonded it because I can't find empirical evidence to support optimizing Airy disk diameters against circle of confusion diameters at a ratio of 2:1.

About three years ago, my 1:1 optimization was challenged very aggressively by a well-known and very knowledgeable contributor to the rec.photo.* newsgroups. This drove me to searching through hundreds of references to diffraction to find and compile unsolicited comments on when diffraction becomes visible under various combinations of format size, enlargement factor and viewing distance. I only came up with a handful of Internet sources that evidenced thoroughness in their testing, but they supported my 1:1 approach. You'll have to take my word for it that I was eagerly seeking the truth, not an affirmation of my thinking. I don't want to be "right" as much as I want my technique to be right. You can be sure of this.

Consider these real-world affirmations: My math says we shouldn't stop down below f/16 when shooting fullframe 35mm with the intention of making an 8x enlargement. That's supported by many people who have no knowledge of my optimization philosophy. It can be argued that those who avoid using f/22 with 35mm cameras do so because of factors other than "visible" diffraction, but my recommendation doesn't hurt where the 2:1 MTF math would, were one to rely on it alone as a means of identifying a minimum aperture.

Several digital cameras with integral lenses have an f/8 minimum aperture. My math correlates nicely with their design choice, given the sensor size, their pixel density and the assumption that we want 5 lp/mm in the final print. The MTF approach would say they could have allowed a smaller stop. Again, there might be other reasons they chose not to offer anything below f/8.

The Mamiya 7 lenses don't offer f/32. Despite several articles I've read where owners are lamenting this "weakness", I'm not disappointed because my optimization says I shouldn't stop down to f/32 when shooting 6x7 - it's worse for 6x6. Did Mamiya avoid the inclusion of f/32 soley because of diffraction? I don't know.

Lastly, I confess my numbers may be conservative, but I sure do like the results I'm getting. My field techniques are almost the reverse of photogrammetry in execution, so I have a lot of images taken with strict adherence to my having avoided Airy disks that are larger than my chosen maximum for CoC's. I routinely use a laser rangefinder to measure the distance from camera to Near and Far Sharps, then calculate the distance to the plane of sharpest focus and the aperture that provides just enough DoF using a programmable calculator (an HP48G+). (The laser rangefinder is also used to find a target on which to focus at the calculated PSF distance.)Having also calculated the aperture at which diffraction's Airy disk would equal the chosen CoC diameter, I'll back away from the Near or use some other technique to lessen the need for DoF, if necessary to maintain the 1:1 optimization. If use of a laser rangefinder seems excessive, let me explain that I'm also using the measured Near and Far distances to calculate stereo base - the necessary separation between lens axes of a twin-camera rig (with which I shoot stereo pairs) that matches the geometry of the subject space.

The results speak for themselves, but so do some people who have seen my work. Their opinions are completely subjective and do not directly address this discussion, but at the very least, it's evident they weren't disappointed by what they saw. Here are some reviews my medium format stereography has received:

http://www.primenet.com/~zilch0/reviews.htm

I confess it's quite possible my 1:1 optimization of Airy disk diameters to CoC diameters is coincidentally avoiding other sources of image degradation - problems that are not inhibited when stopping down further than my approach recommends. I recognize that none of what I've written here solidly refutes what you have offered, so I very much welcome any followup comments you may have.

Thanks!

Mike Davis

[dgweiss]

Let's inject some economics into this.

I ran a few back-of-the-excel-workbook calculations on die (chip) cost for sensors of two sizes.

I assumed:
die size = 25x17 (small) and 38x26 (large)
wafer dia. = 300mm (state of the art)
$10K = wafer production cost
.8/.7 = geometric yield (small/large)
.8/.7 = process yield (small/large)
4 = MSRP cost/internal cost

result:
MSRP chip cost = $376/1142 (small/large).

So it looks to me that with the present state of the semiconductor art, Canon would have to charge almost $800 more for a camera with the same number of pixels but with the larger sensor.

[zilch0md]

Interesting numbers D. Thanks! Staying away from f/16 and smaller stops with the D60 isn't a bad compromise given the cost of doing it "right."

Mike Davis

[CJMORGAN59]

zilch0md wrote:
Consider this before purchasing a Canon EOS D60: If your goal is to achieve a resolution of 5 lp/mm in an 8x10 print, you will not be able to stop down further than f/11, thanks to the visible diffraction that will be magnified from the D60's tiny CMOS. Quite simply, this camera has too many pixels for its sensor size.

I've done the math. Wake me up when someone is making $1,000 digital cameras with 60.7 Megapixels on 61x77.5mm (MF) sensors, for 7 lp/mm resolution, 20x25-inch prints that will have no visible diffraction at f/16. Until then, I'll stick with 6x7cm Provia 100F and Mamiya 7II's.
Mike Davis

Respectfully Mike, it seems you gone to great lengths to make a mountain of an issue out of a mole hill of a problem.

I'm not at all debating your math. But the practical conclusions are drawn not from math, but rather from observing this seeming problem in print -- specifically comparative prints from D60 camera images, like one shot at f/9.5 and another shot at f/19.

I performed such a comparative test last night, and indeed, if one magnifies two images large enough, we can see that the one shot at f/9.5 is sharper than then one shot at f/19.

But I should point out that the results were only readily apparant to my observations because I was looking at comparative prints of a cropped section from what would full frame be 40x60 inch prints (a size much larger than what I ever imagine I'll blow my own D60 images up to and try to look at a view distance of 8-12 inches).

So I cannot dispute your mathematical findings since I have now observed them myself in an actual D60 two image comparsion test.

The question remains, however, about how significant or insignificant this problem really is for us photographer who are out there shooting in the real world.

Over the years, I have come across a lot of images where I could easily say that the composition sucked or that the lighting of that image sucked. But I've yet to find myself saying, "That would have been such a good photograph... if not for the diffraction problem."

While the results of this diffraction issue are apparent when I compare two images size by size which are the eqivalent of full frame 40x60 inch prints, I'm not at all concerned about this if I only blow up my images to 12x18, or 16x24 inches in size. It just altogether becomes a non-issue.

Moreover, even in a 16x24 inch print, most any of us are more going to observe objects out of focus because we used a depth-of-field of, for example, f/9.5 rather than using a greater depth-of-field of, for example, f/19. And we will notice this much, much more than any very, very slight loss of overall shapeness which results from this diffraction problem.

So from where I sit, this whole issue is a non-issue. What you've been saying here and the math you have performed may indeed be perfectly correct, but in as much as there are so many other factors -- truly important factors -- which go into the making of a good image, I don't at all find myself troubled by this issue.

And I'll let my images speak for themselves... some recent ones, from a trip to Algonquin Provincial Park (Ontairo) which can be found here:

http://ca.photos.yahoo.com/bc/cjmorgan59/lst?.view=t&.dir=/Algonquin

So by all means Mike, hold on to your film camera if this diffraction issue seems significant to you and to your image making. For me, it's bascially insignificant compared to other factors (like good composition and light, for example) and so at least for me, I'm quite thrilled to give up any further use of film so that I can otherwise enjoy what the D60 affords me.

As the saying goes, "To each his own".

With regards,

CJ

[zilch0md]

Well said CJ!

It's definitely is a subjective choice and I would say that most people aren't going to be disappointed with the performance of the the D60 at f/22. Even I wouldn't welcome the cost of the larger sensor necessary to avoid visible diffraction at f/22. Canon's decision to increase pixel density without increasing sensor size (in going from the D30 to the D60) was not unwise in my opinion, but definitely compromised image quality below f/11.

Thanks!

Mike

[zilch0md]

PS for CJ: Your Algonquin images are wonderful! I'm humbled! Thanks for sharing,

Mike

[CJMORGAN59]

zilch0md wrote:
Well said CJ!
It's definitely is a subjective choice and I would say that most people aren't going to be disappointed with the performance of the the D60 at f/22. Even I wouldn't welcome the cost of the larger sensor necessary to avoid visible diffraction at f/22. Canon's decision to increase pixel density increasing sensor size (in going from the D30 to the D60) was not unwise in my opinion, but definitely compromised image quality below f/11.
Thanks!
Mike

For whatever it's worth, all you've been saying here won't unnoticed by me (i.e. at the very least, I'll keep it in the back of my mind when shooting).

If I come across a situation where I need the depth-of-field of f/19 instead of f/9.5, then I'll probalby still use f/19.

But there are sometimes where the image we are making doesn't require us to use a greater DOF than something like f/9.5, that we have nothing to gain by closing our aperture way down. It is at these moments when your words will probably come back to mind, and when I realize that stopping down to f/19, for example, isn't giving me any more DOF (than I really need) and that it is in fact actually making the situation worse because the resulting images will suffer from diffraction and thus be less sharp overall.

All of which is to say that there is a time and place where I have no doubt your words will come back to mind -- at least for me -- and that this diffraction issue will be remembers as I go about my work.

For whatever any of that is worth.

CJ

[CJMORGAN59]

zilch0md wrote:
PS for CJ: Your Algonquin images are wonderful! I'm humbled! Thanks for sharing,
Mike

Thanks Mike. That was kind of you to say. And good to know that if I didn't become an engineer like my father wanted years ago, then at least I have something to show for it.

CJ
____________________

"What the heck do you need to study photography for?
Just point the camera and press the button."
-- Paul Morgan (1978)

[NickH]

I can just about follow the maths and I was absolutely intrigued so I tried to find evidence of this in the Photographs from my D60 - I stopped down to F36 on a Canon 28-135 IS USM lens, 15 second exposure at 135mm (ignoring the 1.6x crop due to the sensor size) and the results were crystal clear, all 16 subjects.

Perhaps you can tell us how our eyes manage to produce clear images with all that jelly, blood vessels etc in the way of the randomly ordered and often flawed sensor at the back of our eyeballs - I guess it's in the post processing.

My advice is get hold of a D60 and show us an image where this is apparent, the physics of light and the sensor pixel size are only part of the story.

The smaller the aperture, the longer the exposure - even when locking up the mirror and using a remote shutter release the risk of camera shake and hence loss of sharpness gets higher. I do believe that this is a non-issue but this is the humble opinion of a very satisfied D60 owner.

[mrchips]

NickH wrote:
I do believe that this is a non-issue but this is the humble opinion of a very satisfied D60 owner.


I second your humble opinion!

Denny

[CJMORGAN59]

NickH wrote:
Perhaps you can tell us how our eyes manage to produce clear images with all that jelly, blood vessels etc in the way of the randomly ordered and often flawed sensor at the back of our eyeballs


How do you know the images your eyes are producing are truly clear? I mean we have only one vision and so nothing to use as a reference for comparison. But if we did, we might just discover that our vision actually sucks, that what we thought was clear vision only seemed that way because we had no reference for contrast.

Still, there is the situation where the iris of our eye is closed right down to a small aperture setting on, for example, a sunny day. And where if we put on sunglasses, for example, our iris, the aperture will open up. And perhaps our vision is improved. And perhaps we just attribute this to the filtering the glasses. And it may well be this. But it also might be, at least in part, because with a wider iris opening, we are experiencing less light diffraction.

Just a thought.

CJ

[NedLofton]

Snoooooorrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrre eeeeeee!!!!!

[zilch0md]

Hi Nick,

We tolerate visible diffraction more readily than visible circles of confusion because diffraction affects the entire image uniformly. When the circles of confusion at the near and far limits of DoF reach a size that is resolvable (by the human eye) for a given combination of enlargement factor and viewing distance, their failure to deliver apparent sharpness becomes obvious in the presence of those areas of the subject space that were closer to the plane of sharpest focus. When circles of confusion get too big, they are readily detectable against acceptably sharp surroundings. Resolvable diffraction softens the entire image and thus goes unnoticed unless we have a comparison print alongside, that has Airy disks smaller than can be resolved. Visible diffraction is destructive to image clarity even when it goes unnoticed by some. An experienced eye will see the Airy disks when they exceed the reciprocal of about 7 lp/mm in the final print.

I have no problem with your being satisfied with the results you get at f/36. When I look at the sample image referenced with a link posted earlier in this thread (portrait of a woman), I am not satisfied with the diffraction I see at f/22, which isn't nearly as severe as it would be at f/36. Without question, your tolerance of visible diffraction is greater than mine.

As an anology, I have a friend who insists, "All women are beautiful, just some more than others." I wish I had his eyes.

Mike Davis
http://www.accessz.com

[actualD60user]

Looks like I have come to the part late, but this thread still gets linked to from other places so I thought I would log an opinion. I usually try to avoid pointless discussions like this but I will make an exception here because a great camera is getting a bad rap.

The original post isn't very readable but I think I can translate for those that don't understand. When we photograph a distant point source (like a star) the recorded image(airy disk) is blurred due to the difraction of the light passing through the (nearly) circular lens iris. The blurring is actually a series of rings around the point source that diminish in intensity. This spreading effect can be seen by watching the behaviour of waves on water as they pass through openings. It turns out that as the lens is stopped down the size of the airy disc at the focal plane is increased.

The idea that the original poster is trying to convey is that the additional effective pixels in todays 6Mp DSLRs has magnified the "airy discs" if you assume a uniform printed pixels/inch. I really don't like this argument because most photographers have not automatically increased the size of their prints since purchasing a D60 versus a D30. A better comparison would be to compare the two with a fixed print size. A better explanation of what is really going on is to explain that the D60 sensor is better able to resolve small features which can reveal optical diffraction effects when the lens is stopped down. Because the sensor of the D60 is better it resolves the diffraction effects at larger apertures than the D30. The blurred image is produced by the optical lens/iris system, not the sensor. At a given aperture, blahblah, the D30 sensor was blurring the recorded image more than the optical lens/iris was so I don't see how this makes the D60 an inferior camera, even for use at small apertures. It is just able to record problems that the D30 couldn't even see.

I understand the original post but he has ignored many theoretical and practical factors in his conclusion. If you really want to know if a DSLR is for you and your type of photography try one out. Unfortunately you will have to get in line.

[Aussie Gal]

Why don't you lot just go out and enjoy a great camera and stop wasting time with all this madness.
I have blown pics up to poster size from D60 and they beat film anyday!

spend your time taking great pics!

[Jerry White]

edhofler wrote:
Mike

Have you considered how the Bayer algorithm fits into this?


I've not considered that but I did take two Bayer asprin to kill the headache that I got from trying to understand what everyone is talking about.

Ya'll keep on doing the figgering, and I'll keep on shooting and selling and everything will work out just fine.... :)

Jerry

[jmamer]

zilch0md wrote:
Hi!

sudaplatov wrote:
But he is right.
Couple months ago I decided to buy D30 instead
of D60 (I knew it would be available soon) because
of described reason.
-snip-


Thanks! I'm glad it made sense to someone. Yes, the D30's pixel density is perfectly matched to its sensor size - I once calculated that its sensor is just large enough to permit use of f/22 without causing Airy disks to be larger than 5 lp/mm in a 300 dpi print for the file sizes it generates. I remember writing a friend about it, saying how impressed I was that Canon had made the D30's sensor exactly the right size relative to its resolution to avoid visible diffractiona at f/22. Now they've gone and blown it with the D60. I guess the D30's design was a fortuitous accident in this regard - either that or they figured nobody would catch the diffraction problem when they decided to save bucks by avoiding a larger sensor as they increased the pixel density.

But we're wide awake out here... Back to the drawing board guys!

Mike Davis

This exchange got me to wondering....It seems like I can simulate the less dense sensor of the D30 on my D60 simply by taking photos in Middle/Fine mode instead of RAW or Large/Fine. In Middle/Fine one gets 2048x1360 pixels, not far off of the D30's 2160x1440. I'm assuming that the reduced pixel count
does not change the effective dimensions of the sensor, just the number of pixels recorded. One problem with this has to do with how the lower resolution files are created, if the raw sensor data is evenly sampled at a rate of 44% and then compressed, this might work. If, on the other hand, the sampling rate is variable, one might get effective pixel densities that are too large in portions of the picture.

Taking this a bit further, it seems like one could take a full size RAW file (3072x2048) and sample it down to the maximum density allowable for the F-stop you have used. Shooting at F22 would require a lower sampling rate than F16, etc. This could be handled in software (if one understood the RAW format), or by processing a full size tiff file.


Maybe neither approach is feasible, but I'm curious about the idea of trying to turn off approximately 50% of the pixels when shooting above F16. Would it work? Could it be done?

thanks
John

[petiot]

Are we still talking about photography here? i am not sure...

[zilch0md]

jmamer wrote:

[snip]

Taking this a bit further, it seems like one could take a full size RAW file (3072x2048) and sample it down to the maximum density allowable for the F-stop you have used. Shooting at F22 would require a lower sampling rate than F16, etc. This could be handled in software (if one understood the RAW format), or by processing a full size tiff file.

Maybe neither approach is feasible, but I'm curious about the idea of trying to turn off approximately 50% of the pixels when shooting above F16. Would it work? Could it be done?

thanks
John


Hi John!

All you have to do to avoid visible diffraction is reduce the enlargement factor when printing shots taken at f/16 or f/22. That's the real crux of the problem with the D60 - its pixel count encourages one to make larger 300 dpi prints than can be made with the D30 and at that enlargement factor, the Airy disks produced at f/16 and f/22 become visible. Reduce the enlargement factor and the Airy disks become invisible.

The EOS D60's 3200 x 2048 file will print to a 300 dpi print size = 10.67in. x 8.27in.

To avoid visible diffraction at f/22, you can still shoot at 3200x2048, but just don't enlarge it beyond 1/2 the 300 dpi size, which would be 5.33in. x 4.135in. (Or, as you correctly suggested, just record half as many pixels, saving memory, and print at 5.33in. x 4.135in. - you'll have a data density of 300 dpi instead of 600 dpi.)

Similarly, to avoid visible diffraction at f/16, you can still shoot at 3200x2048, but just don't enlarge it beyond 3/4 the 300 dpi size, which would be 8.0in. x 6.2in. (Again, you could just record 3/4 as many pixels, saving memory, and print at 8.0in. x 6.2in. - you'll have a data density of 300 dpi instead of 450 dpi.)

Another solution is to just increase the viewing distance. Go ahead and make a 10.67in. x 8.27in. 300 dpi print, but don't view it from a distance of 10 inches, at which the 0.2mm (5 lp/mm) Airy disks will be resolvable by the average adult with healthy vision. Instead view an image made at f/22 from a minimum viewing distance of 20 inches and the Airy disks won't be detectable. The problem with this solution is: How do you enforce a minimum viewing distance of 20 inches?

Again, If the D60's sensor were physically larger, using the same number of pixels, a 300 dpi print produced from its 3200x2048 pixel files would have a smaller enlargement factor, thus smaller Airy disks in the final print.

Mike Davis

[zilch0md]

Good news!

Canon Europe announed the 11.1 megapixel EOS-1Ds on 9/10/2002. See:

http://www.digitalfocus.net/sections/views/1DsRumour/1DsRelease.htm

The new EOS-1Ds will have a CMOS sensor described as "full frame." That means the 11.1 megapixels will map to the 24x36mm sensor at a resolution of approximately 2720 x 4080.

Quoting my April 30th post:

-----
For any combination of sensor height and pixel height (or diagonals or widths), the following apertures will be the diffraction limit at various quotients (pixels divided by millimeters):

Pixels/Millimeter vs. Aperture at which Airy Disks will reach 0.2mm diameter (5 lp/mm) in a 300dpi print

77.2 pixels/mm - f/22 (which is actually f/22.6)
115.8 pixels/mm - f/16
154.4 pixels/mm - f/11 (which is actually f/11.3)
231.6 pixels/mm - f/8
308.4 pixels/mm - f/5.6

This shortcut will help you figure out where visible diffraction will kick in with any digital sensor.
-----

So what is the pixel density of this new EOS-1Ds?

2720 pixels / 24mm = 113.33 pixels/mm

-or-

4080 pixels / 36 mm = 113.33 pixels/mm


Compare this to the EOS D30's ratio: 1440 pixels / 14.9mm = 96.6 pixels/mm

And to the EOS D60's ratio: 2048 pixels / 15.1 = 135.6 pixels/mm



5 lp/mm visible diffraction kicks in with 300 dpi prints at the following f-stops for these four cameras:

EOS-D60: f/12.9 (about f/11 + 1/3 stop)
EOS-1Ds: f/16
EOS-D30: f/17.8 (about f/16 + 1/3 stop)
Contax N (the first with a 24x36mm sensor): f/20.7 (about f/16 + 3/4 stop)

With the EOS-1Ds we'll be able to use f/16 without visible diffraction in a 9.1 in. x 13.6 in. 300 dpi print viewed at a distance of 10 inches, but we won't be able to use f/22. That's no worse than what we've suffered with 35mm film for years and although it's not as good as the D30 or Contax N, it's a definite improvement over the D60.

The EOS-1Ds has taken pixel density about as far as they dare for a 24x36mm format. We can not avoid visible diffraction in 300 dpi prints viewed at 10 inches without going to even larger sensors as the number of pixels is increased. Future 24x36mm sensors containing more than 11.1 megapixels will require avoidance of apertures wider than f/16. If Canon is willing to repeat the diffraction suffererd by the EOS-D60, they could go as high as 135.6 pixels/mm on a 24x36mm sensor: 3254 x 4882 pixels = 15.9 megapixels.

Mike Davis

[zilch0md]

Another bit of news quoting an anonymous source:

-----
Sinar has announced the joint development with Kodak of a 22 Megapixel CCD imaging chip for medium format camera backs. Some web sites are erroneously reporting this as a "digital back". Not yet. The chip measures 4080 X 5440 pixels and is 38.8 x 50.0 mm in size, close to the size of 645 format film. The implication for photographers is that while the new Canon 1Ds and Kodak 14n at 11MP and 14MP respectively boost 35mm format digital SLRs into medium format territory, medium format is now moving upwards as well. No indication as yet of when we'll see this in a commercial back, and for which cameras, or of price. But, you can be sure that it will not be inexpensive.
-----

I'd like to point out that despite having 22 Megapixels, this sensor has a pixel density of only 107.4 pixels/mm.

5440 pixels / 50.0 mm = 108.8 pixels/mm
4080 pixels / 38.8 mm = 105.2 pixels/mm

Using the diagonal:

6800 pixels / 63.3 mm = 107.4 pixels/mm


This means this new Sinar/Kodak sensor can support use of f/16 + 1/4 stop without forcing visible (5 lp/mm) diffraction in a 300 dpi print (13.6 x 18.13 inches) viewed at a distance of 10 inches.

Quoting my April 30th post again:

-----
For any combination of sensor height and pixel height (or diagonals or widths), the following apertures will be the diffraction limit at various quotients (pixels divided by millimeters):

Pixels/Millimeter vs. Aperture at which Airy Disks will reach 0.2mm diameter (5 lp/mm) in a 300dpi print

77.2 pixels/mm - f/22 (which is actually f/22.6)
115.8 pixels/mm - f/16
154.4 pixels/mm - f/11 (which is actually f/11.3)
231.6 pixels/mm - f/8
308.4 pixels/mm - f/5.6

This shortcut will help you figure out where visible diffraction will kick in with any digital sensor.
-----

Anybody see a trend in censor design here?

Contax N Digital can use f/16 + 3/4 stop without visible diffraction
Canon EOS-1Ds can use f/16 without visible diffraction
Sinar/Kodak MF sensor can use f/16 + 1/4 stop without visible diffraction

These engineers know what they're doing and they didn't have to read this thread to understand what's required to avoid visible diffraction.

Mike Davis

[adamsmith]

Is diffraction after f/11 a practical concern? I see a whole lot of math and argument in this thread, but so far I don't see anyone backing up their claims with a real example of a shot at f/8 vs. say, a shot at f/22. Are we talking about a theoretical defect, or an effect that a human can actually observe in the photograph?

-Adam

[zilch0md]

Hi Adam,

adamsmith wrote:
Is diffraction after f/11 a practical concern? I see a whole lot of math and argument in this thread, but so far I don't see anyone backing up their claims with a real example of a shot at f/8 vs. say, a shot at f/22. Are we talking about a theoretical defect, or an effect that a human can actually observe in the photograph?

-Adam

Many of the legions of photographers who choose NOT to shoot at f/22 and smaller stops with their 35mm gear would say that they can see the effects of diffraction with this format at that aperture. Some of them may have no knowledge of the math discussed here, but they do know they don't like what they see at f/22.

Many camera manufacturers like Sony, who are building digital cameras with integrated lenses (instead of mating digital bodies to lenses originally designed for larger formats), don't include apertures smaller than f/8 in their lenses. Are their designs impractical or does this decision suit some purpose? Answer: They know better than to offer smaller stops with the tiny sensors they are using. And I submit that manufacturers of sensors to be used with 35mm lenses, actually know better than to jam more pixels on them than the laws of diffraction will allow. There's no way around it - sensor size has to grow with pixel count or we'll see diffraction.

The aforementioned Contax N Digital, Canon EOS-1Ds and the Sinar/Kodak MF sensor are all pushing it as far as they dare - F/16 can be used without causing visible diffraction, but it's already degrading the image at f/22. The EOS-D60 went too far - jamming too many pixels on that size sensor to avoid visible diffraction at f/16.

Many large format photographers know they can't stop down below f/45 with a 4x5 camera or f/90 with an 8x10 camera - because of diffraction. The larger the format, the further you can stop down without concern for it.

Diffraction is real and I for one can see it in the EOS-D60 sample taken at f/22 (available at the URL referenced several times higher up in this thread.) As for backing up my claims... The math I'm using is very well documented in several books I referenced earlier in this thread, as well as in Jacobsen's well-known Lens Tutorial (an online resource that was also referenced earlier in this thread) not to mention many other references, no doubt, that I've never even heard of. I haven't made any new discoveries nor derived never before seen formulas from thin air. I've just put to good use some stuff that's as old as the hills.

Ten years from now, ask yourself why we never saw any 100 Megapixel sensors measuring 24x36mm. (Hint: That's a pixel density of about 330 pixels/mm. We would have to shoot at f/4 or wider apertures to avoid visible diffraction in 300 dpi prints made from such a sensor. There goes the Depth of Field.)

Mike Davis

[zilch0md]

Another contender goes too far.

http://www.dpreview.com/news/0209/02092304kodakdcs14n.asp

Kodak's new DCS-14n gives us 13.89 Megapixels on a 24x36mm (fullframe 35mm) sensor - a resolution of 4536 x 3024 pixel (effective).

What's the pixel density?

4536 pixels / 36mm = 126 pixels/mm
3024 pixels / 24mm = 126 pixels/mm

Quoting my April 30th post, yet again:

-----
For any combination of sensor height and pixel height (or diagonals or widths), the following apertures will be the diffraction limit at various quotients (pixels divided by millimeters):

Pixels/Millimeter vs. Aperture at which Airy Disks will reach 0.2mm diameter (5 lp/mm) in a 300dpi print

77.2 pixels/mm - f/22 (which is actually f/22.6)
115.8 pixels/mm - f/16
154.4 pixels/mm - f/11 (which is actually f/11.3)
231.6 pixels/mm - f/8
308.4 pixels/mm - f/5.6

This shortcut will help you figure out where visible diffraction will kick in with any digital sensor.
-----

The Kodak DCS-14n's 126 pixels/mm will cause diffraction to become visible in a 300 dpi print viewed at 10 inches whenever the user stops down below f/11 + 2/3 stops. This is almost as bad as the Canon EOS-D60's limitations in regard to diffraction (with its even higher pixel density of 135.6 pixels/mm - where diffraction becomes visible at only f/11 + 1/3 stop), and now, with the larger sensor, we lose the argument some folks made for the D60's smaller sensor - that we don't need the DoF offered by f/16 or f/22. Ooops!

I suppose some manufacturers will keep testing our tolerance for diffraction until the majority of their market complains.

Mike Davis

[bradleyphillip]

Three points:

Sorry to start with a beef, but:

#1:
I'm always a little puzzled as to why some feel the need to tell others not too think too deeply about the craft, but 'just go out and shoot', instead. I know many people who take beautiful photographs and do not understand the relationship between shutter speed and apeture. But they have a good eye for composition, color, and timing, and have managed to acquire a feel for how the camera might respond. If that is enough for them, then that's fine-- I think it would be imposing my own value system if I were to imply that they 'should learn more' or that there's 'something wrong' with their approach.

I feel that the same is true with people who discuss things at a deeper level. I think the thread is suitably titled, and if the discussion doesn't suit your particular style, what is the harm in simply moving on?

(end of rant)

#2:
Thank you Mike, for putting the time in to share your thoughts with us. I, as I'm sure others do as well, appreciate the knowlegeable discusson you've promoted, as well as those who've also been contributing. I was able to follow it until Yves weighed in! :) Wow!

#3:
Mike, can you (or someone) be so good as to provide a link of two images illustrating the loss of actuance caused in an image due to diffraction? I don't know what I'm looking for, so I'm at a loss to determine how significant a loss it is to my images.

I think I speak for more than myself when I say that it would go a long way to helping to actually see an f/8 side-by-side with an f/16 image where you could provide 100% crops (even in .bmp, if JPEG loss is an issue-- at least some browser will read that natively) and point out where you see degradation.

It needn't be with the D60 (since you may not have one). I'd be willing to take the shots as per your instructions using my 1D and, say, prime L glass. Your points would then be visible, and everyone could decide for themselves how big an issue it was for them.

Let me know, OK? And thanks again,
Brad

[normkoren]

I haven't read every post in this forum, so I'm not sure if anybody has pointed this out, but there is an error in the original post.

"To convert the diameter of a spread function to its equivalent in lp/mm, just take the reciprocal:
f/11 Airy disk at sensor = 1 / 0.0149mm = 67.1 lp/mm"

The error is that the Rayleigh limit in lp/mm is the reciprocal of the RADIUS of the Airy disk, not the diameter. It is therefore 154 lp/mm at 0.000555 mm wavelength.

This may explain a lot of the confusion in ensuing posts. If science says the bumblebee won't fly, check your equations. I have an introduction to image sharpness and MTF on
http://www.normankoren.com/Tutorials/MTF.html
I say more about this issue on my Depth of field page,
http://www.normankoren.com/Tutorials/MTF6.html

[zilch0md]

Hi Norman!

normkoren wrote:
I haven't read every post in this forum, so I'm not sure if anybody has pointed this out, but there is an error in the original post.

"To convert the diameter of a spread function to its equivalent in lp/mm, just take the reciprocal:
f/11 Airy disk at sensor = 1 / 0.0149mm = 67.1 lp/mm"

The error is that the Rayleigh limit in lp/mm is the reciprocal of the RADIUS of the Airy disk, not the diameter. It is therefore 154 lp/mm at 0.000555 mm wavelength.

This may explain a lot of the confusion in ensuing posts. If science says the bumblebee won't fly, check your equations. I have an introduction to image sharpness and MTF on
http://www.normankoren.com/Tutorials/MTF.html
I say more about this issue on my Depth of field page,
http://www.normankoren.com/Tutorials/MTF6.html

Indeed, the Rayleigh limit is typically expressed in terms of the RADIUS of the Airy disk, but I'm not interested in comparing the RADIUS of Airy disks to my chosen maximum permissible DIAMETER for circles of confusion. I'm not alone in wanting to know at what aperture the DIAMETER of diffraction's Airy disks have reached the same size as my chosen limit for the DIAMETER of circles of confusion.

Actually, I can't find any evidence on your page at

http://www.normankoren.com/Tutorials/MTF6.htm

that's contrary to my thinking. In fact, your page actually references one of the sources I used earlier in this thread - David Jacobsen's Lens Tutorial. Have a look at this link:

http://www.photo.net/learn/optics/lensTutorial

where readers can find David Jacobsen's statement on this subject about half-way down the page:

"As was mentioned above, the normally accepted circle of confusion for depth of field is .03 mm, but .03/0.00135383 = 22.1594, so we can see that at f/22 the diameter [DIAMETER, not RADIUS] of the first zero of the diffraction pattern is as large is the acceptable circle of confusion. "

So, if I want to know at what aperture diffraction's Airy disks reach the same diameter as my chosen limit for circles of confusion, I use the following formula, just as Jacobson does:

N = CoC Diameter / 0.00135383

I quote this from your page:

"The diameter of the corresponding circle, known as the Airy disk, is,
CAiry = 2.44* N *W (The 1.22 term in the Rayleigh limit comes from the radius.)"

If we supply a value of 0.000555mm for W (or 555 nanometers, for the wavelength of the yellow-green light at the middle of the visible spectrum), we can reduce the formula you are using to the same one I'm using:

CAiry = 2.44 * N * 0.000555

CAiry = N * 0.0013542

Which is real close to the formula I've been using (certainly not off by a factor of two):

N = CoC Diameter / 0.00135383

-or-

CAiry = N * 0.00135383

I don't believe we are in disagreement. You just didn't understand what the goal of my calculation was.

Thanks,

Mike Davis

[Dan Honemann]

Mike,


zilch0md wrote:

Here are the 5 lp/mm, 2:3 aspect ratio print sizes (in inches) from various formats, sorted by print size. (For digital cameras this assumes we're making 300dpi prints. For film formats this assumes we have at least 45 lp/mm resolution at the film plane to give us a 5 lp/mm print resolution with a 9x enlargement factor.):

[. . .]
35mm: 8.5 x 12.8
[. . .]


What I don't understand about these figures is that my Polaroid SS 4000 film scanner generates a 4100 dpi (3600 x 5488 pixels) image from 35mm slide film, which translates to a 12 x 18.3 inch print at 300 dpi--quite a bit larger than the 8.5 x 12.8 you list here.

Does the scan actually have more information than the film? Or does the 300 dpi print from the scan not resolve to the 5 lp/mm minimum you're using for your film-based sizes above?

Confused (but interested!),
Dan

[zilch0md]

Hi Dan!

Dan Honemann wrote:
Mike,


zilch0md wrote:

Here are the 5 lp/mm, 2:3 aspect ratio print sizes (in inches) from various formats, sorted by print size. (For digital cameras this assumes we're making 300dpi prints. For film formats this assumes we have at least 45 lp/mm resolution at the film plane to give us a 5 lp/mm print resolution with a 9x enlargement factor.):

[. . .]
35mm: 8.5 x 12.8
[. . .]


What I don't understand about these figures is that my Polaroid SS 4000 film scanner generates a 4100 dpi (3600 x 5488 pixels) image from 35mm slide film, which translates to a 12 x 18.3 inch print at 300 dpi--quite a bit larger than the 8.5 x 12.8 you list here.


The dimensions 8.5 x 12.8 inches equate to a 9x enlargement from fullframe 35mm format. I personally don't believe today's best lenses and color films can deliver more than a 9x enlargement without using digital tools like Grain Surgery, nik Sharpener Pro and Genuine Fractals.

Dan Honemann wrote:
Does the scan actually have more information than the film? Or does the 300 dpi print from the scan not resolve to the 5 lp/mm minimum you're using for your film-based sizes above?

Confused (but interested!),
Dan


The scan doesn't have more information than the film, but many would agree that at 4000 dpi, you've pulled just about all the information that's worth pulling. At 8000 dpi, you can actually get stuff you don't want (or so I've read in several places.)

Surely you must be exploiting some kind of digital enhancement to take your 4100 dpi scans to a 12x18-inch , 300-dpi print (a 12x enlargement) - a little USM, at least. If that's the case, then I can't speak to what you will actually see in the way of degredation due to diffraction, but I can say this:

Whatever you do end up with in an enhanced (or unenhanced) 12x 300-dpi print, it would look much better still if you didn't start out with Airy disks that were so large as to prohibit 5 lp/mm resolution in an unenhanced 9x 300-dpi print.

Mike Davis

[donb]

Got to this party late, but I'm intrigued by one of the first statements in this thread (by the originator of the thread):

"It's difficult to notice diffraction without doing a careful side-by-side comparison of a print... "

Seems a bit like the vacuum tube vs. transistor wars a few decades ago only this time it's visual instead of audible.

[Rayz]

Hi! Mike,

I've been reading this thread with great interest and a certain degree of puzzlement. I have a D60 and my next project will be to take a few shots at F16 and F22 to see if I can pick up these sharply defined Airy discs you're talking about.

The reason I'm puzzled is this. Anyone who's concerned about image quality simply doesn't shoot at larger F stops than F11 - with 35mm, that is. Most 35mm lenses are sharpest at somewhere between F5.6 and F8. As I understand it, F11 with 35mm format is equivalent to F22 with 6x7cm, F45 with 4x5" and F90 with 8x10".

Ansel Adams raised a few eyebrows when he suggested that F64 be used with 8x10. I believe most standard lenses for 8x10 have optimum performance at F22.

Your argument appears to me to be essentially a tautology. You're simply giving a mathematical description to a well known phenomenon. Diffraction limits resolution no matter how good your lens and no matter how high the resolving power of the sensor or film. One can't solve the problem of diffraction. It's a limit due to the nature of light and the laws of Physics. As sensor pixel density increases, ie. as the resolving power of digital sensors increases, then MANY of the defects of lenses will become more apparent - not just Airy discs but a whole host of aberrations. This will spur manufacturers to produce better lenses which can be used at larger apertures without noticeable aberrations.

Those really sharp enlargements from 8x10" film with fine detail that takes your breath away are probably shot at F22. They're probably distant scenes at infinity and if there's a reasonable DOF, it's been achieved through the tilt mechanism. Large format F22 is equivalent to a 35mm F3.5 and Canon, as you probably know, have a selection of 3 tilt & shift lenses for their EOS cameras.

Finally, there are very good reasons for having sensors that might appear to exceed the resolution of the lenses used. You don't need an anti-aliasing filter. The Kodak 14n is a move in that direction. As you know, anti-aliasing filters reduce resolution. There's a trade-off. It's better if you can do without them.

Cheers!, Ray

[zilch0md]

Hi Ray!

Rayz wrote:
Hi! Mike,

I've been reading this thread with great interest and a certain degree of puzzlement. I have a D60 and my next project will be to take a few shots at F16 and F22 to see if I can pick up these sharply defined Airy discs you're talking about.

You'll be looking long and hard. I've never said they were *sharply defined*.

Rayz wrote:
The reason I'm puzzled is this. Anyone who's concerned about image quality simply doesn't shoot at larger F stops than F11 - with 35mm, that is. Most 35mm lenses are sharpest at somewhere between F5.6 and F8. As I understand it, F11 with 35mm format is equivalent to F22 with 6x7cm, F45 with 4x5" and F90 with 8x10".

I appreciate the support you've given me with that statement!

Rayz wrote:
Ansel Adams raised a few eyebrows when he suggested that F64 be used with 8x10. I believe most standard lenses for 8x10 have optimum performance at F22.

That may be, but diffraction doesn't kick in until about f/90 with the 8x10 format, as you've said above, and personally, I welcome the very real DoF benefits available between f/22 and f/90. Who cares if the lens delivers its best resolution at f/22, if using that stop will force the circles of confusion in some portions of the scene to become visible at the anticipated viewing distance?

Rayz wrote:
Your argument appears to me to be essentially a tautology.

From your perspective, my efforts here may seem unnecessary, even pointless, but many contributors to this thread have revealed there's a great need to discuss this - most people are ignorant of how to determine where diffraction will become visible for their choice of print resolution and viewing distance.

Rayz wrote:
You're simply giving a mathematical description to a well known phenomenon. Diffraction limits resolution no matter how good your lens and no matter how high the resolving power of the sensor or film. One can't solve the problem of diffraction. It's a limit due to the nature of light and the laws of Physics.

You write this as if I am unaware of what you are saying and yet I myself wrote the following in this very thread:

Quoting my 30 April post:
"The math I'm using is very well documented in several books I referenced earlier in this thread, as well as in Jacobsen's well-known Lens Tutorial (an online resource that was also referenced earlier in this thread) not to mention many other references, no doubt, that I've never even heard of. I haven't made any new discoveries nor derived never before seen formulas from thin air. I've just put to good use some stuff that's as old as the hills."

I had to write that precisely because my earlier statements were being challenged by so many people. The principles aren't so well known, apparently.

Rayz wrote:
As sensor pixel density increases, ie. as the resolving power of digital sensors increases, then MANY of the defects of lenses will become more apparent - not just Airy discs but a whole host of aberrations. This will spur manufacturers to produce better lenses which can be used at larger apertures without noticeable aberrations.

But as you've written above, "One can't solve the problem of diffraction." - so increasing the resolving power of digital sensors must also be accompanied by an increase in sensor size. Again, I thank you for affirming this. That being the case, however, your prophecy that manufacturers will be spurred "to produce better lenses which can be used at larger apertures without noticeable aberrations" is irrelevant to this discussion. Is it not? Using larger apertures can only be accompanied by a loss of depth of field. And it is the quest for depth of field (smaller apertures required) that will drive one quickly into suffering visible diffraction if manufacturers don't keep the pixel density down on their sensors.

Rayz wrote:
Those really sharp enlargements from 8x10" film with fine detail that takes your breath away are probably shot at F22. They're probably distant scenes at infinity and if there's a reasonable DOF, it's been achieved through the tilt mechanism. Large format F22 is equivalent to a 35mm F3.5 and Canon, as you probably know, have a selection of 3 tilt & shift lenses for their EOS cameras.

I'd rather spend my money on larger sensors with pixel densities at or below 77.2 pixels/mm than on tilt optics. You don't get the larger image circle necessary to employ movements without a loss of overall resolving power. That's a fact. Have a look at the dismal performance of Canon's TS-E 24 f/3.5 (tilt/shift) versus their EF 24 f/2.8 (no tilt/shift):

http://www.photodo.com/prod/lens/detail/CaTS-E24_35L-116.shtml

http://www.photodo.com/prod/lens/detail/CaEF24_28-61.shtml

The TS lens has a Photodo grade of 3.3 vs. 3.9 for the zero-movement lens. Only Canon's zoom lenses test more poorly than the TS-E 24 f/3.5.

Their 90mm tilt/shift isn't bad, but hey, for less money I can get their 100mm f/2 USM with a Photodo grade of 4.2 versus their TS-E 90 f/2.8 with a grade of 3.9.

Lastly, relying on tilt to get sufficient sharpness is frought with pitfalls - the zone of acceptable sharpness becomes wedge-shaped as positive tilt is applied to reposition the plane of sharpest focus such that it reaches from the foreground to the background instead of being parallel to the film plane. Thus, any tall object in the foreground or perhaps even in the midground portions of the subject space can easily intersect and protrude above the ceiling of this wedge of acceptable focus. "Honey! This picture you took of me in the Tetons is horrible! My feet are sharp but my head looks like a giant cotton ball!"

No thanks. I'd much rather enjoy the broader selection of focal lengths, the superior performance and ease of use of non-tilt lenses. Please don't give the manufacturers any encouragement toward higher pixel densities. I have no use for it. Give me more pixels, but give them to me on larger sensors (with densities no greater than 77.2 pixels/mm so that I can use f/22 without causing visible diffraction in a 300 dpi print to be viewed at 10 inches.)

Rayz wrote:
Finally, there are very good reasons for having sensors that might appear to exceed the resolution of the lenses used. You don't need an anti-aliasing filter. The Kodak 14n is a move in that direction. As you know, anti-aliasing filters reduce resolution. There's a trade-off. It's better if you can do without them.

The only way to take advantage of that without a loss of quality is to increase your print data density by the same ratio as the sensor density exceeds the visible diffraction threshold. In other words, if the sensor's pixel density is 154.4 pixels/mm instead of the desired 77.2 pixels/mm and you want to use f/22 without suffering visible diffraction, you can enjoy avoiding the use of an anti-aliasing filter (as made possible by the high pixel density) only if you simultaneously limit your print size to that had at 600 dpi instead of the larger print you may be tempted to produce at 300 dpi. If you try to print at 300 dpi, you'll be forcing visible diffraction in the print. As you have pointed out, there's no way around the problem of diffraction.

Mike Davis
http://www.accessz.com

[Rayz]

Mike,
I certainly have to take off my hat to you for being able to refute almost every argument thrown at you. I'm sorry if some of my points had already been addressed. It's a long thread, but my main point seems to have got through your net. I'll elaborate as follows.

You might well prefer to use F90 with a 300mm LF lens in order to get greater depth of field and in order to avoid using the tilt mechanism which, as you say, is not without its own problems, but F90 with 8x10" is equivalent to F11 with 35mm in terms of Airy disc size on prints of equal size. The D60 has no problems with F11 but F stops greater than F11, say, F16 which is equivalent to F128 with 8x10 format. I think most large format photographers would try to avoid using F/128.

My main point is this. F/3.5 with 35mm has DOF equivalent to F/22 with 8x10". Distortion due to diffraction is much greater at F22 than at F3.5 in absolute terms but not in relative terms (ie. relative to the larger image size of 8x10). If it were not for the degrading effects of film, a good quality 35mm lens, diffraction limited at F3.5, would produce results as sharp and equal in every way to a 300mm LF lens with 8x10'.

It is perhaps not widely realised that big enlargements from large format film look better, sharper and more detailed than 35mm for one main reason - the image quality tends not to be degraded or limited by the film (well, not much anyway). What you get is essentially what the lens is capable of. Not so with 35mm. What you get is what the film allows you to get. There's a severe compromise which can be described by a simple, rule of thumb formula 1/S = 1/F + 1/L where S is system resolution, F is film resolution and L is lens resolution.

In spite of this limitation, there's an interesting experiment at Photodo's web site which compares 4x5 at F22 with 35mm at F5.6. Depending on the film choice, the high quality 35mm lens was capable of producing slightly sharper results, although admittedly grainier. Who would have believed it! 35mm sharper than 4x5"! Of course, the reason is not just film choice. Any lens is severely handicapped at even F22, never mind F90 or F128. That's why it's probably unlikely we'll ever have large format digital sensors. Nevertheless, the larger format sensor with larger pixels has the advantage of lower noise (for any given process). But technology has a way of overcoming such obstacles. The D60 is no noisier than the D30, yet it has smaller pixels.

I might be wrong. My reasoning might be faulty and my facts incorrect, but it seems to me, as the pixel density of sensors increases we get closer to the perfect film which allows us to see just what our 35mm lenses are really capable of.

BTW, the Canon 90mm T&S lens with a Photodo rating of 3.9 has the same rating as the Hassie F2.8 90mm Planar tested by 35mm standards. The Canon T&S 90mm suffers from a similar disadvantage to all MF lenses in that it has a bigger image circle. In relation to the diameter of the image circle, 3.9 is an excellent rating.

Cheers!, Ray

[Rayz]

Mike,
Further to my above post, I've just had a look at some test shots of a newspaper I taped to the wall - the financial pages of a broadsheet containing a mixture of big and small type.

I used my TS-E 90mm because this is the sharpest lens I've got. I also wanted to see just how sharp this lens is at the corners at big apertures. The larger image circle should ensure there's no fall off in light or resolution, especially with the small D60 sensor. The results are surprising. When I get the time, I'll repeat them using proper test charts instead of newspaper.

I used a sturdy tripod, remote shutter release and mirror lock-up. I compared images at up to 600% magnification in Photoshop. The preliminary results are as follows.

From F2.8 to F16 there is no significant difference in the clarity, contrast and readability of the newspaper text. However, there are subtle differences but one would not notice them on a print without a magnifying glass.

For example, centre resolution at F2.8 is marginally better than centre resolution at F16. However, corner resolution is very marginally better at F16 than at F2.8.

Very surprisingly, centre resolution at F2.8 is also marginally better than centre resolution at F8 but not at the corners where F8 wins - but again, not by a significant margin.

F5.6 was very marginally better than F2.8 at the centre. F4 was very close to F2.8 at centre and corners. Too close to call.

I would guess from these preliminary results that the TS-E 90 is diffraction limited at F5.6. That a lens should appear to perform approximately equally well from F2.8 to F16 doesn't make much sense. The only explanation I can think of is that the D60's sensor is the lowest common denominator. It doesn't have the resolving power to show up any significant differences between the aperture range of F2.8 to F16.

Resolution at F22 was decidedly blurry and F32 even more so.

Ray

[zilch0md]

Ray,

Rayz wrote:

I might be wrong. My reasoning might be faulty and my facts incorrect, but it seems to me, as the pixel density of sensors increases we get closer to the perfect film which allows us to see just what our 35mm lenses are really capable of.

The manufacturer of Gigabit-Film claims it can resolve 450 lp/mm, but load it into a Minox and you're still diffraction- limited to 5 lp/mm in a 13.4 x 18.4-inch print shooting at f/3.5 (the only aperture available on an 8x11mm format Minox) and the DoF with a normal focal length lens to produce circles of confusion no larger than 5 lp/mm in this same print isn't anything to get excited about, despite the tiny format: 18.44 feet to Infinity.

Before rushing out to buy a Minox equipped with Gigabit film, please note all of this assumes that the lens+film resolution, together as a system, can deliver 450 lp/mm, which is impossible, since the lens resolving power would have to be infinitely greater than 450 lp/mm to make this happen.

The formula for calculating total resolution is 1/r + 1/r + 1/r... = 1/r total

Assuming we had a lens that could resolve 450 lp/mm to go with our 450 lp/mm film (or sensor?), taking into account only the lens and film resolutions, we would get:

1/450 + 1/450 = 1/x

Thus, x = a 225 lp/mm lens+film combined resolving power. Even with this lens and film, our print size just fell to a 21.25x enlargement instead of a 42.5x enlargement: The dimensions necessary to deliver 5 lp/mm at the print would be only 6.7 x 9.2-inches. Fine grain (or tiny pixels with low noise) can not defeat diffraction.

The problem here is enlargement factor. Small formats can not produce large prints without enlarging diffraction's Airy disks by the same amount. There's no way around it Ray. The smaller your sensor, the greater will be your enlargement factor to achieve a desired print size, and the greater will be the enlargment of the Airy disks that were present at the sensor plane.

The "perfect film" you're looking forward to having with digital technology will come with increased sensor dimensions, not increased pixel density.

Mike Davis

[zilch0md]

Ray,

Rayz wrote:
Mike,
Further to my above post, I've just had a look at some test shots of a newspaper I taped to the wall - the financial pages of a broadsheet containing a mixture of big and small type.

snip

The only explanation I can think of is that the D60's sensor is the lowest common denominator. It doesn't have the resolving power to show up any significant differences between the aperture range of F2.8 to F16.

Resolution at F22 was decidedly blurry and F32 even more so.

Thanks for submitting some "real" data, for those who have been hungry for it. There are so many variables affecting your results, however, that I can not eagerly embrace your conclusions as proof that use of f/22 with the D60 compromises image quality. Your findings could be easily refuted by similarly casual testing, but I do appreciate the effort you've made.

For me, the math is much more solid. It tells me precisely where diffraction will become visible. I know some might be annoyed by my confidence in what they see as an intangible, but real data DOES exist, generated under tightly controlled conditions, that confirms the validity of the mathematical model I'm using. As you wrote, diffraction is "a well known phenomenon." It is but one of many degradations affecting image quality, but it can be a showstopper all by itself.

Mike Davis

[hmhm]

This appears to be perfectly valid analysis. My concern is that
some readers may mis-interpret the conclusions as a condemnation
of the D60. I don't believe it should be interpreted as such.

Let's take the declaration "D60 can't do f/16". Okay, I'll buy
that, but an f-number must be interpreted in the context of the
format. I certainly don't care whether I can "do" f/16 on any
given platform, as it means different things on each format,
though I might be concerned with whether I can achieve depth of
field on my camera comparable to what could be achieved on a
35mm film camera at f/16, without greater effects due to
diffraction.

So consider two shots taken of the same subject from the same
distance, but with these two cameras:
35mm film camera, 50mm focal length, f/16
compared to:
D60, 31mm focal length, f/10

These shots will have equivalent field of view, perspective,
and depth of field (though perhaps many people haven't banged
their heads against a wall enough times to convince themselves
of this). Per the calculations presented at the start of this
thread, these shots will also have identical effects due to
diffraction.

There is a valid point in this thread, which shouldn't be missed,
namely a reminder that you need to re-adjust your habits with
respect to aperture "numbers" when you move from one format to
another. But don't misinterpret this as a condemnation of a
particular format, because in this case the same wide depth of
field effects can be achieved with the same lenses and with no
greater diffraction, they'll just "appear" at different aperture
numbers.

[Rayz]

hmhm,
I agree completely. The D60 is essentially a slightly smaller format than 35mm despite the fact it uses 35mm lenses. Adjustments to F stop in relation to DOF have to be made as is the case with any change of format. But Mike seems to be using this fact to explain why the pixel density of digital sensors can be too great to the detriment of image quality, and this just doesn't make sense to me.

So, to Mike, here's my response to your last 2 posts.

Mike ,
I still can't understand your argument. When this sort of thing happens and people appear to be going round in circles, it's usually because one party, unbeknownst to the other, has a misconception regarding the basic facts of the issue and is therefore arguing from false premises. So, if you'll indulge me, I'll set out below what I understand to be the basic principles of diffraction, depth of field and their relationship to F stop and lens performance, and maybe you can point out where I've gone wrong. (This is as much for my benefit as anyone else's, so I can get matters clear in my own mind.)

1. Diffraction is a function of F stop. As F stop increases, distortion due to diffraction increases. As F stop gets smaller, diffraction gets smaller. Diffraction is at a minimum at maximum aperture and at a maximum at minimum aperture.

2. Other aberrations which affect lens performance tend to work in the opposite direction with regard to F stop. As F stop increases, lens aberrations decrease.

3. Ideally, with the perfect lens, sharpest results would always be obtained at the maximum aperture of the lens, since this is the aperture at which diffraction is least (and diffraction is not a problem that can be solved by lens design).

4. In practice, for most lenses, there is an F stop range at which the degree of lens aberration (such as chromatic aberration) is in balance with the distortion due to diffraction. Movement out of this range in one direction will degrade image quality as a result of increased diffraction, and movement in the other direction will degrade image quality due to various aberrations which could not be removed in the design and manufacture of the lens.

5. This range of F stops, sometimes known as the sweet spot, will vary from lens to lens. For many 35mm lenses, it's a narrow range centred around F8. For some really high quality lenses, such as some of the Leica Summicron and Elmarit standard lenses, the sweet spot extends from F4 to F8 and even at F2.8 sometimes the performance compared to F8 can be only very marginally worse. I recall once reading a test report on one 50mm lens which claimed performance at F2.8 exceeded performance at any other F stop. Can't remember the details though.

6. The fact that such high quality 35mm lenses already exist would suggest that, as technology advances, it would be possible to produce such lenses at an affordable price.

7. Following is a table showing the diffraction spot size in relation to F stop. This table has been copied from Roger N. Clark's excellent website. What this table shows is that there is at least a loose correlation between diffraction spot size and relative DOF's across the formats. For example, comparing LF 8x10" with 35mm 1"x1.5", we get the following relationships of DOF and Diffraction Spot size.

DOF of Large Format at F45 = DOF of 35mm at F5.6

Diffraction spot size at F45 = 50 microns; Diffraction spot size at F5.6 = 6.3 microns

50/6.3 = 8 (in round figures)

8 x (1"x1.5) = 8" x 12"

The inescapable conclusion from the above facts (if indeed they are facts broadly speaking - let's not nitpick) is that a good 35mm standard lens could theoretically give you the same performance as a good 300mm standard 8 x10 lens PROVIDED THE FILM OR DIGITAL SENSOR HAS SUFFICIENT RESOLVING POWER.

This is why I'm all in favour of increased pixel density. I realise that the trade-off in noise and dynamic range as pixel density increases is a huge technological challenge and it may well be that, say, 48 megapixel 35mm sized sensors will never become a reality for this reason.

Now, Mike, can you seriously debunk any of the above statements or highlight a chink in my logic?

F/ratio Diffraction spot size
2 2.2 (microns)
2.8 3.1
4 4.5
5.6 6.3
8 8.9
11 12
16 18
19 21
22 25
32 36
45 50


And another quote from Norman Koren's site:-


When a lens is stopped down so that it becomes diffraction-limited, increasing the format size does nothing to increase the image sharpness, i.e., total resolution. For example, an 8x10 image taken at f/64 will be no sharper than a 4x5 image taken at f/32.
The only exception is for small formats, particularly 35mm, where image sharpness is limited by film resolution.

Cheers!, Ray

[zilch0md]

Hi Ray,

Rayz wrote:

snip

1. Diffraction is a function of F stop. As F stop increases, distortion due to diffraction increases. As F stop gets smaller, diffraction gets smaller. Diffraction is at a minimum at maximum aperture and at a maximum at minimum aperture.

True

Rayz wrote:
2. Other aberrations which affect lens performance tend to work in the opposite direction with regard to F stop. As F stop increases, lens aberrations decrease.

True

Rayz wrote:
3. Ideally, with the perfect lens, sharpest results would always be obtained at the maximum aperture of the lens, since this is the aperture at which diffraction is least (and diffraction is not a problem that can be solved by lens design).

True

Rayz wrote:
4. In practice, for most lenses, there is an F stop range at which the degree of lens aberration (such as chromatic aberration) is in balance with the distortion (degradation) due to diffraction. Movement out of this range in one direction will degrade image quality as a result of increased diffraction, and movement in the other direction will degrade image quality due to various aberrations which could not be removed in the design and manufacture of the lens.

True

Rayz wrote:
5. This range of F stops, sometimes known as the sweet spot, will vary from lens to lens. For many 35mm lenses, it's a narrow range centred around F8. For some really high quality lenses, such as some of the Leica Summicron and Elmarit standard lenses, the sweet spot extends from F4 to F8 and even at F2.8 sometimes the performance compared to F8 can be only very marginally worse. I recall once reading a test report on one 50mm lens which claimed performance at F2.8 exceeded performance at any other F stop. Can't remember the details though.

OK

Rayz wrote:
6. The fact that such high quality 35mm lenses already exist would suggest that, as technology advances, it would be possible to produce such lenses at an affordable price.

Yes

Rayz wrote:
7. Following is a table showing the diffraction spot size in relation to F stop. This table has been copied from Roger N. Clark's excellent website. What this table shows is that there is at least a loose correlation between diffraction spot size and relative DOF's across the formats. For example, comparing LF 8x10" with 35mm 1"x1.5", we get the following relationships of DOF and Diffraction Spot size.

DOF of Large Format at F45 = DOF of 35mm at F5.6

I agree - see the spreadsheet at: http://www.primenet.com/~zilch0/tools/DoFDiff.xls

Rayz wrote:
Diffraction spot size at F45 = 50 microns; Diffraction spot size at F5.6 = 6.3 microns

50/6.3 = 8 (in round figures)

8 x (1"x1.5) = 8" x 12"

The inescapable conclusion from the above facts (if indeed they are facts broadly speaking - let's not nitpick) is that a good 35mm standard lens could theoretically give you the same performance as a good 300mm standard 8 x10 lens PROVIDED THE FILM OR DIGITAL SENSOR HAS SUFFICIENT RESOLVING POWER.

True

Rayz wrote:
This is why I'm all in favour of increased pixel density. I realise that the trade-off in noise and dynamic range as pixel density increases is a huge technological challenge and it may well be that, say, 48 megapixel 35mm sized sensors will never become a reality for this reason.

Now, Mike, can you seriously debunk any of the above statements or highlight a chink in my logic?

I can't debunk any of your premises, but I can debunk the conclusion you're reaching.

An 8x10 view camera can deliver beautiful 40x50-inch prints with an enlargement factor of only 5x. The images from your imaginary 35mm-sized sensor, if enlarged to 40x50, would suffer an enlargement factor of 42.33x (after a crop to 24x30mm)!

Any Airy disk projected onto that sensor will be enlarged 42.33x in the final print.

Question: How wide an aperture must we use to avoid seeing Airy disks in the 40x50-inch print?

The maximum permissible Airy disk diameter at the sensor must be 42.33x smaller than in the final print.

In the final print, it must be no larger than the reciprocal of 5 lp/mm (1/5th of a millimeter or 0.2mm)

So, at the sensor, before enlargement, our Airy disks (and our circles of confusion) must not exceed a diameter of:

0.2mm / 42.3333 = 0.0047244mm

Divide this by 0.00135383 (See Jacobsen's Lens Tutorial or several other references) and we get the f-number at which diffraction's Airy disks will reach this size at the sensor:

0.0047244m / 0.00135383 = 3.5

Wow! We have to shoot at f/3.5 or WIDER to achieve a measly 5 lp/mm in the final print. And I consider this to be a barely acceptable resolution.

I routinely shoot to produce 7 lp/mm in my images, because I, and many others, can SEE the difference between 5 lp/mm and 7 lp/mm at a viewing distance of 10 inches. I'll spare you the math, but using a 35mm format sensor, an attempt to achieve 7 lp/mm in the 40x50-inch prints an 8x10 film camera can readily deliver at only 5x enlargement, you will have to shoot at f/2.8 or WIDER.

Now here's where it really gets ridiculous: I hinted above that our circles of confusion would have to be limited to 0.0047244mm at the sensor just as our Airy disks must. I'm not going to do the math for you - just plug that diameter into any DoF calculator that lets you specify the CoC diameter required and you'll see for yourself that a 50mm lens, used at f/3.5, will require that our nearest subjects be 248 feet away from the camera when focused at the hyperfocal distance of 496 feet, with our far sharp at Infinity.

To achieve my preferred 7 lp/mm in the final print, shooting at f/2.8 instead of f/3.5, both spread functions must be limited to an even tinier 0.00337mm at the sensor. DoF calculation shows that my nears at f/2.8 must be no closer than 429.66 feet (focusing at the hyperfocal distance of 859.32 feet)!

Lovely! I can't WAIT to get my hands on one of these ULTRA-HIGH resolution 35mm-format digital cameras!

And how many pixels would it take to compete with the 8x10 camera you suggested?

300 dpi * 40 = 12,000
300 dpi * 50 = 15,000


12,000 * 15,000 = 180 Megapixels.

That's definitely "a huge technological challenge." It looks like we'll be coming up a bit short with only 48 Megapixels.

No thanks! I'll take your 8x10 with 300mm lens, even if it's a beat up old Deardorf covered with electrical tape to patch light leaks in the bellows.

If it's still not sinking in, have a look at the spreadsheet at: http://www.primenet.com/~zilch0/tools/Sensor1.xls

This will let you compare the 35mm sensor to some other formats and print sizes.

Rayz wrote:
F/ratio Diffraction spot size
2 2.2 (microns)
2.8 3.1
4 4.5
5.6 6.3
8 8.9
11 12
16 18
19 21
22 25
32 36
45 50


And another quote from Norman Koren's site:-


When a lens is stopped down so that it becomes diffraction-limited, increasing the format size does nothing to increase the image sharpness, i.e., total resolution. For example, an 8x10 image taken at f/64 will be no sharper than a 4x5 image taken at f/32.

The only exception is for small formats, particularly 35mm, where image sharpness is limited by film resolution.

Irrelevant.

The aperture at which we run into VISIBLE diffraction can be MUCH wider than the aperture at which a lens becomes "diffraction-limited." (Hint: The aperture at which a lens becomes "diffraction-limited" has nothing to do with enlargement factor, but the aperture at which diffraction becomes visible is inexorably tied to enlargement factor.)

35mm is CURRENTLY lmited only by film resolution. Drive the resolution up and you'll be shaking hands with Mr. Airy disk.

Mike Davis

[Rayz]

Mike,
Well, now we're getting somewhere. Let me try to separate the rhetoric and ridicule from the facts of the matter. You've agreed with my example comparing Airy disc (or diffraction spot) diameter at F45 and F5.6. You've agreed that DOF at F45 on 8x10 is roughly equal to DOF at F5.6 on 35mm. You've agreed with my deduction that a 35mm image at F5.6 can be enlarged 8x before the Airy disc reaches the diameter of the Airy disc on 8x10 at F45 with a standard 300mm lens - and yet you imply that, because the 8x10 film has to be enlarged only 5 times to reach a 40"x50 enlargement it must be sharper than the 35mm image that has to be enlarged 40 times. Since we've already established that the Airy disc on the 35mm image is 8 times smaller, we can enlarge the 35mm image 8 times more - and 8x5 = 40 (You've arrived at 42.3 by a different route, but let's not quibble.)

I'm beginning to think that you might be blinded by your own maths and are unable to see the woods for the trees. I think you're in love with all those figures that follow the decimal point - or have you forgotten we're talking about theoretical possibilities using an ideal, exceptionally high resolution film or sensor.

I admit my suggested pixel density of 48 megapixels was a mistake. This was a figure off the top of my head. I had in mind a system with about 4x the resolution of the 1Ds not 4x the number of pixels which, of course, is only double the resolution. You're right. To take full advantage of my ideal lens at F2.8, you would need about 180 megapixels. With such a lens and such a sensor you would (theoretically) be able to produce a 40x50 enlargement equal in every way to a 40x50 enlargement from an 8x10 image at F22. Agreed?

Now, I agree that the prospect of us ever having a 180 megapixel 35mm sized sensor seems dim. But, if you'd asked me ten years ago if I thought there was any possibility of being able to buy a 100GB hard drive that occupied no more space than my then current 200MB hard drive (500x the capacity) and at half the price of the 200MB drive, I would have said - "I can't imagine it. Sounds preposterous!" Technology has a way of surprising us all and Moore's Law still applies.

But, in any case, you've already ridiculed the poor depth of field at F2.8. With your beat up old Deardorf which you would claim to prefer to my 'super' lens (that's a real mystery in itself) you would presumably not be shooting at the sharpest aperture of F22, equiv. to 35mm F2.8, because of the poor DOF and the fact that you don't think much of the tilt facility which you rubbished earlier. So what F stop would you mostly use with the Deardorf? I'll select one to illustrate my next point. The revered Ansel Adams tried to promote an F64 club. Seems a good compromise to me. LF F64 has the same DOF as 35mm F8. For this illustration we don't even have to use my super lens because most 35mm lenses seem to be best at F8. In order to determine the maximum resolution at these F stops we'll bring in Rayleigh's Law which is often used by astronomers. We're getting into 'rule of thumb' stuff here, but that's fine by me because the maths is simpler. It's the concepts, relativities and relationships I'm trying to illustrate rather than precise real world results which, from experience, are generally much lower.

I know you know this stuff already so forgive me if I appear to be teaching you how to suck eggs. From Rayleigh's Law we can derive a simple formula that describes how diffraction limits resolution at a particular F stop. The formula varies according to the wave length of light, so lets take the lower figure which is probably closer to real world results. Dividing the F stop into 1000 gives you, in line pairs per mm, the maximum resolution that any lens can have at that F stop. (We'll ignore all the complexities of MTF curves and varying contrast ratios. Let's keep it simple.)

At F8, maximum resolution is 1000/8 = 125 lp/mm (for any lens). At F64, max. res. is 1000/64 = 15.6 lp/mm (for any lens). And guess what! 8x15.6 = 125. This is no coincidence. This is another confirmation of my earlier assertion that 8x10 format is sharper than 35mm for one predominant reason - less film degradation. Okay! So next question. What number of pixels do we need to capture that 35mm F8 resolution of 125 lp/mm? According to Nyquist theory it takes 2 pixels for each line pair, ie. 250 pixels per mm. So, (250x24) X (250x36) = 6000x9000 = 54 megapixels. Now that's a big difference from 180 megapixels but that's all that you, Mike, are going to need because of your deep concerns about DOF. You can't eat your cake and still have it.

Cheers!, Ray

[Rayz]

Mike,
Furthermore, this Rayleigh's derived formala for determining maximum resolution at a given F stop sheds some light on my test results of the TS-E 90mm lens which I found had a very similar performance between F2.8 and F16.

1000/16 = 62.5 lp/mm = 125 pixels/mm (Nyquist theory).

125x22.7 (length of D60 sensor) = 2837 pixels.

This is not far off from the quoted 3072 pixels of the D60. Taking into consideration that the Nyquist theory works better with sound frequencies than light frequencies and that in practice it takes somewhat more than 2 pixels to describe 1 line pair, it's easy to come to the conclusion that the D60 sensor can not resolve more than a good lens at F16. Your lens might be capable of producing sharper results at F5.6, but the D60 sensor is not. We need greater pixel density.

Ray

[zilch0md]

Hi Ray,

The following two cameras do indeed produce approximately the same results:

1) A 35mm format camera with 50mm lens at f/3.5 limiting CoC's and Airy disks to 0.00472mm on-film will yield 5 lp/mm resolution in a 40x50 print after ~40x enlargement.

2) An 8x10 camera with 310mm lens at f/28.2 limiting CoC's and Airy disks to 0.03819mm on-film will yield 5 lp/mm resolution in a 40x50 print after ~5x enlargement.

And yes, the Airy disks are 8x smaller in the 35mm format, as is the f-stop number it uses to produce the same results as the 8x10.

I've been over it thoroughly and regret not having calculated the DoF for the 8x10 at f/28.2 (the stop at which the 8x10 will suffer visible diffraction in the 40x50 print.) If I had done so, I would have seen that I had painted myself up a flagpole.

The DoF is, of course, identical - the 8x10 at its visible diffraction stop (f/28.2) will yield the same DoF as the 35mm at its visible diffraction stop (f/3.5) - a near of 248 feet with the far at Infinity.

I feel much better. Was it as good for you as it was for me? :-)

I appreciate your perseverance.

Now... Does my having backed myself into a corner during this sidebar alter the contention of my original post?

It probably does, but its 1:00 AM here, on a work night, so I'm going to go to bed before committing hari-cari.

If you like, feel free to jump in and finish me off in my sleep.

I'll be back...

Mike

[Rayz]

Mike,
Thanks also for YOUR perseverance. You started this thread and carried it through to its logical conclusion. To be forced to think things through in order to rebutt an argument that doesn't quite make sense is always good. It's been a learning experience for me. I'm more interested in clarifying matters in my own mind than winning the argument. Thanks for giving me that opportunity.

Cheers!, Ray

[edhofler]

Been following this from the beginning and would like to thank both of you. It has been very educational.

Ed

[jmamer]

Say, this is a "little" off topic, but our discussion of the D60's proclivity to revealing diffraction effects got me to thinking about something else.

To encapsulate the story so far, it's a matter of image magnification to get from sensor size to print size, and sensor density. You can have very dense sensors (pixels per mm) but you'd better be careful about how you enlarge the image.

Why does the same idea not also apply to camera shake?

I imagine a reasonable first order model of camera shake is deflection around the center of mass of the lens-camera body system. Visible shake occurs when the image of a stationary point in the scene projected on th sensor moves while the shutter is open. How far the projected image will move for a given deflection of the camera would seem to depend on the type of
lens being used and distance to the object. However, all things being equal, the same movement on at the plane of the image will be more noticable the larger
the magnification factor. Thus we digital photographers should be using our tripods and monopods more often than our 35mm colleagues (for the same ISO and focal length, of course).

What am I missing?
thanks
j.

[Morden]

What am I missing?

As far as I can see, you aren't missing much; the effect of camera shake should be greater on a smaller sensor. This is something that I had not previously considered, so thank you for spotting it. Well done!

Of course, one extra factor that must be considered is the mass of the camera; if you are lugging around 4 Kilos of camera/lens/flash then a positive consequence is that slight shakes are 'damped' by the sheer mass of the device. This doesn't apply solely to the D60 - it applies to any camera.

Neil D.

[Rayz]

Good point about camera movement. This occurred to me during my (duel!!) with Mike Davis but I didn't mention it because I thought it might dilute my argument and add confusion. (One shouldn't bring in too many variables at once.)

As I see it, there's usually a big gap between what is theoretically possible and what is practicable. Whilst a really high quality F50mm 35mm lens, diffraction limited at F2.8, could theoretically have a resolving power of 1000/2.8 = 357 lp/mm, which in terms of total image resolution and DoF is equivalent to 1000/22 = 45 lp/mm with 8x10 and a 310mm lens, this is all mathematical and theoretical. But, so was Mike's argument from the beginning. I was trying to find the flaw in Mike's reasoning by approaching the issue from my own perspective.

However, I'm here to confess that I don't really believe there's a 'snowball in hell's' chance of ever being able to capture a resolution of 350 lp/mm on film or sensor outside a laboratory.

First of all, the 180 megapixel sensor that Mike suggested would be required (a figure that I agreed with) is far too low. It's more like 450 megapixels. (If Mike had not been so busy trying to extricate himself from the flagpole, he might have picked me up on that.)

Secondly, assuming it might eventually be possible to make such a sensor, we would need to extend, expand and refine the 'Image Stabiliser' concept by a similar degree. The slightest vibration could have disastrous results. Mirror lock-up would not be sufficient. Vibration from the shutter itself could ruin the results, not to mention the vibrations from a passing truck or one of the numerous and frequent and imperceptible earth quake tremours that are happening all the time in areas that are susceptible to earth quakes.

Maybe we could have an 'image stabiliser' tripod head that would block or filter such vibrations. Hey! I've just talked myself into it. Yep! It might indeed be possible if technology advances equally on different levels.

[hmhm]

jmamer wrote:
... Thus we digital photographers should be using our tripods and monopods more often than our 35mm colleagues (for the same ISO and focal length, of course)...


Camera shake issues between full-frame and "small sensor" cameras
are identical if you consider "effective focal length" on the digital camera.
A film camera with a 50mm lens and a D60 with a 31mm lens will
have identical effects due to camera shake. They'll also have identical
field of view, and take identical compositions from the same distance.

Camera shake isn't a "bigger issue" with digital SLRs, but if you use
the rule of thumb of "shutter speed

[jmamer]

In my original question, I was assuming that the lens focal length was the same between the two cameras.
But, I certainly agree with your point. The 1.6 can also be seen as the effective additonal magnification needed (beyond the magnification you would need to do to a 35mm negative) to get from the D60 sensor to any given print size. Borrowing some of Mike Davis' figures, to go from the D60 sensor to and 8x10, I have to enlarge the longer axis of the picture by a factor of 11.189, for a 35mm negative this would only be a factor of 7.055. Taking the ratio here gives the additional magnification factor of 1.58 (the 1.6 comes back). So I'll use the rule of thumb 1/(focal length x 1.6).

And all this time I thought it was the price of the equipment that was making me shake more. It's
really the additional 1.6x magnfication factor.
What a relief.


j.

[Rayz]

hmhm wrote:

Camera shake issues between full-frame and "small sensor" cameras
are identical if you consider "effective focal length" on the digital camera.




Whilst I agree this is broadly true, there are other issues that come into play as one decreases sensor size and increases pixel density. Already with 35mm and MF, photographers who want to get the highest resolution from their system choose their tripods very carefully, some preferring, for example, wooden legs as opposed to metal legs because wood is worse at transmitting vibration. Some go to the extreme of hanging sand bags around the tripod collar for greater stability. Mirror lock-up is considered essential but some even worry about never being able to remove entirely the initial vibration cause by the shutter going off.

Add to this a whole host of very subtle background vibrations that are there constantly, a bit like background noise in a room that appears to be totally quiet, but if you were to measure it, the sound pressure level would probably be about 25dB or more, then it's not difficult to appreciate the more sensitive the instrument the more of a problem these factors become.

I note from 'rootcausefound's' post on page 2 of this thread, there's a table of basic specs of a number of digicams. I was surprised to learn that the pixel size of the Powershot G2 is only 3.12 microns, as opposed to 10.5 microns for the D30. Both cameras have a similar number of pixels (the G2 slightly more), but the pixel density of the G2 is much greater. In fact, if you extrapolate the 3.87 megapixels of the G2 on its 7.1x5.3mm sensor to a full frame 35mm sensor with the same pixel density of the G2, you get something like 96 megapixels, mathematically double the resolution of the 1Ds.

Now I'm not suggesting the Powershot G2 needs greater use of a tripod than the D30, although for all I know it might. These two cameras are of different quality. G2 pixels are noisier for a start. However, if these two cameras WERE of the same quality, I can imagine it might be more difficult to get the best out of the G2. For example, a tiny 1 micron (0.001mm) jolt during shutter release would cause a 33% degradation in resolution on the G2 (1/3.12). The same jolt or vibration with the D30 would cause only a 10% image degradation (1/10.5).

Ray

[hmhm]

Rayz wrote:
However, if these two cameras WERE of the same quality, I can imagine it might be more difficult to get the best out of the G2. For example, a tiny 1 micron (0.001mm) jolt during shutter release would cause a 33% degradation in resolution on the G2 (1/3.12). The same jolt or vibration with the D30 would cause only a 10% image degradation (1/10.5).

Ray


I don't think a relationship as direct as that would be pertinent
unless vibration could somehow cause the sensor to move with
respect to the lens (i.e. the sensor is shifting around relative
to the image projected onto it).

I don't know how to best model "typical" camera shake, but I'd
think that a sensible start would be to assume that the parts of
the camera (lens and sensor) don't move with respect to each other,
but that the entire camera moves with 2 types of motion, rotational
and translational.

The rotational motion could be modeled after rotation of the camera
about some axis through the nodal point of the lens (i.e. holding the
camera's position constant, but changing the direction in which it
is pointed). In this model, shake can be quantified by the angular
displacement of the camera during the duration of the shutter speed,
and we want to consider the resulting magnitude of the "blur" of
the subject across the sensor. This blur is, of course, how far
the subject's image moves across the sensor during the exposure,
the difference between its positions at the opening and closing
of the shutter.

The magnitude of the shift of the subject across the sensor is
going to depend on the relative magnitude of the shake's "angular
displacement" to the field of view of the lens. You can think of
the lens as converting an "arc" in front of the lens to a (typically)
smaller "arc" behind the lens, and the conversion factor is
dependent on the lens' field of view.

For instance, if you rotate the camera by .01 degrees during the
exposure, the shift of the subject across the sensor will be
significant if the lens has a field of view of 8 degrees (roughly
300mm for 35mm full frame), as the shift represents about 1/800th
of the field of view, and thus the blur will track across
(approximately) 1/800th of the extent of the sensor in that
direction. Note that this 1/800th is 1/800th of the sensor's
dimensions; for a smaller sensor it will be a smaller physical
distance, for a larger sensor it will be a larger physical distance,
but the important point is that it is proportional to the size of
the sensor. This blur will effect approximately 1/800th of the
sensor's pixels in that direction, so the number of pixels affected
by the blur is identical for two sensors of different size but with
identical pixel count. At 1/800th of the pixel count (in the
appropriate direction), this level of shake will be perceptible
on any multi-megapixel sensor, the image's resolution will be
limited by the shake and not by the sensor.

If you apply this same level of "shake" when the camera has a lens
with field of view of 115 degrees (roughly 14mm), then the .01
degrees of angular displacement is very small relative to the field
of view, less than 1/10000. That corresponding "shift" across the
sensor will not be noticeable on any sensor that exists today
(you'd need a sensor with something like 10000 pixels across).

So assuming an "angular displacement" model (rotating the camera
during the exposure), the number of pixels impacted by a subject's
blur can be calculated based only on the shutter speed, the rate
of the rotation, the field of view of the lens, and the total
pixel count of the sensor. It is not in any way dependent on
the pixel density; a pair of sensors of different size but the
same total pixel count will see an identical number of pixels
affected due to an identical shake.

If we consider a "translational displacement", one where the
camera's orientation remains the same but the camera itself is
moved slightly to the left or right (or up or down), then things
get a little more complicated, because the effect at the sensor
is dependent on the subject's distance. For instance, if you're
using a macro lens to shoot a close-up of a small insect at minimum
focusing distance, with the bug silhouetted against the moon, if
you shift the camera a few inches to the right without changing
its direction, the bug will have completely shifted off frame
while the moon will still appear to be in the same position as
before. We're measuring "parallax" here, and the effect diminishes
as the subject gets further away, as the angular change is dependent
on the magnitude of our change in position relative to the distance
to that remote object.

So when we shift the camera to the left by 1mm, we can convert
that into an angular shift for a particular subject by taking
into account the distance to the subject and using a little
trigonometry, it's the inverse sine of 1mm/subject-distance (it
may be easier to think of the camera staying still and the subject
moving 1mm to the right).

So we can convert a translation displacement into an angular
displacement considering only the distance to the subject and
the magnitude of the shift. We know that a given angular displacement
results in a blur across the sensor that is proportional to the
physical size of the sensor (e.g. blurring across 1% of the
sensor's size), and that this proportion is derived from the
proportion of the angular displacement to the field of view of
the lens.

I'd think that real-world camera shake could be modeled accurately
by the cumulative effects of some combination of rotational and
translational movement. In both of these modes of movement,
the camera-dependent factors were limited to the field of view of
the lens, and never to the pixel density of the sensor.
The field of view of the lens can be calculated from the combination
of focal length and sensor size. If we use 35mm film cameras as a
frame of reference, we can calculate an "effective focal length"
for a lens by multiplying its focal length by some multiplier
(e.g. 1.6X for a D60), calculating the focal length of a lens that
would yield the same field of view on a 35mm full-frame camera.
And if you buy all of this so far, then you can convince yourself
that any two cameras using lenses with the same "effective focal
length" will have identical "blur" resulting from identical shake,
even if they have different sensor sizes.

Of course a sensor with 11 megapixels will be able to detect
low levels of camera shake that are imperceptible on a sensor
with 1 megapixel, because it has a higher ability to resolve
the blur resulting from this shake. In other words, an image's
resolution can be "camera-shake limited", preventing an 11 megapixel
sensor from providing higher resolution than a sensor with lower
resolution (though it will be no worse).

At least, this is the logic I've used to convince myself. :)

[Rayz]

hmhm wrote:


So when we shift the camera to the left by 1mm, we can convert
that into an angular shift for a particular subject by taking
into account the distance to the subject and using a little
trigonometry, it's the inverse sine of 1mm/subject-distance (it
may be easier to think of the camera staying still and the subject
moving 1mm to the right).

So we can convert a translation displacement into an angular
displacement considering only the distance to the subject and
the magnitude of the shift. We know that a given angular displacement
results in a blur across the sensor that is proportional to the
physical size of the sensor (e.g. blurring across 1% of the
sensor's size), and that this proportion is derived from the
proportion of the angular displacement to the field of view of
the lens.





hmhm,
I'll have to think about this for a while and perhaps brush up on my maths. Your argument that a 1mm sideways shift at the sensor translates to a 1mm shift of the subject seems at first sight preposterous.

However, I just deleted my first reply to you because I'm having second thoughts about this. If one considers the cone in front of the lens and the much smaller cone behind the lens as a fixed, rigid system of light rays, then a transitional movement of 1mm will be the same at both ends. Whether the camera shifts by 1mm and the subject's stationary, or the subject shifts by 1mm and the camera's stationary is immaterial. Is this what you're saying? This is a beguiling idea.

Let's take a specific example. We're using a G2 with a 7mm wide sensor. The subject is a landscape 700 metres wide. The G2 gets a sideways jolt of 1mm at the time of exposure. Converting this transitional displacement to an angular displacement, we find that a leaf on a tree 700 metres away (and everything else 700 metres away) has shifted about 1mm in relation to the camera. I think this might be true. But is it relevant?

The point I would make is that the 700 metre wide subject has been compressed to a 7mm wide image whithin the camera and a 1mm jolt would be devastating to image quality. There is no two way communication from subject to camera and camera back to subject.

Using the same example with a larger camera, say 8x10 (200x250mm), it's easy to see that a 1mm jolt during exposure would be far less damaging to image quality. No need to get out your slide rule, calculator or maths tables to appreciate this point.

It still seems clear to me that what counts is the movement of the sensor in relation to the compressed image inside the camera and NOT movement in relation to the subject outside the camera. As the sensor gets smaller, a given fixed size movement gets bigger and more significant and more damaging to image quality in RELATION TO THE SIZE OF THE SENSOR.

On the other hand, as one moves down in format size one also moves up in shutter speed. 8x10 at F64 and 100 ISO is likely to require a shutter speed of 1/4 sec.
Equivalent DoF with the G2 is around F2.8 which in the same circumstances would require 1000th sec.

Whilst camera movement becomes more significant for the smaller format, this is offset by the capacity to use smaller F stops and therefore faster shutter speeds. A faster shutter speed is the best deterrent to camera shake. That's why I agreed with your original statement that format size, broadly speaking, does not have a bearing on the effects of camera shake. If your above argument is correct, then you would have to conclude that smaller formats are in fact more stable and less susceptible to the effects of camera shake, not just because of the opportunity to use higher shutter speeds but because of the necessity of having to use higher shutter speeds.

Ray

[edhofler]

I have to side with hmhm on this one.

If you had two cameras, different formats but the same effective focal length, side by side and applied the same shake to each the resulting blur would be the same.

Keep in mind I said the same effective focal length not field of view. In the case of the D60/30 versus a 35mm film body you would use the same focal length lens (do not compensate for the different field of view) because you are effectively cropping the negative by using a smaller sensor.

Ed

[hmhm]

Another approach to thinking about this that may be more
intuitive and less mathematical is to consider that the image
in the viewfinder is identical to the image on the sensor. Think
of the viewfinder as being the sensor, the left edge of the
viewfinder is the left edge of the sensor, etc. Take two cameras
with different sized sensors, and put lenses on them that yield
identical field of view for those formats (e.g. a 50mm lens
on a 35mm full-frame and a 31mm lens on a D60). Stand the same
distance from your subject, compose the frame the same way. You
should see the exact same composition through your viewfinder,
and of course you'll get the exact same composition in the
exposure.

Now, rotate each camera's "aim" by 1 degree to the right.
The composition has shifted slightly, but you once again
have the exact same image in each viewfinder. If your
cameras have lenses that yield an 8 degree field of view,
then everything in your viewfinder will seem to have shifted
to the left by about 1/8th of the width of the viewfinder,
or about 12%. If your cameras have lenses that yield a 50 degree
field of view, then everything in the frame will have shifted
to the left by about 1/50th of the width of the viewfinder,
or about 2%.

For each camera, that 1 degree rotate to the right caused
the subjects to move 2% (for the second case above) across
the viewfinder to the left. Each sensor is recording exactly
what the viewfinder sees, so the subjects have necessarily
moved 2% across the sensor to the left as well. Whether this
is a large and dense sensor, or small and dense, or small and
not dense, it doesn't matter, the subject will still have
"tracked" across 2% of the sensor. Whether 2% of the sensor
is a lot of pixels or just a few depends on how many pixels
the sensor has in that direction; it will be 2% of that number
regardless. Similarly, whether that "track" is several millimeters
across the sensor or just a small fraction of a millimeter depends
on the physical size of the sensor, it will be 2% of the size of
the sensor in that direction (so the jolt yields a larger physical
track across a larger sensor, and a smaller physical track
across a smaller sensor).

As long as the two cameras have identical field of view,
you'll see the same thing in the viewfinder, and "jolts"
of the camera have identical effect on that viewfinder
image, it doesn't matter what the size of the format is.
The sensor/film is "seeing" the same thing the viewfinder
is.

A 1mm "translational" shift of the camera doesn't necessarily
lead to a 1mm shift of the image across the sensor. As a
super-extreme example, consider a digital camera with a 1mm
wide sensor, and with a 180 degree fisheye lens attached.
If you shift the camera 1mm to the right, will the entire
image have shifted off the sensor? To be replace with what?

[Rayz]

Ed,
You might be right but I can't see it. The image in front of the lens can be described as a cone with its base at the subject converging to a point at the lens. The much smaller cone inside the camera has its base at the sensor converging to a point at the lens. If you change formats but retain the equivalent focal length each time, the cone on the outside will remain the same size - same field of view, but the cone on the inside will get progressively smaller as the format gets smaller.

One can argue about which type of shake has a greater effect on image quality, but once the light has passed through the lens, once that BIG cone on one side of the lens has been converted to the SMALL cone inside the camera, then it seems to me, all camera movement has to be considered in relation to the small cone. Using sines and cosines etc to extrapolate and convert displacements at the sensor to displacements outside the camera seems a complete red herring to me. The image or subject outside the camera is completely impervious to all camera shake and its effects.

Could be I'm failing to understand some basic concept.

Ray

[Rayz]

hmhm,
I see where I've gone wrong. I didn't pay enough attention to the first part of your explanation. As you said, my theory would only be pertinent if the sensor moved in relation to the lens. In most cases this doesn't happen. Camera shake applies equally to both sensor and lens. All my reasoning has been based on some idea of a fixed stream of photons passing through a fixed lens with the rest of the camera susceptible to movement - a ridiculous oversight.

Thanks for your helpful explanations.

Ray

[harmlessl]

zilch0md wrote:
Hi!

edhofler wrote:
I think you're supposed to use the numerical aperture not the fstop in Diameter Airy Disk = N * 0.00135383mm.

To solve for the radius (r) of the central disk in the Airy pattern you would use the following:

r=(1.22 x wavelength)/(2 x n.a.)

and n.a. = 1/2 x fstop

Try your formula with the numerical aperture and the results are very different.

David Jacobson's Lens Tutorial (http://www.photo.net/learn/optics/lensTutorial ) shows the formula used as I am using it - with N being the stop (5.6, 8, 11, 22, etc.)

Another reference that supports this formula is my favorite text on photography: "Basic Photographic Materials and Processes" by Stroebel, Compton, Current and Zakia; (c)1990 Focal Press. See the section on Diffraction (pp 168 to 170).

I'm confident my math is correct.

Thanks,

Mike Davis



Hi!
It's very funny you 2. You have same result! That is:
diameter=2 X radius
!!!

[zilch0md]

I'm back!

Rayz wrote:
Mike,
Thanks also for YOUR perseverance. You started this thread and carried it through to its logical conclusion. To be forced to think things through in order to rebutt an argument that doesn't quite make sense is always good. It's been a learning experience for me. I'm more interested in clarifying matters in my own mind than winning the argument. Thanks for giving me that opportunity.

You're welcome! Now, where were we? (Getting back on-topic...)

Lest anyone conclude from following recent events in this thread that diffraction offers no threat whatsoever in our quest for increased pixel densities, let's have a look at what we've learned.

zilch0md wrote:
The following two cameras do indeed produce approximately the same results:

1) A 35mm format camera with 50mm lens at f/3.5, limiting CoC's and Airy disks to 0.00472mm on-film, will yield 5 lp/mm resolution in a 40x50 print after ~40x enlargement.

2) An 8x10 camera with 310mm lens at f/28.2, limiting CoC's and Airy disks to 0.03819mm on-film, will yield 5 lp/mm resolution in a 40x50 print after ~5x enlargement.

And yes, the Airy disks are 8x smaller in the 35mm format, as is the f-stop number it uses to produce the same results as the 8x10.

The DoF is, of course, identical - the 8x10 at its visible diffraction stop (f/28.2) will yield the same DoF as the 35mm at its visible diffraction stop (f/3.5) - a near of 248 feet with the far at Infinity.

Let's make this a more realistic example, by reducing our final print size from 40x50 to 16x20:

1) A 35mm format camera with 50mm lens at f/8.7, limiting CoC's and Airy disks to 0.001181mm on-film, will yield 5 lp/mm resolution in a 16x20 print after ~16x enlargement.

2) An 8x10 camera with 310mm lens at f/70, limiting CoC's and Airy disks to 0.09548mm on-film, will yield 5 lp/mm resolution in a 16x20 print after ~2x enlargement.

And yes, the Airy disks are 8x smaller in the 35mm format, as is the f-stop number it uses to produce the same results as the 8x10.

The DoF is, of course, identical - the 8x10 at its visible diffraction stop (f/70) will yield the same DoF as the 35mm at its visible diffraction stop (f/8.7) - a near of 39.9 feet with the far at Infinity.

Ignoring for the moment that a 5 lp/mm 16x20 print from either camera, equipped with their respective "normal" focal length lenses, requires the nearest subject to be 39.9 feet away (nearly as difficult to achieve as the 248-foot nears required to produce a 40x50 5 lp/mm print), there's something else worth noting here which lends credence to the title of this thread: If pixel densities DO increase sufficiently to produce 5 lp/mm 16x20 prints from a 35mm-sized sensor, we won't be able to stop down below f/8.7 without forcing visible diffraction.

Sensors smaller than 24x36 only exacerbate the need to be wary of using the smallest apertures available on lenses originally made for 35mm film.

So even if Canon, Nikon, et al, managed to increase densities a hundred-fold, they can't shrink their sensors to dimensions smaller than 24x36mm without simultaneously discouraging the use of smaller stops on their 35mm-format lenses.

Which takes us back to my original contention - the D60's sensor is too small to stop down below f/11.

Comments?

Mike Davis

[hmhm]

zilch0md wrote:

Which takes us back to my original contention - the D60's sensor is too small to stop down below f/11.



Contention: "D60's sensor is too small to stop down below f/11"
IMHO:
"Okeydokey, given a chosen target resolution, fine. But who
cares? If the US switched to the metric system, I wouldn't
be able to buy a gallon of milk any more, and then what would
I pour on my cereal? What I lose with a smaller sensor is
shallow depth of field, not wide depth of field, given
identical lenses. Diffraction limits my pixel density,
a smaller sensor limits my total pixel count given
that max pixel density, but the D60 is nowhere near that
max density any way. With today's technology, pixel density is
limited by noise, so we're not butting heads with the
diffraction wall, but hopefully we will some day. Obviously the
goal is a full-size 35mm format at that max density, at which
point we'll have exhausted what the format can do (and anybody
needing more will have to move up to medium format, like
always, only there will be fewer applications that require it
(digital is improving its noise faster than film is improving
its grain)).

Contention: "Consider this before purchasing a Canon EOS D60..."
IMHO:
"Okay. I'm losing access to narrow depth of field,
losing wide angles, gaining telephoto, gaining instant
feedback, losing grain, gaining noise, losing film & processing costs,
gaining a lot of new sw/hw costs. I'll have to remember to use
wider apertures to get the same DoF and diffraction. Consider it
considered, seems like a pretty good deal to me!"

Contention (paraphrased): "There are limits to how dense a
sensor can get before you hit diminishing returns."
IMHO:
"Yup, though we don't seem to be there yet, certainly the D60
isn't past that limit. Anybody who thought that maybe all larger
formats would disappear with the advent of 35mm-sized
gazillion-pixel sensors will be disappointed, we're not going
to be able to go above a few tens of megapixels with 35mm
format before further density doesn't help any more as we
hit the diffraction (and lens impairment) wall. Anyone who
needs "more" will have to move to medium format, which
will continue to exist, it will 'go digital' as well (already
started to), it will have analogous advantages (more image
data) and disadvantages (cost, bulk) as it does today.
Digital will provide higher ISOs and lower noise than film,
film will become a niche medium."

[Rayz]

Mike,
I have to agree with hmhm's post above. Makes complete sense to me. I think many of your statements in this thread give the impression there has been an engineering blunder with the D60 and that the D30 was just right, whether by accident or design. I think that's where you've gone off at a tangent and arrived at some erroneous conclusions.

The D60 and D30 are both the same formats and yet the D30 can (supposedly) be used way down to f22 before diffraction becomes a problem whereas the D60 begins to show a diffraction problem at f16. Why is this?

Seems to me, because the pixel density of the D30 is not sufficient to show any resolution higher than what any good quality lens can deliver at f22 (or thereabouts). Resolution at f22 will be the same for both cameras. At f22 the D60 has no advantage over the D30. But at f8 the D60 will clearly show better resolution than the D30 as a result of its higher pixel density.

I should add that these mathematically derived thresholds of, for example, F11 for the D60 are in part based on the notion that 2 sensor pixels are equivalent to one line pair and that the D60's sensor has a maximum resolving power of 67 lp/mm. In practice it probably takes more than 2 pixels for each line pair. Norman Koren quotes 3 pixels. This could explain why I do not see any significant differences between identical shots taken at f11 and f16 with my D60 (although I admit I haven't done any properly controlled tests with charts yet).

In summary, I do not see a problem, in practice, using f16 with the D60 - resolution wise.

[zilch0md]

Hi Ray,

Rayz wrote:
Mike,
I have to agree with hmhm's post above. Makes complete sense to me. I think many of your statements in this thread give the impression there has been an engineering blunder with the D60 and that the D30 was just right, whether by accident or design.

No matter what density a person chooses for their prints, be it 240 dpi, 300, 360 or whatever, if they make two prints at the same density, one from the D30 and the other from the D60, the D60 print will be larger, right?

Since the D30 and D60 sensors share the same dimensions, the D60 suffers greater enlargment than the D30 when they are both printed to the same print density, right?

Can you agree that this difference in enlargement factor makes diffraction more of a problem at f/22 with the D60 printed to your chosen print density than at f/22 with the D30 printed to that same density?

And since the D60's prints at a given density are half again as large as the D30's prints and you personally find the use of f/22 to cause visible degredation in D60 prints, then wouldn't you have to stop down to f/32 to find the D30's prints equally compromised at that same print density?

And if Canon were to have created say a D90, that had twice the pixel density of the D30, instead of half again the pixel density, again on the same size sensor, wouldn't you find the use of f/16 with this D90 sensor to cause visible degredation - a two-stop difference from the D30's f/32 boundary?

We can infer that by your own judgement, the D30 can use f/22, at whatever print density you prefer, but the D60 must open up to f/16, and my ficticious D90 would have to open up to f/11. Right?

Would you welcome a D120 or a D180 equipped with lenses that stop down to f/22?

By your standards, they will poop out at f/8 and f/5.6 respectively when prints are made at the same density you chose for your D60 tests, and yet you encourage the manufacture of ever-higher pixel densities.

How many apertures wider than f/22 must become compromised for prints enlarged to your preferred print density before you would no longer think me confused for bringing this to people's attention?

Quoting my original post: Canon isn't the only manufacturer running into this problem of having lenses that will stop down into ranges that produce visible difrfraction.

I have NEVER called it a blunder. They know what they're doing. They just aren't bringing it to the attention of the market. Now that the rush is on to produce 35mm-sized sensors, the bar has been moved, but eventually, despite the appeal of ever-increasing pixel densities, the manufacturers will have to offer some lenses with wider minimum apertures, just as many integrated digicam manufacturers do already. (Sony's cameras don't stop down below f/8, for example, due to the very high density of their tiny CCD's.) It's either that, or let the public find out the hard way that they'd better stay away from the smaller stops on their 35mm legacy lenses.

Rayz wrote:
The D60 and D30 are both the same formats and yet the D30 can (supposedly) be used way down to f22 before diffraction becomes a problem whereas the D60 begins to show a diffraction problem at f16. Why is this?

My argument makes sense because people like to make the biggest prints they can from their digital cameras. As the pixel count goes up, so do their print dimensions. If pixel count goes up without simultaneously increasing sensor dimensions, enlargement factor goes up and the smallest acceptable f-number goes down. Your contention would only make sense if D60 owners routinely limited their enlargement factor to that of the D30 at their preferred print density. I wonder how many D60 owners who previously owned D30's are actually doing that...

Rayz wrote:
Seems to me, because the pixel density of the D30 is not sufficient to show any resolution higher than what any good quality lens can deliver at f22 (or thereabouts). Resolution at f22 will be the same for both cameras. At f22 the D60 has no advantage over the D30. But at f8 the D60 will clearly show better resolution than the D30 as a result of its higher pixel density.

Yes at f/8, fine! Just keep increasing the pixel densities and you'll be making that argument at f/4!

Rayz wrote:
I should add that these mathematically derived thresholds of, for example, F11 for the D60 are in part based on the notion that 2 sensor pixels are equivalent to one line pair and that the D60's sensor has a maximum resolving power of 67 lp/mm. In practice it probably takes more than 2 pixels for each line pair. Norman Koren quotes 3 pixels. This could explain why I do not see any significant differences between identical shots taken at f11 and f16 with my D60 (although I admit I haven't done any properly controlled tests with charts yet).

In summary, I do not see a problem, in practice, using f16 with the D60 - resolution wise.

The argument I made above is true no matter how many pixels are equivalent to one line pair and no matter where you believe diffraction becomes visible.

Mike Davis

[Rayz]

zilch0md wrote:


Since the D30 and D60 sensors share the same dimensions, the D60 suffers greater enlargment than the D30 when they are both printed to the same print density, right?

Can you agree that this difference in enlargement factor makes diffraction more of a problem at f/22 with the D60 printed to your chosen print density than at f/22 with the D30 printed to that same density?




Mike,
Still as dogged as ever! I wouldn't agree that the D60 'suffers' greater enlargement. You make it sound as though one is compelled to make a certain size print in accordance with the sensor's pixel densitiy. I don't think that D30 owners restrict themselves to 5x7 prints at 300 dpi or D60 owners restrict themselves to 7x10 prints at 300 dpi, which is all you get without interpolation.

But okay, let's go through the comparison. Two prints of images at f22 and 300 dpi, the D30 being 5x7 and the D60 being 7x10. Is diffraction more of a problem with the larger print, which is another way of asking - does the smaller print 'appear' to be sharper?

Well, I guess the answer is both 'yes' and 'no'. Both prints will contain the same amount of detail. In the case of the D30, the resolving power of the sensor matches the resolving power of the lens at f22. In the case of the D60, the resolving power of the sensor is LIMITED by the resolving power of the lens at f22, or to put it another way, the resolving power of the D60 is GREATER than required for any lens at f22.

In such a situation, the proper, or more objective, or more sensible way to make a comparison would be to compare prints of the same size by either discarding the 'redundant' pixels of the D60 or interpolating the D30's pixels. If you were to do the comparison this way, you would find that both prints are equally sharp.

Comparing different size prints introduces a whole set of new problems. As a general rule, a smaller print will 'appear' sharper if viewed from the same distance as a larger print containing the same amount of detail. A huge billboard from the other side of the street can look razor sharp. However, if you walk up close to it, the individual ink droplets might look like widely spaced peas leaving one to wonder how such a coarse process could ever look sharp.

If you're going to be so mathematically precise about the effects of diffraction, then you should continue with the same precision when viewing the prints. If you do, and adjust the viewing distance in accordance with the print size, then 'no' the greater enlargement from the D60 does not make diffraction more of a problem. If you wish to skew the results, discard all scientific rigour and view different size prints from the same distance, then 'yes' the bigger print will not look as sharp.

Ray

[zilch0md]

Ray,

You might as well tell us we don't have to worry about ANY factors affecting image quality because all such evils can be compensated by making smaller prints or by increasing the viewing distance.

Mike

[Rayz]

Mike,
Not at all! I'm simply explaining that the D30 has no advantage over the D60 at f22 and that when comparing two prints it's more accurate and meaningful to compare two prints of the same size from the same distance, otherwise lots of other factors come into play which can skew the results.

It's YOU who are attempting to compensate for such evils by making one print smaller than the other. If that's not clear, extend the analogy a bit. Imagine a D15. Same size sensor but 1.5 megapixels. According to your reasoning such a camera could go down to f32 (or thereabouts) without diffraction becoming a problem (which is the same as saying stopping up will not improve sharpness).

Are you seriously saying it would be fair and proper to compare a 4x3 print (approx.) with a 7x10 print in order to assess which is sharper? How are you going to do it? If you use the same loupe with each print, the larger print will have the advantage of greater magnification. The task of searching for the smallest detail that might exist on one print but not on the other (or less clear on the other) will be hampered by unequal magnification.

Nevertheless, a thorough scrutiny of each print would reaveal that both prints contain the same information and the same detail.

C'mon now Mike. Admit it when you're wrong. We all make mistakes.

Ray

[zilch0md]

Ray,

As pixel densities continue to increase in digicams equipped with 35mm-based lenses that include stops down to f/22, how do you expect us to avoid visible diffraction in our prints? There are only three choices and you seem to have an affinity for the first two:

1) Keep our prints the same size as those we made with the D30 so we can continue to stop down at least as far as f/16. (Look how sharp my 5x7 print is! Yippee! I knew all those pixels were gonna be good for something!)

2) Let the size of our prints increase in proportion to the increase in pixel density - but simultaneously increase our viewing distance by that same ratio. (All we have to do is put fences around our prints after we hang them on the wall so that nobody gets too close, 'cause we just can't bring ourselves to admit that the smaller apertures on our 35mm lenses have been compromised by visible diffraction!)

-OR-

3) Intelligently abandon the use of f/22, then f/16, then f/11, then f/8... in proportion to increases in pixel density.

I appreciate your suggestions Ray, but there's no mistake about it, I'll take what's waiting for us behind door number 3: Making big prints and viewing them at nose length.

Eventually, even this option will run its course, though: It's going to be a real drag having 24x36mm sensors and no way to get any depth of field without inducing visible diffraction. Say goodbye to DoF as the pixel densities go up and diffraction forces us to shoot at ever-wider stops. But as you've suggested, we can make a pretty good stab at solving that problem by rushing out and buying Canon's Tilt/Shift lenses. We won't be able to stop down with these lenses either, but at least we'll have a better shot at fitting the ever-dwindling DoF to our subjects.

We are already at pixel densities that threaten the usefulness of the smallest stops on our 35mm lenses. What good will a 35mm sensor be to us if its pixel density is so high we have to shoot at f/4 or wider to avoid visible diffraction in a print that's nominally sized to exploit all the pixels we've paid for yet still look sharp at close range (~300 dpi)?

Mike Davis

[Rayz]

zilch0md wrote:

We are already at pixel densities that threaten the usefulness of the smallest stops on our 35mm lenses. What good will a 35mm sensor be to us if its pixel density is so high we have to shoot at f/4 or wider to avoid visible diffraction in a print that's nominally sized to exploit all the pixels we've paid for yet still look sharp at close range (~300 dpi)?



Mike,
I thought we'd already established that F64 with 8x10 format has the same DoF as F8 with 35mm format and that if you want a really impressively sharp 24x30 print from 8x10 film you'll probably have to shoot at f22 which has the same DoF as f2.8 on 35mm.

I thought you'd also agreed that the Airy disc at F64 is about 8x the diameter of the Airy disc at F8 and that the maximum possible resolution of a lens at F8 is 8x the resolution of a lens at F64. Is large format not good enough for you?

You seem to have got hold of the wrong end of the stick. Higher resolution sensors do not restrict use of smaller apertures. The restriction is in the lens. You seem to be blaming pixel density for diffraction limitations. The maximum resolution of any 'good' lens at, say, F22 is given by the Rayleigh's formula discussed previously - ie. 1000/22 = 45 lp/mm (no doubt a theoretical maximum at high contrast). There's nothing much you can do about this. Your sensor either has the resolving power to capture this resolution or it doesn't. If 45 lp/mm is not good enough with 8x10 or 360 lp/mm is not good enough at F2.8 with 35mm (same result in both cases), then we'll have to wait for a major breakthrough in lens technology. No point in complaining about lack of DoF at F2.8 with 35mm. If you want the resolution, that's where you have to go. If you want more DoF you either have to sacrifice some resolution or use a tilt mechanism. Those are the rules of the game or the laws of Physics and they apply to all formats equally after establishing the relativities, ie. 35mm F2.8 = MF F5.6 = 4x5 F11 = 8x10 F22 and so on.

Now you may scoff at the notion that pixel densities of 35mm sized sensors will ever be great enough to capture the 360 lp/mm that a really good quality lens should be capable of at F2.8 (and you might well be right), but that's another issue isn't it? If it proves to be beyond the limits of affordable technology, then larger sensors in MF backs might become the 'ultimate quality' standard as hmhm suggests.

Can't you see this? Perhaps we'll have to agree to disagree.

Ray

[Rayz]

Mike,
Perhaps the confusion here is caused by our having gotten used to the severely degrading and limiting effects of 35mm film which we have come to consider a normal state of affairs. We so often confuse 'system' performance with actual lens performance and forget that lenses have their own performance independent of the film and that the full performance of our 35mm lenses is never realised except perhaps at very small apertures.

This is not the case with lenses designed for large format 8x10 where the degrading effects of film are insignificant. What you get is what diffraction allows you to get. This is why even old, pre World War ll LF lenses can give surprisingly good results and why certain prints that I have in my possession taken from 6x8 negatives exposed by Frank Sutcliffe in the 1890's, look almost as sharp as a modern 35mm print.

I've never used an 8x10 field camera so I have to apologise in advance if what follows sounds like rubbish. But my understanding is, the large formatter is continually battling with trade-offs between lens resolution, DoF and slow shutter speeds. It becomes very apparent that maximum DoF at F128 (if this is the smallest aperture) produces substandard results (resolution wise, just in case some one thinks we're equating overall picture quality with resolution alone).

Maximum resolution at F128 is 1000/128 = 7.8 lp/mm. Yes! That's seven point eight, not seventy eight. In practice it's probably less.

YET F128 WITH 8X10 HAS THE SAME DOF AS F16 WITH 35MM. Furthermore, maximum resolution at F16 is 1000/16 = 62.5 lp/mm. We've already agreed that 35mm has to be enlarged 8x more than 8x10 for equivalent sized prints and (co-incidentally?) 8x7.8 = 62.4. Is that close enough?

Conclusion? If the degrading effects of film or sensor are not a consideration, then shooting at F16 with 35mm format will give you the same c****y results as shooting at F128 with 8x10 format. Yet you are complaining that higher pixel density sensors might deprive you of the opportunity to produce these, to be polite, substandard results only achievable at F16 and below!!!

Well it won't! No matter how high the pixel density of your 35mm sensor, you'll still have the opportunity to continue taking fuzzy photos at F16 and even larger F stops, if that's your forte and if your lens has them.

Mike, sometimes I wonder about you.

Ray

[zilch0md]

Rayz wrote:

Mike, sometimes I wonder about you.

Ray

What do you wonder?

Mike

[Rayz]

I wonder if you really understand this stuff as clear as a bell but you're just having a bit of fun and pretending you don't.

Ray

[zilch0md]

Ray,

I could say the same about you and I don't mean that spitefully. In fact, your having said that means neither one of us is yanking the other guy's chain and that's very comforting to know, given the headlock we have on each other.

From my perspective, your argument that different sized formats produce identical amounts of DoF and diffraction at proportionate f-stops in like-sized prints is absolutely true, but it's a subset of what I'm talking about - not the contradiction you believe it to be. I'm not talking about sharpness in like-sized prints. That was revealed with sarcasm when I wrote:

"1) Keep our prints the same size as those we made with the D30 so we can continue to stop down at least as far as f/16. (Look how sharp my 5x7 print is! Yippee! I knew all those pixels were gonna be good for something!)"

I'm talking about visible diffraction forcing us to use wider apertures as print size increases with pixel count. If you remain steadfast in insisting that we compare like-sized prints, where the data density of one print is different than that of the other, you'll not be able to follow my argument. Please try to step out of that box for a moment and consider the larger scope of what I'm discussing. I'll give it one more try:

We agree that visible diffraction increases with enlargement factor. So without question, if we're willing to avoid increases in visible diffraction by keeping our prints at a fixed size, increasing the pixel density is a welcome thing, but surely we would eventually go to larger prints once we can no longer appreciate an increase in resolution at the size we started with. (Take your first step here...) And when we go to those larger prints, to exploit all those extra pixels, if the sensor size hasn't changed with the increase in number of pixels, the visible diffraction will increase along with the enlargement factor. We can combat that by increasing our viewing distance proportionately, but how can we enforce a doubling of our audience's viewing distance every time the manufacturers double the sensor's pixel density without also doubling the sensor size? (Take another step here...)

Looking at all the variables from THIS perspective, you should be able to clearly see only one solution to the increase in visible diffraction that accompanies sensors with higher pixel densities: Intelligently abandon the use of f/22, then f/16, then f/11, then f/8... in proportion to increases in pixel density. (Quoting my previous post.)

If you are unwilling to accept my contention that people will make larger prints as pixel count increases, you are still in the box.

If you are unwilling to accept my contention that people will not enforce increased viewing distances as pixel count increases in like-sized sensors, you are still in the box.

Outside this box that demands fixed print sizes and viewing distances that increase with pixel count, sensors MUST increase in size in proportion to increases in the number of pixels to continue using all the stops available on our 35mm-based lenses. Since 24x36mm sensors are the largest sensors we can use with our 35mm format lenses, we're stuck with having to abandon smaller apertures as the manufacturers continue to increase pixel density. We'll be saying good-bye to DoF every time we retire the use of an aperture, but the only alternative (outside the box) is to seek DoF at the expense and hassle of purchasing and using Tilt/Shift lenses. Either way, we will lose our zeal for increased pixel densities long before they force us to shoot wide open to avoid diffraction in nominal-density prints viewed up close.

I personally have no interest in using a 35mm-based system where the DoF is constrained to that had at even f/11, much less f/8 or wider apertures. Pixel density can not conquer diffraction, it is enslaved by diffraction. Just as with film, if we want larger prints, we'll have to go to larger sensors in medium format systems. Increasing the pixel densities on our 35mm digicams won't get us there.

Mike Davis

[bglic]

Ray, I certainly appreciate your tenacity. It seems you understand all the issues here, but somehow, in my opinion, you are missing the conclusion, but I am not sure how this is occuring?

I shoot all formats from 35mm through 8x10. I constantly struggle with this diffraction issue. Unfortunately it remains unchanged for the past 200 years. I will try to explain from a different angle, then maybe it will shed new light on the subject.

For starters, this discussion revolves around two issues, the first is lens diffraction and the second is, "on film resolution". (in the case of digital, "on sensor resolution") I will set aside the max. on film/sensor resolution issue for now and try to address what this thread is about, diffraction.

You agree that each jump in format size represents two jumps in f stops to maintain the same DOF, right? However, as you know, there is a limit to how far this can be pushed. This limit is diffraction, hence the reason you sometimes can NOT get a sharper print on larger formats vs. smaller formats, as the f stop on the larger format is costing you more than the gain in film size.

Resolution of the final print has two factors, "on film/sensor resolution" and enlargement factor. I am sure you would agree this, right? I am also sure you would agree that as you continue to stop the lens down, the "on film resolution" is now limited by the physics of diffraction not the resolution of the glass. Considering the same enlargement factor, images that were taken with less "on film/sensor resolution" (from diffraction) will obviously have less "on print" resolution! This seems to be the point you are missing. The only remaining question lies in where this point occurs.

In the very begining of this thread, Mike worked backwards from the final print resolution and determined how much on film/resolution would be required to acheive such. If you follow this math, you will find that constantly increasing the enlargement factor will limit how far you can stop the lens down to achieve the same "on print" resolution. This is a very simple concept. If it was not for diffaction, you can do this forever and shoot at f256.

The other reason enlargement factor increaces is due to the film / sensor size being smaller than ideal. So Mikes point is, unless you get larger sensors (or film) than the only way one can increase final print size is by increasing enlargement factor, which constantly demands more "on film / sensor" resolution. And this is not possible at the higher f stops as "on film resolution" keeps falling...the greater the enlargement factor the earlier diffraction kicks in, and yes, some day they may have a camera that may be limited at f8, which is fine for wedding and sports shooters, but not for landscape shooters. So this is not always a bad thing, it depends on the use of the camera.

The other issue is how much "on film / sensor" resolution is possible. With film the generally accepted formula has been 1/R = 1/r1 + 1/r2.... whereas R is the Resolution of the entire camera system and r1 is the lens resolution, r2 is the films resolution, r3 filters, etc. This formula drastically limits even the best lenses in the world to acheive only moderately better "on film" resolution vs. mediocre lenses. This is why better lenses in smaller format NEVER can overcome a jump in format size using outdated lenses. Now with digital, no such formula seems to exist now... however, the final results have proven the formula has not changed too much, meaning the films MTF is somewher close to sensors MTF. Unless there is a huge breakthrough in this area, we will be foriced to follow a lot of the ol rules that have been around for 150 years with film. So the point of this is.... even in digital, the rules of film still apply. However, digital sensors have been recently prove to appreciate higher resolving lenses, hence the newer digital lenses which are being produced. However, this is a marginal breakthrough, it will not radically change this discussion.

Just think about cameras. Why would anyone jump from 35mm to MF? The anwer is sharper prints vs. 35mm at the same final print size! Why? ... less enlargement factor required to acheive the same size final print. Why jump to 4x5? Same justification...why jump to 810? Well, same justification, however the images that can be shot are now a bit limited due to diffraction / DOF. Why jump to 16x20 format, or 20x24 format? Now the images you can shoot are pretty much limited to infinity, due to diffraction. This is why LF film today has practical limits, mainly 4x5 and 8x10.... as diffraction spoils the craft at sizes larger, unless one only shoots at infinity or shoots flat objects like repro work, or brick walls.

So the bottom line in digital today is, we either accept diffraction rearing its ugly head at lower f stops as we try to exploit enlargement factor on small formats - just like film. The only way we can avoid it - using larger sensor sizes to reduce the enlargement factor.

Of course my dream is to see Canon and Nikon eventually pass the 24x36 sensor size and move into the 50x60 sensor size... (they are no longer limited by film and now they can trample on the over priced MF camera makers) then we will have reasonably priced cameras with all the bells and whistles of 35mm with great enlargement potential and acceptable diffraction issues... someday...

[jmamer]

I have a fairly trivial question that's been nagging me from about the middle of this thread. Is there some way to get a "effective pixel density" for 35mm film?
Say for mundane Kodak 100 ISO print film and for slide film?
thanx
john

[Rayz]

bglic wrote:
Ray, I certainly appreciate your tenacity. It seems you understand all the issues here, but somehow, in my opinion, you are missing the conclusion, but I am not sure how this is occuring?



bjlic,
I'm also not sure how I'm missing the conclusion, but I'm willing to keep trying. I understand everything you've just written although I would probably take issue with your assumption that the basic formula 1/S = 1/F + 1/L also applies to digital sensors. This formula is very revealing of the degree to which film degrades final image quality and it doesn't take much maths ability to play around with it. However, I believe the resolving power of digicams is similar in principle to film scanners and the resolving power of both can be determined using the Nyquist Theory which essentially says 2 pixels are required to resolve one line pair. In practice, I believe it's more, perhaps as many as 3 pixels per line pair, but if we stick to 2 pixels, that agrees with the often quoted 67 lp/mm maximum resolution of the D60. I don't think this figure of 67 is meant to be included in the 1/S=1/F+1/L formula. System resolution would then be far too low.

Mike,
Let me go through this once again and this time use a bit of your own maths to see where we get.

But first let's clarify what you really mean with the D30/D60 comparison. What I think you're saying, if I can paraphrase, is that any photo taken at f22 with a digicam whose sensor is only 22.7 x15.1mm does not merit enlargement beyond 5x7 because to do so would cause diffraction distortion to be visible. The diameter of the Airy disc would exceed 0.2mm and the idea is to keep it smaller than that or at least no bigger - at normal viewing distances.

Using a D60 at f22 would result in a native enlargement (at 300dpi) of about 7x11. For people like you and me who are super critical, such an enlargement would look slightly fuzzy, not up to scratch, below par, when held at, say, arms length.

If that's all you're saying, I would essentially agree. I did suggest an obvious way around this is to view the larger print from a greater distance. We do it with TV sets. You're not going to sit as close to a 36" screen as you would to a 14" screen. I think there's a natural reaction, even when holding prints in the hand, to extend the arm and view the larger print from a greater distance. Nevertheless, I can see you have a point. If we extend the analogy to really high density sensors, say a 48 megapixel sensor the same size as the D60, and we print out all the pixels at 300 dpi, we get a print that's almost 30x20 and that's definitely too big, except perhaps from the other side of the room. It's not ideal, for sure.

However, I would contend, and this is the point where we really disagree, that this is the sacrifice you have to make if you want the DOF that F22 gives you with a D60/D30 format. There's no way around it.

Let's look at the alternative which you and bjlic seem to favour. Rather than a 48 megapixel 22x15mm sensor, I take it you'd rather have a 48 megapixel sensor 16x the size of the D30's sensor with the same pixel density of the D30. That works out almost exactly to MF 6x9cm.

Now there may be many advantages of such an arrangement such as greater dynamic range and lower noise and certainly at F22, 30x20 prints are going to be much, much sharper. No diffraction problems there.

But, wait on! It's not just F22 you're after. What you really want is the DOF that F22 gives you with the much smaller D30 format. As a general rule, to get the equivalent DOF of a larger format you multiply the F stop by the difference in focal lengths of the 2 standard lenses. Standard lens for the D30, taking into account the 1.6 multiplier, is 30mm. Standard lens for 6x9 is 90mm. Equivalent F stop to give same DOF as F22 with the D30 is 3x22=F66. Call it F64. So far, so good.

But, hang on! I've got a couple of second hand MF cameras. Can't see F64 on any of my lenses. Nothing bigger than F32. I'm two stops short. Why is that? Could it be that nobody would want to use F64 with an MF camera because diffraction would be too much of a problem?

Let's have a look at your formulas at the biginning of this thread.

Diameter of Airy Disk = F stop x 0.00135383

At F64 we get 64 x 0.00135383 = 0.08664512

Now a 48 megapixel image from a 6x9cm sensor (3.6x2.4 inches) will produce almost a 30x20 inch print without interpolation. That represents an 8.33x enlargement factor.

From your first post, the size of the Airy disk on the print will be 8.33 x 0.086645 = 0.72mm

Wow! Wow! Wow! Isn't it supposed to be 0.2mm.

Well, let's see what degree of enlargement we can tolerate before exceeding the 0.2mm limit.

E x 0.086645 = 0.2 E = 0.2/0.086645 = 2.3

Maximum print size from our 3.6x 2.4 inch sensor before Airy discs become visible will be (2.3 x 3.6) x (2.3 x 2.4) = 8.28 x 5.52.

Wow! again. There IS an improvement. With the D30 we were limited to 5 x 7.5 prints at F22. With the larger format at equivalent DOF we can get 5.5 x 8.25 prints.

Have I missed something? Have I made a mistake in my calculations? Let me know.

Regards, Ray

[bglic]

Ray, I know you responded to Mike. But I will try to tackle this one. I have no arguments with your presentations. But as I mentioned in my post above, the exact same thing applies to film!

One of the points I was trying to make above is...... you ONLY benefit from increasing format size, or sensor size, when the jump upwards in f stops did not bump the ceiling of diffraction. This is why there is a limit to how big you can push a format size - mean ol diffraction! Although I carry 35mm, MF, 4x5, and 8x10 into the field with me, I rarely use the 8x10. I always want to use it, but it quite often provides no benefit over the smaller formats as diffraction limits its resolution, but does not limit the resolution on the smaller formats. Now, in the example you gave, you started with a 35mm frame at f22 (at the edge of diffraction) and proved larger film / sensor would not benefit us! Right! You have clearly identified the limits of optics from diffraction.

So jumping up in format size will only benefit us (in terms of resolution) when we can at least record resolution greater than "x" of the format jump. Example, 4x5 to 8x10 format jump...if we record 40 lpmm on 4x5 and the jump is 2x, we need to record an amount greater than 1/2 (reciprocal of jump) of 40 lpmm if there is benefits in resolution on the final print. This is what I refferred to when I say, I struggle with diffraction everyday.

I think what Mike was saying was this..... he identified at what f stops you had to reduce the size of the final print to maintain the same print resolution. Meaning you can't maximize the sensors enlargement capability at f stops much earlier than people think. Although he did no mention this, but I think the benefits of larger sensors sizes produce benefits at some point below this diffraction limit.

Now, about your other assumption that sensors do not follow the same "on film resolution" math as film does - 1/R. I would like to beleive you are right, but I see no "real world" evidence that you are right about this. And of course the digital world offers us virtually no support documentation in this area. However, here is my justification why I beleive digital does follows the same math, or at least very close.

A good 35mm lens can deliver 250 lpmm aerial resolution...if the sensor could record anywhere near this resolution, it would provide for a 50x enlargement while still maintaining 5 lpmm to the final print, 50" x 75" ?? I think you would agree this is not possible. In reality, it does not matter if you shoot at f2 or f11 with digital cameras, the enlargement factor remains quite constant while maintaining the same print resolution. However, if the sensor could record higher resolutions, you could create much bigger enlargements from wider f stops shots vs. smaller f stops (excluding the point were diffraction comes into play) And I have not seen this, have you? Hence the reason I mentioned that lens / sensors share a similar or very close relationship to 1/R used for lens / film.

If anything, the digital images seem to be cleaner, meaning it is more software friendly, offering a slight enlargement benefit over the same size scanned film file. But still, no where near the aerial resolutions I mentioned above. Your comments?

[zilch0md]

Ray,

Rayz wrote:

Mike,
Let me go through this once again and this time use a bit of your own maths to see where we get.

But first let's clarify what you really mean with the D30/D60 comparison. What I think you're saying, if I can paraphrase, is that any photo taken at f22 with a digicam whose sensor is only 22.7 x15.1mm does not merit enlargement beyond 5x7 because to do so would cause diffraction distortion to be visible.

That's incorrect.

Any photo taken at f/22 with a D30 or D60 does not merit enlargement beyond 4x6 (not 5x7) because to do so would cause visible diffraction (at a viewing distance of 10 inches, assuming our eyes can resolve 5 lp/mm at that distance).

Rayz wrote:
The diameter of the Airy disc would exceed 0.2mm and the idea is to keep it smaller than that or at least no bigger - at normal viewing distances.

I would say, "- at a viewing distance of 10 inches."

Rayz wrote:

Using a D60 at f22 would result in a native enlargement (at 300dpi) of about 7x11.

I would say, "Using a D60 at any aperture would result in a 6.83x10.25-inch print at 300 dpi (about 7x11)."

Rayz wrote:
For people like you and me who are super critical, such an enlargement would look slightly fuzzy, not up to scratch, below par, when held at, say, arms length.

If that's all you're saying, I would essentially agree.

I've never said anything about viewing prints at arm's length, but if that were to result in a viewing distance of 24-inches, then a 6.83x10.25-inch print that requires f/12.9 with the D60 to deliver 5 lp/mm at a viewing distance of 10-inches, could tolerate use of f/30.9 (almost a full stop beyond f/22) if we have some way of enforcing arm's length viewing.

So, you've not agreed with me; you're still in the box where print size and viewing distance aren't considered with the diligence they deserve.

Rayz wrote:
I did suggest an obvious way around this is to view the larger print from a greater distance. We do it with TV sets. You're not going to sit as close to a 36" screen as you would to a 14" screen. I think there's a natural reaction, even when holding prints in the hand, to extend the arm and view the larger print from a greater distance.

Especially for those with uncorrected myopia.

Rayz wrote:
Nevertheless, I can see you have a point. If we extend the analogy to really high density sensors, say a 48 megapixel sensor the same size as the D60, and we print out all the pixels at 300 dpi, we get a print that's almost 30x20 and that's definitely too big, except perhaps from the other side of the room. It's not ideal, for sure.

A 48-Megapixel sensor the size of the D60's would be a 5656x6464-pixel sensor with a pixel density of 374.6 pixels/mm, which is 2.76x greater than that of the D60's 135.6 pixels/mm. This would provide an on-sensor resolution of 187.3 lp/mm and a 300 dpi print would be 28.3x18.9, not 30x20, but that's in the ballpark.

Such a sensor is not ideal because we would have to shoot at apertures no smaller than f/4.7 for this 300 dpi, 28.3x18.9-inch print to survive scrutiny at 10 inches (assuming our eyes can resolve 5 lp/mm.) Shooting at f/4.7 with a lens at the same focal length as the format diagonal (27.3mm), our DoF will require our nearest subjects to be at least 41.12 feet away if we want Infinity subjects to be resolved at 5 lp/mm also.

Rayz wrote:
However, I would contend, and this is the point where we really disagree, that this is the sacrifice you have to make if you want the DOF that F22 gives you with a D60/D30 format. There's no way around it.

Yes, this is the point where we disagree. I would retire the D60 and purchase something with a larger sensor long before I would suffer 41-foot near sharps at f/4.7 -or- viewing "from the other side of the room" at f/22.

Rayz wrote:
Let's look at the alternative which you and bjlic seem to favour. Rather than a 48 megapixel 22x15mm sensor, I take it you'd rather have a 48 megapixel sensor 16x the size of the D30's sensor with the same pixel density of the D30. That works out almost exactly to MF 6x9cm.

That's incorrect.

6x9cm film has a useful area of 56x84mm and that's only 3.7x larger (not 16x larger) than the D30's sensor.

Rayz wrote:
Now there may be many advantages of such an arrangement such as greater dynamic range and lower noise and certainly at F22, 30x20 prints are going to be much, much sharper. No diffraction problems there.

But, wait on! It's not just F22 you're after. What you really want is the DOF that F22 gives you with the much smaller D30 format. As a general rule, to get the equivalent DOF of a larger format you multiply the F stop by the difference in focal lengths of the 2 standard lenses. Standard lens for the D30, taking into account the 1.6 multiplier, is 30mm. Standard lens for 6x9 is 90mm. Equivalent F stop to give same DOF as F22 with the D30 is 3x22=F66. Call it F64. So far, so good.

Tightening it up a bit: The focal lengths equal to the format diagonals would be 27.3mm and 101mm, respectively, for the D30/D60 and a 6x9 camera. So the DoF had at f/22 with the smaller sensor could only be had at f/81.4 with the larger sensor (the multiplier is 3.7x, not 3x).

Rayz wrote:
But, hang on! I've got a couple of second hand MF cameras. Can't see F64 on any of my lenses. Nothing bigger than F32. I'm two stops short. Why is that? Could it be that nobody would want to use F64 with an MF camera because diffraction would be too much of a problem?

Precisely! That's especially true for the f/81.4 figure I came up with. Which begs the question: "What good is a lens that can stop down to f/22 on a D30/D60-sized sensor?"

If the majority of photographers had your willingness to view prints from "the other side of the room" our MF gear probably would be equipped with f/81.4. If the majority of photographers actually felt that such behavior is "the sacrifice you have to make if you want the DOF that F22 gives you with a D60/D30 format", the MF lenses we use today might even have f/90 or f/128! But most don't go beyond f/32. Why is that? Could it be that the majority of photographers want their prints to survive scrutiny from viewing positions on the same side of the room as that where the print is hanging?

Rayz wrote:
Let's have a look at your formulas at the biginning of this thread.

Diameter of Airy Disk = F stop x 0.00135383

At F64 we get 64 x 0.00135383 = 0.08664512

Using the "real" 6x9cm equivalent to the D60/D30-sized sensor's f/22:

At f/81.4 we get 81.4 x 0.00135383 = 0.110201762

Rayz wrote:
Now a 48 megapixel image from a 6x9cm sensor (3.6x2.4 inches) will produce almost a 30x20 inch print without interpolation. That represents an 8.33x enlargement factor.

Tightening it up again...

A 48-Megapixel image (5656 x 8484 pixels) from a 56x84mm sensor (true size of a 6x9 frame) will produce an 18.9 x 28.3-inch, 300 dpi print without interpolation. That represents an 8.57x enlargement factor.

Rayz wrote:
From your first post, the size of the Airy disk on the print will be 8.33 x 0.086645 = 0.72mm

The size of the Airy disk on-print will be 8.57 x 0.110201762 = 0.94mm.

Rayz wrote:
Wow! Wow! Wow! Isn't it supposed to be 0.2mm?

In order to achieve 5 lp/mm on-print, YES IT IS supposed to be 0.2mm! Thanks for pointing out that the 6x9cm sensor you've described would have far too great a pixel density at 48-Megapixels to support use of f/81.4! The same f/81.4 that requires we stand across the room to enjoy. I don't NEED f/81.4 on a 6x9 digicam. I'm content to shoot at f/22 with my MF gear! If I NEEDED f/81.4, my MF lenses would have stops that small! Where are you taking us Ray?

Rayz wrote:
Well, let's see what degree of enlargement we can tolerate before exceeding the 0.2mm limit.

E x 0.086645 = 0.2 E = 0.2/0.086645 = 2.3

Maximum print size from our 3.6x 2.4 inch sensor before Airy discs become visible will be (2.3 x 3.6) x (2.3 x 2.4) = 8.28 x 5.52.

That's incorrect.

Using the real numbers...

E x 0.110201762 must equal 0.2mm

E must equal 0.2 / 0.110201762, which is an enlargement factor of 1.815x (not 2.3)


Rayz wrote:
Wow! again. There IS an improvement. With the D30 we were limited to 5 x 7.5 prints at F22. With the larger format at equivalent DOF we can get 5.5 x 8.25 prints.

That's incorrect.

With the D30/D60-sized sensor at f/22, we are limited to 4x6-inch prints.
With the 56x84mm 6x9 sensor (1.815x larger), at equivalent DoF, we are limited to 7.26 x 10.89-inch prints.

There IS an improvement. Not surprisingly the print dimensions increase by the same factor as increases in sensor size.

Rayz wrote:
Have I missed something?

Yes.

Rayz wrote:
Have I made a mistake in my calculations?

Yes.

Rayz wrote:

Let me know.

Done.

Mike Davis

[Rayz]

bglic wrote:


One of the points I was trying to make above is...... you ONLY benefit from increasing format size, or sensor size, when the jump upwards in f stops did not bump the ceiling of diffraction.

bdlic,
I sense a bit of confusion about diffraction limits. We're so used to statements that lenses tend to perform best at F8 and that diffraction kicks in below F11 or F16 (in the case of 35mm) that we have forgotten that these 'ceilings' only have meaning in relation to the poor performance of film and the poor design of lenses.

A 35mm lens that has optimum performance at F8 has either been deliberately designed that way because of the limitations of film, or is a relatively cheap lens.

Because of this relationship between film resolution and lens resolution which is described by the formula 1/S = 1/L+ 1/F, we never get to appreciate the increasing resolution that lenses are capable of at smaller F stops (larger apertures). There's sometimes a wide range of F stops which produce very similar results if one ignores the tendency of fall off in resolution at the extreme corners at large apertures.

The aerial resolution of lenses describes clearly, without muddying the waters with film, what the lens is truly capable of. But we generally don't get that information. It's not considered to be useful because the degrading effects of film make it irrelevant.

Most consumer grade lenses and probably even some Canon L series lenses, have significant aberrations at full or close to full apertures. Distortion due to diffraction is insignificant in comparison with coma, chromatic aberration and field curvature etc. However, these aberrations tend to be reduced as one stops down and eventually distortion due to diffraction becomes the main culprit.

Perhaps what is not realised, is that it is already possible to reduce the various types of lens aberrations so that AT ALL APERTURES the main limit to lens resolution is diffraction. As you know, diffraction exists at ALL apertures. It's just less at larger apertures.

I can think of no finer example to illustrate this point than an experiment carried out at Photodo by Lars Kjelberg and colleagues. They compared a really high quality 35 mm lens, a Carl Zeiss Planar 50mm F1.4, with a Sironar 150mm lens on 9x12cm format. Thay used equivalent DOFs in both cases, F5.6 for 35mm and F22 with the Sironar. They chose a high resolution B&W film, T-Max 100 and found to their great surprise that the 35mm print was 'almost' as sharp as the same size print from the 9x12cm format (except the 35mm print was significantly grainier, as you would expect). When they substituted Illford Tri-X for T-Max in the 9x12 camera (admittedly a lower resolution film, but still reasonable by colour film standards) the 35mm print showed actually higher resolution than the print from 9x12 format.

Well, I'll leave it to you to work out the implications of this very careful and meticulously carried out experiment when one considers the advantages of digital over film, especially with regard to grain.

I could go on, but I'd better reply to Mike.

Regards, Ray

[Rayz]

Mike,
I think you're descending into nit picking in order to defend your position. We're talking about a theoretical situation which almost certainly doesn't match the practical realities. To start quibbling over the true dimensions of 6x9 format is really scraping the bottom of the barrel. I arrived at 6x9 by multiplying 22.7 by 4 = 90.8mm or 9cm. I'm still wondering about you.

I won't go through each objection you've expressed because I'm really concerned with the genral thrust of the argument and the concepts that apply, and I think once again that you've lost sight of the woods for the trees.

But, I will pick you up on one point which might be misleading for other readers who can't see through the subterfuge. By reworking my figures and trying to be as presice as possible you ended up with an enlargement factor of only 1.815. That would appear to be in my favour because if you multiply 1.815 by your 'pedantic' 56x84mm (the true image size of 6x9) you get a print size of 6.2 inches x 4.2.

However, for some mysterious reason you've applied that multiplier factor to the D30 maximum prints size of 4x6. That's not how it's supposed to work by your own definitions in your first post. The multiplier factor applies to the sensor size. Who's yanking whose chain?

Ray

[zilch0md]

Ray,

Rayz wrote:
Mike,
I think you're descending into nit picking in order to defend your position.

I checked your math and gave you the answer you requested in the previous post:

Rayz wrote:
Have I made a mistake in my calculations?

Did you expect me to treat that as a rhetorical question?

Rayz wrote:
We're talking about a theoretical situation which almost certainly doesn't match the practical realities.


That's why we aren't clicking Ray. I'm very much concerned about the practical application of these principals, while you prefer to refer to this whole effort as "theoretical". This latest reply, like several before it, makes no attempt to offer a tangible rebuttal to my contentions. Instead you counter with impractical "solutions" to diffraction's impact on the usefulness of 35mm-based lenses - solutions like making like-sized prints as pixel densities increase or viewing prints from "across the room" and then urging "this is the sacrifice you have to make if you want the DOF that F22 gives you with a D60/D30 format. There's no way around it."

The way around the diffraction problem is a larger sensor.

Rayz wrote:
To start quibbling over the true dimensions of 6x9 format is really scraping the bottom of the barrel. I arrived at 6x9 by multiplying 22.7 by 4 = 90.8mm or 9cm. I'm still wondering about you.

I won't go through each objection you've expressed because I'm really concerned with the genral thrust of the argument and the concepts that apply, and I think once again that you've lost sight of the woods for the trees.


I suspect you won't go through each objection because you know you don't have a foot to stand on. If you REALLY believe in what you're doing, you'd better debate this with some elbow grease. Don't blow off all the work I've done to answer YOUR hypotheticals on the excuse that I am blinded by the numbers. Your decision to avoid my challenges will only undermine your credibility in the eyes of others.

Rayz wrote:
But, I will pick you up on one point which might be misleading for other readers who can't see through the subterfuge. By reworking my figures and trying to be as presice as possible you ended up with an enlargement factor of only 1.815. That would appear to be in my favour because if you multiply 1.815 by your 'pedantic' 56x84mm (the true image size of 6x9) you get a print size of 6.2 inches x 4.2.

However, for some mysterious reason you've applied that multiplier factor to the D30 maximum prints size of 4x6. That's not how it's supposed to work by your own definitions in your first post. The multiplier factor applies to the sensor size. Who's yanking whose chain?

Ray, that was an innocent mistake. I haven't spent all these months presenting this material for the purpose of deceiving you and the rest of the world. I dearly wish I hadn't made that slip because you've already made more of it than it is, but YES, both systems (D30 vs. 6x9cm) produce equivalent DoF and visible diffraction in like sized prints at equivalent f-stops.

That sure sounds like the D60 vs. 8x10 argument you made several days ago - an argument which I've explained is but a subset of the big picture I'm talking about - an explanation which you have YET to counter. You've brought nothing new to this table since then and when I go to the effort to explain that I agree with this thing which you believe contradicts my findings, making an effort to guide you out of the box you're in, you can get no closer than to say this:

Rayz wrote:
Nevertheless, I can see you have a point.


Then you jumped into making the same argument you've made before, which only shows you're still stuck on comparing like-sized prints. Of what value is your assessment of my conclusions when you insist on debating a a different set of circumstances?

This is a rough anaology, but it's as if I had said, "When water is heated to 212 degrees F, at a pressure of one atmosphere, it will boil" but you've rushed in to say, "If you leave it at room temperature, it won't boil." That's true, but you carry on as if it contradicts what I've said!

I'm talking about the very real, very common practice of exploiting every last pixel at one's disposal to make the largest print possible. More pixels = bigger prints in the real world Ray. We don't make every print as large as possible, but we sure don't restrict ourselves to the maximums of yesterday's sensors. No one is going to trade in a camera for one with more megapixels only to make nothing but the same sized prints. (No one's going to put water in a pot and bring it to the stove only to leave it at room temperature.) And people aren't always going to stand so far away from a larger print that it occupies the same angle of view as the smaller one. (No one is going to wait for the water to come back to room temperture before making themselves a pot of tea.) If they make the print even a little bit larger and/or stand even a little bit closer than a distance proportional to the increase in print size, the water hasn't been left at room temperature.

We're wasting each other's time Ray. I'm content to give you the last word and the second to the last and however many more shots you want to take, without further effort on my part. I'll not react to anything short of a dilligent response to all the arguments I've made that remain unchallenged.

By the way, here's some genuine nit picking: My protagonist's username is "bglic", not "bjlic" or "bdlic".

Thank you bglic for joining in when you did. I needed a breath of fresh air.

Mike Davis

[bglic]

Ray

> I sense a bit of confusion about diffraction limits. We're so used to statements that lenses tend to perform best at F8 and that diffraction kicks in below F11 or F16 (in the case of 35mm) that we have forgotten that these 'ceilings' only have meaning in relation to the poor performance of film and the poor design of lenses.

Yes, very true, but these are the only films and lenses on the market? I do agree, that film is the limiting factor, more so than lenses, (mainly color) however, the same seems to be true with digital as I have defended in my last post. The optimum apt. of a lens varies based on the lens design, sometimes its f2.8 and sometimes as in LF lenses, f32.


A 35mm lens that has optimum performance at F8 has either been deliberately designed that way because of the limitations of film, or is a relatively cheap lens.

> Because of this relationship between film resolution and lens resolution which is described by the formula 1/S = 1/L+ 1/F, we never get to appreciate the increasing resolution that lenses are capable of at smaller F stops (larger apertures).

VERY TRUE! Yes, I agree, this sucks... but once again, its reality :-(

> The aerial resolution of lenses describes clearly, without muddying the waters with film, what the lens is truly capable of. But we generally don't get that information. It's not considered to be useful because the degrading effects of film make it irrelevant.

Agreed, but we get enough information so as to perform the 1/R calcs. For example, Mamiya USA tested M7 lenses and the 80mm performed at 235 lpmm aerial. High end 35mm perform even better.

> Perhaps what is not realised, is that it is already possible to reduce the various types of lens aberrations so that AT ALL APERTURES the main limit to lens resolution is diffraction. As you know, diffraction exists at ALL apertures. It's just less at larger apertures.

You may find it interesting that Schneiders and Rodenstocks digital lenses are just that, diffraction limited at every f stop. I am in the process of buying some, I too am curious how much better the performance will be after being drug down by the film! I hate 1/R !

> I can think of no finer example to illustrate this point than an experiment carried out at Photodo by Lars Kjelberg and colleagues. They compared a really high quality 35 mm lens, a Carl Zeiss Planar 50mm F1.4, with a Sironar 150mm lens on 9x12cm format. Thay used equivalent DOFs in both cases, F5.6 for 35mm and F22 with the Sironar. They chose a high resolution B&W film, T-Max 100 and found to their great surprise that the 35mm print was 'almost' as sharp as the same size print from the 9x12cm format (except the 35mm print was significantly grainier, as you would expect). When they substituted Illford Tri-X for T-Max in the 9x12 camera (admittedly a lower resolution film, but still reasonable by colour film standards) the 35mm print showed actually higher resolution than the print from 9x12 format.

This is possible, but a bit improbable considering the Sironar 150mm is a good lens. But I get your drift, but I beleive this test was a bit flawed. As you know, when doing these tests, there is many issues that can alter the results, such as, film flatness, vibration, shutter diffraction, distance to target (some lenses are desgined to focus at infinity), lens MTF variance (i.e. not using the optimum apt. for each lens) focus capabililty of the user, ground glass and film alignment, etc. etc...

I am not trying to be argumentative on this one Ray, but if you look at Chris Perezes lens tests where he tries to keep all the variables the same, since he is the same guy testing all the lenses, you will see his results vary from a high of 90 lpmm to film, to a low of about 35 lpmm to film, using high resolving B&W film. Of course the 35 lpmm lenses are 1920's vintage whereas the 85 lpmm lenses are the most expensive and modern MF lenses made. Even with this huge spread, these lousy 1920's lenses on 4x5 can almost match MF lenses enlarged to 4x5. But these 1920's lenses on 8x10 will supercede the MF lenses when enlarged to 8x10. Which just goes to prove, there is no substitute for format size!!!

> Well, I'll leave it to you to work out the implications of this very careful and meticulously carried out experiment when one considers the advantages of digital over film, especially with regard to grain.

Well, I would like you hear you comments about my justifications of 1/R still applying to digital. As I mentioned, the end results is the only data we can draw upon. If you feel I am missing something, I am all ears on this one.

> jmamer - I have a fairly trivial question that's been nagging me from about the middle of this thread. Is there some way to get a "effective pixel density" for 35mm film?
Say for mundane Kodak 100 ISO print film and for slide film?

This question can best be answered by scanning 35mm film till the point the film offers no additional resolution. For example, if you scanned a chrome that has a lens chart recorded, at some point in the scanning process, you will stop seeing the smaller lines. This represents the max amout of resolution the film can hold with a given lens. Of course this considers you are using a high end scanner that is capable of scanning much higher resolutions. For most color chrome films, this resolution is about the 2500 dpi range...maybe Velvia can be pushed to 3000 dpi. At 2500 dpi, or ppi, this would equate to a full size 35mm sensor having 2500 pixels in the vertical dimension and 1.5x or 3750 pixels on the horizontal for a total of 9.4 Mega Pixels and 13.5 MP for Velvia comparison. However, since digital files are more software friendly to sharpening, it has a slight edge over film when pixel count (or dpi) is equal. This estimate vaires from 10% - 40%. Hope this answers your question.

Bill

[bglic]

Mike

I re read your posts above, and I do agree with your meticulous math regarding this issue. For those readers that do not want to get burried in the math, I offer the following....

Your point is, bigger sensors of equal pixel densities can make bigger prints. This of course means, each print must be compared with the same "on paper" resolution. This is one of the main points of your latter posts.

Now, just like film, this is perfeclty true, ASSUMING the increase in f stop you need to use (for same DOF) to accomodate the longer fl lens, does not jump into the diffraction ceiling. Of course you need to increase the f stop to maintain the same DOF using the smaller fl lens.

Your earlier point in this thread, was regarding pixel density. Your point was adding more pixels to the same physical size sensor reduces the number of f stops you can shoot at before the final print is diffraction limited. I totally agree with this assessment. Same is true with film, except we don't have these options in film (except color vs. B&W) so most photographers don't think in terms of film / sensor density (resolving capability).

The reasoning behind this is quite simple. By adding resolution capacity to the same size sensor, you are increasing the amount of lpmm the sensor can hold. Diffraction, on the other hand, is working in the opposite direction, being lowest (lpmm) at the highest f stops and getting higher (lpmm at lower (wider) f stops. The higher resolving capability of the film / sensor, the sooner (going up the f stop scale) this intersection will occur. (intersection is referring to the point at which lens diffraction is limiting what the film / sensor can record) So greater pixel density always equates to diffraction being the limiting factor at lower f stops. Of course, all of this is dependent on some version of the 1/R not being the limiting factor.

So in theory, by making a sensor with super high resolving capacity (pixel density), you can hit diffraction at f 5.6. Which for wedding, wildlife and sports shooters this would still be an ideal camera. (meaning compact in size with great enlargement potential - and these markets may be big enough to support such a camera) But Mikes point is, for landscape shooters, or general shooters, such a camera would be nothing short of a nightmare being limited to only a few f stops to take advantage of the super high and super expensive pixel density. And those who are not adept to the math can get burnt real easy on a purchase such as this.

Mike, does this sum up your points?