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

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

Re: D60's sensor is too small to stop down below f/11
 

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

Re: D60's sensor is too small to stop down below f/11
 

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.

Re: D60's sensor is too small to stop down below f/11
 

Re: Re: D60's sensor is too small to stop down below f/11
 

Hi 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

Re: Re: D60's sensor is too small to stop down below f/11
 

Hi!

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

Re: Re: D60's sensor is too small to stop down below f/11
 

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

Mike Davis

Re: D60's sensor is too small to stop down below f/11
 

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.

Re: Re: Re: D60's sensor is too small to stop down below f/1
 

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

Re: D60's sensor is too small to stop down below f/11
 

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

Re: D60's sensor is too small to stop down below f/11
 

it shure do make pertty piktures, dont it

Re: Re: D60's sensor is too small to stop down below f/11
 

Hi!

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

Re: Re: Re: Re: D60's sensor is too small to stop down below
 

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

Re: D60's sensor is too small to stop down below f/11
 

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/j...rayleighdisks/

Ed

Re: D60's sensor is too small to stop down below f/11
 

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

Re: D60's sensor is too small to stop down below f/11
 

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!

Re: Re: D60's sensor is too small to stop down below f/11
 

Hi 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

Re: D60's sensor is too small to stop down below f/11
 

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

http://www.canon.com/camera-museum/t...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....)

Re: D60's sensor is too small to stop down below f/11
 

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

Re: Re: D60's sensor is too small to stop down below f/11
 

Hi!

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

Re: Re: D60's sensor is too small to stop down below f/11
 

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

Re: D60's sensor is too small to stop down below f/11
 

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

Re: D60's sensor is too small to stop down below f/11
 

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

Re: D60's sensor is too small to stop down below f/11
 

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

Re: Re: D60's sensor is too small to stop down below f/11
 

Hi 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

Re: Re: D60's sensor is too small to stop down below f/11
 

Hi 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

Re: Re: Re: D60's sensor is too small to stop down below f/1
 

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"?

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/S..._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

How about Macro lenses?
 

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

Re: D60's sensor is too small to stop down below f/11
 

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

For Gary Shepard
 

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.

Re: Re: D60's sensor is too small to stop down below f/11
 

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

For soumya63
 

"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

Re: D60's sensor is too small to stop down below f/11
 

Mike

Thank you...

Ed

Re: D60's sensor is too small to stop down below f/11
 

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

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

Re: D60's sensor is too small to stop down below f/11
 

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!

Re: D60's sensor is too small to stop down below f/11
 

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

Re: D60's sensor is too small to stop down below f/11
 

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?

Re: For Gary Shepard
 

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

Re: D60's sensor is too small to stop down below f/11
 

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

Re: D60's sensor is too small to stop down below f/11
 

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