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

I'll take that as a "Yes" response to my question. Again, you've made it clear that you believe diffraction need not be considered when contemplating how many pixels to put on a sensor.

The diameter of an Airy disk at the sensor plane (or film plane) can be calculated as follows:

Airy disk diameter in millimeters = N * 0.00135383

Source: http://photo.net …/optics/lensTut​orial.html

So, you're right when you say that diffraction is dependant on the aperture setting. For any camera, any lens, any sensor, if we shoot at f/8, the diameter of the Airy disks at the sensor plane will be 0.01083mm (because 8 * 0.00135383 = 0.01083).

Now let's compare the use of two 10 megapixel cameras to produce 8x10 prints from exposures made at f/8.

The high-density sensor (511 pixels/mm) in a Casio Exilim EX-Z1000 will require an enlargement factor of 35.4x to produce an 8x10 print.

The low-density sensor (164 pixels/mm) in a Sony DSLR-A100 will require an enlargement factor of only 10.8x to produce an 8x10 print.

Now let's look at the impact these disparate enlargement factors have on the Airy disk diameter...

Both cameras will have Airy disk diameters at the sensor plane of 0.01083mm when shooting at f/8.

The low-density Sony will enlarge those Airy disks to a diameter of 0.117mm in the 8x10 print (because 10.8 * 0.01083 = 0.117).

The high-density Casio, however, will enlarge those Airy disks to a diameter of 0.383mm (because 35.4 * 0.01083 = 0.383).

Thus, thanks to diffraction at f/8 and more than three times the enlargement factor necessary to achieve an 8x10 print, the Casio, with its high-density sensor, having just as many pixels as the low-density sensor, will be diffraction-limited to a print resolution of only 2.61 lp/mm (because 1 / 0.383 = 2.61).

But with the same Airy disk diameter at the sensor plane, thanks to the smaller enlargement factor, the Sony, with its low-density sensor, will be diffraction-limited to the far greater resolution of 8.55 lp/mm (because 1 / 0.117 = 8.55).

When you argue that sensor size or pixel density or print size has nothing to do with diffraction, you are absolutely right as long as you confine your discussion to what's happening inside the camera. But I'm talking about how we perceive the final print after enlargement. Enlargement factor and viewing distance are critical variables in any assessment of the factors affecting image clarity.

Does this help?

Mike Davis

This has been like watching a tennis match, with a volley that belongs in the Guinness Book of World Records. We've seen it all, drop shots, kills, balls just inside the foul line, those that flick the net. Yet the ball keeps going back and forth.

But, really, enlargement size is at the heart of all format discussions. And this is a format discussion more than a pixel-density discussion. Hear me out:

Back in the old days, similar arguments raged between small-format (i.e., 35mm) photographers and large-format (i.e., 4x5) photographers. In the press corps, for example, both camps overlapped considerably in the 1960's. The standard press camera prior to that time was a Speed Graphic or something similar, while after that time it was the Nikon F. (Medium format was then a transition or compromise between the portability and quick handling of the small format and the image quality of the large format.)

In many ways, it was an argument about meeting requirements. It was rather difficult to traipse around Viet Nam or up and down football-field sidelines with a Speed Graphic. But setting aside functional requirements, the arguments would go like this:

Assertion: Small format is better, because film has improved so much that the high enlargements are no longer an issue.

Response: But if the film improves for small formats, it also improves for large formats. And improvement often comes at a cost, such as lower film speed.

(It was the same in the audio world in those days with the argument between cassettes and open-reel magnetic tape.)

Small sensors of a given pixel count have high pixel densities, just as film optimized for small formats has small grain. But there is a price to be paid, and in digital photography it is as much about ISO performance as it was with film.

But the bigger issue has to do with the print size. When you enlarge a small original to a big print, every flaw in the process is also enlarged. Those flaws include lens aberrations, camera shake, grain (or noise), dust, and, if you are lucky enough so that those other issues are not overwhelming, diffraction. The more you have to enlarge to achieve a given print size, the more important it is to control those flaws (or lower expectations).

One argument states that more pixels may only record those flaws in more detail, as opposed to capturing more image detail. I think that's the case in this thread (though I'm forgetting who's on which side, seasick as I am with the to and fro), and thus the higher pixel density is wasted.

The countering argument is that you never know exactly where those flaws will become critical for a given situation or image, and therefore you need as many pixels as possible to at least deliver the full potential of the lens, camera, and photographer. Both positions are defensible, and both can lead to reasonable buying strategies. Thus, the argument can have no winner, it seems to me, because it is now an argument about requirements and needs, rather than an argument about design. And everyone has different needs and requirements. (Sorry--I do systems engineering for a living and can't think outside the needs and requirements box.)

It is the same with scanners. Some buy film scanners to support a given enlargement capability, while others buy film scanners in an attempt to model everything on the film, including grain, image flaws--everything. It could be argued that only the latter approaches an accurate scan, but for most practical applications it exceeds requirements.

When asked what camera size he preferred, Ansel Adams said, "The biggest one I can carry!" That response tells me that he wanted to be able to support the largest possible prints, WHATEVER THAT HAPPENS TO BE. He took his well-known image of Georgia O'Keeffe with a Leica, and then stated that the largest acceptable print of that image was 8x10. But it is still a famous image.

For me, I don't size my equipment based on print size, I carry the biggest camera I can and then print it as large as the image quality will allow. A larger format will always support a bigger print at a given quality level. That should not be subject to argument.

If I was a commercial photographer and was hired to make prints of a certain size for a certain viewing distance, or if I were an art photographer known for selling prints of a given size looking for a general-purpose camera, then I have specific requirements that I can choose equipment to meet. But most of us go the other way--getting what we can carry or afford and then living with the resulting constraints.

Rick "thinking the combatants mistakenly believe this is an argument about fact" Denney

Hi Rick,

First I have to say that I enjoyed reading your post.

I understand what you're saying, but I feel compelled to clarify your summary of my argument as follows: Adding pixels does not record diffraction's Airy disks in greater detail. Adding pixels without increasing the sensor dimensions proportionately leads to an increase in enlargement factor, which causes the Airy disks to be larger in the final print than they would be with a lesser enlargement factor. As Airy disk diameters are increased, print resolution decreases.

That argument is not "defensible" because we know the apertures offered by a given lens; we know the sensor dimensions; we can calculate the diameter of Airy disks at the sensor plane and we can calculate the enlargement factor that must be endured to reach a given print size. Astronmers have been doing this stuff for decades. Many experienced 35mm photographers will tell you that to avoid visible diffraction in 8x10 prints, they stayed away from f/22 and smaller apertures. The aperture at which diffraction will inhibit your desired print resolution is easily calculated:

Maximum N = 1 / desired print resolution / enlargement factor / 0.00135383

Your summary of "the countering argument" at least hints at the possibility that diffraction can "become critical" under certain situations. I'm sure Rayz would agree with that, but your summary fails to embody arguments like this:

Rayz is saying that so far as the effects of diffraction are concerned, we can increase pixel density all we want to. He acknowledges that lens resolution, noise, and other factors may limit the detail resolved in the final print, but not pixel density. He has argued that a camera having 10 megapixels on a small sensor will be no more vulnerable to a loss of detail caused by diffraction after enlargement to an 8x10 print than a camera having the same number of pixels on a larger sensor. THAT is the argument with which I am in contention. It is not a defensible argument.

If you really want to understand why Rayz' argument is not defensible, read, study, and/or ask me questions about my most recent recap:

zilch0md wrote:
The diameter of an Airy disk at the sensor plane (or film plane) can be calculated as follows:

Airy disk diameter in millimeters = N * 0.00135383

Source: http://photo.net …/optics/lensTut​orial.html

So, you're right when you say that diffraction is dependant on the aperture setting. For any camera, any lens, any sensor, if we shoot at f/8, the diameter of the Airy disks at the sensor plane will be 0.01083mm (because 8 * 0.00135383 = 0.01083).

Now let's compare the use of two 10 megapixel cameras to produce 8x10 prints from exposures made at f/8.

The high-density sensor (511 pixels/mm) in a Casio Exilim EX-Z1000 will require an enlargement factor of 35.4x to produce an 8x10 print.

The low-density sensor (164 pixels/mm) in a Sony DSLR-A100 will require an enlargement factor of only 10.8x to produce an 8x10 print.

Now let's look at the impact these disparate enlargement factors have on the Airy disk diameter...

Both cameras will have Airy disk diameters at the sensor plane of 0.01083mm when shooting at f/8.

The low-density Sony will enlarge those Airy disks to a diameter of 0.117mm in the 8x10 print (because 10.8 * 0.01083 = 0.117).

The high-density Casio, however, will enlarge those Airy disks to a diameter of 0.383mm (because 35.4 * 0.01083 = 0.383).

Thus, thanks to diffraction at f/8 and more than three times the enlargement factor necessary to achieve an 8x10 print, the Casio, with its high-density sensor, having just as many pixels as the low-density sensor, will be diffraction-limited to a print resolution of only 2.61 lp/mm (because 1 / 0.383 = 2.61).

But with the same Airy disk diameter at the sensor plane, thanks to the smaller enlargement factor, the Sony, with its low-density sensor, will be diffraction-limited to the far greater resolution of 8.55 lp/mm (because 1 / 0.117 = 8.55).

When you argue that sensor size or pixel density or print size has nothing to do with diffraction, you are absolutely right as long as you confine your discussion to what's happening inside the camera. But I'm talking about how we perceive the final print after enlargement. Enlargement factor and viewing distance are critical variables in any assessment of the factors affecting image clarity.

Does this help?

I have no such mistaken belief. This is, most assuredly, an argument about fact.

Mike Davis

Yes it is, Mike. It's all about facts, not theoretical mathematical calculations that impress the naive and uninformed.

You've started the thread as an egotistical expression of your mathematical knowledge, which may well be greater than that of most of us. But reality proves you wrong. Get real and accept the facts.

Today I did some more tests with a Canon 50/1.8 lens, better than the 100-400L IS. The results are incontrovertible. At f22, the high pixel pitch, high density, 20D records more detail than the lower pixel pitch 5D, with the same lens from the same position.

Basically, I would say that's the end of the story.

It's difficult to display such differences on this web site because of the 800x600 limitation to image resolution. I've posted the results on Luminous Landscape at http://luminous-landscape.com …index.php?showt​opic=11651

All the best. Sorry for blowing you out of the water.

Sorry - Major misunderstanding or extremely sloppy wording here.

If you add pixels without changing the dimensions of the sensor as a whole, the degree of magnification required for a given print size does not change. The pixels get smaller, so they record smaller parts of the overall image. So you get, as Rick says, a much more detailed and high resolution capture of the image, flaws and all.

If the individual sensor sites don't change dimensions but you add sensor sites to the sensor, the overall sensor dimensions have to increase, so you reduce the degree of magnification required for a given print size. In that case you would see less image degradation,for the same reason you'd see less effect from camera shake, or greater depth of field, under the same circumstances. Because you're not magnifying the blur (from whatever cause) as much as you would with a smaller sensor.

You've not disproven the facts I've presented. Where would we be if everyone considered the use of mathematics to be unfactual?

This equation...

Maximum N = 1 / desired print resolution / enlargement factor / 0.00135383

... is just as concrete and unspeculative (though not as profound in scope, of course) as this equation:

E = mc^2

The merit and capacity for practical application of these equations can not be reduced by a failure to understand them.

Revisiting my prior mention of 35mm shooters avoiding diffraction in an 8x10 print by never shooting at f/22 and smaller apertures, let's examine the efficacy of the equation I've been using throughout this thread. Many photographers can testifty that "things go soft" when shooting at f/22 with 35mm format, so I consider this common practice to be the result of literally millions of real world tests.

We can easily calculate the resolution limit imposed by diffraction when using f/22 for an 8x10 print made from a 35mm negative (cropped to 24x30mm), as follows:

N = 1 / resolution limit imposed by diffraction / enlargement factor / 0.00135383

For an 8x10 print made from a cropped 35mm negative that was exposed at f/22..

22 = 1 / resolution limit imposed by diffraction / 8.47 / 0.00135383

Rearranging the equation to solve for the unknown resolution limit:

Resolution limit = 1 / 8.47 / 0.00135383 / 22

Resolution limit = 3.96 lp/mm

Thus, when legions of 35mm users practiced avoiding the use of f/22 when the goal was to make a "sharp" 8x10 print, they were striving for a resolution higher than 4 lp/mm.

At f/16, the same mathematics will tell us they enjoyed a diffraction limited resolution of 5.45 lp/mm. With 5 lp/mm considered by many to be at the lower end of what the human eye can appreciate at a viewing distance of 10 inches, this makes sense.

So... kick and scream all you want to about how this use of mathematics is unrealistic or only "theoretical", but the FACTS speak more loudly than your immaterial challenges.

Mike Davis

Hi Jon,

When the enlargement factor is maintained as pixel count is increased, the Airy disk diameters after enlargment will remain unchanged. Similary, the resolution-limit imposed by diffraction will not change. That's why I wrote, in response to Rick's attempt to summarize my argument: "I understand what you are saying." The impact on print resolving power does not change just because you've got more pixels sitting under each Airy disk. The Airy disks themselves must get larger on-print to reduce print resolution - this requires an increase in enlargement factor. A 10 megapixel sensor that's physically 1/3 the size of another 10 megapixel sensor will suffer 3 times the enlargement factor to achieve a given print size, and thus, a 3x reduction in print resolution. Which of the these two sensors has the higher density? The one that's smaller, of course. It's absolutely valid to say that high-density sensors are more vulnerable to diffraction (and noise) than low-density sensors when comparing the final products, after enlargement.

Mike Davis

Sorry. You can't have it both ways. Adding pixels without changing sensor dimensions allows you to capture the image projected by the lens in finer detail. This applies no matter what quality the projected image is. As a thought experiment, consider an APS-C sensor of 6 Pixels. Compare the image from that to another APS-C sensor of 6 MegaPixels. Which will show lens qualities and flaws better? That's what Rick was saying when you disagreed with him.

You are contrasting statements I made for two entirely different situations - one where the enlargement factor doesn't change, and one where it does. The two statements you've highlighted in red do not contradict each other in the least. I CAN "have it both ways".

Again, I understood what Rick was saying, and said so. I understand what you are saying. But that "truth", in and of itself, falls far short of summarizing the scope of my argument.

Mike Davis

Of course all of photography is a series of compromises. If optical resolution were the only concern then we would all be using view cameras the exact size of the prints we wanted and making contact prints. And truth be told there are some who won't accept anything less than that. Of course the trade off is no photojournalism, no sports photography, very limited travel and fashion photography.

Still, I glad to see the theoretical issue addressed as well as the practical upshot of it without any rancor!

Then you need to work on the quality and clarity of your argument.

You're right, Jon.

With an open mind I went looking for a lack of "clarity" in the text you had quoted in red and it was suddenly obvious that my choice of words was less than ideal.

Specifically, this sentence requires further explanation: "Adding pixels without increasing the sensor dimensions proportionately leads to an increase in enlargement factor..."

This begs the queston: How can the enlargement factor change if the sensor dimensions don't?

Answer: It's the print that's getting larger in this scenario, not the sensor.

To normalize my comparisons of sensors that have different pixel counts and different dimensions, I calculate the impact of diffraction against the enlargement factor had with each sensor's 300 ppi print dimensions. (I've covered this before...) To make the comparisons at a fixed print dimension, would be unrealistic because doing so assumes that people with 16 megapixel cameras make prints no larger than the prints made by people with 3 megapixel cameras -and- any camera will suffer less diffraction when operating at print sizes that are smaller than what the camera is intrinsically capable of producing. The more pixels a sensor has, the larger will be its 300 ppi print dimensions. I could just have easily have normalized the comparisons at 150 ppi, so there's nothing special about 300 ppi, but by using an enlargement factor based on each sensor's nominal print size at some fixed ppi, a fair comparison is made.

Mike Davis

I was not trying to summarize your argument, but rather capture the essence of both sides of the issue in the context of the old format vs. resolution debate that has raged for decades. There are aspects where you two guys crossover in my summary, perhaps. Frankly, I have not attempted to understand everything you are saying in that much detail, but to frame the discussion in terms understandable and usable by the rest of us.

Adding pixels without increasing sensor dimensions does not lead to greater enlargement. The degree of enlargement is the same. If the sensor is 15x23mm, and the print is 8x12 inches, then the enlargement factor is 13.9. That will be true if the sensor has 6 million or 12 million pixels.

It could be argued that the sensor should have more resolution that any potential image flaw (and for convenience I'll call diffraction a flaw though we both know it is not), so that the pixel density is never the limiting factor in making enlargements. At what point does a sensor have enough pixels so that pixel resolution is never the limiting factor? That's a debate for the ages, because the factors it might limit are so variable.

High pixel density can't make a poor lens better, and it can't overcome the effects of diffraction. But neither does it contribute to those faults. At best, it allows them to be more visible as enlargement increases, but the limit of acceptability depends on the standards applied to the enlargement.

We always wanted film with high enough acutance and resolution to allow our maximum print size to be limited by optics and technique. We want the same thing with digidal sensors.

Also, as you know, an Airy disk is not a hard-sided circle. It's a fuzzy spot, and the fuzziness makes it subject to various interpretations. Thus, another factor that decides the tipping point between pixel density and the limitations of optics and technique is the required standard of the photographer. Some photographers are just plain pickier than others, and some situations demand higher standards than others. Nobody will care if the 10x15" front-page enlargement of a wide receiver catching a football is sharp to 5 lines/mm, so that it will appear sharp when viewed from 10 inches. The newsprint can't even print it that sharp. Nobody will care if the mural-size landscape is sharp to 5 lines/mm--because it's going up on the wall where nobody will even be able to get within 10 inches without a ladder.

I have images (some even in large format) where diffraction caused disappointing results because I stopped it down too far. I just deal with the smaller maximum print. But the increased depth of field that I bought with that small aperture was critical in getting at least that level of enlargeability.

I just bought a new (to me) scanner--a Nikon 8000 ED. It scans medium-format film at 4000 pixels/inch. That's a pixel density of 157 pixels/mm, and it gives me an 80-megapixel scan of a 6x6 negative or transparency. Is there a film made that can support such resolution? Probably not--I'm just describing detailless clumps of grain with more precision. And my medium-format optics are also probably not up to it. But I wanted that much resolution, so that whatever my optics could do, I could use, even if I pull a roll of ISO50 Velvia out of the freezer. Considering only pixel density, I should be able to make a 30" square print from a 6x6 negative. I guarantee you that those prints will not stand up to a standard of 5 lines/mm. But they may still find useful application at sizes that large.

That depends on the definition of "visible", which depends on the requirements imposed by the viewing conditions.

Astronomers have a different set of requirements. They are always working at the limits imposed by diffraction, and measure their scope's performance in microscopic terms (Can I see the Cassini division? How about the light spot in the middle of the Ring Nebula?).

A photographic lens is not evaluated by viewing a tiny bit of the projected image in air using a 4.8mm Nagler eyepiece. The vewer of a photograph has to get far enough away to see the whole image, and the image is appreciated as a whole image, not microscopically. Only photographers look at really big prints from 10 inches. Different requirements lead to different designs.

So, while your formulas may be factual, they may not be relevant to the situations, standards, and objectives of all photographers. Therefore, it's quite difficult to use them in support of sweeping statements in the form of buying advice, such as the title of this thread. If the strategy is to have more pixels than is needed by the optics, then more is better until you reach the tipping point, but that point isn't that easy to define. If it's high enough so as not to be critical, then the lens and technique will limit the degree of enlargement, and that's how it should be for those folks.

A BIGGER sensor, on the other hand, requires less enlargement, again no matter how many pixels it has. Thus, the flaws are smaller in the print. But those things can only be evaluated on the print.

Rick "nothing to see here...move on" Denney

Ahh. You are arguing against the notion that 300 dpi (or 240, or 360, or whatever) controls the maximum print size.

If that's how someone determines their maximum enlargement, then the effects of optics and technique (and diffraction) will loom large in their prints, if their sensors have a high enough pixel density such that the density is not the limiting factor on enlargement.

That's like saying, I have 35mm film which should allow a 8x enlargement to 8x10", even when I use f/45 and a one-second shutter speed on my shaky tripod. It's a sign of someone who does not see the whole picture.

But saying that a 35mm photographer should never use a smaller aperture than f/16, or should never use film with finer grain than Tri-X because the diffraction's airy disks will be bigger than the grain, is approaching the problem from the wrong direction. They should instead understand the interplay of all these factors.

Rick "who thinks it takes experience to understand tradeoffs now more than ever" Denney

The use of mathematics can be very unfactual. It can also be very insghtful.

There's a story about the very brilliant, but underrated physicist, Paul Dirac who discovered the existence of anti-matter through mathematics. As a mathematician, he knew that mathematics could lead one into absurd conclusions and, for a while, refused to publish his findings for fear of ridicule. He was persuaded by friends to publish and be damned. A few years later, the emprical evidence for anti-matter was found and his reputation was sealed.

Your mathematics, Mike, sorry to say, is leading you to absurd conclusions. It's not necessarily that the logical processes are flawed, it's just that there appear to be other issues that your maths is not addressing.

I can only make a guess at what these might be.

You've already admitted that you understand that diffraction limitation occurs gradually over a number of f stops. I would suggest that Airy Disk destruction of detail also takes place over a number of f stops. Two points in an image might begin to merge at, say f8, but are not fully merged till f22 or perhaps even f32. The points at f8 are more clearly delineated, for sure, but may be still visible at f22.

The eye can detect detail with an MTF response as low as (and even lower) than 10% MTF.