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

Of course, you wouldn't shoot both cameras at f/8. This "isn't fair". You're making the tiny-format camera use the small-format camera's aperture. The small-format camera might need f/8 to get the desired depth of field, but the tiny-format camera can achieve that same depth of field using a much larger aperture. In your example, you'd have to compare the low-density sensor at f/8 to the high-density sensor at f/2.6, to equalize the depth of field yielded by the two formats.

When you do your calculations for "what's the biggest print I can produce at XXX lp/mm" for different sensors, you can't use the same apertures when the sensors are different sizes, that's "cheating". Instead, try normalizing the aperture used to be appropriate to the sensor size, and then see what your results are.

What we're really interested in is "what resolution can I put on a print of a given size, at my required depth of field". I think once you frame the question like this, you'll soon find it doesn't matter whether your 10MP camera is high density or low density, they'll hit the "diffraction barrier" at different "f numbers", certainly, but they'll hit it at f numbers that yield identical depths of field, as seen in that identical print.

It is true that the smaller format cameras will be able to use shorter shutter speeds, but that's always been an inherent advantage of smaller formats.
-harry

Now THAT is worth studying as it relates directly to the usefulness of a given aperture setting on a given format.

Things that make you go Hm Hm.

Harry,

I understand everything you're saying, but past, present, or future, in this thread, if I compare two cameras having the same pixel count and shooting at the same aperture (10 megapixels and f/8, for example), my purpose is to show that the low-density, large-sensored, camera can deliver a greater resolution to its 8x10 print than the high-density, small sensored camera.

I fully understand, as you do, that the smaller format digicam will enjoy more DoF and thus, in practice, would not have to use as small an aperture (assuming it's even available on the digicam). What does the digicam have to do to support the SAME desired resolution in the final print? Answer: Indepdendant of DoF requirements, thanks to the difference in enlargement factor and the impact this has on the size of Airy disks in the final print, the small-sensored, high-density camera absolutely MUST use a larger aperture if it is to support the SAME desired resolution in a like-sized print as the larger-sensored, low-density camera.

Going back to my comparison of the Casio Exilim EZ-1000 and the Sony DSLR-A100,
instead of calculating the difference in diffraction-limited print resolution for 8x10 prints for these cameras, with both of them shooting at f/8, let's calculate the apertures at which each camera will no longer support a desired print resolution of
5 lp/mm.

Let me say it again this way: Before, I fixed the aperture and calculated the difference in diffraction-limited print resolution. Now, I'm going to fix the diffrraction-limited print resolution at 5 lp/mm and calculate the difference in aperture required to support that resolution.

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

For the Casio Exilim EZ-1000:

Maximum N = 1 / 5 / 35.4 / 0.00135383

Maximum N = 4.2

Thus, to prevent diffraction from inhibiting a desired resolution of 5 lp/mm in the 8x10 print, the Casio Exilim EZ-1000, with its 35.4x enlargement factor, must not shoot at apertures smaller than f/4.2.

For the Sony DSLR-A100:

Maximum N = 1 / 5 / 10.8 / 0.00135383

Maximum N = 13.7

Thus, to prevent diffraction from inhibiting a desired resolution of 5 lp/mm in the 8x10 print, the Sony DSLR-A100, with its 10.8x enlargement factor, can use any aperture down to f/13.7.

According to DPReview specs, the high-density, small sensored, Casio Exilim EX-Z1000's aperture range is f/2.8 through f/5.4, but to support a desired resolution of 5 lp/mm in an 8x10 print, the diffraction-savvy shooter must operate in the range f/2.8 through f/4.2. (As an aside, to achieve 5 lp/mm in a 9x12-inch print (300 ppi), the Casio's range of diffraction-free stops shrinks to only f/2.8 through f/3.4.)

The low-density, large sensored, Sony DSLR-A100 uses interchangeable Alpha lenses, many of which have an aperture range from f/2.8 through f/22, but to support a print resolution of 5 lp/mm in an 8x10 print, the diffraction savvy shooter must operate the Sony in the range f/2.8 through f/13.7.

Consider the two ranges of diffraction-free stops required to support an 8x10 print resolution of 5 lp/mm:

High-density Casio: f/2.8 through f/4.2
Low-density Sony: f/2.8 through f/13.7

Independant of other factors affecting print resolution, looking only at the impact of diffraction, both cameras can support a desired print resolution of 5 lp/mm in an 8x10 print, but which camera offers the greatest range of f-stops capable of delivering that resolution?

What would happen to the aperture range if Casio decided to increase the number of megapixels on that same sensor, from 10 to 16.6 (to compete with something like the Canon EOS 1Ds Mark II), without increasing the sensor dimensions? Nothing would happen to the range of available diffraction free stops, as long as users of the new 16.6 megapixel digicam continued making only 8x10 prints! But when you give people more pixels, they tend to make bigger prints. 16.6 megapixels are sufficient to produce an 11.1x16.6-inch print at 300 ppi. The enlargment factor would be huge: 58.7x.

Let's calculate the aperture at which diffraction would inhibit a desired resolution of 5 lp/mm in an 11.1x16.6-inch print:

Maximum N = 1 / 5 / 58.7 / 0.00135383

Maximum N = 2.5

If Casio failed to make the new lens faster than the EZ-1000's f/2.8, the lens would not be able to open up to f/2.5 and thus, diffraction would prevent the desired print resolution of 5 lp/mm at any and all stops available to the shooter.

Whether or not any shooters, digicam or dslr, are going to go to the trouble of confining their aperture selection to a range that supports a given print resolution in a given print size is immaterial to my argument. My message is simply that high-density sensors are more vulnerable to diffraction than low density sensors. Rayz and others would have readers believe this is not the case. Diffraction imposes a limit to how many pixels can be added without increasing sensor dimensions. That limit can be accomodated by putting faster, heavier, more expensive lenses on small-sensored cameras, but that's not as economically viable as simply making the sensor larger.

Mike Davis

Okay. So the Sony's sensor is about 3.26X larger (in one dimension) than the Casio's. If we set the two cameras up side-by-side, and use a focal length appropriate to each camera's format (e.g. we use a 10mm lens on the Casio and a 32.6mm lens on the Sony), then we'll see that we achieve comparable angle of view (i.e. the same "stuff" appears in the viewfinder, and in the frame of our 8x10 print). If we shoot the Casio at f/4.2 and the Sony at f/13.7, we'll also find that we achieve identical depth of field in both of those shots.

Now, if we're a Sony salesman, we can say "the Sony can be used all the way up to f/13.7 while still making great 8x10's, meanwhile, that Casio can only be used up to f/4.2. Try to use the Casio at anything beyond f/4.2, and you'll get that nasty diffraction stuff!"

At this point, the customers at Best Buy have lit their torches, and have begun to chase the Casio salesman through the store. The poor Casio salesmen is waving a pair of 8x10s, the ones made in the above shots, and trying to explain how they're identical in terms of field of view, depth of field, and the effects of diffraction, but the angry mob cannot hear his defense!

Any way...

So what are the "truths" that we hold to be self-evident?

Well, one is that as you go to smaller formats, you'll find "equivalence" in terms of depth of field and diffraction at apertures with smaller "f numbers". In other words, if you used to say "f/22 gives a lot of depth of field, but you can get diffraction" in 35mm days, you just need to train yourself to start saying "f/8 gives a lot of depth of field, but you can get diffraction" when using a format that's 1/4 the size of 35mm film. Is diffraction a bigger problem than it was before? No, not at all, it's just that all the "stuff" that used to happen at f/22 now happens at f/8 (or whatever).

Tiny-format cameras seldom provide apertures smaller than f/8 or so. Is this to cover up a big secret? Well, for these cameras, "f/8 is the new f/22". They top out at f/8 for the same reason many 35mm lenses top out at f/22, because there's lots of depth of field there, and because we start to run into diffraction. But this is like currency, I've got 1000 pesos, while you've only got 100 dollars, who's better off? Well, that's about the same amount of money.

Another truth is that since smaller formats allow us to use smaller "f numbers" to achieve the same depth of field, we can use faster shutter speeds. This is true in digital for all the same reasons it was in film. Those large format guys carried around a lot of tripods, didn't they? (Well, okay, their cameras were pretty heavy, too, but they had to use long exposures due to the big f numbers they had to use to get decent depth of field).

The other truth is that since smaller formats skew everything to smaller "f numbers", if we want to get shallow depth of field, we need to use f numbers that sound _really_ small to those used to 35mm. In the 35mm world, f/2.8 is "pretty shallow DoF", but not crazy shallow. Some 35mm enthusiasts play around with f/1.0 lenses to get super-shallow DoF.

But the tiny cameras with their little zoom lenses that peek out like a turtle head whenever it's time to take a photo of Grandma, well, they're not very fast lenses, are they? So these cameras don't provide the ability to get shallow depth of field. I'm not a lens expert, so I don't know what the issues are with building a really fast lens to be mated with a tiny sensor, but presumably this is taking the engine from a Ferrari and stuffing it into a Yugo, these little cameras are designed to be cheap, and so they get cheap lenses.

But note that the "problem" here isn't on the diffraction side of the aperture range, it's on the fast side of the aperture range. Those little cameras are just being shipped with slow lenses. The diffraction "issue" hangs out on the "wide depth of field" side of the aperture range, and the little cameras provide you with just as much rope to diffraction yourself as the bigger cameras do, just the aperture numbers sound smaller.

Now, if you want to take the math a bit further, stick with that comparison of 10MP sensors in small and large sizes, and also consider a comparison of two sensors of the same size, where one is 10MP and another 20MP. But when comparing a pair of sensors, always adjust the apertures you use to be appropriate to the format.

Now, again consider the "8x10 with XXX lp/mm and YYY depth of field" question. My assertion is that you'll find that for any "8x10 with XXX lp/mm and YYY depth of field" problem you come up with, you can calculate a max number of MPs based on your values of XXX and YYY, and this will be the maximum number of MPs that will be "useful" on a sensor to produce that 8x10 image. You'll also find that it just doesn't matter what size of sensor you're using, small sensors and large sensors will all "top out" at that same number of MPs. So diffraction isn't a "pixel density" issue, it's "damn, physics put a ceiling on how many pixels are useful" issue. We can move that ceiling up by accepting shallower depth of field, but our tiny format sensor and our small format sensor are both stuck under that same theoretical ceiling.

So when we contemplate taking our 10MP sensor and bumping it up to a 15MP sensor without increasing the area of the sensor (i.e. making it more dense), we'll certainly find that there are values of XXX and YYY in the "8x10 with XXX lp/mm and YYY depth of field" that tell us that our camera can only use, say, 12MP of its available 15MP. That will tempt us to say "those guys should have also increased the area of the sensor when they went from 12MP to 15MP". But if we revisit the calculation for that new, larger, 15MP sensor, we find that we're now in a different format, and so have to normalize our aperture again to match the depth of field we had before, and we'll soon find that we're identically limited to getting "use" of the same 12MP of our 15MP sensor, even though we made it bigger and thus reduced the density.
-harry

Is that what your purpose is, Mike? Perhaps my memory is not as good as I think it is. I could have sworn you were trying to make the point that an 8mp sensor like the 20D will hit a diffraction wall at f11.2 and that at larger f stops, such as f16 and f22, having fewer than 8m pixels on the (same size) sensor will provide more detail on the print.

Having demonstrated to my own satisfaction that this is not the case, it seems perhaps I've been wasting my time because this was never the point you were trying to make in the first instance. Is that correct?

The 20D with its 8m rather small pixels unequivocally provides greater detail at f22 than a camera with the same size sensor having 4.8m larger pixels. The camera with 4.8mp is the 5D, the image from which was cropped to the same size as the 20D image, having used the same lens at the same distance to target, at the same f stop of 22.

Who the heck cares? I get great images with my second hand 300D as I have with the D60 before that, I couldn't care less about hairy discs and I don't waste my life shooting lpmm charts.

I guess you ought to tell all those poor D60 owners that their pictures are no good.

Hey! Kraterz,
You shouldn't be wasting your time reading this thread, then.

bring back to the top

steve.banks wrote:
bring back to the top

You have an evil sense of humor.

Here are some applicable unsolicited quotes:

"There is also a good reason to use larger sensor arrays. Lenses are limited by diffraction at higher f-numbers, and this effect is independent of focal length. The smaller the light sensitive array, the more the image has to be magnified for a useful picture. That magnifies the effect of diffraction. It is true that the shorter focal length lenses in digital cameras have greater depth of field for the same angle of view and same f-number, so to some extent the diffraction problem can be avoided simply by limiting the highest f-number available. But the manufacturers have not been able to produce acceptable lenses with very small f-numbers for these cameras, so the net result is that the range of f-numbers available is reduced. One solution to this problem is to use larger sensor arrays. "

Leonard Evens
Dept. of Mathematics, Northwestern Univ

http://groups.google.c​om …ital/msg/19a99f​06ffd95e54

---------------

"In real life, 5MP 2/3" dcams had best sharpness at f/5.6 or f/6.3. Pack more pixels into a smaller sensor and even f/5.6 will be problematic due to diffraction, so you are stuck shooting at f/4.0."

David J. Littleboy
Tokyo, Japan

http://groups.google.c​om …ital/msg/7488a7​a61c888105

---------------

"It seems to me that you are saying that one can notice the effect of diffraction on sharpness at f/22 with the 35mm format. I.e., points in the plane of focus produce a COC on the film which is noticeable in, say, an 8x10 at normal viewing distance. It seems to me, then, that with the average consumer digicam, the COC on the sensor would be 1/5 the diameter of the COC for 35mm, and this would occur between f/4 and f/5.6 for the corresponding focal length (i.e., at the same absolute aperture diameter). When multiplied by 5, this would be the same size COC as that for 35mm, and thus the effect on an 8x10 would be the same. I.e., at some aperture slightly smaller than f/4, diffraction effects would affect image quality."

Richard

http://groups.google.c​om …ital/msg/3b1aa2​a7625ba562

---------------

"As calculated above, f/32 is really the limit of what's useful on a 35 camera lens. But because of the scaling, when the sensor is 1/5 the size, the aperture that gives the *same* diffraction-limited sharpness is 32/5, or about f/6. So a digicam lens at f/8 is LESS sharp than your 35 lenses at f/32, when the image is printed the same size. "

Dave Martindale

http://groups.google.c​om …ital/msg/a05e0a​39569ac58e

---------------

Leonard Evens's reply to David Martindale's post (above):

"Let me applaud you for a really excellent discussion. It should convince anyone who is willing to do a little work and is really interested in the optics behind digital photography.

But I suspect you aren't going to convince your debating opponent.

There is an interesting phenomenon going on here. "Practical men" distrust theory and like to rely on their experience. While experience in its totality should always trump theory, such people don't realize that one's preconceptions can significantly affect what one "sees". It isn't that we don't see what we think we see, but we haven't looked at sufficeintly many situations, and we can be misled by limited observations. It is easy to make up some conceptual model to explain in our minds what occurs in common situations we are very familiar with and then overgeneralize to extend them to ranges where they don't apply. One only finally realize that the conceptual model is faulty when one is presented with very different situations. Theory of course must explain everything in the applicable range of observations, not just those of interest to "practical men".

The paradox here is that those of us who do have solid scientific training are usually much more aware that we could be wrong, even about things we thought we knew very well, than the "practical men" we find ourselves debating. I'm sure that statement will enrage some readers who will treat it as being elitist, but science and mathematics are basically not elitist in the sense that anyone who is willing to put in the work has a chance to learn the subject. But there are no short cuts and making it up yourself on the basis of limited knowledge is not allowed."

http://groups.google.c​om …ital/msg/90a685​f7a2040f1e

Mike,
When the theory and observable facts are at odds, then the theory is either wrong, misunderstood, or there are unidentified influences affecting the observations.

It is an observed fact that stopping down beyond f11 with a camera such as the D60 can provide more detail, on screen or print, at 8"x10" or any size print you want to make, than a camera such as the D30 stopped down to the same aperture.

Your theory of Airy Disc size and its affects appears to have been misapplied. I leave it up to you to work out where the error is.

Maybe you've ignored the possibility that Airy Disks are partially transparent. Maybe you've overestimated the degree to which 35mm lenses are fully diffraction limited. In my experience, they are not fully diffraction limited at f8 or f11 and probably not at f16 even.

When you've found the reason for your error, let us know, won't you?

No
NO
thrice NO

Rayz,

Are these people also in error?

zilch0md wrote:
"There is also a good reason to use larger sensor arrays. Lenses are limited by diffraction at higher f-numbers, and this effect is independent of focal length. The smaller the light sensitive array, the more the image has to be magnified for a useful picture. That magnifies the effect of diffraction. It is true that the shorter focal length lenses in digital cameras have greater depth of field for the same angle of view and same f-number, so to some extent the diffraction problem can be avoided simply by limiting the highest f-number available. But the manufacturers have not been able to produce acceptable lenses with very small f-numbers for these cameras, so the net result is that the range of f-numbers available is reduced. One solution to this problem is to use larger sensor arrays. "

Leonard Evens
Dept. of Mathematics, Northwestern Univ

http://groups.google.c​om …ital/msg/19a99f​06ffd95e54

---------------

"In real life, 5MP 2/3" dcams had best sharpness at f/5.6 or f/6.3. Pack more pixels into a smaller sensor and even f/5.6 will be problematic due to diffraction, so you are stuck shooting at f/4.0."

David J. Littleboy
Tokyo, Japan

http://groups.google.c​om …ital/msg/7488a7​a61c888105

---------------

"It seems to me that you are saying that one can notice the effect of diffraction on sharpness at f/22 with the 35mm format. I.e., points in the plane of focus produce a COC on the film which is noticeable in, say, an 8x10 at normal viewing distance. It seems to me, then, that with the average consumer digicam, the COC on the sensor would be 1/5 the diameter of the COC for 35mm, and this would occur between f/4 and f/5.6 for the corresponding focal length (i.e., at the same absolute aperture diameter). When multiplied by 5, this would be the same size COC as that for 35mm, and thus the effect on an 8x10 would be the same. I.e., at some aperture slightly smaller than f/4, diffraction effects would affect image quality."

Richard

http://groups.google.c​om …ital/msg/3b1aa2​a7625ba562

---------------

"As calculated above, f/32 is really the limit of what's useful on a 35 camera lens. But because of the scaling, when the sensor is 1/5 the size, the aperture that gives the *same* diffraction-limited sharpness is 32/5, or about f/6. So a digicam lens at f/8 is LESS sharp than your 35 lenses at f/32, when the image is printed the same size. "

Dave Martindale

http://groups.google.c​om …ital/msg/a05e0a​39569ac58e

Enh, I'm not sure why their quotes are any better than our quotes. I didn't visit the links, but I presume that those quotes are drawn from a 2-sided argument, and thus they must have resided adjacent to contradictory quotes that could have just as easily been chosen, no? But despite not being moved much by quotes,I don't notice anything in these quotes that appears to be grossly incorrect.

But I feel like the "argument" has gotten a bit slippery, squirming from left to right to find a place where it can stick, when shoo'ed away from its previous spots.

Residing purely in the world of mathematics, we can easily demonstrate that when choosing apertures that yield comparable depth of field, a 10MP "tiny sensor" and a 10MP "full frame" sensor will yield 8x10 prints with identical effects due to diffraction. In my mind, this eliminates the argument that susceptibility to diffraction is well-described as a function of pixel density. Instead, once you fix the print size and the depth of field required, the math will spit out an effective number of MPs you can represent in the print, without being specific in any way to your format (i.e. the size of your sensor).

But it is true that "f numbers" must be intrepreted in the context of the format, and it's also true that cameras with tiny sensors are not being shipped by manufacturers with lenses fast enough to provide shallow depth of field. Whether this is truly a technical issue, that there are engineering hurdles involved in making fast lenses at very small focal lengths, or this is purely a marketing issue, I don't know. If you make the argument that the best way to gain access to good lenses is to use a camera with a bigger sensor, well, yes, but is this because you've side-stepped certain lens engineering issues, or is it just that you're now using more expensive cameras, and the vendors have made more expensive lenses available for them. The comparable argument might be that if you want a car with good brakes, you should drive a car with a good engine. The engine isn't making the brakes any better, but the better engine is in the more expensive car, and the vendor packaged that with better brakes.

When you say "small sensors are more susceptible to diffraction", is this argument now fully described by "small formats need faster lenses to get shallow depth of field"? That's certainly a truthful statement, though I don't think of it as being much about diffraction, really. And it appears, to me, to be one of the many "trade offs" that characterize the technical side of photography.

Maybe, after all these years, it would be productive to restate as succinctly as possible, yet in a logically "complete" manner, what the current "argument" is, to see who disagrees with whom.

By the way, I think what the math gives you is "the trend". I don't think it's particularly important whether observation suggests that f/8 is the number when the theory predicted f/5.6, as the theory requires a tiny bit of "hand waving" to gloss over the complicated parts. But the theory predicts the trend properly (how "things go" as you move from large apertures to small, or large sensors to small), and that's what's important for photographers to understand. All the "forget the math stuff, just get out and shoot" neanderthals are correct that it's not worth arguing between f/11 and f/22, but it's extremely important to understand how f/22 differs from f/1.0, and how f/8 differs between a tiny digicam and a large format view camera.
-harry

It pleases me that you can say that about the following text, especially:

zilch0md wrote:
"There is also a good reason to use larger sensor arrays. Lenses are limited by diffraction at higher f-numbers, and this effect is independent of focal length. The smaller the light sensitive array, the more the image has to be magnified for a useful picture. That magnifies the effect of diffraction. It is true that the shorter focal length lenses in digital cameras have greater depth of field for the same angle of view and same f-number, so to some extent the diffraction problem can be avoided simply by limiting the highest f-number available. But the manufacturers have not been able to produce acceptable lenses with very small f-numbers for these cameras, so the net result is that the range of f-numbers available is reduced. One solution to this problem is to use larger sensor arrays."

Leonard Evens
Dept. of Mathematics, Northwestern Univ

http://groups.google.c​om/group/rec.p...a99f0​6ffd95e54

Going back to your post...

Above, you've made it clear there's a maximum number of pixels that diffraction will permit us to use in the scenario given. Thank you! I agree, vigorously. Adding more pixels would achieve no increase in detail, thanks to diffraction. In other words, increasing the pixel density would achieve no increase in detail, thanks to diffraction.

I've already presented the math for the scenario you've described above, when I calculated the apertures at which a digicam and a DSLR both support (at least as far as diffraction is concerned) a desired resolution of 5 lp/mm in 8x10 prints. At these respective apertures, the prints will indeed display identical effects due to diffraction, as well as identical DoF. In that material (below), I also discussed what would happen if the pixel density of the digicam were increased from 10 MP and accompanied by a corresponding increase in print size. Where the larger sensored Sony can make use of an increase in pixel density, to produce larger prints that still support a desired resolution of 5 lp/mm, the small-sensored Casio, would find itself with no available diffraction-free stops.

Mike Davis