Digital, diffraction and DoF

[gkramer]

Dr. Johnson's analysis ("Lens equivalents...") may be OK for film cameras, but not for digital cameras, as it neglects the effect of pixel pitch. Both theory and practical experience suggest that there is an interaction between diffraction and pixel size, and that diffraction becomes quite noticeable when the Airy disk becomes large enough to span more than two pixels; see, for example:

http://www.cambridgeincolour.com/tutorials...photography.htm

For the D2X, or the several recent DSLRs based on Sony's recent 10MP APS-C sensor, the limit is around 11-14 microns, well below the 19-micron figure he gives for an APS-C camera.

All of the optics referencs cited by Johnson, and indeed in most amateur photography forums, date from the film-camera era, and while they cover DoF and diffraction, do not discuss the effects of pixel pitch, and other digital-specific angles; nor do they incorporate the influential MTF-based image-quality criterion developed by Otto Schade in the mid-1980s. I'm sure these subjects are well covered in any modern video-era optics textbook, but the only ones I've found cited are mathematically dense treatises on Fourier optics and the like. Does anyone know of a reasonably accessible textbook (requiring something less then Ph.D.-level mathematics) that covers these topics, as the spply to digital photography?

[bjanes]

Dr. Johnson's analysis ("Lens equivalents...") may be OK for film cameras, but not for digital cameras, as it neglects the effect of pixel pitch. Both theory and practical experience suggest that there is an interaction between diffraction and pixel size, and that diffraction becomes quite noticeable when the Airy disk becomes large enough to span more than two pixels; see, for example:

http://www.cambridgeincolour.com/tutorials...photography.htm

For the D2X, or the several recent DSLRs based on Sony's recent 10MP APS-C sensor, the limit is around 11-14 microns, well below the 19-micron figure he gives for an APS-C camera.

All of the optics referencs cited by Johnson, and indeed in most amateur photography forums, date from the film-camera era, and while they cover DoF and diffraction, do not discuss the effects of pixel pitch, and other digital-specific angles; nor do they incorporate the influential MTF-based image-quality criterion developed by Otto Schade in the mid-1980s. I'm sure these subjects are well covered in any modern video-era optics textbook, but the only ones I've found cited are mathematically dense treatises on Fourier optics and the like. Does anyone know of a reasonably accessible textbook (requiring something less then Ph.D.-level mathematics) that covers these topics, as the spply to digital photography?
[{POST_SNAPBACK}][/a]

You should read a bit further in your reference to find the following quote:

"Are smaller pixels somehow worse? Not necessarily.  Just because the diffraction limit has been reached with large pixels does not mean the final photo will be any worse than if there were instead smaller pixels and the limit was surpassed; both scenarios still have the same total resolution (although one will produce a larger file)."

[a href=\"http://www.clarkvision.com/imagedetail/scandetail.html#diffraction]Roger Clark[/url] has some good information on diffraction on his web site. Note in particular the table showing the diffraction limit at variious MTFs (80%, 50%, Dawes, and Rayleigh). The same laws of optics apply to both film and digital. Digital can have a high MTF below Nyquist, but then MTF drops abruptly as Nyquist is approached. Beyond Nyquist, there is no useful resolution. Film has no such cutoff and continues to resolve at low MTF.

As explained in the Cambridge in Color site, the COC used by most camera makers assumes a visual acuity of less than 20/20 and conservative viewing distances. If you plug in 20/20 vision for the calculations of COC and diffraction and change the viewing distance and print size, the limits change rather drastically.

[gkramer]

You should read a bit further in your reference to find the following quote:

"Are smaller pixels somehow worse? Not necessarily...

...Note in particular the table showing the diffraction limit at variious MTFs (80%, 50%, Dawes, and Rayleigh). The same laws of optics apply to both film and digital. Digital can have a high MTF below Nyquist, but then MTF drops abruptly as Nyquist is approached. Beyond Nyquist, there is no useful resolution. Film has no such cutoff and continues to resolve at low MTF. [sic: at high lp/mm]
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Precisely my point; rather than using any single resolution figure, such as the the lp/mm value at which the system MTF falls to zero (the Dawes limit), or to 50% or some other arbitrary level, Schade proposed taking the (square of) the entire area under the (system) MTF curve as a better measure of overall image quality. He was specifially concerned with comparing digital to film images; since film has a long "shoulder" often reaching up to 150 lp/mm, whereas digital has a sharp cutoff at the Nyquist limit (about 100 lp/mm for the D2X, lower for other DSLRs) its Dawes limit will usually be be better (with a good lens), but the overall image quality, taking account of digital's typically better MTF values at lower frequencies, may well be inferior. See Sony's Tech [digicam] paper at:

[a href=\"http://bssc.sel.sony.com/Professional/production/productsite/files/24PTechnicalSeminar2.pdf]http://bssc.sel.sony.com/Professional/prod...calSeminar2.pdf[/url]

It's pretty easy to show that with a perfect (diffraction-limited) lens, smaller pixels are better than larger ones, yielding a higher Schade index until the "Airey disk = 2-pixel = Nyquist limit" is reached; though, paradoxically, the effect of diffraction is more pronounced with smaller pixels, yielding a proportionately greater falloff as the lens is stopped down. But I'm unaware of any (website or textbook) analysis along these lines, much less one that tries to integrate this with DoF considerations, and am still searching for a suitable reference.

[bjanes]

Precisely my point; rather than using any single resolution figure, such as the the lp/mm value at which the system MTF falls to zero (the Dawes limit), or to 50% or some other arbitrary level, Schade proposed taking the (square of) the entire area under the (system) MTF curve as a better measure of overall image quality. He was specifially concerned with comparing digital to film images; since film has a long "shoulder" often reaching up to 150 lp/mm, whereas digital has a sharp cutoff at the Nyquist limit (about 100 lp/mm for the D2X, lower for other DSLRs) its Dawes limit will usually be be better (with a good lens), but the overall image quality, taking account of digital's typically better MTF values at lower frequencies, may well be inferior. See Sony's Tech [digicam] paper at:

http://bssc.sel.sony.com/Professional/prod...calSeminar2.pdf

It's pretty easy to show that with a perfect (diffraction-limited) lens, smaller pixels are better than larger ones, yielding a higher Schade index until the "Airey disk = 2-pixel = Nyquist limit" is reached; though, paradoxically, the effect of diffraction is more pronounced with smaller pixels, yielding a proportionately greater falloff as the lens is stopped down. But I'm unaware of any (website or textbook) analysis along these lines, much less one that tries to integrate this with DoF considerations, and am still searching for a suitable reference.
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Thanks for the Sony reference and your incisive analysis. Area under the MTF curve was also considered by Grainger at Kodak in the 1970s as explained by [a href=\"http://www.bobatkins.com/photography/technical/mtf/mtf4.html]Bob Atkins[/url] on his web site. Since you are obviously very knowledgeable in this area, I would be interested in your opinion of SQF. One can do a SQF analysis of actual digital images by using Norman Koren's Imitest and integrate the area under the curve by digital image analysis.

Small pixels have their advantages, but suffer in their signal to noise ratio, especially at higher ISO. What are your opinions regarding perceived noise and pixel size as discussed in this: thread  . As the pixel size decreases and the overall sensor size is held constant, noise per pixel increased but is expressed at higher frequency where it may be less apparent.

Bill

[dandill]

I found Nathan Myhrvold's additional comments very helpful, and they led me to Sean McHugh's interactive illustrations of the effects described.

Dan Dill

[dwa652]

I found Nathan Myhrvold's additional comments very helpful, and they led me to Sean McHugh's interactive illustrations of the effects described.

Dan Dill
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Thanks, the McHugh site is very helpful.  What I take from all of this, is that digital photography is unlikely ever to rival my 4x5 with film for scenes such a fields of wildflowers where a large DOF is needed.  Or am I missing something?  I usually shoot at f32-f64 with my 4x5.  Even though a 6x4.5 sensor like a P25 or P45 is smaller and can achieve similar DOF with a lower f-stop, I still doubt an aperture like f8 would cut it even with tilt.  Or does someone have a contrary experience?

Don't get me wrong, I yearn to replace the 4x5 with digital but do not want substantially less sharp photos.  I am willing to trade a little resolution for all the benefits of digital but am not willing to trade a lot of resolution.

Any comments welcome!

[erich6]

One thing to consider is that the diffraction length is only a driver if the MTF is "diffraction-limited".  This means the optics have virtually no aberration.  The MTF will further broaden the spot size on the detector.  The optical response function is what needs to be compared to the pixel pitch.

Having a larger pixel will result in more signal-to-noise ratio which has to be balanced against the mild gain you get from a better sampling ratio of the optical response.

That said, most decent camera lenses are close to diffraction limited so that's a good rule-of-thumb.  Only when the pixel is much larger than this do you have to worry about the pixel pitch affecting the DOF calculation.

Erich

[CSidney]

The discussion of digital resolution versus diffraction broadening continues.  Everyone agrees that diffraction reduces resolution.  The image we see is essentially a diffractionless image convoluted with a 2D Airy function.  There is still the question of what pixel size will do the best job at rendering the image we are stuck with.  Or, in other words, will oversampling help.  The following site considers just this point, though it is not clear how relevant the conclusions are for everyday photos as compared to resolving stars:

http://geogdata.csun.edu/~voltaire/pixel.html

Figures 1-3 on this site clearly show the effects of increased sampling and how multiple exposures with translation can be combined make up for undersampling.  I presume this combination of images is the basis of some of the super-resolution techniques.

[John Sheehy]

Figures 1-3 on this site clearly show the effects of increased sampling and how multiple exposures with translation can be combined make up for undersampling.
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Translation of the sensor will work.  Translation of the camera would only work if everything is at the same depth (or close enough, and of course, with super wide angles, anything more than a few feet away are all close to infinity.).  Far and near objects translate differently if you translate the camera.  Rotation of the camera would probably be better for mixed depths, so long as nothing is very close to the camera (in which case only sensor translation would probably work well).

Translation works best with sensors that have weaker than normal AA filters.

[Ray]

This entire issue is complicated by the factor of real-world conditions of lens quality variability. There's no simple formula. There are merely trends with many exceptions.

I did some test shoots a while back with my Canon 100-400 IS zoom at 400mm, at various f stops, with 1.4x extender, with both 20D and 5D. I was trying to find out how the 20D compared with the 5D for ultimate telephoto reach, and how diffraction effects might vary with both cameras as one stopped down.

I won't repeat the images I posted a year or so ago, of rural scenes. The following images, not posted before, include line charts, and printed text which in some respects is a better guide to resolution than line charts. If you can read it, then that's better than not (or hardly) being able to read it.

First, below is the 20D at f22 compared with the 5D at f22, with 560mm lens. Both images were converted in ACR with default settings (including sharpening at a default 25). The 5D image was interpolated with bicubic sharper, so both images are the same pixel density (on screen). Of course, the 5D image has a greater FoV, but the purpose of the test was to determine the best maximum telephoto reach and at what aperture.

[attachment=1668:attachment]

As you should be able to see, even at f22 the 20D is streets ahead of the 5D, in this respect (okay, maybe just half a street ahead). Call the lens a coke bottle if you like, but that doesn't change the results. We would merely amend our description to include 'coke bottle', along the lines, Even using a coke bottle, the higher-pixel-density 20D delivers more detail at f22 than the 5D. Okay!  

Next, a comparison of text from f8 to f45, with the 5D and 560mm lens.

[attachment=1669:attachment]

What is surprising here is that f32 seems better than f8. If you want to criticise me for not being 'spot on' with my focussing, then repeat the experiment yourself.

Next, a comparison of text from f8 to f45 with the 20D.

[attachment=1670:attachment]

Here we have a situation where f8 is marginally better than f32, but not by much. F22 is still better than f8.

For those who are interested, I'll post a few more comparisons below, which are really self-explanatory because I've labelled each image clearly, something I wish other posters would do when they post their comparison test shots.

[attachment=1671:attachment]  [attachment=1672:attachment]  [attachment=1673:attachment]  

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