f-stop limits for full sensor resolution

[BJL]

Nathan Myhrvold's  addition to the discussion started by Charles Johnson is a useful additional perspective: not really digital specific, but just about what the aperture limits are if one wants to get the full resolution that one's film or sensor is capable of.

I have a disagreement on the actual numbers though, at least for the case of sensors using Bayer CFA's and interpolation, because that process lowers the resolution of the sensor output beyond "green pixel diagonal size", and thus relaxes the diffraction spot size limit a bit.

For example observations of several users of the Nikon D2X, with 5.5 micron pixel spacing, say that difffraction starts to limit resolution at somewhere between f/8 and f/11. Thom Hogan is the author of the f/11 figure, which gives it some credibility. Myhrvold's calculation instead gives about f/5.8.

So I propose a rule of thumb (dependent on how Bayer interpolation is done, details of anti-aliasing filters and such) that diffraction starts to cut into the resolution that a Bayer CFA sensor is capable of somewhere around twice the pixel spacing in microns, or as much as one stop under. That is, I would modify  "Myhrvold's formula" to

max f-stop = P x 1.4 to P x 2 (instead of P X 1.054).

That makes quite a difference in "effective useful pixel counts" at a given high f-stop, by a factor of two to four.

For example, I suggest that full sensor resolution limits one to maximum f-stops of about
- f/8-f/11 for the D2X or the 400D and similar for other new 10MP SLR's
- f/11-f/14 for the 7.2 microns pixel spacing of the 1DsMkII, and for the 6.8 microns of the E-1 (for which Olympus recommends an f/11 limit)
- f/7-f/9 for the current smallest DSLR pixels, 4.75 microns in the Olympus E-400
- f/2.8-f/4 for the current digicam sensors with pixel pitch about 2 microns or a bit under.

Has anyone have sharpness tests at various f-stops on the 1DsMkII, G7 or other cameras, to allow a test of this idea and give us a better estimate of the best constant in Myhrvold's formula?

[madmanchan]

I don't know the answers to your questions, but I have a couple of additional questions of my own that I hope the authors (or someone else with sufficient background) can answer:

- Are the diffraction formulas used in the articles based on the standard "single slit" diffraction model or are they based on the actual kind of diffraction that occurs in camera lenses (e.g., diffraction around the aperture blades)? Does the distinction matter? Intuitively, it seems to me that a linear row of slits is quite different from an octagonal pattern of 8 aperture blades (some blades are somewhat rounded now, too). Does this affect the formulas and/or the results in a meaningful way?

- A lot of sensors (like the ones in DSLRs) have a layer of microlenses in front of them. These are often described as focusing the incoming light more efficiently. Obviously, this must mean the direction of the optical path changes slightly. Is this purely a geometrical result, or does it affect the wave properties of light as well? Do microlenses interact with diffraction? How so?

Eric

[John Sheehy]

For example, I suggest that full sensor resolution limits one to maximum f-stops of about
- f/8-f/11 for the D2X or the 400D and similar for other new 10MP SLR's
- f/11-f/14 for the 7.2 microns pixel spacing of the 1DsMkII, and for the 6.8 microns of the E-1 (for which Olympus recommends an f/11 limit)
- f/7-f/9 for the current smallest DSLR pixels, 4.75 microns in the Olympus E-400
- f/2.8-f/4 for the current digicam sensors with pixel pitch about 2 microns or a bit under.

Has anyone have sharpness tests at various f-stops on the 1DsMkII, G7 or other cameras, to allow a test of this idea and give us a better estimate of the best constant in Myhrvold's formula?
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I just did a quick test.  I filled a soda bottle cap with a layer of glossy, tiny glitter beads, and took shots at f/2.8 through f/22 (in one-stop increments) with my Tamron 90mm macro (probably the most optically perfect lens I own), using flash and 1/250s @ ISO 200 on my Canon 20D.  f/22 is noticeably duller than 16, 16 slightly duller than 11, and 8 is the sharpest of the lot, with 5.6 slightly sharper than 11.  Sweet spot is probably about 7.1 - 8.

I opened all 7 RAW in tandem in ACR, turned off all auto settings, adjusted exposure individually (varied by over a half stop with no changes in frame!), and cropped as a group.

The f/22, though a bit duller than the f/11, tightens up very quickly without significant artifacting with USM, to look like the f/11 with more DOF.

[gkroeger]

- Are the diffraction formulas used in the articles based on the standard "single slit" diffraction model or are they based on the actual kind of diffraction that occurs in camera lenses (e.g., diffraction around the aperture blades)? Does the distinction matter? Intuitively, it seems to me that a linear row of slits is quite different from an octagonal pattern of 8 aperture blades (some blades are somewhat rounded now, too). Does this affect the formulas and/or the results in a meaningful way?
Eric
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Eric:

Most of the calculations use an Airy disc formula for point sources... this is pretty good for a camera lens iris opening, certainly within 25% or so.

I also agree with the previous posts that Nathan's article, although very useful and well written, doesn't account for the effect of the anti-aliasing filters and demosaicing of the Bayer data.  I would agree with BJL that we get about 1 more stop than Nathan's formula predicts.  

Lloyd Chambers has done extensive DOF and diffraction testing of D2X and 1DsMkII and found about 1 stop effective difference.  One was f/11 but I don't remember which, so that's not much help, but BNLs numbers look about right.

Glenn

[EricV]

The tone of the discussion about pixel size and f/stop limits for full resolution seems to suggest that small pixels are somehow worse than large pixels, because they become diffraction limited at larger apertures.  This is actually an advantage of small pixels.  Rather than saying that small pixels only support large apertures, it seems less misleading to say that large pixels do not support large apertures.  

All other factors being equal (sensor size in particular), a sensor with small pixels will have better resolution than a sensor with large pixels.  At worst, this extra sensor resolution will be wasted if the optical resolution does not support it.  A sensor with small pixels requires better optical resolution to attain its full potential because its full potential exceeds that of a sensor with large pixels.

A crucial factor when considering resolution as a function of pixel size is the magnification needed to go from sensor to print.  This depends on total sensor size, not pixel size or pixel count.  This is the real reason cameras with small pixels generally have worse "resolution" than cameras with large pixels -- the total sensor size is generally smaller, requiring higher print magnification.

[alainbriot]

I think the essay has valuable information. Regarding landscape work,  it helps me decide the best f-stop to use when shooting at infinity or shooting relatively flat subjects.  

However, when maximum depth of field is a requirement, such as with a foreground-background wide angle composition, stopping the lens down is necessary.  

This brings an important question: what size sensor/pixel combination is required to be able to close the lens down say to f16 and not lose resolution?

[BJL]

The tone of the discussion about pixel size and f/stop limits for full resolution seems to suggest that small pixels are somehow worse than large pixels, because they become diffraction limited at larger apertures.  This is actually an advantage of small pixels.
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I fall right in the middle on this one: the trade-offs of diffraction and OOF effects on image sharpness are the same with different pixel sizes and formats, with the f-stop needed changing roughly in proportion to pixel size.

I prefer to think in terms of resolution rather than pixel size. The smallest aperture (and highest f-stop) that avoids diffraction limiting the resolution that the sensor is capable of is proportional to sensor resolution in lp/mm (roughly, pixel density). If for example reducing pixel size doubles resolution in lp/mm, the maximum f-stop is halved in order to half the size of the diffraction spots.
Meanwhile, half the focal length is needed to get an equally detailed image, to be combined with twice the degree of enlargement. That halved focal length and halved f-stop makes each circle of confusion on the sensor half the diameter, just as the diffraction spot diameter is halved.
With twice the degree of enlargement one gets an equally detailed image of the same size with the diffraction spots and circles of confusion on the print also the same size.

More generally, with equal aperture size (f-stop adjusted in proportion to focal length) and enlargement adjusted according to focal length to get equal print size, the diffraction effects and OOF effects on the print are the same.
What changes is that
- with larger pixels, equal shutter speed requires higher exposure index (ISO speed)
- if pixels and sensors are too small, this [equal aperture size] might require an aperture ratio so low that lens aberrations are a problem. The diffraction limited aperture ratios of SLR pixels are not low enough for that problem, but with recent digicam sensor pixel sizes, this might be an issue.

[Ray]

A crucial factor when considering resolution as a function of pixel size is the magnification needed to go from sensor to print.  This depends on total sensor size, not pixel size or pixel count.  This is the real reason cameras with small pixels generally have worse "resolution" than cameras with large pixels -- the total sensor size is generally smaller, requiring higher print magnification.
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I don't think this is correct. In the old days of film, the enlargement was a direct physical enlargement of a piece of film. When we make an enlargements from a digital image, the size of the sensor is not enlarged. Everything has to do with pixel count and pixel size; pixel count in relation to degree of enlargement; pixel size in relation to resolution.

[bjanes]

I fall right in the middle on this one: the trade-offs of diffraction and OOF effects on image sharpness are the same with different pixel sizes and formats, with the f-stop needed changing roughly in proportion to pixel size.

I prefer to think in terms of resolution rather than pixel size. The smallest aperture (and highest f-stop) that avoids diffraction limiting the resolution that the sensor is capable of is proportional to sensor resolution in lp/mm (roughly, pixel density).
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Rather than theorizing about these matters, it is often better to perform tests with your own equipment. I have found Imitest a good tool for this purpose. Here are results for my Nikon D200 and the 50 mm f/1.8 expressed as MTF 50% resolution figures with and without sharpening (uncorrected and corrected).

[attachment=1617:attachment]

[a href=\"http://www.photozone.de/8Reviews/index.html]Photozone[/url] gives Imitest results for many lenses. One must be aware that you are testing the resolution of the camera system and not merely the lens. As is evident in my test, optimum resolution is around f/5.6 with significant deterioration beyond f/11.

Bill

[Ray]

As is evident in my test, optimum resolution is around f/5.6 with significant deterioration beyond f/11.
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These results more or less confirm the general consensus that f11 is the limit for stopping down with cropped 35mm format and and f16 the limit for full frame 35mm. Standard 50mm lenses are usually very sharp at f5.6 - f8. With the average zoom lens, the differences between f5.6 and f11 would be less.

Perhaps more relevant than using Imatest is to do real world comparisons with specific lenses. I've done extensive 'real world' comparisons of my 5D with 24-105 zoom and there's no significant resolution difference between f8 and f16, at the plane of focus. I haven't however done similar comparisons using my sharpest lens, the Canon 50/1.4.

[xtoph]

the question of diffraction limits for max rez on a digital sensor is interesting. my results do not conform to the model that myhrvold proposes. i am not an optical theorist; i am just going from empirical results. f/11, or even 16, on my 5d with the 100macro is not worse than f/9 in terms of resolution information. furthermore, i have used f/22 even on my old 20d, which has a higher pixel density, and resolution did not drop down anywhere near as far as myhrvold's model predicts. some of this may be because of the limits of lenses, but that doesn't really work; otherwise we wouldn't be able to get the kind of peak resolving power out of these lenses and sensors that we do at any aperture.

furthermore, we know that the actual photosite is not as large as a straight area density calculation would show; each photosite sits within that area, from what i've seen on a relatively small part of it. even with the latest microlenses, the actual area used for the calculations in this model ought to be significantly smaller... which would mean that diffraction limits on the dsII would kick in even sooner, if this model is correct. and this we know does not happen (innumerable tests confirm that resolution is often at a peak around f/8, which given the adjusted-for-actual-photosite-size calculations ought to be beyond the diffraction limit for this camera). does that sound incorrect to people? am i misinterpreting the model?

perhaps this consideration of actual photosite size drops out, since the model looks at the array rather than each individual photosite. but this is the part of the model i am least clear on; it is not evident to me that the bayer array should enter into the calculation in this way. photosites are not pixels; each pixel of the image, of course, contains information interpollated from many sites. i would guess that this is where the model is breaking down, around misunderstanding of how the bayer array affects the optical construction of the final image.

as i said, i have no particular expertise in optics, but what the model predicts doesn't match my real-world results, and from the other comments and tests posted here, don't match others' either. yes, diffraction becomes a consideration around f/11 in many cases, but we knew that. i get resolution at f/22 that wouldn't be representable in a 2mp image, and furthermore a very high proportion of the diffraction-related blur goes away with application of usm. as a guide to how to get the best rez from our sensors, i think that this article fails, or at most comes close for the wrong reasons (we know our lenses tend to do best at f/8 anyway).

ps i just shot a test sequence to confirm that i wasn't misremembering anything i stated above--i can say with absolute assurance that the notion that shooting at f/22 is like getting 2mp out of your sensor is rubbish. i got lines resolved clearly at barely above a pixel apart at f/22 without even trying--reducing size to 2mp doesn't come close to enough resolution to separate such lines. mr myhrvold, if that's what your model predicts, you really ought to do some empirical tests to check your model. (while you're at it, change "half of the pixel are sensitive only to green light, while the other half are split 25% to red and 25% to blue" to read something like "half of the pixels are sensitive only to green light, while the other half are divided evenly between red and blue".)

[Ray]

furthermore, we know that the actual photosite is not as large as a straight area density calculation would show; each photosite sits within that area, from what i've seen on a relatively small part of it. even with the latest microlenses, the actual area used for the calculations in this model ought to be significantly smaller... which would mean that diffraction limits on the dsII would kick in even sooner, if this model is correct. [a href=\"index.php?act=findpost&pid=97278\"][{POST_SNAPBACK}][/a]

You might have a point there, but I doubt it. Is there a distinction to be made between pixel pitch and pixel size (or microlens size) regarding DoF? Canon have narrowed the gaps between microlenses in their new 10mp 400D so that each microlens is hardly smaller (perhaps no smaller, they don't say) than a 20D microlens. Does this mean that the same f stop (as the 20D) applies for maximum DoF consistent with good resolution? I doubt it.

Of course, the problem is that such small increases in pixel count on a sensor of the same size don't count for much. We're all engaging in rather extreme pixel peeping here.

[Gordon Buck]

I was taught that most devices work "best" near the mid-point of the intended range of application and this generality has been very useful.

[BJL]

Thanks for the data, and I agree about testing, but now see complications from the difference between essentially monochrome data and color data, and the extent to which sharpening can unravel the effects of Bayer interpolation.

I imagine that a sharpening algorithm that concentrates on luminosity using green information as the main measure of luminosity could more or less reproduce the resolution given by the green pixels, at least with near monochrome subjects, leading to more or less the Myhrvold threshold of "f-stop equal to pixel spacing in microns".

Next, to see diffraction effects on other colors, perhaps we need some of those test results that Foveon X3 sensor fans like: red-blue test patterns! Or at least sharpness tests on subjects with colors towards magenta (away from green).

Maybe the synthesis of observations so far is that diffraction effects start being measurable or even visibly noticeable with suitable subject matter once one passes the Myhrvold threshold (f/6 for the D200, close enough to your f/5.6 observation), with significant deterioration typically setting in beyond the "Thom Hogan" threshold of two stops beyond that (f/12 for the D200, close enough to your f/11 observation).

[EricV]

In the old days of film, the enlargement was a direct physical enlargement of a piece of film. When we make an enlargements from a digital image, the size of the sensor is not enlarged.
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Magnification has the same physical meaning for a digital sensor as it has for film: (print size) / (size of image on sensor).  If I make a 16" print from a 1" image, every feature on the image gets magnified by a factor of 16.  Does it really matter whether the image is recorded on a sensor composed of pixels or film grains?

Of course if you do not want to mention sensor size, you are free to substitute (pixel count) x (pixel size).  Both have real physical dimensions.

If I take a picture of a 10m tall tree from a distance of 50m, with a lens of focal length 50mm, stopped down to f/22 (diffraction blur 30um), on a sensor with 2000 pixels of size 5um, then make a print where the tree is 16" high, what is the diffraction blur size on the print?  Hint: calculate the magnification factor and ignore the irrelevant sensor parameters.

[bjanes]

These results more or less confirm the general consensus that f11 is the limit for stopping down with cropped 35mm format and and f16 the limit for full frame 35mm. Standard 50mm lenses are usually very sharp at f5.6 - f8. With the average zoom lens, the differences between f5.6 and f11 would be less.

Perhaps more relevant than using Imatest is to do real world comparisons with specific lenses. I've done extensive 'real world' comparisons of my 5D with 24-105 zoom and there's no significant resolution difference between f8 and f16, at the plane of focus. I haven't however done similar comparisons using my sharpest lens, the Canon 50/1.4.
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Ray,

I agree with you entirely, but establishing the performance of your 24-105 mm would require quite a lot of testing and effort and the results are somewhat subjective. Since perceived image sharpness correlates well with the MTF at 50% contrast, one can get quite a bit of information in a couple of hours with Imitest.

On the otherhand, taking test shots of a high contrast USAF chart would be less likely to give useful information about how the lens performs in actual photographic tests.

Bill

[Ray]

Magnification has the same physical meaning for a digital sensor as it has for film: (print size) / (size of image on sensor).  If I make a 16" print from a 1" image, every feature on the image gets magnified by a factor of 16.  Does it really matter whether the image is recorded on a sensor composed of pixels or film grains?

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Yes, it does matter. In the days of film, a particular type of fine grained film was not restricted to a particular format. You could use Provia F100 in 4x5" sheets or 35mm rolls. When people talked about the advantages of large format over small format, the enlargement factor, directly in relation to the size of the film, was the most significant factor. If we'd had a situation where Kodak Royal Gold 25 was only available for 35mm and Fuji ISO 800 film only available for 4x5" format, the resolution advantages of the larger format would have been either slight or non-existant.

Of course you are right in the sense, if you know any 2 out of the 3 factors, sensor size, pixel count and pixel pitch, you can work out the 3rd factor.

[Ray]

Ray,

I agree with you entirely, but establishing the performance of your 24-105 mm would require quite a lot of testing and effort and the results are somewhat subjective. Since perceived image sharpness correlates well with the MTF at 50% contrast, one can get quite a bit of information in a couple of hours with Imitest.

On the otherhand, taking test shots of a high contrast USAF chart would be less likely to give useful information about how the lens performs in actual photographic tests.

Bill
[a href=\"index.php?act=findpost&pid=97353\"][{POST_SNAPBACK}][/a]

As with many things in photography, the relevance of the technical results (whether from shooting high contrast test charts or using programs like Imatest) has to be assessed in the field and in practice.

The following images at f11 and f16 were taken in the field, partly with the conscious purpose of examining the results back home for DoF and resolution trade-off. I think I've posted similar images before. The conclusion is clear. The Canon 24-105 zoom at 85mm shows no resolution advantage at f11 in any part of the image, compared with the f16 shot, but the f16 shot is significantly sharper at the extremes of the DoF range.

The test might not be without flaws. I didn't use a tripod and the camera is tilted down very slightly in the f16 shot (compared with the f11 shot), so I can't compare the bottom centre edge, which I believe is also sharper in the f16 shot.

However, I did use the same shutter speed of 1/100th for each shot with IS turned on, a shutter speed which I think is more than sufficient to freeze camera shake at this focal length using IS. Both images were converted in RSP with exactly the same settings, including 'detail extraction' of +30 and sharpening of -10.

If you see any flaws or inconsistencies in the results, let me know   .

[attachment=1622:attachment]   [attachment=1623:attachment]   [attachment=1624:attachment]

[attachment=1625:attachment]   [attachment=1626:attachment]

[Kirk Gittings]

I completely agree with Ray's point on film. All film of a particular type and ASA were cut from huge "master rolls" with no difference of film quality between film formats. I.E. there was always an advantage with larger film formats to make prints of a given size. With digital it is important to compare apples with apples as with film.

[bjanes]

The following images at f11 and f16 were taken in the field, partly with the conscious purpose of examining the results back home for DoF and resolution trade-off. I think I've posted similar images before. The conclusion is clear. The Canon 24-105 zoom at 85mm shows no resolution advantage at f11 in any part of the image, compared with the f16 shot, but the f16 shot is significantly sharper at the extremes of the DoF range.

The test might not be without flaws. I didn't use a tripod and the camera is tilted down very slightly in the f16 shot (compared with the f11 shot), so I can't compare the bottom centre edge, which I believe is also sharper in the f16 shot.

However, I did use the same shutter speed of 1/100th for each shot with IS turned on, a shutter speed which I think is more than sufficient to freeze camera shake at this focal length using IS. Both images were converted in RSP with exactly the same settings, including 'detail extraction' of +30 and sharpening of -10.

If you see any flaws or inconsistencies in the results, let me know   .

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Ray,

I agree with your conclusions regarding better depth of field at f/16, but with only two shots I'm not sure that the results are statistically significant. If you take a series of hand held shots with the same shooting parameters, some will be sharper than others.

At f/16 the diffraction spot is 20.7 microns for green light, well over the 2x the pixel spacing of the 5D (8.2 microns), and the system is definitely diffraction limited at f/16.

One way to test for camera shake is to photograph a point source and observe the pattern at 200% or more. Here is a test with Nikons VR 70-200 f/2.8 lens at 1/100 sec at f/5.6 with VR on the right and no VR on the left. It does work as you say. It would be best to examine the green channel of the raw file, but that is for another day. (this shot is of my neighbor's Christmas lights at about 100 meters).

[attachment=1631:attachment]

Bill