Effects of diffraction

[ErikKaffehr]

Hi,

I made a small write up on the effects of diffraction. All had been said before, it's just information collected in a single place. The article will be updated in the coming days.

http://echophoto.dnsalias.net/ekr/index.php/photoarticles/68-effects-of-diffraction

Best regards
Erik

[marcmccalmont]

Erik
Thanks for the summary!
I certainly can verify the accuracy of your conclusions with both the IQ180/Rodenstock HR's and the Nikon D800E/Leica R's
The sweet spot is f5.6 to f8.0 but f4 to f16 is certainly usable and with proper sharpening quite good
Marc

[Ray]

Erik,
That's an excellent description of the problem. Thanks for taking the trouble to do the tests and share your results.
I'm sure many folks who have never hear of the Airy Disk will be aware that their camera produces sharper results at F5.6 than at F16, but your graph of Imatest results demonstrating the differences in resolution at 50% MTF at F stops between F2.8 and F32 (using the same lens with 3 different cameras) is very revealing, and also very credible in my opinion, in relation to my own tests.

You've done a more thorough and comprehensive test than I've done. I simply concentrated on the 10mp Canon 40D and the 15mp Canon 50D, as a result of claims on this forum, some years ago, that the 50% increase in pixel count of the 50D would serve no purpose beyond F8.

Your graph, which I've reproduced here (hope you don't mind) shows results for 3 cameras which have the pixel density of full-frame 13.7mp, 27.5mp and 54.7 mp. What surprises me is that, even at F32, both the Alpha 700 and the SLT-A77 show a slight resolution advantage over the 6mp Dimage 7D, and that resolution advantage is about the same magnitude as the resolution advantage of the 24mp A77 over the 12mp Alpha 700 at F16.

I say I'm surprised because both Guillermo and Bart in this context have claimed that at F16 the D800 will have no resolution advantage. Now such statements do not accord with my own tests, but I would probably have been prepared to accept the truth of such a statement in relation to F32. It now looks as though a comparison between the D800 and the D3 will show very marginally increased detail for the D800 shot even at F32.

When I carried out my tests back in 2009, between the 40D and 50D, it was very apparent that at F22 there was no difference whatsoever in detail, whatever the degree of magnification on the monitor. As a consequence there was no point in testing at F32.

If I ever get around to comparing my Canon 5D with the D800E, I'll test all the way down to F32, and expect to see some subtle increase in detail in the D800E shot, at maybe 300% magnification.

[free1000]

Eric thats a nice and clear explanation.
 
The sharpening information is very interesting, I'd never before realised the relationship between radius and detail. I've always used little of the detail because of an increase in 'grittiness'. I now see that increasing the radius can remove that effect while retaining more detail.

I don't know who found these sharpening recipes but thank you for posting them, the effect on my recent test images is revelatory. It makes the Nikon 24 f2.8 more usable. At f16 the corners aren't too bad at all.

PS: The icing on the cake would be a diagram that showed the size and shape of the airy disk 3d plot at different apertures,  even better an interactive one!

[ErikKaffehr]

Hi,

Detail works as "halo supression" at low values at high values it will switch algrithm to deconvolution.

Best regards
Erik

Eric thats a nice and clear explanation.
 
The sharpening information is very interesting, I'd never before realised the relationship between radius and detail. I've always used little of the detail because of an increase in 'grittiness'. I now see that increasing the radius can remove that effect while retaining more detail.

I don't know who found these sharpening recipes but thank you for posting them, the effect on my recent test images is revelatory. It makes the Nikon 24 f2.8 more usable. At f16 the corners aren't too bad at all.

PS: The icing on the cake would be a diagram that showed the size and shape of the airy disk 3d plot at different apertures,  even better an interactive one!

[Bart_van_der_Wolf]

Your graph, which I've reproduced here (hope you don't mind) shows results for 3 cameras which have the pixel density of full-frame 13.7mp, 27.5mp and 54.7 mp. What surprises me is that, even at F32, both the Alpha 700 and the SLT-A77 show a slight resolution advantage over the 6mp Dimage 7D, and that resolution advantage is about the same magnitude as the resolution advantage of the 24mp A77 over the 12mp Alpha 700 at F16.

I say I'm surprised because both Guillermo and Bart in this context have claimed that at F16 the D800 will have no resolution advantage.

Ray,

That is because of the units used for the vertical axis of the chart. Line Widths per Image Height is a metric that lumps together actual resolution in cycles/mm together with number of (vertical) pixels. More pixels will always help to reduce the need for output magnification.

Using actual resolution in cycles/mm on the vertical axis would give a somewhat different picture, which is what I've been saying all along. Therefore it all depends on what it is that one is comparing, output resolution based on same size output, or same output resolution at different sizes. These are different goals and thus will lead to different evaluations results.

LW/PH is a good criterion for same size output scenarios, Cy/mm is a good criterion for same output resolution at different output sizes. They are different sides of the same coin. LW/PH is more about image quality at a fixed output size (can I improve my image quality at this specific output size?), where Cy/mm is more about enlargement capability (can I produce larger output without sacrificing quality?).

Cheers,
Bart

[Ray]

Ray,

That is because of the units used for the vertical axis of the chart. Line Widths per Image Height is a metric that lumps together actual resolution in cycles/mm together with number of (vertical) pixels. More pixels will always help to reduce the need for output magnification.

Using actual resolution in cycles/mm on the vertical axis would give a somewhat different picture, which is what I've been saying all along. Therefore it all depends on what it is that one is comparing, output resolution based on same size output, or same output resolution at different sizes. These are different goals and thus will lead to different evaluations results.

LW/PH is a good criterion for same size output scenarios, Cy/mm is a good criterion for same output resolution at different output sizes. They are different sides of the same coin. LW/PH is more about image quality at a fixed output size (can I improve my image quality at this specific output size?), where Cy/mm is more about enlargement capability (can I produce larger output without sacrificing quality?).

Cheers,
Bart

Hi Bart,
I have to say, I haven't heard anything so confusing in a long time. You've even exceeded the obfuscation records previously set by BJL.

Whenever I compare images for resolution and detail, I always compare them at equal output size and always from an equal viewing distance. That seems just plain common sense to me. When one starts changing output size of one image in relation to another, or changing viewing distance of one image in relation to another, then one can achieve any result one desires, as regards perception of detail or resolution.

I've dug out the DVD where I recorded my tests of the 40D and 50D in 2009, and reconverted two of the images of the $50 banknote, a 40D shot and a 50D shot both taken at F16.

As far as I can tell, from my position of inexperience, there is no moiré or artifacts in either image. But there is clearly more real detail in the 50D shot, but visible only in certain parts of the images at a high magnification.

Now, how would you like me to display such images to demonstrate my point? If I display them both at 100%, and unequal size, the resolution differences will be ambiguous and uncertain. If I display both images at 200%, and unequal size, the differences will be more obvious. If I display them both at 300%, and unequal size, the differences will be even clearer.

On the other hand, I could display the lower resolution 40D at 242% and the higher resolution 50D at 200%, which would make them equal size. Or I could display the 40D at 300% and the 50D at 245%, which would also make them equal size.

Which would you prefer? I can be very accommodating. 

Cheers!  Ray

[Bart_van_der_Wolf]

Hi Bart,
I have to say, I haven't heard anything so confusing in a long time.

Which is understandable if you prefer to only look at one side of the coin ...

Whenever I compare images for resolution and detail, I always compare them at equal output size and always from an equal viewing distance. That seems just plain common sense to me.

Strange as it may seem to you, looking only at one side of the situation, there are actually people out there who buy a higher megapixel and/or larger sensor array size camera because they have a need for larger output. These are often the same kind of people that resort to stitching when such a larger physical size sensor is not feasible.

When one starts changing output size of one image in relation to another, or changing viewing distance of one image in relation to another, then one can achieve any result one desires, as regards perception of detail or resolution.

I know it must come as a shock that not everybody prints only 8x10 inch images, some have different requirements such as filling the wall of a booth on a tradeshow. A higher pixel or line count alone (LW/PH) only tells one part of the whole story, because one also needs to know the actual resolution in Cy/mm for each of those 'lines' to know what the output resolution (in Cy/mm) will be.

On-sensor resolution (Cy/mm) divided by output magnification factor equals output resolution (Cy/mm). For reference, 5 cycles/mm is considered good output quality for normal reading distances with adequate light levels, 8 cycles/mm is considered to be excellent. Double the viewing distance, and one can half the resolution requirement. Grasping such a concept doesn't come even close to rocket science.

Now, how would you like me to display such images to demonstrate my point?

I have already explained the possibility to represent images/figures with two different requirements in mind. I don't feel the need to repeat myself.

Feel free to post whatever you like to illustrate whatever point it is you are trying to make.

Cheers,
Bart

[Ray]

Which is understandable if you prefer to only look at one side of the coin ...

Strange as it may seem to you, looking only at one side of the situation, there are actually people out there who buy a higher megapixel and/or larger sensor array size camera because they have a need for larger output. These are often the same kind of people that resort to stitching when such a larger physical size sensor is not feasible.

I know it must come as a shock that not everybody prints only 8x10 inch images, some have different requirements such as filling the wall of a booth on a tradeshow. A higher pixel or line count alone (LW/PH) only tells one part of the whole story, because one also needs to know the actual resolution in Cy/mm for each of those 'lines' to know what the output resolution (in Cy/mm) will be.

C'mon now Bart. Everyone knows that you can produce whatever output size you want, whatever the megapixel count of your sensor. The only reason for requiring more megapixels is so that a print at a particular, large size will show finer detail from a closer viewing distance.

There must be thousands of bill boards on the highways that were produced from an old-fashioned 6mp MFDB, or an 11mp 35mm DSLR, that look very detailed from a distance of 20 metres or so. Walk up close, and the image quality is crap.

My plasma HDTV is 65"diagonal. It can display no more than a 2mp image, which is quite pathetic in terms of modern DSLR resolution, and even pathetic in terms of the average P&S resolution, yet from the other side of the living room, say 5 or 6 metres away, I might find it difficult to discern any additional detail in an equal-size print from a 36mp file placed next to the TV.

However, that 2mp image displayed on my HDTV also looks crap from the same close distance one might view an 8"x10"print.

My prints are not coins. They have two sides, but the other side is a blank.

Cheers!  Ray

[bjanes]

Hi Bart,
I have to say, I haven't heard anything so confusing in a long time. You've even exceeded the obfuscation records previously set by BJL.

Whenever I compare images for resolution and detail, I always compare them at equal output size and always from an equal viewing distance. That seems just plain common sense to me. When one starts changing output size of one image in relation to another, or changing viewing distance of one image in relation to another, then one can achieve any result one desires, as regards perception of detail or resolution.

Ray,

Perhaps an example would help clarify the differences. Suppose that you want to take a picture of a bird at some distance and you have only a 200 mm lens and have both the D800 and D7000 cameras. With both cameras you would take the shot and then crop the area of interest. If both crops are of the same pixel dimension, there will be little difference in the images. The Nyquist frequencies of both cameras is slightly over 100 cy/mm. If your crop is 1000 x 800 pixels in the plane of the sensor, you are not using the full picture height of each sensor but are using less of the full picture height of the D800. The resolution in terms of cy/mm is the determining factor.

On the other-hand, if you take a picture so that the full frames of both cameras are used and the views are the same, then the determining factor is cy/PH.

Regards,

Bill

[ErikKaffehr]

Hi,

All the images discussed in the original article were taken with APS-C sensors of different generations, so LW/PH and cy/mm are essentially just related by a constant.

Best regards
Erik

Ray,

Perhaps an example would help clarify the differences. Suppose that you want to take a picture of a bird at some distance and you have only a 200 mm lens and have both the D800 and D7000 cameras. With both cameras you would take the shot and then crop the area of interest. If both crops are of the same pixel dimension, there will be little difference in the images. The Nyquist frequencies of both cameras is slightly over 100 cy/mm. If your crop is 1000 x 800 pixels in the plane of the sensor, you are not using the full picture height of each sensor but are using less of the full picture height of the D800. The resolution in terms of cy/mm is the determining factor.

On the other-hand, if you take a picture so that the full frames of both cameras are used and the views are the same, then the determining factor is cy/PH.

Regards,

Bill

[Ray]

Ray,

Perhaps an example would help clarify the differences. Suppose that you want to take a picture of a bird at some distance and you have only a 200 mm lens and have both the D800 and D7000 cameras. With both cameras you would take the shot and then crop the area of interest. If both crops are of the same pixel dimension, there will be little difference in the images. The Nyquist frequencies of both cameras is slightly over 100 cy/mm. If your crop is 1000 x 800 pixels in the plane of the sensor, you are not using the full picture height of each sensor but are using less of the full picture height of the D800. The resolution in terms of cy/mm is the determining factor.

On the other-hand, if you take a picture so that the full frames of both cameras are used and the views are the same, then the determining factor is cy/PH.

Regards,

Bill

Bill,
Surely you know that sensor resolution is determined by pixel density. LW/PH is a combination of pixel density and sensor size. The D800 has approximately the same pixel density as the D7000 (very slightly less to an insignificant degree), so resolution in terms of line pairs per mm is about the same, but LW/PH is obviously greater for the D800.

When comparing equal size sensors, as in my comparison between the Canon 40D and the 50D, and in Erik's comparisons amongst 3 cropped-format sensors, one Minolta and two Sony, there is no distinction between resolution per mm (cy/mm) and Line Widths per Picture Height. A higher resolution in terms of cy/mm equates to a proportionally higher resolution in terms of LW/PH.

Bart has raised a complete red herring in this respect.

Ps. I see Erik has said more or less the same. Cy/mm is not the same in precise mathematical terms as LW/PH, for same size sensors. Different terminology. But it varies proportionally, assuming that the LW/PH is an extrapolation of centre resolution, which I believe it is.

[Bart_van_der_Wolf]

When comparing equal size sensors, as in my comparison between the Canon 40D and the 50D, and in Erik's comparisons amongst 3 cropped-format sensors, one Minolta and two Sony, there is no distinction between resolution per mm (cy/mm) and Line Widths per Picture Height. A higher resolution in terms of cy/mm equates to a proportionally higher resolution in terms of LW/PH.

Bart has raised a complete red herring in this respect.

You said you "haven't heard anything so confusing in a long time". I'm afraid you are, confused that is, and you also managed to get this thread off-topic. Oh well, what's new.

Erik's three camera models do have virtually similar physical sensor sizes but with quite different sensel pitches. The sensel pitch has shrunk with each generation, but with that, the on-sensor resolution has increased (assuming the same lens performance and similar AA-filter characteristics).

The Maxum 7D has an approx. on sensor resolution at Nyquist of 64 cy/mm, the Alpha A700 has approx. 91 cy/mm, and the SLT-A77 has approx. 128 cy/mm.

That means that for same output resolution the A700 can produce some 42% larger output, and the SLT-A77 can produce output that is 100% larger, twice the size. That is such a significant difference that I wouldn't call it a red herring, but then I'm not claiming to be confused.

BTW the on-sensor resolution of the 40D is approx. 88 cy/mm at Nyquist, and the 50D is 106 cy/mm. So that would allow the 50D to produce approx. 20% larger output with the same output resolution in cy/mm as the 40D, ceteris paribus.

So the differences when expressed as LW/PH which are good for comparison of same size output, tell a somewhat different story than when we compare cycles/mm which is more useful for same output resolution but different magnification and thus output size. Actually it is the same story but seen from two different usage goals/perspectives, hence the two sides of the same coin analogy.

I can also tell from first hand experience that the 2012 'Dutch Herring' tastes excellent, and that it is not red. And yes, we prefer to eat them raw (with chopped onions).

Cheers,
Bart

[ErikKaffehr]

Hi,

I would suggest that these figures explain a lot:

and


The upper figure shows MTF as function of LW/PH for the Dynax 7 at f/5.6 and at f/16. The dotted line is the diffraction limit. So would we have a sensor with MTF == 1.0 and a prefect lens the MTF curve would fit the dotted line. Obviously the MTF curve is quite a bit below the diffraction limit even at f/16 but it also obvious that diffraction affects MTF. If we check 1000 LW/PH, MTF is around 0.55 at f/5.6 but only 0.4 at f/16.

The lower curve shows MTF for the Alpha 77SLT. MTF is still less than what would be due to diffraction alone. If we compare 1000 LW/PH  we can see that we have MTF around 0.7 at f/5.6 and about 0.5 for f/16.

On the other hand, the Nyquist limit for the Dimage 7D is 2000 LW/PH, and here it produces virtually nil MTF at f/16. The Alpha 77SLT still has a significant MTF for 2000 LW/PH.

What I see is that the Dimage 7D is sensor limited at f/16, while the Alpha 77SLT is diffraction limited at f/16 as diffraction limit crosses the horizontal axis at around 3400.

The sample images in the article illustrate that the effect of diffraction is noticable even at f/8.

Contrary to Bart's view I'd say that LW/PH is a good measure, it says what amount of information the sensor can deliver. The MTF curve is much effected by the amount of sharpening, but that is a different can of worms, and a can of worms it is.

Best regards
Erik

Erik,
That's an excellent description of the problem. Thanks for taking the trouble to do the tests and share your results.
I'm sure many folks who have never hear of the Airy Disk will be aware that their camera produces sharper results at F5.6 than at F16, but your graph of Imatest results demonstrating the differences in resolution at 50% MTF at F stops between F2.8 and F32 (using the same lens with 3 different cameras) is very revealing, and also very credible in my opinion, in relation to my own tests.

You've done a more thorough and comprehensive test than I've done. I simply concentrated on the 10mp Canon 40D and the 15mp Canon 50D, as a result of claims on this forum, some years ago, that the 50% increase in pixel count of the 50D would serve no purpose beyond F8.

Your graph, which I've reproduced here (hope you don't mind) shows results for 3 cameras which have the pixel density of full-frame 13.7mp, 27.5mp and 54.7 mp. What surprises me is that, even at F32, both the Alpha 700 and the SLT-A77 show a slight resolution advantage over the 6mp Dimage 7D, and that resolution advantage is about the same magnitude as the resolution advantage of the 24mp A77 over the 12mp Alpha 700 at F16.

I say I'm surprised because both Guillermo and Bart in this context have claimed that at F16 the D800 will have no resolution advantage. Now such statements do not accord with my own tests, but I would probably have been prepared to accept the truth of such a statement in relation to F32. It now looks as though a comparison between the D800 and the D3 will show very marginally increased detail for the D800 shot even at F32.

When I carried out my tests back in 2009, between the 40D and 50D, it was very apparent that at F22 there was no difference whatsoever in detail, whatever the degree of magnification on the monitor. As a consequence there was no point in testing at F32.

If I ever get around to comparing my Canon 5D with the D800E, I'll test all the way down to F32, and expect to see some subtle increase in detail in the D800E shot, at maybe 300% magnification.

[Bart_van_der_Wolf]

Contrary to Bart's view I'd say that LW/PH is a good measure, it says what amount of information the sensor can deliver.

Hi Erik,

Just to make sure, I'm not saying it is bad measure, on the contrary. It is just one way of specifying performance, specifically normalized for 1 picture height (PH), or same output size. That is fine if that is the comparison; does the image quality improve when I choose one system instead of the other? However, there is a limit to how much quality can improve when we exceed a 720 PPI output resolution, because the printer becomes the limitation.

Another way of looking at a system comparison is; how much larger can the output become, before losing image quality? That comparison is not more limiting for one or the other system because the printer resolution will be the same.

Both are good methods to compare systems, they are just anwering the question with a different goal in mind. That's all.

Cheers,
Bart

[Fine_Art]

Good info, thanks Erik.

[Ray]

You said you "haven't heard anything so confusing in a long time". I'm afraid you are, confused that is, and you also managed to get this thread off-topic. Oh well, what's new.

Erik's three camera models do have virtually similar physical sensor sizes but with quite different sensel pitches. The sensel pitch has shrunk with each generation, but with that, the on-sensor resolution has increased (assuming the same lens performance and similar AA-filter characteristics).

As do mine, Bart. I've been quite clear all along that my comparisons relate to equal size sensors with a different pixel pitch. No confusion on my part, old chap.

Whenever a DSLR manufacturer significantly raises the pixel count of its latest model we seem to get the same old concerns about diffraction, raised again and again. Will the extra pixels serve any purpose when the camera is used above F5.6 or F8? Is there a cut-off point at a particular F stop, beyond which no further resolution can be gleaned however large the ouput size?

Erik's graph demostrates that even a camera with the very high pixel density of the SLT-A77, which is equivalent to a 55mp full-frame sensor of the same pixel density, can show a resolution edge at all apertures up to, and including F16, compared with a camera of half the pixel count, such as the Alpha 700. The graph also shows that F22 is the point where no further resolution benefits are to be had from the 24mp A77, compared with Alpha 700.

Now you are quite right to point out, Bart, that the differences in pixel densities between the 12.25mp Alpha 700 and the 24.3mp ALT-A77, are greater than the differences between the Canon 40D and 50D. In the case of the two Sony cameras, one has double the pixel count of the other. In the case of the two Canon cameras, one has only 50% greater pixel-count than the other.

One should therefore not presume from Erik's graph that a sensor with a lower pixel density than the A77, such as the Canon 50D, equivalent to a 38 or 39mp full frame, will also show a resolution edge at F16. And indeed I haven't presumed that. I carried out my own tests back in September 2008, and discovered for myself that even a camera with a modest 50% increase in pixel count over another of fairly similar pixel density to the Alpha 700, will show a very slight resolution edge at F16. (Alpha 700 roughly equivalent to 28mp full-frame; 40D roughly equivalent to 25.6mp. That's close enough).

The question that now remains, will a camera such as the D800 with 3x the pixel count of a D3 show any resolution advantage whatsoever at F32? I doubt it, but I'm fairly confident that the D800 will show a very slight advantage at F22, and a more significant advantage at F16, compared with the D3.

Enjoy your Dutch Herring, Bart. 

Cheers!

[Bart_van_der_Wolf]

The question that now remains, will a camera such as the D800 with 3x the pixel count of a D3 show any resolution advantage whatsoever at F32? I doubt it, but I'm fairly confident that the D800 will show a very slight advantage at F22, and a more significant advantage at F16, compared with the D3.

That is not too difficult to answer, denser sampling will get the most out of any optical projection. However, physics sets a hard absolute diffraction limit, based on wavelength and aperture. No other parameters play a role.

For a 564 nm wavelength (wich is a nice Luminance weighted average between Red, Green, and Blue) and a round aperture, diffraction will limit spatial frequency resolution in the focal plane by a zero modulation at resolutions beyond:

• f/32 is limited at 55.4078 cycles/mm, a sample pitch of 9.0 micron
• f/28 is limited at 62.1932 cycles/mm, a sample pitch of 8.0 micron
• f/25 is limited at 69.8095 cycles/mm, a sample pitch of 7.2 micron
• f/22 is limited at 78.3585 cycles/mm, a sample pitch of 6.4 micron
• f/20 is limited at 87.9544 cycles/mm, a sample pitch of 5.7 micron
• f/18 is limited at 98.7255 cycles/mm, a sample pitch of 5.1 micron
• f/16 is limited at 110.816 cycles/mm, a sample pitch of 4.5 micron

There is zero resolution possible beyond those spatial frequencies, none, nada. The indicated sample pitches have a Nyquist frequency that limits resolution at that same maximum spatial frequency, and as a consequence of diffraction there cannot be any aliasing because there is no signal beyond Nyquist. These are the absolute optical and sampling limits.

Because our sensors are not point samplers but area samplers, and our lenses are not perfect, the optical limits are even a fraction lower, but the above limits cannot be broken no matter how close the small sampling area gets to resembling a point sampler, or how good our lenses are. Only by using shorter wavelength light can we squeeze a bit more resolution out of our diffraction limiting optics. That's why chip manufacturers use UV and X-ray wavelengths to expose the photo resist masking layers, to beat the absolute limits of diffraction.

And again, near those diffraction limits there will only be resolution for very high contrast features because the MTF response is so low. Micro contrast is increasingly limited once the diffraction pattern diameter starts to exceed 1.5x the sensel pitch. A very rough rule of thumb tells us that, for wavelengths around 555 nm, that starting point of low micro contrast loss is at the sensel pitch in microns plus 10%, so for a D800 with a 4.88 micron sensel pitch that would be at approx. f/5.6 . Therefore, for the scenario of magnification capability based on cycles/mm, the per pixel contrast at maximum (for a given purpose) magnification will be low, unless the subject contrast was very high.

Cheers,
Bart

[Ray]

That is not too difficult to answer, denser sampling will get the most out of any optical projection. However, physics sets a hard absolute diffraction limit, based on wavelength and aperture. No other parameters play a role.

For a 564 nm wavelength (wich is a nice Luminance weighted average between Red, Green, and Blue) and a round aperture, diffraction will limit spatial frequency resolution in the focal plane by a zero modulation at resolutions beyond:

• f/32 is limited at 55.4078 cycles/mm, a sample pitch of 9.0 micron
• f/28 is limited at 62.1932 cycles/mm, a sample pitch of 8.0 micron
• f/25 is limited at 69.8095 cycles/mm, a sample pitch of 7.2 micron
• f/22 is limited at 78.3585 cycles/mm, a sample pitch of 6.4 micron
• f/20 is limited at 87.9544 cycles/mm, a sample pitch of 5.7 micron
• f/18 is limited at 98.7255 cycles/mm, a sample pitch of 5.1 micron
• f/16 is limited at 110.816 cycles/mm, a sample pitch of 4.5 micron

There is zero resolution possible beyond those spatial frequencies, none, nada. The indicated sample pitches have a Nyquist frequency that limits resolution at that same maximum spatial frequency, and as a consequence of diffraction there cannot be any aliasing because there is no signal beyond Nyquist. These are the absolute optical and sampling limits.

Because our sensors are not point samplers but area samplers, and our lenses are not perfect, the optical limits are even a fraction lower, but the above limits cannot be broken no matter how close the small sampling area gets to resembling a point sampler, or how good our lenses are. Only by using shorter wavelength light can we squeeze a bit more resolution out of our diffraction limiting optics. That's why chip manufacturers use UV and X-ray wavelengths to expose the photo resist masking layers, to beat the absolute limits of diffraction.

And again, near those diffraction limits there will only be resolution for very high contrast features because the MTF response is so low. Micro contrast is increasingly limited once the diffraction pattern diameter starts to exceed 1.5x the sensel pitch. A very rough rule of thumb tells us that, expressed in microns and for wavelengths around 555 nm, that starting point of low micro contrast loss is at the aperture number plus 10%, so for a D800 with a 4.88 micron sensel pitch that would be at approx. f/5.6 . Therefore, for the scenario of magnification capability based on cycles/mm, the per pixel contrast at maximum (for a given purpose) magnification will be low, unless the subject contrast was very high.

Cheers,
Bart

Hi Bart,
That's an informative table which certainly makes sense to me as long as we emphasise that the sample pixel pitches are maximum sizes in relation to maximum resolutions and that any sensor with a smaller pixel pitch will potentially achieve the same diffraction-limited resolution at those F stops, provided the target is high contrast of course, such as B&W lines or similar contrasty detail one might find on a banknote.

For example, the 50D has a pixel pitch of 4.68 microns and a potential maximum resolution at the Nyquist limit of 106 cy/mm. It looks as though the 50D would be capable of delivering close to its maximum potential resolution at F16, whereas the 40D cannot deliver more than 88 cy/mm at any aperture up to F20.

One would therefore expect the 50D to deliver slightly higher resolution than the 40D at F16, which it does.

The D800 with a very marginally larger pixel than the 50D (4.7 versus 4.68 microns), should deliver a similar resolution to the 50D at F16 (in terms of cy/mm rather than LW/PH of course) especially if we use the D800E.

However, the D3 with a pixel pitch of 8.4 microns, and a maximum resolution at the Nyquist limit of only 60 cy/mm, will deliver worse resolution than the D800 all the way down to F28. At F32, diffraction will prevent it from achieving its full resolution potential under any circumstances. Resolution with both the D3 and D800 at F32 and F28 should be indistinguishable at any degree of magnification. But resolution at F25 could be very slightly better for the D800, viewed at say 200% on screen, I would predict. And if not at F25, then certainly at F22, wouldn't you agree?

Cheers!

[Bart_van_der_Wolf]

Hi Bart,
That's an informative table which certainly makes sense to me as long as we emphasise that the sample pixel pitches are maximum sizes in relation to maximum resolutions and that any sensor with a smaller pixel pitch will potentially achieve the same diffraction-limited resolution at those F stops, provided the target is high contrast of course, such as B&W lines or similar contrasty detail one might find on a banknote.

Yes, they are maximum values. Denser sampling will usually help because it provides a better oversampling of the diffraction pattern, which in turn allows more accurate restoration by deconvolution sharpening.

However, the D3 with a pixel pitch of 8.4 microns, and a maximum resolution at the Nyquist limit of only 60 cy/mm, will deliver worse resolution than the D800 all the way down to F28. At F32, diffraction will prevent it from achieving its full resolution potential under any circumstances. Resolution with both the D3 and D800 at F32 and F28 should be indistinguishable at any degree of magnification. But resolution at F25 could be very slightly better for the D800, viewed at say 200% on screen, I would predict. And if not at F25, then certainly at F22, wouldn't you agree?

Yes, that's how it happens to work out for high contrast detail. But do keep in mind that lower contrast subject matter will be mostly lost already at wider apertures than these limiting ones. Stopping down will kill low contrast micro-detail long before it kills all micro-detail (of any level of contrast). For the D800 it starts at f/5.6 and for the D3 it starts at f/9 .

Cheers,
Bart