f-stop limits for full sensor resolution

[Ray]

Another way of looking at this; 3 people out of 50 were able to tell the difference between the 7, 10 and 16.7mp images. But that presumably does not include David Pogue and Ellis Vener. Making the fairly safe assumption that the person who took the shots and the person who organised the tests were also able to discern the difference, that makes 5 out of 52 or 10%, since we can't have a fraction of a person.

10% of a group who are particularly discerning is fairly typical. For example, 10% of all computer users are Mac users, and just to make the point that I am not being elitist, I belong to the set of 90% non-discerning rabble who use the PC   .

[xtoph]

dude--i already _did_ what you suggest here. look up higher in the thread. the sample pics are posted; they prove conclusively that myrhvold's (sp?) statements (both the 2mp one and the gaussian blur one) are absolutely false. what more do you want? i've already given him the most charitable interpretation conceivable--his claims are complete nonsense (beyond the platitude that most lens-dslr combinations will perform at their peak resolution somewhere close to f/8--which we already know, and not for the reasons myrhvold says).

i am confused as to why this discussion kept on proceeding as though no one had bothered to do real-world tests.

[Ray]

dude--i already _did_ what you suggest here. look up higher in the thread. the sample pics are posted; they prove conclusively that myrhvold's (sp?) statements (both the 2mp one and the gaussian blur one) are absolutely false. what more do you want? i've already given him the most charitable interpretation conceivable--his claims are complete nonsense (beyond the platitude that most lens-dslr combinations will perform at their peak resolution somewhere close to f/8--which we already know, and not for the reasons myrhvold says).

i am confused as to why this discussion kept on proceeding as though no one had bothered to do real-world tests.
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Are you talking to me, dude? If so, what point have I made that you are disputing?

I'm well aware that f16 is a perfectly usable f stop on my 5D, only marginally less sharp than f8 in real world scenes. F22, however, is a noticeable compromise. I rarely use it.

It's clear that Myhrvold is a theoretician. The reason he appears to be wrong is that he hasn't taken into consideration the failings, inadequacies and characteristics of the equipment we use. He's assuming that lenses and sensors are as perfect as his mathematical formulae and optical theories.

Jonathan made an easy experiment by downsampling a 1Ds image at f22 to 2mp and then upsampling back to its original size. I made the point it would have been more relevant if the image which was downsampled had been taken at f8 or f11, and compared with the same scene taken at f22 or f32. But even then, I suspect that the f22 shot would be marginally sharper and more detailed.

The problem as I see it is that no 35mm lens is diffraction limited at f8, whereas many 35mm lenses really are diffraction limited at f22. Additionally, if one did have a lens that is diffraction limited at f8, there is no 35mm sensor capable of capturing all the detail that such a lens would provide above say a 30% MTF cut-off point.

From a theoretical point of view, a lens which is diffraction limited at f8 will have 2.8x the resolution of that same lens at f22. But to capture such resolution at f8 you need 2.8^ x the numer of pixels, ie. 7.8x that you would need at f22.

So yes, Myhrvold is wrong in practice, but it's still useful to work out what he was trying to get at. The reasons why f16 with the 5D seems hardly less sharp than at f8, are (1) lenses are not as good as we think at f8. They are not diffraction limited. (2) the 5D does not have sufficient pixel density to reveal all the differences in lens resolution between these two f stops.

[bjanes]

Are you talking to me, dude? If so, what point have I made that you are disputing?

The problem as I see it is that no 35mm lens is diffraction limited at f8, whereas many 35mm lenses really are diffraction limited at f22. Additionally, if one did have a lens that is diffraction limited at f8, there is no 35mm sensor capable of capturing all the detail that such a lens would provide above say a 30% MTF cut-off point.

[a href=\"index.php?act=findpost&pid=113594\"][{POST_SNAPBACK}][/a]

Ray,

Just a comment on the semantics of diffraction limited resolution.

Every optical lens now in existence is diffraction limited at all apertures--that is diffraction sets a limit on the maximum resolution possible at that aperture. In practice, the resolution limit is often imposed by aberrations rather than diffraction. When we say a lens is diffraction limited at f/8, we mean that aberrations are no longer the limiting factor at this aperture, and that the lens resolves at the limit set by diffraction for that aperture and for smaller apertures. Many current high quality lenses exhibit better resolution at f/5.6 than f/8. In this case, if the resolution at f/5.6 is limited only by diffraction, we say that the lens is diffraction limited at f/5.6.

Bill

[Ray]

Ray,

Just a comment on the semantics of diffraction limited resolution.

Every optical lens now in existence is diffraction limited at all apertures--that is diffraction sets a limit on the maximum resolution possible at that aperture. [a href=\"index.php?act=findpost&pid=113732\"][{POST_SNAPBACK}][/a]

Bill, if we are getting into semantics, I would say that definition serves no purpose other than to point out that there is a concept called diffraction which may be a limit to resolution at a particular f stop.

There are many technological factors which limit the resolution of lenses. Diffraction is one of them. But 'diffraction limitation', in my view, is a situation that arises only when all other abberrations have been reduced to a level that is less significant than the effects of diffraction. In other words, a situation where the only option to improve resolution is to reduce the effects of diffraction; a situation where further reduction in other lens aberrations would serve no purpose.

At the same time, it might well be the case that the finest 35mm prime lenses are fairly close to being diffraction limited at f8, at least at the centre. The Photodo ratings for lenses at f8 seem to vary from about 0.77 to 0.87.

[bjanes]

Bill, if we are getting into semantics, I would say that definition serves no purpose other than to point out that there is a concept called diffraction which may be a limit to resolution at a particular f stop.

There are many technological factors which limit the resolution of lenses. Diffraction is one of them. But 'diffraction limitation', in my view, is a situation that arises only when all other abberrations have been reduced to a level that is less significant than the effects of diffraction. In other words, a situation where the only option to improve resolution is to reduce the effects of diffraction; a situation where further reduction in other lens aberrations would serve no purpose.
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Ray,

I agree with your explanation of diffraction limited and it coincides with with what I was trying to get across.

At the same time, it might well be the case that the finest 35mm prime lenses are fairly close to being diffraction limited at f8, at least at the centre. The Photodo ratings for lenses at f8 seem to vary from about 0.77 to 0.87.
[a href=\"index.php?act=findpost&pid=113738\"][{POST_SNAPBACK}][/a]

Here is where we begin to differ. The new PhotoDo ratings use Imatest to derive their resolution figures, and measure the system resolution, not lens resolution. An idealized system would yield 0.5 cycles per pixel, but a Bayer array sensor can resolve only about 75% of this at 50% contrast, and I assume that the ratios of 0.77 to 0.87 that you mention are derived from this type of analysis.

For example in a recent test of the new [a href=\"http://www.photodo.com/topic_156.html]Nikon AFS 105 f/2.8 MicroNikkor[/url], maximum resolution in the center of the field occurred at f/4 (f/2.8 was not tested), and degrades with stopping down beyond f/4. In this test the lens with the D200 camera resolved about 0.475 cycles/pixel at f/4 (which is dubious). These data would imply that the lens is diffraction limited at f/4, and not the f/8 figure you mention.

Another way to look at resolution is in terms of line pairs/picture height as shown in the test of the same lens and camera at PhotoZone. These data show that maximum resolution in the center is reached at f/4 and that resolution is lost by stopping down further, in agreement with the PhotoDo results.

In both of these test cases, the relative contributions of lens versus sensor and demosiacing algorithms on the test results is not clearly determined.

One can also use the diffraction calculator devised by Sean McHugh with stringent parameters for observer visual acuity and print size and determine whether the limits of diffraction are reached. For example,  the Nikon D200 camera used in the above Imatest reports is 10 MP with a CF of 1.5. Using 36 inches maximal print dimension and vision of 20/20, we see that the system is diffraction limited at apertures above f/1.4. Due to optical aberrations and limitations in the sensor and demosaicing process, degradation of the image is not observed until f/4 and significant degradation does not occur until considerably smaller apertures are used. This is true only for the center of the image; you may have to stop down more to improve resolution at the edges. The Nikon guru Thom Hogan states that diffraction begins to limit the D200 performance beyond f/13, and this is consistent with observations made by others.

Bill

[Ray]

Here is where we begin to differ. The new PhotoDo ratings use Imatest to derive their resolution figures, and measure the system resolution, not lens resolution. An idealized system would yield 0.5 cycles per pixel, but a Bayer array sensor can resolve only about 75% of this at 50% contrast, and I assume that the ratios of 0.77 to 0.87 that you mention are derived from this type of analysis.
[a href=\"index.php?act=findpost&pid=113779\"][{POST_SNAPBACK}][/a]

I don't believe so, Bill. I usually refer to the old Photodo tests which I understand test the MTF of the lens only, in relation to 10, 20 and 40 lp/mm.

These tests are a few years old and it's a pity that Photodo has not continued with the same testing procedures. Their finest result is for a lens which is now discontinued, the Canon 200/1.8 which has an even higher score at f4 (0.90) than at f8 (0.87).

The difficulty I have here is related to a view that a lens is very unlikely to have less aberration at f4 than at f8 or any other larger f stop number. I don't know if this is always true, but it seems a reasonable assumption.

We can therefore deduce that the slightly higher performance at f4 (of this lens) is due to the fact that any increase in aberration at f4 is less than the reduction in diffraction effects at f4.

But we cannot deduce that the 200/1.8 is therefore diffraction limited at f8.

[bjanes]

I don't believe so, Bill. I usually refer to the old Photodo tests which I understand test the MTF of the lens only, in relation to 10, 20 and 40 lp/mm.

These tests are a few years old and it's a pity that Photodo has not continued with the same testing procedures. Their finest result is for a lens which is now discontinued, the Canon 200/1.8 which has an even higher score at f4 (0.90) than at f8 (0.87).

The difficulty I have here is related to a view that a lens is very unlikely to have less aberration at f4 than at f8 or any other larger f stop number. I don't know if this is always true, but it seems a reasonable assumption.

We can therefore deduce that the slightly higher performance at f4 (of this lens) is due to the fact that any increase in aberration at f4 is less than the reduction in diffraction effects at f4.

But we cannot deduce that the 200/1.8 is therefore diffraction limited at f8.
[a href=\"index.php?act=findpost&pid=113917\"][{POST_SNAPBACK}][/a]

Ray,

Your use of the old PhotoDo figures clarifies things, but I think you are misinterpreting the data. The weighted MTF figures merely refer to the percent contrast at a given frequency (resolution), not resolution expressed as a fraction of the diffraction limited resolution. For example the theoretical diffraction limited resolution of a lens at f/2.0 is 160 lp/mm at 80% contrast (0.8 in the PhotoDo charts), 390 lp/mm at 50% contrast, and 820 lp/mm at Rayleigh about 9% contrast). At f/8 the resolutions are 40, 97, and 200 lp/mm respectively. Since the PhotoDo tests max out at 40 lp/mm, there is no way to determine the resolution of the 200/1.8 as compared to the theoretical values with the lens wide open.

At f/8 it the MTF at 80% contrast is about 30 lp/mm by eyeball estimation from the MTF chart, whereas the theoretical diffraction limit is 40 lp/mm, so the resolution is about 75% of theoretical, more or less in keeping with your figures. So, the lens is operating near the diffraction limit at 80% contrast. However, at MTF 50 (the value that correlates best with perceived sharpness) the PhotoDo analysis is not helpful, since testing at anywhere near the theoretical limit of 97 lp/mm was not done.

Bill

[Ray]

For example the theoretical diffraction limited resolution of a lens at f/2.0 is 160 lp/mm at 80% contrast (0.8 in the PhotoDo charts), 390 lp/mm at 50% contrast, and 820 lp/mm at Rayleigh about 9% contrast). At f/8 the resolutions are 40, 97, and 200 lp/mm respectively. Since the PhotoDo tests max out at 40 lp/mm, there is no way to determine the resolution of the 200/1.8 as compared to the theoretical values with the lens wide open.

Bill,
I agree it's not possible to precisely determine from the Photodo figures if the lens is diffraction limited at f8 unless we have the diffraction limited MTF responses at the same resolutions that Photodo have tested, which are 10, 20 and 40 lp/mm, but you have already provided a good indication of what to expect, from your usual sources (Roger Clark, Norman Koren??).

For example, you say a lens which is diffraction limited at f8 should be capable of 80% MTF at 40 lp/mm. Checking the Photodo MTF graphs (one doesn't have to rely upon weighted figures) we can examine the MTF response of what might be the finest lens that Canon ever made, the now discontinued 200/1.8 which at full aperture is as sharp as the Canon 28-135 at its sharpest focal length of 50mm and its sharpest aperture of f8 (weighted rating of 0.82 in both cases).

What do we get? Well, most lenses fall off in MTF response towards the edges, but if we consider just the central part of the image with a diameter of say 18mm, and if we average the sagital and meridional lines, we get an MTF response for 40 lp/mm of approximately 73%. Beyond 9mm from the centre, the MTF falls to about 65% at 18mm, and further beyond that

The conclusion is, the very expensive and probably uneconomical-to-produce 200/1.8 is very close to being diffraction limited at f8 in the central part of the image. Perhaps as close as matters.

Another fine lens, the Canon 50/1.4 doesn't quite make it in any part of the image, having an MTF response at 40lp/mm of just 70%. So I think we can say, on the basis of the accuracy of your figures, that the 50/1.4 is definitely not diffraction limited at f8, but is still reasonably close. The difference between 70% and 80% is probably not particularly significant. Also, the 50/1.4 is very consistent in this response right out to 18mm from the centre.

Lesser quality lenses and zooms rarely seem to rise as far as 70% at f8 in any part of the image.

[BJL]

Ray,

   firstly, the idea that a lens, at any given aperture ratio, is either "diffraction limited" or "not diffraction limited" is a false dichotomy, and the attempt to declare than one particular f-stop (f/8 for almost all good lenses according to you it seems!) is the limit and is therefore the lowest completely "worthy" f-stop is trying to make things far more rigid than they really are. It is a cousin of Myrvold's mistake in apparently declaring that as soon as the pixel size is smaller than the diffraction spot size at a given aperture ratio, resolution is determined mostly or entirely by diffraction, so that decreasing pixel size at that aperture ratio will not increase resolution; contrary to clear experimental evidence.


At any aperture, the resolution of a lens is affected to some extent by both diffraction and by aberrations, with diffraction effects increasing in proportion to aperture ratio, while aberrations almost certainly decrease with increasing aperture ratio. At very high aperture ratios, resolution is determined almost entirely by diffraction, while at very low aperture ratios, the resolution of most or all lenses is probably determined almost entirely by aberrations.

But at the intermediate apertures where the vast majority of photographs are taken, like f/4, f/8 and even f/2.8 and f/11, the resolution of good lenses seems to be significantly affected by both diffraction and aberrations. The simple fact that even good lenses vary noticeably in resolution at f/8 and f/11 (as seen in MTF graphs) shows that aberrations are a significant factor in resolution. Only if the MTF graph of a lens at some aperture ratio was identical to the theoretical MTF graphs calculated from diffraction alone would that lens achieve your holy grail of being "purely diffraction limited" at that aperture ratio.

Rather than debate if and when one limit on lens resolution is dominant, why not just look at the practical bottom line: the angular resolution [see note] performance of the lens as a whole at various choices of aperture. Perhaps in relation to speed and DOF possible at that aperture. If a lens has significantly higher resolution at f/4 than it does at f/8, what is the significance of worrying about it being "not diffraction limited at f/4"?


Note on angular resolution
I prefer, like many astronomers and lens optics professionals, to think of resolution and MTF in terms of angular resolution, as in "cycles per radian" or "line per degree", and MTF at various levels of cycles per radian or such. This a fairly direct measure of the ability of the lens to resolve subject features of a certain size when at a certain distance from the subject, which is my bottom line for resolution in most situations.
It is roughly equivalent to "lines per picture height" when comparing lenses covering the same angular FOV but possibly of different focal lengths and producing different sized images at the focal plane.


P. S. Given that the vast majority of SLR's (and even a clear majority of professional SLRs) are now in formats smaller than 35mm, it puzzles me why you persist in looking only at 35mm format lenses in arguing for your favored f/8. Even with the 18.7x28.7mm format 1D series, the use of only part of the 35mm image circle somewhat invalidates the old PhotoDo measurements, because they to some extent weigh MTF measurements towards the edge of the 35mm format frame. In the now dominant SLR formats, it seems that even some good amateur level zoom lenses achieve peak resolution at f/4 or below, not just a few very expensive prime lenses like the old Canon 200/1.8.

[Ray]

Note on angular resolution
I prefer, like many astronomers and lens optics professionals, to think of resolution and MTF in terms of angular resolution, as in "cycles per radian" or "line per degree", and MTF at various levels of cycles per radian or such. This a fairly direct measure of the ability of the lens to resolve subject features of a certain size when at a certain distance from the subject, which is my bottom line for resolution in most situations.
It is roughly equivalent to "lines per picture height" when comparing lenses covering the same angular FOV but possibly of different focal lengths and producing different sized images at the focal plane.
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BJL,
I get the impression you've just responded to my last post and haven't followed the developing arguments of the last few posts.

I'll recap for you.

(1) I've made the point that the differences in resolution as seen in real world shots at f8 and f16, with a reasonably good 35mm lens, do not seem nearly as great as one might think they would be, using a FF DSLR such as the 5D.

(3) I've suggested the reasons for this are that, whilst the lens at f16 is probably truly diffraction limited and therefore giving as good a resolution as is technically possible within the laws of physics, that same lens at f8 is probably quite far from being diffraction limited. Furthermore, a camera such as the 5D does not have even nearly sufficient pixel density to reveal the full extent of such differences.

(4) Bill has responded with some semantic issues regarding the definition of 'diffraction limitation' but agrees that the term should apply in situations (at f stops) where it is not possible to improve resolution by further reducing lens abberations in the lens design.

(5) Bill has also questioned the accuracy of my assertion that most 35mm lenses at f8 are not in fact diffraction limited. He seems to think they might be, but at the same time has provided the information that a lens should have an MTF response of 80% at 40 lp/mm at f8 if it is diffraction limited at that f stop.

(6) On the basis of the information that Bill has provided, and by examining the MTF curves at the Photodo site, I have made my case and proved my point, I believe   .

Now to your point. Comparing angular resolution or 'lines per picture height' is a valid alternative method and it's a method which would reduce the differences between f16 and f8 even further because f16 tends to produce a more even performance from edge to edge. With such a method, the humble Canon 50/1.4 would have at least as much angular resolution at f8 (from the appropriate closer distance) as that very expensive and discontinued 200/1.8.

The disadvantage to your method is, I simply don't have the information regarding angular resolution to work on. Where are the published results for angular resolution of the lens only? There are data at dpreview regarding lines per picture height, but these are lens/sensor combinations.

[Ray]

   firstly, the idea that a lens, at any given aperture ratio, is either "diffraction limited" or "not diffraction limited" is a false dichotomy, and the attempt to declare than one particular f-stop (f/8 for almost all good lenses according to you it seems!) is the limit and is therefore the lowest completely "worthy" f-stop is trying to make things far more rigid than they really are.

BJL,
Perhaps I should have answered this point first. We have to define terms clearly or we simply go round in circles. I realise there is a transition stage from the first hint of the effects of diffraction to the last hint of other aberrations which are eventually completely obscured by the effects of diffraction.

If you think it is necessary to break up the degree of diffraction limitation into separate descriptions such as 'very slightly diffraction limited', 'moderately diffraction limited', 'significantly diffraction limited', 'completley diffraction limited', then I have a problem with the semantics.

We all know what a 'limit' is. It's a 'stop'; a point beyond which one cannot go. It would be very silly to describe speed limits on the highway as, 'slightly limited to 60km/hour', 'significantly limited to 60km/hour', 'completley limited to 60km/hour etc. etc. Complete confusion would result.

My understanding is, rightly or wrongly, whilst diffraction may have an effect over a range of f stops, there will likely be one particular f stop at which (and beyond which) the effects of diffraction will limit the possibility of further resolution improvements in the design of the lens in question. At such a point, the lens is said to be diffraction limited.

[bjanes]

(4) Bill has responded with some semantic issues regarding the definition of 'diffraction limitation' but agrees that the term should apply in situations (at f stops) where it is not possible to improve resolution by further reducing lens abberations in the lens design.

(5) Bill has also questioned the accuracy of my assertion that most 35mm lenses at f8 are not in fact diffraction limited. He seems to think they might be, but at the same time has provided the information that a lens should have an MTF response of 80% at 40 lp/mm at f8 if it is diffraction limited at that f stop.

(6) On the basis of the information that Bill has provided, and by examining the MTF curves at the Photodo site, I have made my case and proved my point, I believe   
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Ray,

The PhotoDo original MTF charts are not conducive to  determining how the lens performs with respect to the diffraction limit. I made my best attempt previously. I saw a better method of plotting on the [a href=\"http://bobatkins.com/photography/technical/mtf/mtf2.html]Bob Atkins[/url] site. He seems pretty knowledgeable (even though he is somehow associated with Pop Photo). Note the charts from the old German paper.

The disadvantage to your method is, I simply don't have the information regarding angular resolution to work on. Where are the published results for angular resolution of the lens only? There are data at dpreview regarding lines per picture height, but these are lens/sensor combinations.
[a href=\"index.php?act=findpost&pid=114108\"][{POST_SNAPBACK}][/a]

With Imatest one can only determine lens/sensor resolution but here is a test with the EOS 1Ds MII with an 85 mm lens (I don't know which one since I downloaded the test shot from the DPReview web site) with a graphical comparison to Atkins' data for a diffraction limited f/8 lens. The test is without any sharpening.

For real world work with a given camera and lens, one is more interested in determining the optimum aperture for maximum resolution, and one can do this with Imatest. When the image starts to degrade with stopping down, I assume it is due to diffraction.

[attachment=2405:attachment]

Here is the original Imatest plot

[attachment=2374:attachment]

[Ray]

The PhotoDo original MTF charts are not conducive to  determining how the lens performs with respect to the diffraction limit. I made my best attempt previously. I saw a better method of plotting on the Bob Atkins site.

Bill, what part of your explanation do you think I didn't understand?

I well appreciate the fact that those sagital and meridional lines can wander all over the place, but the fact remains, if it is true that a diffraction limited lens at f8 should theoretically have an MTF response of 80% at 40 lp/mm, but the measured MTF response of a particular lens at F8 and 40 lp/mm never reaches beyond say 70% and is well below 70% over most of the image circle, then we can confidently declare that such a lens is not diffraction limited at f8.

Why mince words? Why make things more complicated than they need be? Why introduce other factors such as SQF? You might as well introduce the effects of different sharpening algorithms and the different contrast requirements for big prints and small prints, all of which are other issues.

I note also in the Bob Atkins article you referred to that his definition of Diffraction Limitation seems to coincide with mine. I quote.

Real lenses rarely, if ever, come close to the theoretical maximum MTF at apertures below about f8 as stated above, though a few (expensive) lenses may be an exception to this rule. Performance at the maximum theoretical MTF is called "diffraction limited" performance, since diffraction is the reason why MTF falls with increasing spatial frequency, even for a "perfect" lens - thus diffraction ultimately limits the lens' performance.

I conclude from the above quote that Bob Atkins does not know of any lenses that are diffraction limited at apertures wider than f8, at the same time he allows for the possibility that some may exist.

Bob could have been more helpful if he had mentioned a few lenses that actually are diffraction limited at f8, since his statement appears to imply that such lenses do exist. A perusal of the old Photodo MTF charts will reveal there is at least one lens that reaches 80% MTF at f8 and 40 lp/mm, but only dead in the centre. From there on it's all down hill, so I would agree with BJL here that this does not constitute diffraction limitation.

[BJL]

My understanding is, rightly or wrongly, whilst diffraction may have an effect over a range of f stops, there will likely be one particular f stop at which (and beyond which) the effects of diffraction will limit the possibility of further resolution improvements in the design of the lens in question. At such a point, the lens is said to be diffraction limited.
[a href=\"index.php?act=findpost&pid=114150\"][{POST_SNAPBACK}][/a]

If that is the way that you want to use the words, then essentially you are saying that a lens is diffraction limited when its MTF curves are very close to what you would get from a theoretical calculation based on diffraction effects alone, assuming perfection as far as the "geometrical optics" part of lens performance (no aberrations at all). In that case, none of the MTF curves I have seen fit that, even at f/8 or f/11.

But I repeat my question: if the overall overall resolution keeps rising as one stops downs from f/11 to f/8 to f/5.6 and even to f/4, what is the possible practical significance of whether or not it is truly diffraction limited at f/8, or f/11? The only one I can see is telling me that it is futile to seek resolution improvement at that combination of focal length and aperture by upgrading to a better lens.

What is absolutely does not tell me is that this diffraction limited threshold dictates the maximum possible resolution. To think so would be in the spirit of Mhyrvold's error.

It is a common characteristic of design optimization that the best solution is one in which the several greatest imperfections are roughly in balance (like diffraction and aberration effects roughly equal), so that further reducing one requires increasing the other by a greater amount, making the overall result worse, not better.

It is instead a characteristic of dilettantish technical discussions to insist on an ideal of reducing one particular imperfection like aberrations, shadow noise, or camera weight as much as possible, or to completely insignificant levels, not matter how much other imperfections must be increased in the process.

(Lately, in this misguided over-simplification of seeking a single measure of technical excellence, one debate is whether resolution limits or shadow noise at high ISO is "the" single enemy that should be focussed on exclusively.)

[Ray]

If that is the way that you want to use the words, then essentially you are saying that a lens is diffraction limited when its MTF curves are very close to what you would get from a theoretical calculation based on diffraction effects alone, assuming perfection as far as the "geometrical optics" part of lens performance (no aberrations at all). In that case, none of the MTF curves I have seen fit that, even at f/8 or f/11.

BJL,
What other way is there to use the term, apart from the semantically absurd, "slightly diffraction limited', moderately 'diffraction limited' etc.?

Somewhere on Photodo's site there is (or was) an explanation as to why they did not test lenses at f11. The reason given was, the Photodo team considered all lenses equally bad at f11. Perhaps not to be taken literally, but I think we could interpret that as meaning the differences at f11 amongst all good lenses are so slight that the time, trouble and expense of carrying out MTF tests could not be justified.

My understanding of the term 'diffraction limitation' is not dependent on the condition that the lens should be absolutely free of all other aberrations, but that such aberrations are insignificant compared with the magnitude of the Airy discs.

A good analogy might be 'sensor resolution limitation'. When a sensor's resolution is limited by its pixel density, we do not assume that finer detail does not exist, ie. cannot be transmitted by the lens. We know that detail that is smaller than the pixel simply cannot be recorded by such a sensor. Likewise, aberrations that are smaller than the Airy discs, or that are swamped and effectively completely obscured by the effects of the Airy discs, may still exist, but are not relevant with regard to the recorded image. Those are the conditions for diffraction limitation.

But I repeat my question: if the overall overall resolution keeps rising as one stops downs from f/11 to f/8 to f/5.6 and even to f/4, what is the possible practical significance of whether or not it is truly diffraction limited at f/8, or f/11? The only one I can see is telling me that it is futile to seek resolution improvement at that combination of focal length and aperture by upgrading to a better lens.

It matters in proportion to how closely the resolution at f8 reaches that diffraction limited ideal. I get the impression that the lenses that are closest to being diffraction limited at f8 are the ones that deliver even greater resolution as one stops up to f5.6 and f4, but it's not always the case. You should know better than I do that lenses can be optimised for sharpest results at a particular aperture.

An example would be the Canon 400/2.8 II USM. This lens (or at least the copy that Photodo tested) is sharpest at full aperture of f2.8. Wow! And this is not just sharp in the centre but extends almost to the very edges. The lens has remarkably similar performance at f2.8 to the 50/1.4 at f8.

Unfortunately, this 400/2.8 does not have IS. The IS version does not come near to matching this performance at full aperture, but both lenses are about the same at f8. What does it matter? If you owned both of these lenses would you not experience a degree of indecision   .

Let's suppose the 400/2.8 IS version was actually diffraction limited at f8. It would be noticeably sharper at f8 than the non-IS lens at full aperture. The IS would largely compensate for the slower shutter speed at f8, and if not, an extra stop of ISO would. The images at f8 would be noticeably sharper at the point of focus. The focus point would not be quite as critical because of the greater DoF, yet the DoF would still be fairly shallow if that quality was desired.

What is absolutely does not tell me is that this diffraction limited threshold dictates the maximum possible resolution. To think so would be in the spirit of Mhyrvold's error.

Of course not. Where have I implied that? The diffraction limited threshold dictates the maximum possible resolution at a specified f stop.

It is a common characteristic of design optimization that the best solution is one in which the several greatest imperfections are roughly in balance (like diffraction and aberration effects roughly equal), so that further reducing one requires increasing the other by a greater amount, making the overall result worse, not better.

It is instead a characteristic of dilettantish technical discussions to insist on an ideal of reducing one particular imperfection like aberrations, shadow noise, or camera weight as much as possible, or to completely insignificant levels, not matter how much other imperfections must be increased in the process.

Get off your soap box, BJL   . I merely make the point that the best 35mm lenses cannot quite manage diffraction limitation at f8. Lesser quality 35mm lenses are not even close.

(Lately, in this misguided over-simplification of seeking a single measure of technical excellence, one debate is whether resolution limits or shadow noise at high ISO is "the" single enemy that should be focussed on exclusively.)

Since my views are supported by the hundreds of MTF measurements that are shown on Photodo's MTF charts, I don't see how you can accuse me of seeking a single measure. But the single (weighted) measure can be a useful, quick summary.

The development of high resolution sensors with low shadow noise is definitely the way forward, but lenses have to keep up. Ever since the introduction of the fairly low pixel density 1Ds, photographers have been grumbling about the inadequacy of lenses, so much so that some people seem to have arrived at the erroneous conclusion that further pixel density will serve no purpose.

[bjanes]

Bill, what part of your explanation do you think I didn't understand?
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After a bit of discussion, I think we are pretty much on the same wave length, and I merely thought you might be interested in the information.

Why mince words? Why make things more complicated than they need be? Why introduce other factors such as SQF? You might as well introduce the effects of different sharpening algorithms and the different contrast requirements for big prints and small prints, all of which are other issues.

I note also in the Bob Atkins article you referred to that his definition of Diffraction Limitation seems to coincide with mine. I quote.

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SQF takes human perception into account. The eye is most sensitive to contrast in the frequency range of 3-12 cycles per degree (BJL would be pleased) rather than at its maximum resolution of about 1 minute of arc, and this sweet spot translates to 0.5-2.0 cycles per mm on a print viewed at 34 cm. This correlates to 4-16 cycles/mm on a 35 mm negative or full frame 35mm sensor with an 8x10 inch print (8x magnification). A high MTF in this range is more important than that at 40 cycles/mm. Since you like big prints, the important frequency range for a 16x20 inch print would be 8-32 cycles/mm. SQF is merely the area under the MTF curve between the critical frequencies.

Yes, I think that we are all using Diffraction Limited in the same way.

[BJL]

Ray, there are too many point for me to reply to them all now, so let me be selective. And do not misunderstand; I am happy to work with your definition of diffraction limited.

1. Somewhere on Photodo's site there is (or was) an explanation as to why they did not test lenses at f11. The reason given was, the Photodo team considered all lenses equally bad at f11.

2. It matters in proportion to how closely the resolution at f8 reaches that diffraction limited ideal.

3. Since my views are supported by the hundreds of MTF measurements that are shown on Photodo's MTF charts, I don't see how you can accuse me of seeking a single measure. But the single (weighted) measure can be a useful, quick summary.
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1. That suggest that the (mostly 35mm format) lenses they tested are indeed more or less diffraction limited. The f/11 curve I have seen are for larger format lenses, and definitely showed aberration effects.

2. But what is the practical importance of that? If the goal is to compare to other lenses the MTF curves at various apertures will do the same job more directly. Intermediate questions about being diffraction limited do not seem to add to the final judgement.

3. Are you playing dumb Ray? I said single measure, not single measurement. The "single measure" I refer to is something like overall effect of aberration on resolution, and a one dimensional ideal of "absence of significant aberration so that resolution is detemined mostly by diffraction". Not to any one measurement of MTF.

[Ray]

This correlates to 4-16 cycles/mm on a 35 mm negative or full frame 35mm sensor with an 8x10 inch print (8x magnification). A high MTF in this range is more important than that at 40 cycles/mm. Since you like big prints, the important frequency range for a 16x20 inch print would be 6-24 cycles/mm. SQF is merely the area under the MTF curve between the critical frequencies.

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Bill,
How do we get from 4-16 lp/mm at 8x enlargement, to 6-24 lp/mm at 16x enlargement? Shouldn't that be 8-32 lp/mm for a 16x20 print?

Since I have a 24" wide printer I occasionally make 22x33" prints from a single, uncropped 5D image, in which case the critical resolutions for SQF should be 11-44 lp/mm, resolutions (approx) which the Photodo MTF charts address.

[Ray]

1. That suggest that the (mostly 35mm format) lenses they tested are indeed more or less diffraction limited.

BJL.
I presume you mean more or less diffraction limited at f11. The conclusion I reach is that Photodo does not test lenses at their diffraction limit, but one stop below it so we can see how closely the lenses reach that diffraction limited ideal.

3. Are you playing dumb Ray? I said single measure, not single measurement. The "single measure" I refer to is something like overall effect of aberration on resolution, and a one dimensional ideal of "absence of significant aberration so that resolution is detemined mostly by diffraction". Not to any one measurement of MTF.

You are falling into obscurantism, BJL. The overall effect of aberrations on resolution at any given f stop is the only variable that determines resolution. Diffraction is an invariable property of the aperture chosen. It's in the very fabric of the optics. It is non-negotiable.

The Photodo MTF charts are all about the issue of how successfully such aberrations have been minimised at apertures of f8 and wider. Presumably, if that exceptionally fine Canon 200/1.8 had had a fairly flat MTF response at f8, close to 80% at 40 lp/mm right out to the edges, it would have got a rating of 5.5 out of 5 and Photodo would have had to revise its scales.