Understanding Diffraction

[bjanes]

Michael's post on diffraction with the 180mm f/5.6 Rodenstock APO Sironar HR lens on his p45 back is quite interesting, but he has not really demonstrated that the lens is diffraction limited.

To avoid math and calculations, it is easiest to refer to a table where the needed values are listed, for example:

http://www.clarkvision.com/imagedetail/sca...tml#diffraction

For a f/5.6 lens, we see that the diffraction spot is 6.3 microns, which is a pretty good match for the p45 pixel size of 6.8 microns. Af f/16 the diffraction spot is 18 microns, not a good match for the pixel size.

The Nyquist limit for 6.8 micron pixel spacing is 73 lp/mm. For a diffraction limited f/5.6 lens the resolution at MTF of 80% is 58 lp/mm and the MTF 50%  is 140 lp/mm. The Rayliegh limit is 290 lp/mm. To really make full use of a diffraction limited f/5.6 lens, Michael would need a back with more resolution

[Gary Ferguson]

I don't think the point of the article was to sing the praises of any particular lens, I read it more as as straightforward demonstration of the destructive effects of diffraction on image quality.

The reason it's relevant is that with film we'd arrived, after a hundred years of development and experience, at a fairly useable set of guidelines. We knew that a 35mm could reliably give us high quality 10"x8" prints, that f8 was a pretty good bet, that handholding a lens with a shutter speed slower than the reciprocal of the focal length was asking for trouble, and the engravings on our manual focus lenses gave us at least some insight into depth of field. In other words we weren't just pre-visualising the final image, we were likewise "pre-visualising" the quality we could expect in the finished print.

But digital has changed all the rules, and IMO we're still struggling to get a similarly precise grip on the process. We may well get instant feedback from our LCD screens, but in many ways we're in a complete fog when it comes to predicting the quality we'll get in the final print.

This article gives a clear illustration of one piece in the new digital quality jigsaw. The implication is that managing digital depth of field is problematic. I agree.

Depth of field is intimately tied to enlargement levels, and the fact is that we're enlarging far more with digital than we ever did with film. In the "old" days we all instinctively knew that once we went beyond x7 or x8 enlargements we were skating on thin ice, but today we seem to think that x12 or x15 or even x20 is ours by megapixel right.

It's not. And I think the point of the article is that high quality photography is just as elusive today as it's ever been.

[bjanes]

I don't think the point of the article was to sing the praises of any particular lens, I read it more as as straightforward demonstration of the destructive effects of diffraction on image quality.

But digital has changed all the rules, and IMO we're still struggling to get a similarly precise grip on the process. We may well get instant feedback from our LCD screens, but in many ways we're in a complete fog when it comes to predicting the quality we'll get in the final print.

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The effects of diffraction have been understood for over one hundred years, dating back to the late 19th century and the work of Lord Rayleigh and Sir George Airy, and they apply to digital as well as film and the rules really have not changed. Over the last 100 years, photography has tended toward smaller sensor or film sizes. Due to the greater magnification required by the smaller formats, it is necessary to use a larger aperture to increase resolution in the plane of the image so that the resolution of the magnified image will not suffer. You can't stop down a 35mm film camera to f/45 as with a view camera. Likewise, point and shoot digitals become diffraction limited beyond f/5.6.

We are hardly in a fog--look at the diffraction calculator at the Cambridge in Color web site to which Michael has referred. The calculations are quite precise. My point was that a diffraction limited lens at f/5.6 would outresolve Michael's camera.

[Ray]

Michael's post on diffraction with the 180mm f/5.6 Rodenstock APO Sironar HR lens on his p45 back is quite interesting, but he has not really demonstrated that the lens is diffraction limited.
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I agree. He hasn't. But he has demonstrated that the lens is sharpest at f5.6.

I'm very dubious about claims of diffraction limitation at f5.6 in any lens, even lenses that are used for P&S cameras. The fact is, one simply can't test for diffraction limitation with a digital sensor at f5.6. For all we know, the Rodenstock lens could be close to diffraction limitation, but as you imply, to verify this we would need a sensor with resolution beyond the wavelength of light, which is perhaps impossible.

Whatever the actual resolution of the lens, at a specified MTF response, the 'system' resolution is going to be less.

If you examine Michael's series of test shots, you will see that the f22 shot 'looks' as though it has half the resolution of the f45 shot. Maybe greater than half, but let's call it half.

However, the resolution difference between f22 and f11 is clearly not as great, and the resolution difference between f11 and f5.6 is even less.

There's a process of diminishing returns going on. However, if that Rodenstock lens really is diffraction limited at f5.6 and able to resolve more than Michael's 39MP back is capable of, he should feel pleased because he will not need to replace his lens when he later buys a future 60MP back.  

[bjanes]

I'm very dubious about claims of diffraction limitation at f5.6 in any lens, even lenses that are used for P&S cameras. The fact is, one simply can't test for diffraction limitation with a digital sensor at f5.6. For all we know, the Rodenstock lens could be close to diffraction limitation, but as you imply, to verify this we would need a sensor with resolution beyond the wavelength of light, which is perhaps impossible.

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How so? Look at the diffraction calculator for a compact digital camera with 6 MP and a 1/1.8" sensor using the default (not very stringent) parameters and aperture of f/5.6. The pixel size is 2.6 microns and the Airy disk is 7.5 microns. The system is already diffraction limited. Most of these cameras won't even you set an aperture of much less than 5.6 for this reason. However, due to the small sensor size, the depth of field is good.

[a href=\"http://www.cambridgeincolour.com/tutorials/diffraction-photography.htm]http://www.cambridgeincolour.com/tutorials...photography.htm[/url]

Whatever the actual resolution of the lens, at a specified MTF response, the 'system' resolution is going to be less.

If you examine Michael's series of test shots, you will see that the f22 shot 'looks' as though it has half the resolution of the f45 shot. Maybe greater than half, but let's call it half.

However, the resolution difference between f22 and f11 is clearly not as great, and the resolution difference between f11 and f5.6 is even less.

There's a process of diminishing returns going on. However, if that Rodenstock lens really is diffraction limited at f5.6 and able to resolve more than Michael's 39MP back is capable of, he should feel pleased because he will not need to replace his lens when he later buys a future 60MP back. 
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Quite true. Michael's camera does not have a "sweet spot" like the cameras that most of us use, where one stops down 2 or 3 stops from maximum aperture for better sharpness and depth of field. Of course, he hasn't lost anything but rather has options that the rest of us simply don't have.

[Gary Ferguson]

I agree. He hasn't. But he has demonstrated that the lens is sharpest at f5.6.

That's interesting. But could you explain what the difference is between a lens being sharpest at f5.6, and a lens being diffraction limited from f5.6?

Are there other factors, other than diffraction, operating to reduce the sharpness of the lens as it progresses beyond f5.6?

[32BT]

We are hardly in a fog--look at the diffraction calculator at the Cambridge in Color web site to which Michael has referred. The calculations are quite precise. My point was that a diffraction limited lens at f/5.6 would outresolve Michael's camera.

While the calculations and theory are quite precise, we might still need to gain experience in practical results. For example: we know that a small amount of anti-aliasing results in a better digital image. Overlapping airy discs act as a kind of anti-aliasing filter. How much overlap is optimal? Would there be a theoretical optimum, or is that a matter of taste?

Note for example that the f8 image actually shows more desirable pixels than the f5.6 image. The background on the right seems sharper in the f8 vs the f5.6. Almost as if the focus is slightly off.

In addition, I would like to point out that most lenses wide open don't have the aperture in the light path. It is the lensbarrel or lens entrance that would be causing any effects in those cases.

[Ray]

How so? Look at the diffraction calculator for a compact digital camera with 6 MP and a 1/1.8" sensor using the default (not very stringent) parameters and aperture of f/5.6. The pixel size is 2.6 microns and the Airy disk is 7.5 microns. The system is already diffraction limited. Most of these cameras won't even you set an aperture of much less than 5.6 for this reason. However, due to the small sensor size, the depth of field is good.

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bjanes,
I'm making a distinction between a 'system' that shows the effects of diffraction and a 'lens' that is diffraction limited at a particular f stop. For example, on my 5D I would not expect a shot at f8 to be twice as sharp as the same shot at f16, even assuming I had an expensive 35mm prime that was diffraction limited at f8. Yet, according to Rayleigh's derived formulas the lens, if diffraction limited at f8, should have twice the resulution it has at f16, just as in Michael's example the Rodenstock lens exhibits twice the resolution at f22 as at f45, but not twice the resolution at f5.6 that it has at f11.

Maybe P&S cameras do use lenses that really are diffraction limited at f5.6 and f4 even. Some P&S cameras do stop down as far as f11 (I think), some of the Canon G series perhaps, and if not f11 then certainly f8. If we had the camera we could do a test with line charts. At f4 the camera should capture double the lp/mm count that it captures at f8, shouldn't it?

[bjanes]

bjanes,
I'm making a distinction between a 'system' that shows the effects of diffraction and a 'lens' that is diffraction limited at a particular f stop. For example, on my 5D I would not expect a shot at f8 to be twice as sharp as the same shot at f16, even assuming I had an expensive 35mm prime that was diffraction limited at f8. Yet, according to Rayleigh's derived formulas the lens, if diffraction limited at f8, should have twice the resulution it has at f16, just as in Michael's example the Rodenstock lens exhibits twice the resolution at f22 as at f45, but not twice the resolution at f5.6 that it has at f11.

Maybe P&S cameras do use lenses that really are diffraction limited at f5.6 and f4 even. Some P&S cameras do stop down as far as f11 (I think), some of the Canon G series perhaps, and if not f11 then certainly f8. If we had the camera we could do a test with line charts. At f4 the camera should capture double the lp/mm count that it captures at f8, shouldn't it?
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Of course, all lenses are diffraction limited at all apertures--resolution is limited by diffraction as shown in the table on Clark's website. When we say that a lens is diffraction limited at f/5.6, we mean that aberrations are no longer a factor in degrading image quality at that aperture. Presumably, this lens would be soft at f/2.8, but stopping down to f/5.6 eliminates the aberrations so that resolution at this and smaller apertures is now limited by diffraction and not aberrations. The transition from aberration limited to diffraction limited is not abrupt and we have a "sweet spot", a range of apertures where resolution is good.

With resolution, the figure in lp/mm is not sufficient--one must also specify the contrast. At the  Dawes limit, contrast is zero and resolution is 1/(Fw) in line pairs per mm, where F is the focal ratio and w the wavelength of light. To obtain resolution at the Rayleigh limit (about 9% MTF) we multiply the Dawes resolution by 0.81; the corresponding multipliers for MTF of 80% and 50% are 0.39 and 0.16 respectively. The 50% MTF corresponds best with perceived sharpness.

The resolution scaling at various f/stops are theoretical. Since a real lens does not suddenly go from aberration limited to diffraction limited, the resolution ratios you mention are not seen in practice. Also, elements other than the lens in the imaging chain also affect MTF, and you are correct to separate system resolution from lens resolution. To avoid Fourier transforms, convolution, deconvolution, etc (far beyond my understanding   ), it is a lot easier to measure system MTF with by Imitest or similar programs.

Here is a graphical summary of Imitest results with the D200 and the 50mm f/1.8 Nikkor. Corrected means with standardized sharpening and uncorrected means no sharpening. Optimum performance is at about f/5.6. With larger apertures, aberrations limit MTF, and diffractioin limits performance with smaller apertures.

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[Ray]

The resolution scaling at various f/stops are theoretical. Since a real lens does not suddenly go from aberration limited to diffraction limited, the resolution ratios you mention are not seen in practice.

I agree that theory does not always correspond with practice, but what I'm suggesting is the reason these resolution ratios are not seen in practice is due to the fact that the sensor's (or film's) own limitations always reduce lens resolution to varying degrees, depending on the lens resolution at a particular aperture. It is therefore difficult to tell at what aperture a lens is diffraction limited because we (or general photographers at least) almost always see the results through another limiting prism.

Of course a lens does not suddenly go from being diffraction limited at one aperture to being abberration limited at the next larger aperture. I understand that. But I also think it is misleading to describe a lens as being diffraction limited at say, f5.6 if other aberrations are also visible and identifiable at that f stop. My understanding is, the term 'diffraction limited' means that the effects of diffraction completely obscure, for all practical purposes, other aberrations which might begin to be visible at a larger aperture. In other words, if a lens at a particular aperture consists of 50% Airy disks and 50% of all the other aberrations such as coma, astigmatism, spherical aberration etc which impact upon resolution, then it cannot be said to be diffraction limited at that aperture.

[bjanes]

But I also think it is misleading to describe a lens as being diffraction limited at say, f5.6 if other aberrations are also visible and identifiable at that f stop. My understanding is, the term 'diffraction limited' means that the effects of diffraction completely obscure, for all practical purposes, other aberrations which might begin to be visible at a larger aperture.
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That's not what I understand diffraction limited to mean and apparently Michael does not either:

"Since diffraction cannot be completely eliminated, the finest lens is one that produces an image whose quality is limited only by diffraction. A lens such as this is said to be 'diffraction limited'."

His lens is diffracftion limited at all apertures. No significant aberrations are present. In contrast, a more ordinary lens is diffraction limited only at smaller apertures. At wider apertures, the aberrations prevent the lens from resolving at the diffraction limit.

[BJL]

Firstly, Michael's photographic tests show, better than any theoretical comparison of Airy disc diameters and pixel dimensions, that at apertures of f/11 and smaller, diffraction is reducing the resolution of this combination of lens, sensor and demozaicing algorithms (Bayer interpolation) noticeably below what is possible at f/5.6. Maybe also at f/8, but f/5.6 vs f/8 is a closer call for my eyes.


Secondly, theoretical calculations based on the Nyquist frequency of a given pixel pitch (74lp/mm for the 6.8 micron pitch in this case) ignore the reduction of MTF and resolution caused by anti-aliasing filters and demozaicing algorithms. A rough but pessimistic guideline is three pixel widths per line pair, in stead of the two pixel widths per line pair of the crude Nyquist frequency.

Also, photo-sites are square, not round, so the Nyquist frequency is different for lines at different angles: the standard number only applies to horizontal and vertical lines. I believe that it is lower for any other orientation of the lines: these "6.8 micron" photo-sites are 9.5 microns long on the diagonal.


Thirdly, there is not an abrupt line between "diffraction limited" and "not diffraction limited", just as there is not between "lens out-resolves sensor" and "sensor out-resolves lens". Instead, there is a transition zone where the different factors limiting resolution (sensor, diffraction, geometric aberrations of the lens) have roughly equal MTF at a given spatial frequency, and in this zone, the combined MTF is less than the separate MTF of diffraction alone, or sensor alone, etc.


One thing that Michael's evidence seems to show is that at f/11 and smaller (and maybe at f/8) diffraction is a very visible factor in the overall system resolution, probably the dominant limitation on sharpness, and that for optimum sharpness (ignoring OOF effects) one is better off with larger apertures like f/5.6 and f/8.

[bjanes]

Firstly, Michael's photographic tests show, better than any theoretical comparison of Airy disc diameters and pixel dimensions, that at apertures of f/11 and smaller, diffraction is reducing the resolution of this combination of lens, sensor and demozaicing algorithms (Bayer interpolation) noticeably below what is possible at f/5.6. Maybe also at f/8, but f/5.6 vs f/8 is a closer call for my eyes.
Secondly, theoretical calculations based on the Nyquist frequency of a given pixel pitch (74lp/mm for the 6.8 micron pitch in this case) ignore the reduction of MTF and resolution caused by anti-aliasing filters and demozaicing algorithms. A rough but pessimistic guideline is three pixel widths per line pair, in stead of the two pixel widths per line pair of the crude Nyquist frequency.

Also, photo-sites are square, not round, so the Nyquist frequency is different for lines at different angles: the standard number only applies to horizontal and vertical lines. I believe that it is lower for any other orientation of the lines: these "6.8 micron" photo-sites are 9.5 microns long on the diagonal.
Thirdly, there is not an abrupt line between "diffraction limited" and "not diffraction limited", just as there is not between "lens out-resolves sensor" and "sensor out-resolves lens". Instead, there is a transition zone where the different factors limiting resolution (sensor, diffraction, geometric aberrations of the lens) have roughly equal MTF at a given spatial frequency, and in this zone, the combined MTF is less than the separate MTF of diffraction alone, or sensor alone, etc.
One thing that Michael's evidence seems to show is that at f/11 and smaller (and maybe at f/8) diffraction is a very visible factor in the overall system resolution, probably the dominant limitation on sharpness, and that for optimum sharpness (ignoring OOF effects) one is better off with larger apertures like f/5.6 and f/8.
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I agree that Michael's tests are very informative, but your arguments only bolster my contention that he has not shown that his lens is diffraction limited at f/5.6. To do that, he would have to show an MTF50 of 140 lp/mm, which is pretty hard to do with a sensor having a Nyquist of 73 lp/mm. If you factor in 3 cycles/lp instead of 2, demosaicing, etc, etc, he falls even further short of his assertion.

You may consider the theory boring, but when empirical testing is not sufficient to show what one wishes to demonstrate, then theory fills in the void.

[frdchang]

i was wondering how well does the zeiss 100mm or maybe the 250mm SA for hasselblad resolve relative to these "diffraction limited" lens.  

any opinions? facts?  i just simply assumed them to be the best... and i guess "diffraction limited" as well, but i have no basis for my beliefs... especially since luminouslandscape mentions that the fujiblad glass do not hold up to these digital glass from schneider... if that is the case...then i am figuring that such gems like the 100mm and 250mm SA might not hold up to the digital glass from shcneider as well.

[Ray]

That's not what I understand diffraction limited to mean and apparently Michael does not either:

"Since diffraction cannot be completely eliminated, the finest lens is one that produces an image whose quality is limited only by diffraction. A lens such as this is said to be 'diffraction limited'."

I'm having trouble following your reasoning, bjanes. From the quote above, ...an image whose quality is limited only by diffraction.

By that definition, the aperture at which the effects of diffraction begin to rear their ugly heads would not be the aperture at which the lens could be said to be truly diffraction limited.

I tried doing a Goggle search, typing in 'Definition of Diffraction Limitation in Camera Lenses', and was shocked to find the second entry was a thread on LL started by me, the first one being a link to scholarly articles on the subject which one has to pay for.

After looking at a few other pages replete with complex mathematical equations, I gave up. Who cares! I've got photographs to process and practical things that need attending to.

[ErikKaffehr]

That's easy you can just compare 250mm SA for the Hassy from Hasselblads web-site
http://www.hasselblad.se/Archive/documents...ts/CFE250Sa.pdf
and
http://www.phootos.com/Library/rodenstock_...ses_digital.pdf
Keep in mind that the Rodenstock curves are for 7.5/15/30/60 LP/mm while Hasselblad curves are for 10/20/40 LP/mm.

In my view the Rodenstocks win the MTF-race hands down, and I also think that the Hasselblad H-series 210/4 lens is a little bit better than the SA (from an MTF viewpoint).

Best regards
Erik

i was wondering how well does the zeiss 100mm or maybe the 250mm SA for hasselblad resolve relative to these "diffraction limited" lens. 

any opinions? facts?  i just simply assumed them to be the best... and i guess "diffraction limited" as well, but i have no basis for my beliefs... especially since luminouslandscape mentions that the fujiblad glass do not hold up to these digital glass from schneider... if that is the case...then i am figuring that such gems like the 100mm and 250mm SA might not hold up to the digital glass from shcneider as well.
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