f-stop limits for full sensor resolution

[xtoph]

i figured i might as well supply the quick tests i did to confirm what i know from real-world photographs. here are 4 representative crops (from a longer series, on a tripod), including: full resolution shot at f/8 (f/11 is slightly better, but f/8 is closer to the theoretical limit myhrvold proposes for the 5d, so we will use that as a point of comparison); full res shot at f/22; the same f/22 shot with some sharpening applied; and finally, the f/8 shot resized to 2mp for the full frame (f/8 to give the best-case interpretation to his "2mp" claim).

you can see that at f/22 there is some loss of very fine detail (especially in the tailfeathers) just as we would expect from standard calculations for diffraction limits on film. sharpening helps a lot with much of the detail; since we're looking at 100% crops, we can conclude that sharpening will make up for most softening that you might actually see in a print, even a very, very large print. finally, we can see that myhrvold's claim that f/22 on full digital frame is equivalent to 2mp of resolution is absolutely wrong.

[from myhrvold's article "Now, I don’t think anybody would be very excited about turning their EOS 1Ds Mark II, or Canon 5D or other full frame camera into a 2 megapixel camera. It sounds pretty drastic, but that is exactly what you do when you stop down to f/22 – the diffraction limit imposes this condition. If you shoot with a full frame 24 x 36 sensor at f/22 you are throwing away a lot of resolution. There is no getting around this – it is fundamental in the physics of light."]

there is no getting around this--either the model is wrong (it's not even close), or we have in fact gotten around the "laws" of physics (which, where light is concerned, seem to be rather flexible anyway. which is how we got into this mess in the first place...)

so, conclusion: go ahead and use whatever aperture you need to obtain the depth of field or other results you want. for my 100mm macro, i will use it at f/11 whenever i can get away with it on subjects like insects, since i know that that is the peak of performance for the lens, gives adequate dof, and is occasionally obtainable with the lighting i've got. and lastly, do your own plausibility tests on authoritative info posted on the internet.

[attachment=1633:attachment]
[attachment=1634:attachment]
[attachment=1635:attachment]
[attachment=1636:attachment]

[Herkko]

[from myhrvold's article "Now, I don’t think anybody would be very excited about turning their EOS 1Ds Mark II, or Canon 5D or other full frame camera into a 2 megapixel camera. It sounds pretty drastic, but that is exactly what you do when you stop down to f/22 – the diffraction limit imposes this condition. If you shoot with a full frame 24 x 36 sensor at f/22 you are throwing away a lot of resolution. There is no getting around this – it is fundamental in the physics of light."]

Another quote from Myhrvold's article:
["While Johnson’s treatment works for a fixed size print, the converse is to consider how to get the maximum image quality – i.e. the biggest and best print that you can possibly get. From this standpoint you don’t ask about the final print size, instead you ask what is the best quality that my camera can possibly render."]

Then we should propably define the maximum image quality? For me it's much more depending on chosen aperture for visual impact than optimal resolution on in-focus -area (which can be next to nothing at f8). If I want to deliver a visual message that requires f32, then I either:
- stop down to f32
- where possible use lens movements
- where possible stitch pictures at post processing
.. rather than settle for larger aperture and very different looking picture.

As most of timed photographers already know: the core idea of picture peaks  many times at large or very small apertures. f8 can be excellent choice sometimes, but only sometimes.

If I would be photographing flat test charts as my main hobby, the situation could be different. Resolution: for a low key still life picture with FF and f22 you can spot out dust specks that are hardly visible on bare eye. If someone requires even more resolution and is shy for diffraction, then there are of course digital backs and serious lens movements to be considered in  

[bjanes]

i figured i might as well supply the quick tests i did to confirm what i know from real-world photographs. here are 4 representative crops (from a longer series, on a tripod), including: full resolution shot at f/8 (f/11 is slightly better, but f/8 is closer to the theoretical limit myhrvold proposes for the 5d, so we will use that as a point of comparison); full res shot at f/22; the same f/22 shot with some sharpening applied; and finally, the f/8 shot resized to 2mp for the full frame (f/8 to give the best-case interpretation to his "2mp" claim).

you can see that at f/22 there is some loss of very fine detail (especially in the tailfeathers) just as we would expect from standard calculations for diffraction limits on film. sharpening helps a lot with much of the detail; since we're looking at 100% crops, we can conclude that sharpening will make up for most softening that you might actually see in a print, even a very, very large print. finally, we can see that myhrvold's claim that f/22 on full digital frame is equivalent to 2mp of resolution is absolutely wrong.


[{POST_SNAPBACK}][/a]

There is another way to look at this situation using MTF figures for various apertures as shown in the table on [a href=\"http://www.clarkvision.com/imagedetail/scandetail.html#diffraction]Roger Clark[/url]'s web site. These figures are for green light.

The 5D sensor is 23.9 mm in height and has 2912 pixels in this dimension. The Nyquist frequency is 2912/23.9/2 or 49 lp/mm. A Bayer sensor can resolve to only about 80% of Nyquist, but we will ignore this limitation for now. Frequencies above Nyquist will be removed by the low pass filter and can not be resolved by the digital sensor and result in aliasing, which is why the low pass filter is there. Film has a more gradual roll off and often resolves higher frequencies with low contrast.

When one mentions resolution without further qualification, the specification is incomplete: one must also state the MTF contrast for that resolution. MTF at 50% contrast corresponds well to perceived sharpness. The MTF at Rayleigh is about 9% and one can barely make out the image details at this contrast. If we look at Roger's table (Optical System Resolution Limits) we see that the MTF 50 for f/8 is 97 lp/mm and the MTF 50 resolutions for f/11, f/16, and f/22 are 71, 48, and 35 lp/mm respectively.

By this criterion, f/8 , f/11, and f/16 should give resolution at 50% contrast at or above Nyquist. At f/22 the resolution at 50% contrast is only 35 lp/mm, well below Nyquist. However one can still resolve 75 lp/mm at 9% MTF (Rayleigh) so you may get some detail at low contrast at f/22. At the Dawes limit the MTF is zero and you will have no detail. The Nyquist for the Nikon D200 cropped sensor is 82 lp/mm. The camera should give decent resolution at f/11, but smaller apertures would be suboptimal.

These considerations correlate well with what Ray has observed in the field with his 5D: sharpness is good at f/11 and f/16. The image will suffer at f/22.

Bill

[xtoph]

By this criterion, f/8 , f/11, and f/16 should give resolution at 50% contrast at or above Nyquist. At f/22 the resolution at 50% contrast is only 35 lp/mm, well below Nyquist. However one can still resolve 75 lp/mm at 9% MTF (Rayleigh) so you may get some detail at low contrast at f/22.

These considerations correlate well with what Ray has observed in the field with his 5D: sharpness is good at f/11 and f/16. The image will suffer at f/22.

Bill
[a href=\"index.php?act=findpost&pid=97463\"][{POST_SNAPBACK}][/a]

well, i basically agree with you--and we both agree that the article to which we are replying is dead wrong.

as i stated in my first post, i actually started from what i observe in the field, and just posted the dollar bill tests (green, by the way) to prove the point beyond a shadow of a doubt. frankly i find it worthwhile to just _try_ the things we are talking about. it isn't that i don't think it also worthwhile to understand the physics behind what is happening--that is important. but we are talking about a set of tools--let's try them out. if we accepted what myhrvold wrote, we'd all be worried about turning our 13-17mp sensors into "2mp" sensors. posting articles like his just gives a bad name to those who do try to gain a rigorous understanding of what is happening inside our cameras--because anyone who uses the camera can see he's wrong, and many are prone to conclude that hiphalutin' talk about frequencies and stuff is just so much fertilizer.

[BernardLanguillier]

It is also my feeling that when discussing what realy matters to most photographers - a body AND a lens- f10 is the optimal aperture on a D2x with most lenses.

One aspect that might explain some of the difference between theory and practise  is the presence of an AA filter on the sensors. My uneducated guess is that the presence of an AA filter on the sensor does to some extend contribute to making the effect of diffraction appear later that it would on a perfectly sharp filter, since the image is always blurred to some extend - even at optimal lens/difraction aperture.

sharpening works wonders on this because of the lack of noise of modern sensors at low ISO. It is also my feeling that diffraction is overall easier to correct by sharpening with digital images than with film, which tends to compensate for the smaller size of pixels as well.

Regards,
Bernard

[francois]

...
One aspect that might explain some of the difference between theory and practise  is the presence of an AA filter on the sensors. My uneducated guess is that the presence of an AA filter on the sensor does to some extend contribute to making the effect of diffraction appear later that it would on a perfectly sharp filter, since the image is always blurred to some extend - even at optimal lens/difraction aperture...

Bernard,
Would a Leica M8 (or MF digital backs) be closer to the theory since it has no AA filter?

[bjanes]

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

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

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

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

BJL,

Your synthesis makes sense to me. Drs. Myhrvold and Johnson are both accomplished scientists and I'm not certain that their analyses are necessarily contradictory, but rather they are approaching the problem from different perspectives. Dr Johnson states in response: "I conclude that the Canon 1Ds, Mark II, with a pixel pitch of 7.2 microns, can use all of its resolution to describe an image at f/22, and that at f/2.8 aliasing would be severe without an anti-aliasing filter". This statement appears to be true: the sensor can largely capture the degraded image presented to it at f/22, but it would do better with an image presented at a larger aperture.

Aliasing can be severe when one is taking pictures of fabrics or other subjects with regularly repeating patterns at a certain frequency, but in nature shots these patterns do not frequently occur and the aliasing may not be that apparent. The Leica M8 seems to do well in most circumstances without a low pass filter as did the full frame Kodak sensor that failed largely due to its high noise.

With regard to Bayer color array sensors, there are many complications as you mention and these are analyzed in Dr. Johnson's reference ([a href=\"http://white.stanford.edu/~brian/papers/ise/CMOSRoadmap-2005-SPIE.pdf]Stanford Paper[/url]). The mathematics of point spread functions and convolution kernels are pretty exotic to me and I would expect to most photographers. For the time being, we need some rules of thumb and your synthesis appears reasonable to me.

Bill

[Tim Gray]

A crucial factor when considering resolution as a function of pixel size is the magnification needed to go from sensor to print.  This depends on total sensor size, not pixel size or pixel count.  This is the real reason cameras with small pixels generally have worse "resolution" than cameras with large pixels -- the total sensor size is generally smaller, requiring higher print magnification.
[a href=\"index.php?act=findpost&pid=97197\"][{POST_SNAPBACK}][/a]

wow

Just making sure I understand what you're saying:

The reason a small 10 mpx P&S has lower apparent resolution (same as "less sharp?) than a 5d full frame  is because the sensor in the P&S is so much smaller (about the size of a thumb nail) than the full 35mm in the 5d, and the size and number of pixels doesn't matter?  Did I paraphrase that correctly?

If that's correct it would seem logical to conclude that a 35mm sensor with 4 pixels, would be sharper than the P&S with 10 mpx?  Giving you the benefit of the doubt, you MIGHT be claiming that a 10 mpx P&S isn't as sharp as a 10 mpx full frame because, keeping the pixel count the same, the sensor (hmm - I guess that means the individual pixels since we've kept the count the same) is smaller?

Either way it's 100% wrong.

[bjanes]

wow

Just making sure I understand what you're saying:

The reason a small 10 mpx P&S has lower apparent resolution (same as "less sharp?) than a 5d full frame  is because the sensor in the P&S is so much smaller (about the size of a thumb nail) than the full 35mm in the 5d, and the size and number of pixels doesn't matter?  Did I paraphrase that correctly?

If that's correct it would seem logical to conclude that a 35mm sensor with 4 pixels, would be sharper than the P&S with 10 mpx?  Giving you the benefit of the doubt, you MIGHT be claiming that a 10 mpx P&S isn't as sharp as a 10 mpx full frame because, keeping the pixel count the same, the sensor (hmm - I guess that means the individual pixels since we've kept the count the same) is smaller?

Either way it's 100% wrong.
[{POST_SNAPBACK}][/a]

I have to agree with Tim here. A digital image consists of pixels and really has no physical size in millimeters. If the pixels are of equal quality, it makes no difference whether they were derived from a small or large sensor. However, in the real world, the effects of diffraction and noise often favor large pixels as Michael points out in his essay and as [a href=\"http://www.clarkvision.com/imagedetail//does.pixel.size.matter2/]Roger Clark[/url] demonstrates on his web site.

Bill

[Rob C]

I completely agree with Ray's point on film. All film of a particular type and ASA were cut from huge "master rolls" with no difference of film quality between film formats. I.E. there was always an advantage with larger film formats to make prints of a given size. With digital it is important to compare apples with apples as with film.
[a href=\"index.php?act=findpost&pid=97388\"][{POST_SNAPBACK}][/a]

Ray, Kirk

I'm a little unhappy with your statement/belief that films of the same name, in different formats, are the same thing.

It's been been my experience that this is simply not the case: sometimes the film is on a thicker base, other times the results look quite different. For example, in b/w I would use TXP 120 and get great results (Hass/Zeiss) whilst on 35mm it was far too contrasty for my purposes; Ilford's FP3/4 were excellent on 35mm (Nikon/Nikkors) but did not work nicely for me on 120. Both were processed by me in D76 1+1. In colour transparency material I found 35mm Velvia 50 (Nikon/Nikkors) to be very attractive but not so in 120 (Pentax/Pentax) 6x7. I do not believe this to be anything significantly to do with the lenses, more a function of the films bearing a common name but not common properties. As far as the b/w examples go, even the ASA ratings didn't pan out the same for films of the same name - the 120 seemed to need more exposure/lower ASA rating than the similarly named 35mm.

Ciao - Rob C

[EricV]

A digital image consists of pixels and really has no physical size in millimeters. If the pixels are of equal quality, it makes no difference whether they were derived from a small or large sensor. However, in the real world, the effects of diffraction and noise often favor large pixels ....
Bill
[a href=\"index.php?act=findpost&pid=97652\"][{POST_SNAPBACK}][/a]

A digital image is a record of an optical image, which most certainly does have physical size, and the optical image has characteristics like diffraction blur which do have physical size.  When this information is tranferred into pixels, it is not lost.  I guess you can forget about the physical size of the pixels and the sensor, provided you keep track of something equivalent, like the size of the diffraction blur measured in pixels.  With this understanding, we proabably have no real disagreement.

(I still maintain though that there is no fundamental difference between recording an image on digital pixels or analog film, at least in the limit where the recording medium has finer resolution than the optical image.  So why maintain that film size is significant, but digital sensor size is not?  Is it just because film physically reminds you how large it is, but a digital file makes it easy to forget?)

Let me give a simple example where I would claim sensor size matters and I imagine you would claim it does not.  I think we will agree on the final conclusions, if not on the semantics :)  

A) 50mm lens at f/11 on 1/2" sensor with 4um pixels
B) 50mm lens at f/22 on 1/2" sensor with 4um pixels
C) 100mm lens at f/22 on 1" sensor with 8um pixels

All three images have the same field of view and perspective.  All three images have the same pixel count.  However, the digital images are not equivalent.  

Image A will produce a sharper print than image B (but with less depth of focus), because the optical resolution is higher (less diffraction).

Image C will also produce a sharper print than image B, even though the optical resolution is the same.  From my viewpoint, this is because less magnification is required to make the final print.  In your view, I suppose it is because the diffraction blur spreads across fewer pixels.

Images A and C will produce similar prints, with comparable sharpness and depth of focus.  I concede that in this comparison sensor size does not matter, because optical resolution was scaled to match the sensor size.

[Tim Gray]

So you're suggesting a 5" (diagonal) print from the 1/2" sensor @ f22 would have the same apparent sharpness as a 10" print from the 1" @ f22 sensor?

What would happen at the wider end, where diffraction isn't an issue - eg: f2.8 rather than F22 (obviously ignoring abberation)?  Given the same size prints, the 1" should produce sharper results than the 1/2"?  I don't think so.

[Kirk Gittings]

Rob C, That is how film is manufactured. Now, if one is on a different base (thicker say) that of course is from a different roll but may be coated with the same emulsion or perhaps not. In order to make the multi format cross referenced comparisons that you are stating, all your shutters and meters would have to be calibrated to an exact standard, and the differences of all lens coatings and film processing differences factored in. For one example Schneider lenses from the 70"s to now are a whole paper grade more contrasty and significantly more neutral in color. Plus between lens systems over time color varies significantly in addition to contrast as multicoatings advanced. I own a dozen modern view camera lenses about half and half Schneiders and Nikons. If I shoot a building in 4x5 (I am an architectural photographer by trade) mixing those lens brands, I get widely varying color which is disturbing in a magazine layout (by my standards). The Nikons are warmer and less contarsty than the Schneiders. On the same shoot I may also shoot some 35mm and 120 details. Those will have a different look, but it is the because of the variation in lenses and shutters.

I routinely shoot both 4x5 and 120 (switching backs) with the same lens, in the same camera, at the same time, with the same scene. If the film is the same ( I primarliy use Fuji Provira) the results are identical.

[Rob C]

Kirk

Thanks for your reply - your example of using the same name of film in two formats on the same lens/camera combo seems to make good sense as a definitive test, at least of the film you quote. That was something I couldn't do with my own equipment so your experience there certainly sounds convincing.

Come to think of it, it might be part of the same argument that led to Nikon cameras and lenses replacing the Leicas of war photographers lo those many years ago: more bite, more contrast for printing in LIFE!

Yet there we go again: I mention Leica being replaced by Nikon but Leica glass still seems to be considered as producing a more MF kind of look than do other makes of optics for 35mm, at least on colour transparency.

Funny old world.

Ciao - Rob C

[EricV]

So you're suggesting a 5" (diagonal) print from the 1/2" sensor @ f22 would have the same apparent sharpness as a 10" print from the 1" @ f22 sensor?

What would happen at the wider end, where diffraction isn't an issue - eg: f2.8 rather than F22 (obviously ignoring abberation)?  Given the same size prints, the 1" should produce sharper results than the 1/2"?  I don't think so.
[a href=\"index.php?act=findpost&pid=97675\"][{POST_SNAPBACK}][/a]

Comparisons should always be done for the same print size, otherwise too many other factors like viewing distance must be considered.  I am claiming that a 10" print from a 1"sensor will be sharper than a 10" print from a 1/2" sensor, provided the lens focal length is adjusted to cover the full sensor with the same field of view in both cases, provided the optical resolution is the same in both cases (which is the case if both lenses are stopped down to f/22), and provided the pixel size is much smaller than the optical resolution in both cases.  I think everyone on this forum will agree with this claim.  If you change some of these assumptions (like making the pixel size ridiculously large), then the conclusion will change.

What will happen if diffraction is not an issue?  In the extreme limit where optical resolution is much smaller than pixel size, the advantage goes to whichever camera has more pixels, independent of sensor size.  This is a pretty extreme case.  A diffraction limited lens at f/2.8 still has a resolution of 4um, which is not negligible compared to pixels on most sensors.  

In your example, do both cameras get to use diffraction limited f/2.8 lenses?  Does the larger sensor still get to use a longer focal length lens, to provide the same field of view, and does its sensor still have the same pixel count?  Then the larger sensor will still produce a sharper print, because the optical blur is not negligible and it is magnified less.

If you want to create a situation where the large sensor has no advantage over the small sensor, simply pick a wider lens aperture (better optical resolution) for the small sensor (as I noted in my previous post).

[bjanes]

A digital image is a record of an optical image, which most certainly does have physical size, and the optical image has characteristics like diffraction blur which do have physical size.  When this information is tranferred into pixels, it is not lost.  I guess you can forget about the physical size of the pixels and the sensor, provided you keep track of something equivalent, like the size of the diffraction blur measured in pixels.  With this understanding, we proabably have no real disagreement.

(I still maintain though that there is no fundamental difference between recording an image on digital pixels or analog film, at least in the limit where the recording medium has finer resolution than the optical image.  So why maintain that film size is significant, but digital sensor size is not?  Is it just because film physically reminds you how large it is, but a digital file makes it easy to forget?)

[a href=\"index.php?act=findpost&pid=97667\"][{POST_SNAPBACK}][/a]

I never said that sensor size was more important with film than with digital. However, 35 mm film is the limitation for a 35 mm film camera. If we had better film and diffraction limited lenses, 35mm at f/11 would be about equal to f/45 for a 4x5 camera with current film. To keep the diffraction blur the same with respect to pixel size, you do have to use larger apertures with small pixels and you reach a limit as you approach f/1.0.

Bill

[xtoph]

wow. this myhrvold guy just isn't listening. or looking. bad enough to post one article proposing a flawed model, but then we all make mistakes. to post yet again, and with such a condescending tone, insisting that your original mistake was right all along... well, that's really unfortunate. and reichmann isn't helping by 'sticking to the sidelines'--neutrality is fine in matters of opinion or indeterminacy, but this is a case of settled fact. the cropped images i posted above prove conclusively what most of us already knew from experience--that myhrvold's predictions were incorrect; a 5d at f/22 is not equivalent to a 2mp sensor. now myhrvold claims that at f/22 the image is equivalent to f/8 with a gaussian blur of 1.5 applied. well, here is the same crop from above at f/8, with gaussian blur. you can plainly see that it has lost the ability to distinguish fine detail, and usm will not bring it back. myhrvold is consistent at least--this image is almost indistinguishable from the one based on his original claim of 2mp.

the problem is, it bears no resemblance to the actual image you get from the 5d at f/22 (see above post). in fact, on the 'cambridge in color' website myhrvold links in his latest post to support his claim that at f/22 we will lose massive amounts of detail, we can read the following statement clearly disagreeing:
"Recall that a digital sensor utilizing a bayer array only captures one primary color at each pixel location, and then interpolates these colors to produce the final full color image.  As a result of the sensor's anti-aliasing filter (and the Rayleigh criterion above), the airy disk can have a diameter approaching about 2 pixels before diffraction begins to have a visual impact (assuming an otherwise perfect lens, when viewed at 100% onscreen)."

this author actually agrees with johnson and about the source of myhrvold's misunderstanding of the situation. their explanation sounds plausible to me. but more to the point, the empirical tests prove that myrhvold is wrong.

really, he ought to retract his posts and issue an apology at this point.
[attachment=1677:attachment]

[Tim Gray]

I wonder if Michael has his contributors sign a waiver acknowledging the slings and arrows they are liable to be subjected to    I remember a tutorial by Mitch? on, I think, selective desaturation - or something like that.  Never heard from again...

Having said that, if you set yourself up as an authority, then you're inviting this kind of controversy.   I guess it's a little bit like academic peer review, with the gloves off.  The  advantage of the "traditional model" is that review happens before publication - in today's internet world publication and review happen simulaneously - which means the review process can be a bit spirited.  

I do think, in the end, that our overall understanding and appreciation for what's really going on does increase - but we have to be a lot more diligent in exercising our own critical analysis.   What we read here isn't from Nature Journal.

[bjanes]

wow. this myhrvold guy just isn't listening. or looking. bad enough to post one article proposing a flawed model, but then we all make mistakes. to post yet again, and with such a condescending tone, insisting that your original mistake was right all along... well, that's really unfortunate. and reichmann isn't helping by 'sticking to the sidelines'--neutrality is fine in matters of opinion or indeterminacy, but this is a case of settled fact.

this author actually agrees with johnson and about the source of myhrvold's misunderstanding of the situation. their explanation sounds plausible to me. but more to the point, the empirical tests prove that myrhvold is wrong.

really, he ought to retract his posts and issue an apology at this point.
[attachment=1677:attachment]
[a href=\"index.php?act=findpost&pid=97893\"][{POST_SNAPBACK}][/a]

This myhrvold guy is not your typical crackpot who posts ill conceived messages. If you look at his bio on Wikipedia: "studied physics at Princeton (PhD) and held a postdoctoral fellowship at Cambridge working under Stephen Hawking for one year, but left to join a computer startup in Oakland, California. The company, Dynamical Systems Inc., sought to produce a clone of IBM's TopView graphical user interface. Microsoft purchased Dynamical Systems in 1986 and Myhrvold worked there for 13 years" and held the position of chief technology officer.

Johnson also holds a PhD in chemistry and has authored 150 scientific papers. One could say these men may not be expert in optics and digital imaging, but they do understand the scientific method and rigorous analysis and are without doubt highly intelligent.

Now, I am puzzled by Dr. Johnson's statement that the EOS 1D M2 can use all of its resolution to resolve an Airy disc at f/22. I'm sure the Airy disc would be resolved in exquisite detail, but overall image resolution would suffer IMHO. Myhrvold's analysis of resolution at f/22 makes more sense to me, but I do not understand the complex mathematics discussed in the Stanford reference they quote. I think Michael is wise to keep out of this "argument" and I am not qualified to mediate either, and I suspect that very few forum members so qualified. I hope we can learn from a few more exchanges by these two experts. However, when a complicated scientific argument contradicts common experience, we can and should make comments.

Bill

[Ray]

However, when a complicated scientific argument contradicts common experience, we can and should make comments.

Bill
[{POST_SNAPBACK}][/a]

That's a very reasonable argument to make, Bill. Science is based upon empirical evidence. No matter how 'impressive' and 'high faluting' the the theory appears to be, if it doesn't accord with real world conditions, or practice, then it has to be junked.

The fact that someone who has 6 PhDs (or whatever) can be simply wrong, is a difficult accusation to make. However, if the theory does not agree with the empirical evidence, then we have a problem.

In the Middle Ages in England, and later, when someone disagreed with the official (PhD sanctioned) position, they were often tortured, mutilated and burned.

I'm glad we have progressed from that situation   .

In general, I see a lack of empirical evidence in these discussions. Okay! Maybe I and one or two others post a few images, but the discussions are mostly hot air rhetoric.

Maybe I posted the following images in the wrong thread.

[a href=\"http://luminous-landscape.com/forum/index.php?act=ST&f=3&t=14317&st=0]http://luminous-landscape.com/forum/index....=3&t=14317&st=0[/url]