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### AuthorTopic: f-stop limits for full sensor resolution  (Read 79773 times)

#### 01af

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##### f-stop limits for full sensor resolution
« Reply #80 on: February 19, 2007, 11:44:19 am »

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Your formula applies only for MTF around the Rayleigh resolution criterion for contrast of 9 %. For a more realistic MTF of 50 % one must convert [blah blah]. This is explained by Norman Koren on his web site.
You're right. But exactly that is also where Norman explains my formula is a good first-order approximation. And that's all we need here in our context.

The point is: Of course does pixel count have an effect on absolute resolution (as I said). But it does NOT have an effect as to where the limiting f-stop for a given lens is. The lens has an optimal f-stop where it has the highest resolution. And this resolution peak will "show through" the sensor, no matter what its own resolution is. If the sensor's resolution is high enough to make the difference between the optimal f-stop and one f-stop away from the optimum visible, then all higher-resolving sensors will show the optimum at the very same f-stop.

The only possible difference between two sensors might be the accuracy they nail down the lens' optimum. With a lower-resolving sensor we might be able to find the lens' optimum somewhere between, say, f/8 and f/11. With a higher-resolving sensor we might be able to find it between f/9 and f/10. That's all. If you're willing to call the difference between f/11 and f/10 the advantage of the higher-resolution sensor ... fine. But still the f-stop limit definitely is by far not linear to the pixel pitch, as Myhrvold has suggested.

-- Olaf
« Last Edit: February 19, 2007, 12:29:02 pm by 01af »
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#### bjanes

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« Reply #81 on: February 19, 2007, 11:44:40 am »

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Your MTF 50 figures are what is preposterous;

I don't know exactly what the error is, or where it is, but there certainly is an error somewhere.
[{POST_SNAPBACK}][/a]

Hardly preposterious, why don't you look at these references?

[a href=\"http://www.clarkvision.com/imagedetail/scandetail.html#diffraction]Roger Clark[/url]

Norman Koren

Furthermore, these MTF calculations agree with what is observed in actual testing. For example, the above referenced test of the Canon D350, as summarized in the following table:

[attachment=1884:attachment]

The Nyquist frequency of this sensor is 78 lp/mm and at f/4.0 the system resolves at 91.5% of Nyquist with a contrast of 50%. As one stops down, the resolution of the system becomes diffraction limited and the system MTF50 tracks the theoretical MTF50 of the lens within reasonable limits. At f/32, the observed system resolution is 32 lp/mm at 50%, whereas the MTF 50 of the lens is 24 lp/mm. Resolution beyond the theoretical limit of the lens is due to sharpening artifact and limitations of the slanted edge method used by Imatest, as Norman Koren explains. The MTF 50 best correlates with perceived image sharpness, but  if you want to use MTF 0 at the Dawes limit, that is OK with me.

It is very difficult to debate with a person who ignores established facts and does not follow a scientific approach, instead injecting subjective philosophical arguments into the discussion. Unless you come to your senses, I see no point in further discussion. It reminds me of the ancient Greek philosophers trying determine the number of teeth in a horse's mouth by deduction rather than actually looking into the animal's mouth.

Bill
« Last Edit: February 19, 2007, 11:57:12 am by bjanes »
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#### bjanes

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« Reply #82 on: February 19, 2007, 11:49:26 am »

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You're right. But exactly that is also where Norman explains my formula is a good first-order approximation. And that's all we need here in our context.

-- Olaf
[a href=\"index.php?act=findpost&pid=101669\"][{POST_SNAPBACK}][/a]

Your formula is a good first order approximation for MTF of 9% as with resolution tests with the USAF target, but it fails for MTF 50, where the Fourier transform and multiplication is necessary.

Really, I do not see why all this argument is necessary. All you have to do is look at the measured MTF 50 responses for various f/stops as shown in tests.

Bill
« Last Edit: February 19, 2007, 11:58:30 am by bjanes »
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#### 01af

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« Reply #83 on: February 19, 2007, 12:09:01 pm »

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Your formula is a good [...], but it fails for MTF 50, where the Fourier transform and multiplication is necessary.
It doesn't fail; it just becomes less accurate ... but still a good-enough approximation.

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Really, I do not see why all this argument is necessary. All you have to do is look at the measured MTF 50 responses for various f-stops as shown in tests.
Now this is really funny! Why don't you take a look at real images made through real lenses on real sensors? You remind me of the ancient Greek philosophers trying determine the number of teeth in a horse's mouth by deduction rather than actually looking into the animal's mouth.

-- Olaf
« Last Edit: February 19, 2007, 12:16:51 pm by 01af »
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#### Jonathan Wienke

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« Reply #84 on: February 19, 2007, 12:22:47 pm »

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It reminds me of the ancient Greek philosophers trying determine the number of teeth in a horse's mouth by deduction rather than actually looking into the animal's mouth.

And that's exactly what you are doing; citing the same formulas as the individual that sparked this thread, while ignoring a real-world example that clearly shows somebody is miscounting the horse's teeth. The hair detail in the spider shots I posted clearly show that 1-pixel-wide image features can be successfully resolved with a 1Ds at f/32. Those hairs are NOT aliasing artifacts. I've gone to the horse's mouth and actually counted the teeth. You're the one citing formulae without evaluating whether those formulae accurately predict or reflect real-world results.

What is your explanation for the results I show? You haven't even attempted to explain them, other than a quasi-ad hominem attack. If you are right, there shouldn't be any significant difference between the before and after crops, other than the sizing artifacts. The "before" shot clearly shows more detail than the one reduced to 2MP and back. If you want to criticize my conclusions, at least have the decency to point out the flaws in my methodology and explain why my examples (and the conclusions I draw from them) aren't meaningful or valid.
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#### 01af

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« Reply #85 on: February 19, 2007, 01:05:28 pm »

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If you want to criticize my conclusions, at least have the decency to point out the flaws in my methodology and explain why my examples (and the conclusions I draw from them) aren't meaningful or valid.
Jonathan, don't hold your breath! He'll never do that. Because he can't. Because your example and your conclusions are perfectly valid (albeit your methodology---down- and upsizing to mimic a 2-MP shot---is not).

The resolution you got from the lens stopped down to f/32 sure is a bit lower than what you'd gotten from the same lens at f/11 or f/16. But it's by far not as low as a 2 MP image would be. Myhrvold's statement simply was an exaggeration.

Assuming an APS-C-sized 8 MP sensor and a lens that has its optimum aperture at f/16 (super-zoom lens at very close distance). Then stopping down beyond the optimum to f/32 will yield a resolution that comes close to a 4 MP sensor's, not a 2 MP one. You'll get the 2 MP figure when applying the "weakest-link theory" ... which however is wrong, as I explained in my first post.

And all this does not mean your photograph of the spider (Black Widow?) would have come out better at f/11 or f/16. Maximum sharpness would have been slightly better but depth-of-field not---and that would have a detrimental effect on that macro shot.

-- Olaf
« Last Edit: February 19, 2007, 01:13:34 pm by 01af »
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#### Paul Kay

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##### f-stop limits for full sensor resolution
« Reply #86 on: February 19, 2007, 01:11:55 pm »

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Now this is really funny! Why don't you take a look at real images made through real lenses on real sensors?
[a href=\"index.php?act=findpost&pid=101676\"][{POST_SNAPBACK}][/a]

Forgive me for saying so, but generally this is what we did in those olden days of film, and it seemed to work ok! Unless there is an exceedingly good reason for mathematical analysis of resolution (ie for purely scientific or technical results which require this precise data) then I'm not sure what all the fuss is about. Although I trained as a scientific photographer/Photoscientist (many years ago I should add) I now use my own eyes and experience to determine whether the results that a particular lens/camera system produce are acceptable to me for my applications.
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#### Jonathan Wienke

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##### f-stop limits for full sensor resolution
« Reply #87 on: February 19, 2007, 02:22:49 pm »

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The resolution you got from the lens stopped down to f/32 sure is a bit lower than what you'd gotten from the same lens at f/11 or f/16. But it's by far not as low as a 2 MP image would be. Myhrvold's statement simply was an exaggeration.

I've never claimed otherwise, and previously noted that I had to boost contrast and sharpen more agressively with this image than what is typical for an image shot at f/8 or so. It's the magnitude of the effect that I'm disputing, not the existence of the effect. We're in agreement here.

And yes, it is a black widow spider. There was a bumper crop of them one year where I lived, so I took advantage of the opportunity.
« Last Edit: February 19, 2007, 02:25:10 pm by Jonathan Wienke »
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#### jani

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##### f-stop limits for full sensor resolution
« Reply #88 on: February 19, 2007, 03:10:34 pm »

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I've never claimed otherwise, and previously noted that I had to boost contrast and sharpen more agressively with this image than what is typical for an image shot at f/8 or so. It's the magnitude of the effect that I'm disputing, not the existence of the effect. We're in agreement here.
It seems that there still is a misunderstanding regarding the use of MTF, though.

It also seems to me that you're confusing two different cameras; you're talking about a 1Ds (pixel pitch 8.8 microns), bjanes about the 1Ds MkII (pixel pitch 7.2 microns, different AA filter, too).

If you don't boost contrast and sharpen before you do the crop and resize, and if you do so according to the theoretical background that bjanes has put forward, what are your results then?

I'd also appreciate it if you would test with images with different contrasts, not just high-contrast ones. Then you can claim to be looking in the horse's mouth and not just theoretizing about what a horse's mouth looks like, from looking at a frog.
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Jan

#### bjanes

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« Reply #89 on: February 19, 2007, 03:30:34 pm »

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And that's exactly what you are doing; citing the same formulas as the individual that sparked this thread, while ignoring a real-world example that clearly shows somebody is miscounting the horse's teeth. The hair detail in the spider shots I posted clearly show that 1-pixel-wide image features can be successfully resolved with a 1Ds at f/32. Those hairs are NOT aliasing artifacts. I've gone to the horse's mouth and actually counted the teeth. You're the one citing formulae without evaluating whether those formulae accurately predict or reflect real-world results.

What is your explanation for the results I show? You haven't even attempted to explain them, other than a quasi-ad hominem attack. If you are right, there shouldn't be any significant difference between the before and after crops, other than the sizing artifacts. The "before" shot clearly shows more detail than the one reduced to 2MP and back. If you want to criticize my conclusions, at least have the decency to point out the flaws in my methodology and explain why my examples (and the conclusions I draw from them) aren't meaningful or valid.
[{POST_SNAPBACK}][/a]

I note that you have responded selectively, and omit anything about my MTF 50 figures being way off and affecting my analysis. What was your point?

The hairs on the spider's back can be seen in the image even though they are beyond the resolving power of the camera, just as a distant star (essentially a point source) can appear in the image. However, if two hairs on the spider's back were placed more closely than the camera could resolve, they would not be distinguishable in the image, just as a binary star beyond the resolving power of a telescope would not be resolved.

I have already agreed that the first of your images shows more detail than the second and that the 2 MP figure is wrong. My own calculations based on my MTF 50 calculations would be closer to 5.6 MP for your 16 MP camera at f/22 and 2.7 MP at f/32 (36% and 17% of base resolution respectively). Your statement that a decent lens at f/32 can still capture 11MP of image data with an MTF somewhere on the sunny side of 50% is completely without basis, and you are counting teeth by deduction rather than observation.

Furthermore, you may have seen the tests reported on by [a href=\"http://query.nytimes.com/gst/fullpage.html?res=9507E1DD113FF93BA35751C0A9619C8B63]David Pogue[/url] in the NY Times. He used downsampling from 13 MP to 8 and 5 MP followed by printing with a Durst Lambda, which up-reses the image to 400 ppi for printing. Observers could see no differences in the print and he concluded that MP counts do not correlate well with perceived image quality. A pro photographer repeated his test with a 16.7-megapixel Canon EOS-1Ds Mark II and got the same results.

How can this be? The answer is that MTF at relatively low resolution determines the perceived sharpness of prints.

Bill
« Last Edit: February 19, 2007, 03:48:16 pm by bjanes »
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#### BJL

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« Reply #90 on: February 19, 2007, 03:30:45 pm »

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Generally, the optimal f-stop roughly correlates to image size (among other things, the most important being lens quality) ... but not to pixel count or pixel pitch.
[a href=\"index.php?act=findpost&pid=101659\"][{POST_SNAPBACK}][/a]

I think you are right that the resolution of the sensor (including film as a type of sensor) does not affect the f-stop at which resolution is optimal. That still leaves the question of how much resolution one gets at that optimal f-stop, or at any specified f-stop, where we agree that sensor resolution is relevant.

When DOF needs come into play, the optimal choice of f-stop can be considerably smaller than the values you talk about, which are based on optimizing the sharpness of images of subjects lying at the focal distance, ignoring OOF effects for subjects at other distances.

However, when one stops down for greater DOF, sensor resolution becomes even less significant in overall resolution, with diffraction and OOF effects becoming the main considerations at small enough apertures.

The main connection to sensor resolution is that, if a given aperture is chosen on the basis of best handling aberrations, diffraction and OOF effects, there is a resolution limit, no better than that due to diffraction alone, which means that increasing sensor resolution too much beyond diffraction based resolution has little benefit for overall resolution. My 1.4*N to 2*N estimate is thus mostly a guideline for that "maximum useful sensor resolution at a given aperture ratio."

For example, landscapes are one of the dominant examples of the most extreme resolution needs, and typically have DOF needs leading to use of apertures f/8, f/11 or smaller with 35mm. At such apertures, there is little benefit to reducing photo-site size much below about  4 to 5.6 microns, or about 27 to 54MP.

But it gets worse: when one wants to make use of new higher resolution of sensors 16MP and up, seeing that resolution requires a combination of larger prints and closer viewing than with lower resolution images, which makes OOF effects more noticeable, so that adequate sharpness across the desired DOF will tend to push the needed f-stop higher. Once one needs about f/14 or higher, for adequate DOF in the desired "big, closely viewed prints", diffraction and other effects limit useful pixel counts to about that 16MP.

Since landscapes are almost the dominant example of photography that can benefit from high pixel counts, this makes me wonder how much use there will be for pixel counts significantly higher that 16MP. (Larger sensors do not change these DOF/diffraction based limits on useful pixel counts at all, since higher f-stops are needed for equal DOF with the larger focal lengths of a larger format increasing the diffraction spot size in proportion to focal length).

I wonder how the artistic effect of landscapes and such is changed by the step from 16 or 22 up to 31 or 39 MP. I do not mean "print peeping" comparisons showing greater sharpness at the focal plane when using the same aperture with a higher pixel count, but the overall artistic impression, including more noticeable OOF effects when one looks closely enough to see that extra sharpness. Maybe it still works because
1. "Overall viewing", from far enough away to see the whole image, looks at least as sharp with fewer pixels, and probably with as much DOF.
2. Closer scrutiny shows some parts of the scene at least with more sharpness and detail, even though this benefit is limited to subjects only within a part of the "overall in-focus range".

And I suppose that other specialties like architectural images often benefit from high resolution without very much DOF.
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#### bjanes

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« Reply #91 on: February 19, 2007, 03:42:07 pm »

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Jonathan, don't hold your breath! He'll never do that. Because he can't. Because your example and your conclusions are perfectly valid (albeit your methodology---down- and upsizing to mimic a 2-MP shot---is not).

The resolution you got from the lens stopped down to f/32 sure is a bit lower than what you'd gotten from the same lens at f/11 or f/16. But it's by far not as low as a 2 MP image would be. Myhrvold's statement simply was an exaggeration.

Assuming an APS-C-sized 8 MP sensor and a lens that has its optimum aperture at f/16 (super-zoom lens at very close distance). Then stopping down beyond the optimum to f/32 will yield a resolution that comes close to a 4 MP sensor's, not a 2 MP one. You'll get the 2 MP figure when applying the "weakest-link theory" ... which however is wrong, as I explained in my first post.

-- Olaf
[a href=\"index.php?act=findpost&pid=101684\"][{POST_SNAPBACK}][/a]

I have already posted my own photographic resolution tests with a Nikon D200 and the 50 mm f/1.8 lens (post #9 in this thread). The optimum system resolution (MTF 50) peaks at f/5.6 to f/8 and falls off appreciably at f/22. The lens does not go to f/32, but Photozone has published similar results for an APS sized Canon with a high grade macro lens.

No one is applying the "weakest link" theory here. You multiply MTFs and system resolution can and does exceed the weakest link. According to Norman Koren, your reciprocal method is not adequate for MTFs in the range of 50% and you have presented no evidence to the contrary, rather than stating that the approximation is "good enough". What a joke.

Bill
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#### 01af

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« Reply #92 on: February 20, 2007, 01:48:25 pm »

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I have already posted my own photographic resolution tests with a Nikon D200 and the 50 mm f/1.8 lens (post #9 in this thread). The optimum system resolution (MTF 50) peaks at f/5.6 to f/8 and falls off appreciably at f/22.
So we can now rest reassured that your 50 mm standard lens basically behaves just like any other 50 mm standard lens.

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No one is applying the "weakest link" theory here.
Myhrvold did.

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... and system resolution can and does exceed the weakest link.
That's what I am saying.

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According to Norman Koren, your reciprocal method is not adequate for MTFs in the range of 50 % and you have presented no evidence to the contrary ...
I am under the impression that you are trying to make a point which is not the point of this thread, is it?

Myhrvold stated that in order to fully exploit a sensor's resolving power, you must not stop down beyond the pixel pitch's diffraction limit. At larger apertures, you'll get the full resolution. At smaller apertures, you'll get a limited resolution that is not up to the pixel count's potential.

And I say he's wrong.

Assume a pixel size that, after Myhrvold, implies a diffraction limit at f/11. Also assume a fine lens that is diffraction-limited at f/5.6. According to Myhrvold, you can stop down to f/11 without losing image quality. But in fact the lens-sensor system will yield best performance at f/5.6 (the lens' limit); at f/8 you'll notice a slightly degraded image quality, and at f/11 degraded even more. The decreasing lens performance will show, even though the sensor has not yet reached his own "Myhrvold limit."

So Myhrvold's formula does not help to get the best-possible image quality out of a given camera. My advice is: Stop down no further than to the lens' diffraction limit, period ... no matter what the pixel size is.

-- Olaf
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#### Ray

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« Reply #93 on: February 20, 2007, 06:54:49 pm »

I'm surprised that I'm the only one who sees the complete irrelevance to Myhrvold's article of Jonathan's Black Widow spider experiment. Jonathan has clearly misunderstood the point Myhrvold is making with his '2 megapixel camera' analogy.

I agree that Myhrvold is not as clear as one would like and the fact that Jonathan has misunderstood Myhrvold's point is not entirely Jonathan's fault.

However, if you read the whole article it should be clear that Myhrvold precedes his '2 megapixel camera' analogy with statements to the effect that f8 to f9 gets you the sharpest results with cameras such as the 1ds2 and 5D and that as you stop down you are effectively throwing away resolution to the point where at f22 you could have got the same result with a 2 megapixel camera but not necessarily with a 2 megapixel camera used at f22. Where has Myhrvold stated that?

When there's some doubt as to what is meant precisely, you might as well cut the guy some slack and consider the more sensible interpretation of what was meant rather than the less sensible interpretation.

Myhrvold is really trying to say that a 2 megapixel camera used at f8 will give you the same sharpness at the plane of focus as a 1Ds2 at f22. However, the fact that the DoF at f8 will be different seems to have escaped Myhrvold. This is no doubt due to the fact that Photography is a new field to him. He seems to be under the impression that stopping down beyond f8 reduces resolution in all parts of the image, as implied in the following quote from his article.

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The bottom line is that the Canon EOS 1Ds Mark II will suffer lower resolution from diffraction at any f-stop above f/8, at which point both red and green light are at their diffraction limited resolution.

Another way to say this is that if you stop down below f/8 with this camera, you will reduce the resolution everywhere – including in the plane of perfect focus.

What Jonathan should do is take another couple of shots at f11 and f32, with his 1Ds, of scenes where DoF considerations are not significant (in order not to confuse the issue). Downsize the f11 shot to 2mp then upsize and compare to the f32 shot.
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#### bjanes

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« Reply #94 on: February 21, 2007, 06:23:46 pm »

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I'm surprised that I'm the only one who sees the complete irrelevance to Myhrvold's article of Jonathan's Black Widow spider experiment. Jonathan has clearly misunderstood the point Myhrvold is making with his '2 megapixel camera' analogy.

I agree that Myhrvold is not as clear as one would like and the fact that Jonathan has misunderstood Myhrvold's point is not entirely Jonathan's fault.

However, if you read the whole article it should be clear that Myhrvold precedes his '2 megapixel camera' analogy with statements to the effect that f8 to f9 gets you the sharpest results with cameras such as the 1ds2 and 5D and that as you stop down you are effectively throwing away resolution to the point where at f22 you could have got the same result with a 2 megapixel camera but not necessarily with a 2 megapixel camera used at f22. Where has Myhrvold stated that?

When there's some doubt as to what is meant precisely, you might as well cut the guy some slack and consider the more sensible interpretation of what was meant rather than the less sensible interpretation.

Myhrvold is really trying to say that a 2 megapixel camera used at f8 will give you the same sharpness at the plane of focus as a 1Ds2 at f22. However, the fact that the DoF at f8 will be different seems to have escaped Myhrvold. This is no doubt due to the fact that Photography is a new field to him. He seems to be under the impression that stopping down beyond f8 reduces resolution in all parts of the image, as implied in the following quote from his article.
What Jonathan should do is take another couple of shots at f11 and f32, with his 1Ds, of scenes where DoF considerations are not significant (in order not to confuse the issue). Downsize the f11 shot to 2mp then upsize and compare to the f32 shot.
[{POST_SNAPBACK}][/a]

Ray,

I agree that we should cut Myhrvold some slack, since he probably knows more physics than the rest of us combined. I also agree that his 2MP figure was not well explained and is on the low side, but not entirely unreasonable.

In any case, people are deluding themselves when they think that their camera has an effective resolution of anywhere near that indicated by the nominal pixel count. Consider for example, the Canon 1DsM2, which is the current resolution champ in 35 mm style cameras with 16.6 MP.

Lets look at an Imatest MTF 50 plot of that camera (taken from the test shot published on DpReview):

[attachment=1903:attachment]

An ideal digital camera would resolve 0.5 cycles per pixel at Nyquist, but in the real world one gets about 0.33 cycles per pixel with sharpening. Without sharpening, the figure is worse. The 1DsM2 gets 0.344 cycles/pixel with standardized sharpening for MTF 50, which is a very good figure. In terms of idealized MTF 50 pixels, the effective megapixel count is 6.93 MP. This illustration shows how important sharpening is for MTF, and any analysis which does not take sharpening into account is incomplete.

Now lets look at the Nikon D200 with the 50 mm f/1.8 lens at f/5.6 (which is the optimum aperture in my tests):

[attachment=1904:attachment]

This camera resolves 0.324 cycles/pixel with standardized sharpening at MTF 50, for an idealized MTF megapixel count of 4.21.

Now, let's consider this combo at f/22:

[attachment=1905:attachment]

The resolution is now 0.193 cycles/pixel for an effective idealized MP count of 1.5 MP.  Stopping down to f/22 costs 64% of my resolution. Instead of MTF 50 idealized pixels one could use the Rayleigh criterion of 9% MTF, but the results would again show a dramatic loss of resolution. Jonathan cound take another picture of the spider, if the specimen is still available. However, in keeping with Lord Kelvin's quote, I think that quantitative analysis is appropriate.

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So we can now rest reassured that your 50 mm standard lens basically behaves just like any other 50 mm standard lens.

[a href=\"index.php?act=findpost&pid=101950\"][{POST_SNAPBACK}][/a]

No, I did not really determine the behavior of my standard 50 mm lens, but rather the behavior of the camera and lens combination and quantititated the loss of resolution incurred by stopping down from f/5.6 to f/22. So far, all you have contributed is a lot of conjecture without any data.

For further explanation of the Imatest terms, please refer to Norman's [a href=\"http://www.imatest.com/]web site[/url]. The latest version of Imatest now contains an SQF (subjective quality factor) module, which has been shown in extensive tests at Kodak to correlate well with perceived image quality and when I upgrade I might show these results for 16 by 20 inch images at the two f/stops.

Bill
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#### 01af

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« Reply #95 on: February 22, 2007, 10:20:19 am »

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I agree that we should cut Myhrvold some slack ...
"Some" slack!? You're kidding! Make that "a mountain of slack," then we'd get closer to the truth.

Myhrvold said, "Now, I don’t think anybody would be very excited about turning their EOS 1Ds Mark II, or Canon EOS 5D, or other full frame camera into a 2 megapixel camera." And that's pure nonsense.

It may (repeat: MAY) come closer to reality if he'd said, "At f/22, a full-frame DSLR has an effective resolution that corresponds to an ideal MTF-50 2 MP image." And that would have been a completely different statement (although one might still argue about the 2 MP figure). After all, a 2 MP camera (as opposed to a MTF-50 2 MP ideal) is subject to the same ideal-vs-real-world limitations as everything else is.

So, all your calculations of MTF-50 megapixel equivalents are very nice but pointless. It still remains a fact that a real-world 16 MP camera has a higher resolution than a real-world 10 MP camera has a higher resolution than a real-world 6 MP camera has a higher resolution than a real-world 2 MP camera. And a low-performing lens (be it due to poor quality or due to diffraction at too-small an aperture) tends to level these resolution differences but won't cancel them out completely ... provided the lens still offers at least some reasonable resolution.

Myhrvold also said, "we need to consider the pixel size. The formula is max f-stop = P x 1.054, where P = pixel size in microns". And that's nonsense, too.

This formula computes the f-stop where the lens' resolution limit starts to limit the output resolution more than the sensor's resolution limit does. But "more" does not mean the sensor's limit suddenly was irrelevant after that f-stop ... nor does it mean the lens' limit wasn't relevant before. So it does not (repeat: NOT) tell you at what f-stop you'll get the best-possible output resolution. The output resolution is always affected by both input resolutions ... only to varying degrees.

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In any case, people are deluding themselves when they think that their camera has an effective resolution of anywhere near that indicated by the nominal pixel count. Consider for example the Canon EOS 1Ds Mk II ...
This is an absolutely pointless consideration. It doesn't matter what some freaks consider "the effective pixel count" by some obscure definition. The point is: with a good-enough lens the effective pixel count of  a 16 MP camera is twice the effective pixel count of an 8 MP camera, period. With a lesser lens, 16 MP effectively is not twice as much but still more than 8 MP effectively. The "Myhrvold f-stop" approximately indicates where the higher pixel count's advantage starts to become less than the quotient of the two pixel counts. Still the higher pixel count will always keep an advantage over the lower pixel count, even at f/22 or f/32.

Don't get me wrong: I do agree that the effective pixel count (whatever that may be exactly) always is somewhat less than the nominal pixel count. But please don't let scholastic arguments fool you into thinking higher pixel counts were no better than lower ones. Better take a good look into the horse's mouth

-- Olaf
« Last Edit: February 22, 2007, 10:54:19 am by 01af »
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#### Ray

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##### f-stop limits for full sensor resolution
« Reply #96 on: February 22, 2007, 10:36:46 am »

Bill,
The test charts and imatest results are useful for predicting what we might expect from certain lenses and cameras, but we still need to check out the significance of these numbers in real world scenes.

For example, it's implied in a Roger Clark graph of diffraction limitation at various f stops, you posted a couple of pages back, that a lens diffraction limited at f8 should resolve 40 lp/mm (it looks about 40) at 80% MTF.

The best Canon lenses can manage only 70% MTF at 40 lp/mm. Medium quality lenses like the 100-400 IS at 400mm are at best 60% in the centre, falling significantly, away from the centre.

I would expect all good lenses to be equal at f22, but clearly not equal at f8.

It would be interesting to see some real world results comparing images at f8, downsampled to 2mp then upsampled back to the original size, with the same scene at f22. Just how close would such images be (at the focal plane)?

I'm disappointed that BJL has not taken up this challenge. He's written so much about the superiority of the Zuiko lenses. If any lens is likely to be diffraction limited at f8, then surely it's a Zuiko lens   .

ps. My excuse: I'm not at my studio at present.
« Last Edit: February 22, 2007, 10:39:41 am by Ray »
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#### bjanes

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##### f-stop limits for full sensor resolution
« Reply #97 on: February 22, 2007, 11:51:48 am »

Quote
So, all your calculations of MTF-50 megapixel equivalents are very nice but pointless. It still remains a fact that a real-world 16 MP camera has a higher resolution than a real-world 10 MP camera has a higher resolution than a real-world 6 MP camera has a higher resolution than a real-world 2 MP camera. And a low-performing lens (be it due to poor quality or due to diffraction at too-small an aperture) tends to level these resolution differences but won't cancel them out completely ... provided the lens still offers at least some reasonable resolution.

Myhrvold also said, "we need to consider the pixel size. The formula is max f-stop = P x 1.054, where P = pixel size in microns". And that's nonsense, too.
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I do not know your level of photographic sophistication, but I do note that you have made only a few posts on this forum. Many unsophisticated or beginning photographers fall into the [a href=\"http://query.nytimes.com/gst/fullpage.html?res=9507E1DD113FF93BA35751C0A9619C8B63]Megapixel Myth[/url]. Extra MP are nice since they allow bigger prints and some freedom in cropping. However, for prints that most of us make, the extra MP may not mean much. Furthermore, resolution varies with the square root of MP: a 16MP sensor has 1.4 times the resolution of an 8MP sensor, not double the resolution.

As an illustration I post the following SQF analyses for the D200 50 mm f/1.8 combo at f 5.6 and f/22 along with the Canon EOS 1DsM2. For details concerning the test method click here.

D200, f/5.6
[attachment=1907:attachment]

D200, f/22
[attachment=1908:attachment]

Canon 1DsM2
[attachment=1909:attachment]

Interpretation criteria
[attachment=1910:attachment]

As is apparent from the graph, f/5.6 on the Nikon enables excellent print quality up to  a picture height of 34 cm or 13.23 inches. At f/22, one can get equivalent quality only by decreasing the picture height to 13 cm or about 5 inches. The Canon enables excellent quality up to 40 cm (16 inches). For smaller prints, the prints from the Canon might not show much advantage, since it takes a SQF difference of about 5 to be significant.

Quote
This formula computes the f-stop where the lens' resolution limit starts to limit the output resolution more than the sensor's resolution limit does. But "more" does not mean the sensor's limit suddenly was irrelevant after that f-stop ... nor does it mean the lens' limit wasn't relevant before. So it does not (repeat: NOT) tell you at what f-stop you'll get the best-possible output resolution. The output resolution is always affected by both input resolutions ... only to varying degrees.
This is an absolutely pointless consideration. It doesn't matter what some freaks consider "the effective pixel count" by some obscure definition. The point is: with a good-enough lens the effective pixel count of  a 16 MP camera is twice the effective pixel count of an 8 MP camera, period. With a lesser lens, 16 MP effectively is not twice as much but still more than 8 MP effectively. The "Myhrvold f-stop" approximately indicates where the higher pixel count's advantage starts to become less than the quotient of the two pixel counts. Still the higher pixel count will always keep an advantage over the lower pixel count, even at f/22 or f/32.

Don't get me wrong: I do agree that the effective pixel count (whatever that may be exactly) always is somewhat less than the nominal pixel count. But please don't let scholastic arguments fool you into thinking higher pixel counts were no better than lower ones. Better take a good look into the horse's mouth
[a href=\"index.php?act=findpost&pid=102370\"][{POST_SNAPBACK}][/a]

I wouldn't consider Norman Koren to be a freak, but rather a very knowledgeable scientist and photographer. Let Myhrvold defend his statements, but the fact is that it is useful to consider the camera as sensor or lens limited. In practice, as shown by the Photozone tests on the Canon, stopping down the lens does not have a major effect on system resolution until the diffraction limit of the lens drops below the resolution of the sensor. Above that point, increased lens resolution makes a relatively minor change in system resolution.

It is always better to look into the horses mouth than make predictions from a scientific model, but that model has been thoroughly tested. Perhaps you can publish some images to show your point rather than employing intuition.

Bill
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#### bjanes

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##### f-stop limits for full sensor resolution
« Reply #98 on: February 22, 2007, 11:57:46 am »

Quote
The test charts and imatest results are useful for predicting what we might expect from certain lenses and cameras, but we still need to check out the significance of these numbers in real world scenes.
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Ray,

Something like Michael's megapixel shootout would be informative, but that would require everyone to get together, shoot the same scene, and use similar processing. Optimum sharpening is critical and would be hard to standardize since it depends on many factors, including the anti-aliasing filter that most 35 mm style cameras use. Even with all the efforts Micheal and his expert colleagues took, many still criticized the results. IMHO, the methodology was outstanding.

Quote
What Jonathan should do is take another couple of shots at f11 and f32, with his 1Ds, of scenes where DoF considerations are not significant (in order not to confuse the issue). Downsize the f11 shot to 2mp then upsize and compare to the f32 shot.
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I agree with your post that it would be useful for Jonathan to make the tests you suggest. The suggested method is similar to that used by [a href=\"http://query.nytimes.com/gst/fullpage.html?res=9507E1DD113FF93BA35751C0A9619C8B63]David Pogue[/url] with somewhat surprising results. Can you comment on that analysis?

Bill
« Last Edit: February 22, 2007, 12:22:38 pm by bjanes »
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#### Ray

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##### f-stop limits for full sensor resolution
« Reply #99 on: February 22, 2007, 07:00:06 pm »

Quote
The suggested method is similar to that used by David Pogue with somewhat surprising results. Can you comment on that analysis?
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Bill,
I did comment on that analysis when the article was first mentioned on this site in another thread.

The explanation for these results is that the general public at large is not particularly interested in matters of resolution and image sharpness. It's not something they give much thought to. I wasn't there, in the library where the 3 different shots from the 1Ds2 were shown. However, 3 observers were able to see the resolution differences between the 3 enlargements. To put it another way, 6% of the participants knew what to look for. The rest, quite possibly, didn't have much of a clue.

These results are consistent with the general public's attitude to the introduction of high definition television. When digital broadcasting was first implemented in Europe, there was no provision for HD broadcasts. It was thought (by people who had done some market research) that the general public was not sufficiently interested to spend the extra money on a new display that would (initially only partially) support HD broadcasts. Furthermore, it was thought that the smaller, more affordable HDTV sets, say 32" diagonal, would be too small to have any impact with the increased resolution.

Bearing in mind that an HDTV image has at least double the resolution of  standard definition (and much more than double if one is comparing the full spec of 1920x1080p), it is not surprising that some people, when asked to compare images that differ by considerably less than double the resolution, might have some difficulty.
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