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Author Topic: f-stop limits for full sensor resolution  (Read 78173 times)

xtoph

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f-stop limits for full sensor resolution
« Reply #40 on: January 29, 2007, 03:40:46 am »

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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
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with all due respect, myhrvold is obviously not an expert on the question of optical diffraction effects on digital sensors. take a look at the crops i've posted here, or do them yourself (in order to test his assertions, you need to have detail visible at less than the width of two pixels). he says that while such details can be resolved at f/8 or 9, by the time you reach f/22 your full-frame sensor cannot resolve more than 2mp worth of detail. or, in his second post, he substitutes what turns out to be a similar claim; that at f/22 such an image is equivalent at best to the f/8 performance with a gaussian blur of radius 1.5 applied.

these at least have the merit of being testable assertions. i've tested them, and they are wrong. i used a lens that comes close to its peak performance at f/8 (and is darn good), so we avoid the problems with samples coming from an extreme telephoto that is struggling to perform at f/8 (ie, near wide open, including teleconverters). such a test is invalidated (especially if looking at detail much larger than 2 pixels across) because it is a poor approximation of the ideal (diffraction limited) lens. in other words, such a test would mainly reflect the (expected) performance of a less than ideal lens, ie, it gets better when stopped down.

i think it is silly to assume that just because a person is making an argument from authority and invoking some essoteric information we should stay out of the discussion. he's made clear predictions; we can test them; let's do it and move the discussion forward. sitting on the sidelines hoping to 'learn' something here is pointless--unless you're mainly interested in ego psychology.

the problem is that the one who ought to be looking to learn something here is myhrvold. but clearly he isn't. case in point: johnson pointed out that the way the sensor interpollates informatino from multiple photosites to calculate the value of single pixels may be the souce of the confusion; the cambridge in color website makes the same point (i quoted it above); and in fact i made the same suggestion in my first post, before these two got involved. so, myrhvold's prediction based on his model is demonstrably wrong; at least three people have suggested a plausible source of the error; and myhrvold is just closing his eyes and repeating that the laws of the universe are on his side.

it is very hard not to see it all as a grand political metaphor.
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BernardLanguillier

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f-stop limits for full sensor resolution
« Reply #41 on: January 29, 2007, 04:29:36 am »

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Bernard,
Would a Leica M8 (or MF digital backs) be closer to the theory since it has no AA filter?
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That would indeed be my guess. At least it should be more useful as an experiment subject than a 1s2 or D2x.

It would of course still not account for the influence of the lens.

Regards,
Bernard

francois

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« Reply #42 on: January 29, 2007, 08:16:51 am »

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...It would of course still not account for the influence of the lens.
...
Of course, we all know that Leica lenses are perfect! At least, that's what the local camera store owner told to a potential M8 customer.
« Last Edit: January 29, 2007, 11:41:20 am by francois »
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Francois

marcmccalmont

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« Reply #43 on: January 29, 2007, 10:24:54 am »

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That would indeed be my guess. At least it should be more useful as an experiment subject than a 1s2 or D2x.

It would of course still not account for the influence of the lens.

Regards,
Bernard
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I did a quick test with a 5D that has no AA filter, F8 was a bit sharper than F22 what one would expect from the lens in its sweet spot not drastic like 13 mp to 2 mp?
Marc
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Marc McCalmont

jani

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« Reply #44 on: January 31, 2007, 05:52:24 pm »

Even though people have PhDs and whatnot, they can still make mistakes. That's what friends, colleagues and editors are for. Unfortunately, the peer review process apparently is a bit less stringent when posting to a website, so it's entirely possible that mistakes don't get caught.

In Myhrvold's calculations, it could be something as simple as a missing square root somewhere, which also seems to match the difference he notes between his usage and that of Cambridge in Colour.

Now for the 1.5 radius gaussian blur statement; that was for the 1Ds MkII, not the 5D, which xtoph (Christoph(e)?) posted images for.

Let's pretend that there was a square root error, and that in addition, we need to divide by the factor of minimum f-stops between the 1Ds MkII and the 5D (1.125), to find the correct gaussian blur radius to use. That would then be a radius of 0.943 instead of 1.500.

Here's xtoph's f/22 picture:

[attachment=1710:attachment]

And here's the f/8 with a 0.9 radius blur:

[attachment=1707:attachment]

Okay, that's still a bit off.

But what if Myhrvold confused radius and diameter?

The f/8 with a 0.7 radius blur:

[attachment=1708:attachment]

And what if we assume that Cambridge in Colour is right (1.414 factor reduction), as well as that Myhrvold confused radius and diameter?

The f/8 with a 0.5 radius blur:

[attachment=1709:attachment]

Hmm ...

Edit: A consistent typo, AKA "brainfart", of 1.5 instead of 0.5 would also explain the observations.
« Last Edit: January 31, 2007, 05:54:29 pm by jani »
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xtoph

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f-stop limits for full sensor resolution
« Reply #45 on: February 09, 2007, 04:01:50 am »

well jani, i appreciate the effort to track down where myhrvold went wrong. i agree that even the titled are 'entitled' to make mistakes (though if someone politely points out that you're wrong, and you rudely insist you haven't made any mistake, well, that's a different case). i realize that the 1.5 gaussian blur radius factor was probably based on the 1dsII, but i don't have one handy to do that test (my old 20d though, with even greater pixel density than the 1dsII, gives remarkably similar results to the 5d, better than the example on the cambridge site shows--not sure what is going on with that and can't do further tests, as i gave the 20d to my brother. but we don't know what lens the cambridge site used, and we don't really know much else--raw or jpg, noise reduction or not, etc, which may have affected that image. i don't deny that the 20d captures less detail at f/22 than the 5d--i just didn't see the very dramatic kinds of effects illustrated on their textured fabric). what i found interesting was that the results of a 1.5 radius blur on the f/8 5d image look exactly the same as the image which myhrvold first suggested, ie that at f/22 you had only 2mp worth of resolution (a statement he applied to both the 1dsII and the 5d--see his original post).

so here's the problem: myhrvold actually was completely consistent (and equally wrong) in both of his posts. this makes it harder to believe that the way he got there was through misplacing decimals on the radius calculation, or confusing radius and diameter (though perhaps that was a factor).

i still suspect, as i stated in my first post, that the problem is related to misunderstanding how the interpolated data from multiple photosites relates to 'pixels'. that would be an interesting subject to take up, in my opinion. it would be helpful to know how interpollation affects the diffraction limits (and i am unconvinced by myhrvold's dismissal of it given my tests). i could read the papers johnson references; i bet they would help. but it just isn't that high on my list of things to do. in the meantime i will continue to get results from my camera at f/16-22 which, according to myrhvold, violate the laws of physics.
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jani

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« Reply #46 on: February 15, 2007, 05:57:06 pm »

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well jani, i appreciate the effort to track down where myhrvold went wrong. i agree that even the titled are 'entitled' to make mistakes (though if someone politely points out that you're wrong, and you rudely insist you haven't made any mistake, well, that's a different case).
To put it this way: even a title in computer science doesn't mean that you've done anything worth s... in programming, or know your way around complex algorithms.

That being said, even if you had the relevant experience, you could still mess up and don't realize it.

It's a core human problem that when we've written something of our own, it's very hard to find fault with it. Most people -- even among the experts -- will need a second set of eyes, a peer reviewer if you like, who can find these faults.

Neither Johnson nor Myhrvold appear to have had anyone review their articles/musings before they were published, which the general quality of what they wrote speaks volumes about.

If they'd been submitting a scientific paper, you can bet that they'd both been more thorough.

Instead, the tone was informal.

That's why I think it's entirely likely that a basic mistake can sneak into the text and remain there, in spite of any number of doctorates the person holds.

But enough said about that; Myhrvold was clearly wrong in the factual details of what he wrote, whatever the reason.
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Ray

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« Reply #47 on: February 15, 2007, 06:26:52 pm »

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Neither Johnson nor Myhrvold appear to have had anyone review their articles/musings before they were published, which the general quality of what they wrote speaks volumes about.
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One could consider the posting of their articles on LL a form of seeking second opinion. I notice that professor Charles Johnson has now invited comments on a book he's preparing on the science and technology of photography. No-one (except me) seems to have shown much interest on this site so far. The thread is [a href=\"http://luminous-landscape.com/forum/index.php?showtopic=14767&hl=]http://luminous-landscape.com/forum/index....topic=14767&hl=[/url] and Charles Johnson's first 3 chapters of his book are at http://photophys.com/photophys/
« Last Edit: February 15, 2007, 06:28:45 pm by Ray »
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Jonathan Wienke

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« Reply #48 on: February 15, 2007, 06:32:44 pm »

I've done macro shots at f/36 with a Canon 35-350 L zoom, which is far from the sharpest lens Canon makes, and the resulting images still have significantly more than 2MP of detail. Myhrvold is clearly off in his calculations somewhere.
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BJL

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« Reply #49 on: February 15, 2007, 06:51:26 pm »

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I've done macro shots at f/36 with a Canon 35-350 L zoom, which is far from the sharpest lens Canon makes, and the resulting images still have significantly more than 2MP of detail. Myhrvold is clearly off in his calculations somewhere.
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I think he is off in his interpretation: the "brick wall" fallacy that the resolution of an optical system is equal to the resolution of the lowest resolution component. Some reading about the multiplicative nature of MTF might be in order.

Maybe at f/22, diffraction spots are about as large as the photo-sites of a 2MP 35mm format sensor, but reducing the pixel size (increasing pixel count well beyond 2MP) will still increase overall resolution. Given the soft edges of diffraction spots (so that they do not have a single clear cut diameter), I am fairly sure that one could reduce pixel size to half that much and still be gaining in overall resolution, so maybe about 8MP in 35mm format is more like the resolution limit of f/22.

That seems to fit the data better anyway: film matching about 8MP to 16MP in 35mm format and f/16 to f/22 being where diffraction srarts to significantly reduce resolution with film.
« Last Edit: February 15, 2007, 06:52:19 pm by BJL »
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Ray

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« Reply #50 on: February 15, 2007, 08:57:19 pm »

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I've done macro shots at f/36 with a Canon 35-350 L zoom, which is far from the sharpest lens Canon makes, and the resulting images still have significantly more than 2MP of detail.
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More significant detail than which 2MP, with which lens at which f stop?

This entire issue is confused by 2 factors. What the heck do we mean by 'diffraction limitation' and what the heck is a pixel?

We know that a Foveon pixel (consisting of red, green and blue element) carries far more weight than a Bayer type pixel which is in fact monochrome.

True diffraction limitation is something one perhaps never sees demonstrated. My understanding of diffraction limitation at a particular f stop is that an image will show no trace of aberration at that f stop. A diffraction limited lens is, in a sense, bearing in mind the limitation of Physics, a perfect lens.

That is, at f16 diffraction is more predominant than at f8, but there may still be traces of other aberrations at that f stop. At f8 aberrations such as spherical aberration , coma and chromatic aberration may predominate, with aperture diffraction taking a back seat but still contributing to the degradation of the image.

I think we kid ourselves if we think that even the best 35mm lenses are truly diffraction limited at f8 or f11 or even f16. All we can say is that they are more diffraction limited as we stop down, and more aberration limited as we stop up.
« Last Edit: February 15, 2007, 09:17:21 pm by Ray »
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Ray

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« Reply #51 on: February 15, 2007, 09:58:37 pm »

Looking at it another way, if one defines 'diffraction limitation' as the f stop at which image degradation due to diffraction is greater than 50% of all the factors, in aggregate, that conspire to reduce image sharpness, then the f stop at which diffraction limitation applies will vary enormously with the lens used.

Am I right or am I right?
« Last Edit: February 15, 2007, 10:01:50 pm by Ray »
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BJL

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« Reply #52 on: February 16, 2007, 10:50:23 am »

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Looking at it another way, if one defines 'diffraction limitation' as the f stop at which image degradation due to diffraction is greater than 50% of all the factors ...
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I prefer to avoid attaching a single number to what is in fact a gradual transition: a range of values is a better indication of the situation. (What scientists and engineers might call specifying an "error bar" for a result.)  The physical reality is that at _any_ aperture, diffraction has some effect, though very slight at large apertures, and the effect increases is a continuous way as aperture is increased, with no sudden onset of diffraction effects at some particular aperture.

I am happy with the following two stop range, supported by observation and theory:
- diffraction effects are negligible at f-stops less than the the pixel spacing of standard Bayer CFA sensors.
- diffraction effects are clearly significant at f-stops greater than twice this length scale.

E.g. the transition zone for current 10MP 6 micron SLR sensors is about f/6 to f/12.
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Ray

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« Reply #53 on: February 16, 2007, 12:05:59 pm »

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E.g. the transition zone for current 10MP 6 micron SLR sensors is about f/6 to f/12.
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There are some lenses that are sharper at f12 than at f6. If you are very lucky, you might have a lens that is marginally sharper at f4 than at f8.
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BJL

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« Reply #54 on: February 16, 2007, 01:41:14 pm »

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There are some lenses that are sharper at f12 than at f6.
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It might be better to say that "some lenses are less sharp at f/6 than at f/12", which is almost certainly due to aberration problems at f/6: they in no sense have an advantage over other lenses at f/12, but only a disadvantage relative to other lenses at f/6. The discussion of diffraction versus sensor resolution ignores such poor lens performance as a factor.

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If you are very lucky, you might have a lens that is marginally sharper at f4 than at f8.
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Perhaps I am lucky then with my Olympus 50-200/2.8-3.5, for which this is reportedly the case. However I am not sure if it is a matter of luck so much as a matter of choice of lenses and formats. The f-stop giving best resolution tends in general to increase as focal length and image circle size increases, due to natural scaling laws applied to lens designs, so absolute statements about particular f-stops like f/4 and f/8 are at best applicable only to one format or some specific range of formats.  Resolution tests I have seen show that many new "digital specific" lenses for formats smaller than 35mm (DX, EF-S, FourThirds, etc.) have their best resolution at f/4 or lower, and certainly at below f/8.
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Ray

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« Reply #55 on: February 16, 2007, 07:20:17 pm »

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.... they in no sense have an advantage over other lenses at f/12, but only a disadvantage relative to other lenses at f/6. The discussion of diffraction versus sensor resolution ignores such poor lens performance as a factor.
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Except in the case where a lens is sharper at f16 than it is at f12. I believe there are such lenses. They tend to be budget telephoto zooms. Michael has reviewed such a lens using the DXO analyzer.

Ignoring such factors of course is what Myhrvold does and consequently his calculations appear to be at odds with real world experience.

Without getting into the complication of trying to equate Airy disc size with pixel size, the following statements appear to be true.

1. A lens that is fully and completely diffraction limited at f8 will also be fully and completely diffraction limited at larger f stops of f11 and f16 and so on.

2. A lens that is fully diffraction limited at f8 will have twice the resolution, at f8, as it has at f16.

3. An 8mp sensor has twice the resolution of a 2mp sensor, all else being equal.

4. This same lens, fully diffraction limited at f8, will have 1.4x the resolution at f16 as it has at f22.

5. A 16mp sensor has 1.4x the resolution of an 8mp sensor.

Put briefly, this ideal lens, which probably doesn't exist, has 2.8x the resolution at f8 as it has at f22. A 16mp sensor has 2.8x the resolution of a 2mp sensor. Quadruple the pixel count and you double the resolution. Double the pixel count and you increase resolution by a factor of 1.4x.
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Ray

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« Reply #56 on: February 16, 2007, 07:54:27 pm »

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Perhaps I am lucky then with my Olympus 50-200/2.8-3.5, for which this is reportedly the case. However I am not sure if it is a matter of luck so much as a matter of choice of lenses and formats. [a href=\"index.php?act=findpost&pid=101246\"][{POST_SNAPBACK}][/a]

I was of course referring to 35mm lenses. There are very few that would be sharper at f4 than at f8. One should also bear in mind that such lenses, whether they are rare examples of 35mm lenses or more common examples of Zuiko lenses, are nowhere near diffraction limited at f4.
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BJL

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« Reply #57 on: February 17, 2007, 06:21:49 pm »

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whether they are rare examples of 35mm lenses or more common examples of Zuiko lenses, are nowhere near diffraction limited at f4.
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I am not sure that I care about whether it is diffraction or something else that primarily limits resolution; I mainly care about what the overall resolution is, either in "lines per picture height", or in "lines per mm" (the latter particularly when my longest focal length is not enough to fill the frame, so I need to use some combination of tele-convertors and cropping). But to what extend that resolution limits come from diffraction, aberration, OOF effects, etc. is not of much significance to the end product.
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Ray

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« Reply #58 on: February 17, 2007, 07:51:47 pm »

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But to what extend that resolution limits come from diffraction, aberration, OOF effects, etc. is not of much significance to the end product.
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It has great significance in the context of Myhrvold's claim that using a lens at f22 with a 16mp camera such as the 1Ds2, is equivalent to using a 2mp camera of the same pixel pitch at f8, a claim that is widely disputed in this thread.

There might be a number of reasons why this does not appear to be true in practice, but I think a major reason is that a lens at f22 is much closer to being diffraction limited than a lens at f8, generally, in practice.

An interesting experiment would be to shift the range of apertures down so we can be more confident that the lens at those apertures really is diffraction limited.

For example, my 100-400 IS, at 400mm, stops down to f40. I think we can be confident that at this aperture the lens is diffraction limited. 3 stops up from f40 we get (approx.) f14 which, with this lens, might not be a fully diffraction limited f stop, but is much closer to being fully diffraction limited than possibly any 35mm lens at f8.

To give Myhrvold's assertion a fairer test, I would propose the following experiment.

1. Shoot a detailed subject at f40 with the 100-400 IS and 1Ds2.

2. Step back the appropriate distance so that a 2mp crop of the same scene will have the same FoV. (Requires a bit of mathematical calculation.)

3. Shoot the same scene at f14. Crop that shot to the same FoV as the first shot.

4. Compare detail.
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Jonathan Wienke

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« Reply #59 on: February 18, 2007, 04:08:34 am »

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To give Myhrvold's assertion a fairer test, I would propose the following experiment.

1. Shoot a detailed subject at f40 with the 100-400 IS and 1Ds2.

2. Step back the appropriate distance so that a 2mp crop of the same scene will have the same FoV. (Requires a bit of mathematical calculation.)

3. Shoot the same scene at f14. Crop that shot to the same FoV as the first shot.

4. Compare detail.

There's a much easier and faster option:

1. Shoot a detailed subject at  f/22 or smaller.
[attachment=1865:attachment]

2. Downsize the the shot to 2MP.

3. Upsize the shot back to the original pixel dimensions.
[attachment=1866:attachment]

4. Compare the original and the downsized-upsized images. If Myhrvold's assertions are correct, there won't be much difference between the two. But if the original is significantly better, he misplaced some decimal points or something.

The attached images are crops of a 1Ds macro shot with the 35-350L at f/32, which I sharpened and processed normally, saved the first crop, downsized to 2MP (1154x1734), upsized back to original size, and saved the second crop. I'll let you all compare for yourselves and come to your own conclusions.
« Last Edit: February 18, 2007, 04:17:19 am by Jonathan Wienke »
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