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Geek Articles

More Ultra High-Resolution MTF Experiments

GEEK ALERT!!

Let’s be absolutely clear; this is not a practical or useful article. It won’t help your photography or cinematography become better. It won’t help you choose equipment any time in the next couple of years. It won’t provide any fodder for your next Forum War. It’s just a geek article that may interest some people. It may give a little peek into what may come in the future, and some insight into the kind of work we’re actually doing behind the scenes at Olaf. So if you’re interested in that kind of stuff, read along

A couple of years ago, a testing customer asked us to find which lenses could get maximum resolution from a 150-megapixel sensor. Many people assumed that the highest resolving lenses at standard resolutions would be the highest resolving lenses at higher resolutions. Assumptions are the dark matter of the internet; we can’t see them, but we know they account for most of the mass.

We try hard not to assume, so we tested a bunch of lenses at high frequencies on the MTF bench (high-frequency MTF is basically high resolution on the camera). This requires testing MTF at ultra-high resolutions, way higher than any camera of today. The manufacturer wanted 240 lp/mm (compared to the 50 lp/mm we use currently). I wasn’t sure that was necessary, and actually wasn’t sure we could do it, so we settled on 200 lp/mm. If you want some understanding of what all that means, you can read the above post or Brandon Dube’s excellent post. Or you can just accept it and move on.

There was no photo or video lens that could resolve 200 lp/mm wide-open. (Our standard for ‘resolve’ was an MTF 0f 0.3; an MTF of 0.2 was borderline. There’s some evidence to support those cut-offs, but someone could argue them. Wait, this is the internet. Someone WILL argue them; it’s what someone lives for.)

We did find several prime lenses that could meet those criteria stopped down to f/4 in the center of the image, but none could near the edges. The best results were for the Zeiss Otus 85mm f/1.4 lens at f/4. A few other lenses (Zeiss 135mm f/2 APO-Sonnar; Sigma 135mm f/1.8 DG HSM Art; Zeiss 55mm f1.4 Otus) were acceptable at f/4 in the middle portion of the image. Nothing wider than 50mm was really acceptable, although the Canon 35mm f1.4 Mk II and Sigma 35mm f/1.4 Art were close.

Back to the Future

Two years later, that customer asked us if we knew of any other lenses that they should consider. There’ve been a lot of lenses released since we did these tests, and some of those lenses fit the criteria for possible ‘ultra-high’ resolution; primes with focal lengths of 85mm or more. The manufacturers are obviously making these lenses with at least moderately higher resolution cameras in mind. So perhaps some of the newer lenses would resolve ‘ultra-high’ frequencies better than some of the older lenses we had tested.

So we checked some new lenses all the way up to 240 lp/mm, something sufficient to make a 200 megapixel FF camera worthwhile. To be clear, this is NOT coming to a camera near you anytime soon; it’s a research project. But if the researchers are making such a sensor, it makes sense they want to know which lenses would get the best results from the sensor. It is not a test for if the lens or sensor out resolves the other, because that doesn’t happen.  (For those of you who believe in perceptual megapixels or that the earth is flat, I’ve included an appendix to clarify this a bit – with no math more complicated than multiplication.)

The Best We Found Last Time

Last time we found some tendencies: longer focal lengths perform better, and f/4 is the minimum aperture that any lens can resolve such high frequencies. To give you a reference, here are several lenses that met our criteria last time (notice on these we set the highest frequency at 200 lp/mm).

Sigma 135mm f/1.8 DG HSM Art at f/4

Lensrentals.com, 2017

Zeiss 85mm APO-Planar Otus at f/4

Lensrentals.com, 2017

Zeiss 55mm Otus Distagon at f/4

Lensrentals.com, 2017

Canon EF 35mm f/1.4 Mk II USM

Lensrentals.com, 2017

The 35mm Lens Whose Name Cannot Be Spoken

You’ve seen the best results we had from lenses you could actually buy and use. We did see one lens that you can’t purchase, a prototype lens that will probably never be made, that was truly amazing, particularly for a 35mm focal length.

Olaf Optical Testing, 2017

So here is a 35mm lens that is as good as the 55m Otus; it’s that it’s this good at f/2.8 and doesn’t improve much at f/4. I put this up just to show that current lenses are not designed to do their best at ultra-high resolution, but they could be.

 We Wanna Take it Higher

Last time around, we set our peak at 200 lp/mm, even though the client really wanted 240 lp/mm. We didn’t think the higher number was really necessary, and honestly, we weren’t sure that any of our lenses would adequately resolve even 200 lp/mm. This time, though, we felt comfortable we could test at 240 lp, and doing that, let us also test at 192 lp/mm, which is pretty close to the original 200 lp peak.

For starters, we repeated the test using a Sigma 135mm f1.8 Art. You can compare it to the one done at 200 lp up above. Remember, these are single copy tests, so there is a little sample variation, but you can see the light blue line of this run (192 lp/mm) is comparable to the purple line of the previous lens (200 lp/mm). Even at 240 lp/mm, the MTF still exceeds our ‘borderline’ MTF cut-off of 0.2, at least in the center, but it doesn’t quite reach and MTF of 0.3.

Lensrentals.com, 2019

We’ll consider this our standard for the new tests, then, and see if any of the other lenses do as well.

Results for New Lenses

Sony 135mm f1.8 GM

We’ll start with the usual “Roger had expectations and was disappointed” part, because, after all, disappointment is the sole purpose of expectations. One of the reasons I was excited about testing new lenses was that the Sony 135mm f/1.8 GM had the best normal-range MTF scores we’d ever seen, besting the Sigma 135mm f/1.8 Art. It seemed logical that it might also best the Sigma in ultra-high resolution tests. Reality 1, Logic 0. We tried the lens at f/4, but it was actually a bit better at f/5, which we show below. At high frequency, it’s not as good as the Sigma.

Lensrentals.com, 2019

Let me repeat, for those of you who want to mistake this test as having something to do with, say, the 60-megapixel full-frame camera you’re shooting; it doesn’t. Somewhere around 80 lp/mm would be more than sufficient for that. If you compare the orange lines of the Sony and Sigma 135mm graphs, you’ll see that at 96 lp/mm the Sony is actually a bit better than the Sigma. At ridiculously high frequencies, the Sigma is better. The takeaway message is important: better MTF at one frequency doesn’t mean better MTF at all frequencies.

So let’s look at a couple of other candidates I thought might do really well.

Sigma 105mm f1.4 Art at f/4

Even though this copy was slightly tilted, in the center, at least, it is the first lens to make, albeit barely make, our ‘acceptable’ cut-off of MTF 0.3 at 240 lp/mm. At 192 lp/mm, it actually touches MTF of 0.4. So we have a new high-resolution champion, and that’s despite, as you can see below, this copy of the lens having a slight tilt.

Lensrentals.com, 2019

Zeiss APO Sonnar 100mm f/1.4 Otus at f/4

Another good contender; not quite as good as the Sigma 105mm, but very similar to the Sigma 135mm.

Lensrentals.com, 2019

Canon 90mm f2.8L TS-E Macro

This one I had low expectations for, but we had one handy, so we thought we’d give it a try. Set your expectations low, and they will be met. Again, don’t get me wrong, this is a really, really good lens, it’s just not as good at ultra-high resolutions.

Lensrentals.com, 2019

Sigma 40mm f1.4 Art

We learned from earlier testing that wider-angle lenses don’t do as well at these frequencies. But the Sigma 40mm Art tested so spectacularly at normal MTF that we thought it was worth a shot, at least.

Lensrentals.com, 2019

Here’s a case where good at normal resolution translates to good at ridiculously high resolution. This is close to, although not quite as high in the center as the Otus 55mm. It stays acceptable further away from the center than the Otus 55mm does, however.

Summary:

I say summary, because there are no practical or useful conclusions to be made. The only thing of interest, probably, is that only really good lenses can resolve ultra-high resolutions you’ll never need. However, even among these really good lenses, you can’t assume how a lens will perform at ultra-high resolutions based on its results at normal resolutions. You can also see that ultra-high-resolution performance is a bit easier to obtain in short telephoto focal lengths than in standard or wide-angle lengths.

Oh, yeah, and you can also wonder why someone, somewhere, is wondering what lenses will perform well at resolutions more than twice as high as what you might need today.

 

Roger Cicala, Aaron Closz, and Brandon Dube

Lensrentals.com

October, 2019

Appendix: Why Perceptual Megapixels are Stupid

I get asked several times a week if this lens or that is ‘capable of resolving’ this number of megapixels. Some people seem to think a lens should be ‘certified’ for a certain number of pixels or something. That’s not how it works. That’s not how any of it works.

How it does work is this. Any image you capture is not as sharp as reality. Take a picture of a bush and enlarge it to 100%. You probably can’t see if there are ants on the leaves. But in reality, you could walk over to the bush (enlarge it if you will) and see if there are ants by looking at a couple of leaves.

What if I got a better camera and a better lens? Well, theoretically, things would be so good I could see the ants if I enlarged the image enough. MTF is somewhat of a measurement of how sharp that image would be and how much detail it contains. (The detail part would be the higher frequency MTF.) That would, of course, be the MTF of the entire system, camera, and lens.

Lots of people think that will be ‘whichever is less of the camera and lens.’ For example, my camera can resolve 61 megapixels, but my lens can only resolve 30 megapixels, so all I can see is 30 megapixels.

That’s not how it works. How it does work is very simple math: System MTF = Camera MTF x Lens MTF. MTF maxes at 1.0 because 1.0 is perfect. So let’s say my camera MTF is 0.7, and my lens MTF is 0.7, then my system MTF is 0.49 (Lens MTF x Camera MTF). This is actually a pretty reasonable system.

Now, let’s say I get a much better camera with much higher resolution; the camera MTF is 0.9. The system MTF with the same lens also increases: 0.7 X 0.9 = 0.63. On the other hand, I could do the same thing if I bought a much better lens and kept it on the same camera. The camera basically never ‘out resolves the lens.’

You could kind of get that ‘perceptual megapixel’ thing if either the lens (or the camera) really sucks. Let say we were using a crappy kit zoom lens with an MTF of 0.3. With the old camera; 0.3 X 0.7 =.21. Let’s spend a fortune on the newer, better camera, and we get 0.3 X 0.9 = 0.27. So our overall system MTF only went up a bit (0.07) because the lens really sucked. But if it had been just an average lens or a better lens (let say the MTF was 0.6 or 0.8), we’d have gotten a pretty similar improvement.

If you have a reasonably good lens and/or a reasonably good camera, upgrading either one upgrades your images. If you ask something like ‘is my camera going to out resolve this lens’ you sound silly.

Roger’s rule: If you have either a crappy lens or crappy camera, improve the crappy part first; you get more bang for your $. I just saw a thread for someone wanting to upgrade to the newest 60-megapixel camera, and all of his lenses were average zooms. I got nauseous.

Author: Roger Cicala

I’m Roger and I am the founder of Lensrentals.com. Hailed as one of the optic nerds here, I enjoy shooting collimated light through 30X microscope objectives in my spare time. When I do take real pictures I like using something different: a Medium format, or Pentax K1, or a Sony RX1R.

Posted in Geek Articles
  • That looks like what is called a “Barn Swallow.”

    As far as I know, there is no species called “American Swallow.”

  • In the future, we’ll have gigapixel sensors on 360° optics, and all the work of photography will be done in post-processing. 🙂

  • How about “Witless Transfer Function,” or WTF? 🙂

  • Mark Harris

    Another awesome article! Yet I am still confused why my Sigma 135mm art is sharper than 3 copies of the 105mm Art I have tested on flat surfaces of course to prevent the DOF differences to influence the results. I need to send you my Sigma 135mm to be tested 😀

  • Carleton Foxx

    So how small of an object will these lenses be able to capture when we get these 100 mp or 200mp bodies?
    Are we talking the ability to image individual skin cells (25 micrometers across) when you photograph a person at normal portrait distance? Smaller than that?
    Would the level of detail these lenses capture allow me to read the newspaper on the desk of someone in an office 1km away? (Newspaper type is about 4 mm high).
    Or are we looking at the potential to take a single photo of the Golden Gate Bridge and use some kind of AI to examine it for cracks and corrosion?
    Is that anywhere in the ballpark.

  • Hi Roger, first installment is great work. You really delivered! Looking forward to part number two!

    But, all that must have been hard work, team, MTF-bench and computers may need some rest… 🙂

  • Dave Hachey

    This beast will take some effort to tame. My main reason for the purchase was for portrait and landscape work, which will require a good tripod. I have an A73 and an A9 for wildlife and general photography.

  • Idahodoc

    Absolutely! I have the Sony a7R4 and it is a devil of a camera to get really sharp pictuees with! Now what do I mean? If I only had 24MP to play with, they would all look good. But I was cussing my 24-70 f/2.8 for being unsharp at pixel peeping ranges until I realized it was ME! Throw away those rules for sharp shooting (inverse focal length = shutter speed for hand holding). It seems I can easily blur images at beyond 1/500 on that rig. Now, that only appears at the “bonus” pixel level, it prints OK at lower res. But to extract that last ounce of sharpness needs really excellent technique. And shooting bursts. On the plus side, all my GM lenses appear to produce more detail, sometimes much more, on the 60 MP sensor. Can’t wait to try my adapted Sigma 105 f/1.4!

  • Samuel Edge

    Please do share….

  • But I did give you a nice segue, didn’t I?

  • Brandon Dube

    There is insignificant spherical aberration at greatly reduced apertures like f/5.6. It is also field constant, so the result is quite boring in these graphs.

  • Brandon Dube

    Descartes used geometrical optics in the same manner in dioptrique, which is from the early 17th century.

    It would be unwise for a mathematician of no prominence in the field of optics to try to redefine our grammar, and even more foolish to take their modifications as gospel. They have, quite clearly, not taken given that recent revisions of reference texts use geometrical optics in the same manner I have, for instance the fourth edition of the seminal “intro to fourier optics,” or perhaps principles of optics, which as the most cited textbook in all of physics is quite inarguable in its authority.

  • David Remington

    I enjoyed reading this piece and the other lens performance and testing articles. I’m a photographer not an engineer or scientist but I understand most of the core principles discussed and always learn something interesting and often useful. I’ve read the blog for a few years now but have not posted before. I thought that I would today to provide what may be a unique perspective. I work in the cultural heritage imaging field. Our work involves digitizing items from the collections for access and preservation. Projects can last from days to years and involve capturing hundreds to millions (literally) of images. We have used many digital camera systems over the years. In chronological order, Leaf, Betterlight, Sinar, Canon, Nikon, Hasselblad, Phaseone, and Sony. More pixels have generally been welcome though it is not a free lunch. Our camera system needs are different from those of the typical commercial or personal photographer. We are concerned with what sampling rate (achieved) on the original is required to reproduce the level detail that will make the image useful for study and preservation. This might be reproducing printed or hand written text, names and symbols on a map, every line on an etching, textiles, figures and objects in photographs, physical condition documentation, etc. We have to reproduce the ants. We also “scan” film with a camera and light box setup. Cameras with greater pixel density allow us to image larger items at the necessary sampling rate, or smaller items at a higher sampling rate. As has been so clearly demonstrated and discussed here however, the camera is only half of the system. Lens performance is critical and is often the point of failure. We need to sample at the necessary rate and those samples have to contain meaningful information. For our purposes a lens that is exceptional in the center and “acceptable” in the corners is of no use. Better to be excellent in the center and very good (though preferably also excellent) in the corners. Wide maximum apertures are not necessary. Significant astigmatism is a deal breaker. We most often work at camera to subject distances of less than six feet and often less than four feet. As you might have guessed, we use macro lenses on the 35mm cameras. The Zeiss 50mm and 100mm f2 Macros both the Milvus and the original style. We also have a 55mm Otus we break out once in a while and a few specialty lenses. Of the lenses we have tested, the Zeiss Macros perform the best for general copy work. In resolving capability and also minimal distortion, and astigmatism. Not much CA either. Nothing that can’t be fixed in post. One significant limitation we have to work with is that we are working on copy stands most of the time and cannot use longer focal length lenses. The 135mm Sony and Sigma lenses look great. Alas. I have observed everything discussed here. Our default practice is to work out the best compromise focusing point where center and corner focus are as equal as possible. We give up a bit in the center to bring the corners up. Roger’s test and related posts nailed it and has a real world application in our studio! We shoot at f//5.6 to f9 for 2d work depending on how flat the original is. After that diffraction quickly becomes a trade off. Setup involves laser alignment of the camera to the copy plane and eliminating/minimizing vibration. We manually focus in live view. The Sony Alpha 7r3 is the best 35mm camera so far for our work. No mirror, no slap. e-shutter/e font curtain shutter. The camera is inert. We use the same Nikon mount Zeiss macro lenses with Metabones adapters. I remember Roger raising on flag on this practice but see no noticeable misalignment focus degradation. The Sony also performs sensor shift multi-shot which is much better at reproducing fine line and screen printed detail without moire. We use multi-shot with our Hasselblad and Sinar cameras as well. We use the H5d 50c MS Hasslebald cameras with Hasselblad HC 50mm and 120mm Macro lenses. Yes, the 50mm is not ideal but it is better than the 80mm using their lens profile to correct for distortion and we need the shorter focal length. The 120mm is terrific. I’ll note here that the primary (there were a few) reason that we did not purchase a 400c MS camera is lack of a suitable lens. While the 50mm works well enough on the 50c MS, it does not on 400c MS. It is a physically larger sensor but the lens flaws are also magnified by the higher pixel density. In this case a “good” lens and a “better” sensor added up to less not more. We use Schneider Digitar lenses on our Phaseone camera. The 72mm and 120mm Macro. We use the 120mm for close up and film capture and the 72mm for general copy work. The 72mm Digitar is a good lens but on the 100MP Phase back you really have to pick the sweet spot for placing focus and still leave some space to crop the edges of the frame. Phaseone has been looking for a replacement to use with the 150MP back as it is acknowledged that the 72mm doesn’t cut it. Again, what had worked well enough… We used Schneider enlarger lenses on our Sinar medium format backs. The 90mm and 60mm Componon HM. No complaints there though the 60mm was not at its best at close distances. For film “scanning” with the Nikons we use Rodnestock Rodagon D duplication lenses. The 75mm and 120mm with adapters and extension tubes. For this type of work these lenses perform much better than the 100mm Zeiss or other standard Macro lenses. I hope they was of interest to the group and keep up the good work.

  • Ilya Zakharevich

    (Looks like I need to redo without links)

    > “… geometrical is that it uses geometrical optics.”

    See above. These words meant very different things in 18th century comparing to now. High school physic classes keep the obsolete meaning. Now we know how the symplectic geometry of the rays encodes the “main” terms of the diffration (as in “the first few terms of Taylor–Puiseux series” in ? or ?).

    (For example, see Geometric Asymptotics by Guillemin, Sternberg; ISBN=0821816330 etc. However, while I learned A LOT from it, now I do not like the exposition.)

    > “to treat them as gaussians you first have to define their standard deviations”.

    Not necessarily. There are more way to fit a Gaussian to a function than matching the Taylor series at 0. For an obvious way, match the Gaussian to the aperture, then take a Fourier transform.

  • Keith Cooper

    Thanks – far more maths than for me too 😉
    The benefits do show up as real detail, but obviously the multi-shot limits applications. Worked really well photographing an old 8086 and a few other chips with the top removed and using the Laowa 100mm macro.

  • P.A. Hawk

    Very interesting test, although maybe not too relevant for current generation of cameras. I would like to see what kind of results fe. the Nikkor 105mm 1.4E ED would get. Atleast it seems very very sharp @ f4 on a 45 megapixel sensor.

  • Keith, I honestly don’t have a clue. Somebody with way more math than I have probably can figure it out.

  • Not really true, remember we have a random sampling of a few lenses out of thousands we’ve tested. The two Zeiss in this example are tilted. At these high frequencies, almost everything is. Also remember, the higher the resolution, the more obvious the tilt.

    At more standard resolutions, tilt is less obvious, but the WORST for tilt, by miles, of the expensive primes is the Sony 35mm f/1.4 ZA. Never had one without tilt and I’ve tested around 100.

  • SpecialMan

    Given your shocking confession that technique is so important wouldn’t a better investment be a lighter, faster-to-set-up, more rigid yet more vibration absorbing, taller-yet-more compact tripod? And a rigorous program of shutter-finger exercises?

  • kirkmoon

    One thing jumps out at me: every single one of the Sigma plots shows some degree of lens tilt (or at least some asymmetry). This is not present in the Zeiss, Canon or Sony lens samples. Food for thought.

  • David Remington

    Roger and others,

    I enjoyed reading this piece and the other lens performance and testing articles. I’m a photographer not an engineer or scientist but I understand most of the core principles discussed and always learn something interesting and often useful. I’ve read the blog for a few years now but have not posted before. I thought that I would today to provide what may be a unique perspective. I work in the cultural heritage imaging field. Our work involves digitizing items from the collections for access and preservation. Projects can last from days to years and involve capturing hundreds to millions (literally) of images. We have used many digital camera systems over the years. In chronological order, Leaf, Betterlight, Sinar, Canon, Nikon, Hasselblad, Phaseone, and Sony. More pixels have generally been welcome though it is not a free lunch. Our camera system needs are different from those of the typical commercial or personal photographer. We are concerned with what sampling rate (achieved) on the original is required to reproduce the level detail that will make the image useful for study and preservation. This might be reproducing printed or hand written text, names and symbols on a map, every line on an etching, textiles, figures and objects in photographs, physical condition documentation, etc. We have to reproduce the ants. We also “scan” film with a camera and light box setup. Cameras with greater pixel density allow us to image larger items at the necessary sampling rate, or smaller items at a higher sampling rate. As has been so clearly demonstrated and discussed here however, the camera is only half of the system. Lens performance is critical and is often the point of failure. We need to sample at the necessary rate and those samples have to contain meaningful information. For our purposes a lens that is exceptional in the center and “acceptable” in the corners is of no use. Better to be excellent in the center and very good (though preferably also excellent) in the corners. Wide maximum apertures are not necessary. Significant astigmatism is a deal breaker. We most often work at camera to subject distances of less than six feet and often less than four feet. As you might have guessed, we use macro lenses on the 35mm cameras. The Zeiss 50mm and 100mm f2 Macros both the Milvus and older style. We also have a 55mm Otus we break out once in a while and several specialty lenses. Of the lenses we have tested, the Zeiss Macros perform the best for general copy work. Very good resolving capability and also minimal distortion, and astigmatism. Not much CA either. Nothing that can’t be fixed in post. One significant limitation we have to work with is that we are working on copy stands most of the time and cannot use longer focal length lenses. The 135mm Sony and Sigma lenses look great. Alas. I have observed everything discussed here. Our default practice is to work out the best compromise focusing point where center and corner focus are as equal as possible. We give up a bit in the center to bring the corners up. Roger’s test and related posts nailed it and has a real world application in our studio! We shoot at f//5.6 to f/9 for 2d work depending on how flat the original is. After that diffraction quickly becomes a trade off. Setup involves laser alignment of the camera to the copy plane and eliminating/minimizing vibration. We manually focus in live view. The Sony Alpha 7r3 is the best 35mm camera so far for our work. No mirror, no slap. e-shutter/e font curtain shutter. The camera is inert. We use the same Nikon mount Zeiss macro lenses with Metabones adapters. I remember Roger raising on flag on this practice but see no noticeable misalignment focus degradation. The Sony also performs sensor shift multi-shot which is much better at reproducing fine line and screen printed detail without moire. We use multi-shot with our Hasselblad and Sinar cameras as well. We use the H5d 50c MS Hasslebald cameras with Hasselblad HC 50mm and 120mm Macro lenses. Yes, the 50mm is not ideal but it is better than the 80mm when using their lens profile to correct for distortion and we need the shorter focal length. The 120mm is terrific. I’ll note here that the primary (there were a few) reason that we did not purchase a 400c MS camera is lack of a suitable lens. While the 50mm works well enough on the 50c MS, it does not on 400c MS. It is a physically larger sensor but the lens flaws are also magnified by the higher pixel density. In this case a “good” lens and a “better” sensor added up to less not more. We use Schneider Digitar lenses on our Phaseone camera. The 72mm and 120mm Macro. We use the 120mm for close up and film capture and the 72mm for general copy work. The 72mm Digitar is a good lens but on the 100MP Phase back you really have to pick the sweet spot for placing focus and still leave some space to crop the edges of the frame. Phaseone has been looking for a replacement to use with the 150MP back as it is acknowledged that the 72mm doesn’t cut it. Again, what had worked well enough… We used Schneider enlarger lenses on our Sinar medium format backs. No complaints there though the 60mm was not at its best at close distances. For film “scanning” with the Nikons we use Rodnestock Rodagon D duplication lenses. The 75mm and 120mm with adapters and extension tubes. For this type of work these lenses perform much better than the 100mm Zeiss or other standard Macro lenses. I hope they was of interest to the group and keep up the good work!

    David

  • Well, if you assume internal consistency, that would be true. But really, it would be more like “we combine EPA gas mileage, 0-60 times, curb weight, luggage space, cornering ability, subjective attractiveness, and seat comfort as measured by our ideal ass size” and rate this car a 92, so it’s the car you should buy. Even if it’s valid, are many people really interested in that ideal combination of cornering ability and luggage space?

  • Carleton Foxx

    I’ve always thought of them like the old EPA gas mileage numbers, no external validity but nevertheless useful for rough comparison of one combo to another, no?

  • Carleton Foxx

    Thanks…
    So many factors to keep track of and balance off against each other. We’re not photographers, we’re photon jugglers.

  • Lee Wooten

    I just realized the second reason that Roger’s articles about arcane photography subjects suck me in (the first reason being the quality of his expressed cynicism) – life lessons. I have added the following to my list of principles to guide me through the trials of day-to-day existence:

    “disappointment is the sole purpose of expectations”
    &
    “If you have either a crappy lens or crappy camera, improve the crappy part first; you get more bang for your $.”

    Thank you!

  • Brandon Dube

    What means it geometrical is that it uses geometrical optics. If you want to treat them as gaussians you first have to define their standard deviations, which is (to me) undoable. The second moment of an airy disk is undefined.

  • Ilya Zakharevich

    To me, your ideas about “what makes a model geometric” look like some high-school.simplifications. I would prefer to say that “geometric” means something similar to what Andre Yew said here earlier: when you treat all “defects” (including diffraction) as if they were “independent Gaussians”, so combine them as ?(a²+b²) (instead of doing the honest Fourier optic).

    About the rest: I still cannot collect the shards of my head together. What *I* get *now* is that using your criterion (MTF20-width), the DoF goes as 1/F for small F, and switches to GROWING as 1/?(F?-F) for F close to the cut-off frequency F?. (But since I do calculations in my head, I could have missed some “?” sign easily?—?which would make my calculations completely bogus. The high-frequency answer above does not [immediately?] match the graphs in your thesis! Need to sleep my flu off… And: sorry for not paying attention to the “grade” of your thesis; I usually review the PhD level, so got a wrong assumption…)

    Anyway, note that you did not provide any shard of evidence for your
    “QED, … monotonically decreasing quadratic regime.”

  • Ilya Zakharevich

    cos(2?/14) is about 0.9. So does not it indicate that MTF at 200 lp/mm should be somewhere about 0.9×72?65%?

  • Brandon Dube

    It means the RMS wavefront error is less than one fourteenth of a wave.

  • Ilya Zakharevich

    “Diffraction limited at ƒ/2” means what, about 72% at 200lp/mm? (I hope I did not make mistake…) Roger, why do not you mention it above, then?!

    (Of course, as you said, the precise answer depends on the spectrum of incoming light. But still, if what you say is right, this should be WAY better than ?20–30% Roger claims!)

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