Are the large format lens test results of Perez / Thalmann realistic?
Almost everybody who got into comparing LF lenses or even own testing knows the large format lens test of Perez / Thalmann ( http://www.hevanet.com/cperez/testing.html ).
The values at f/22 for the best lenses for instance a Symmar-S 150 f/5.6 mm are about 60 lpm or slightly higher than 60 lpm. In the case of the Symmar even 67 lpm.
For the theoretically maximum resolution of a perfect lens at f/22 I find 75 lpm (diffraction limit). Tmax 100, the film Perez / Thalmann used for their test, should resolve a maximum of 200 lpm at high contrast (1:1000).
If I calculate the maximum system´s resolution for that with 1/max system resolution = 1/max resolution film + 1/max resolution lens at f/22. This is the result I find:
max system resolution = 1 /(1/max resolution film + 1/max resolution lens)=1/(1/200+1/75)=54,5 lpm
This theoretical value of about 55 lpm is below the often seen values of 60 lpm or even slightly higher for different (very best) lenses at f/22 that were observed in the testing.
Any thoughts to this "paradox"?
That's no great paradox for traditional resolution tests involving human interpretation. Also, the traditional diffraction limit formula does not allow for variations in many film characteristics.
The results for diffraction limit is variable depending on whether you use points or lines and a figure of 1/100 for f/22 isn't impossible. Likewise, the MTF of the film is very difficult to read 'accurately' as it depends on contrast.
Developer will make a difference also and getting absolute accuracy is difficult. However, you should read that at the bottom they say that the survey is intended as a 'relative' comparison of the lenses on test..
Make sure all your calculations are in either lines per millimeter or line-pairs per millimeter.
Thank you for your reply. What do you exactly mean with "1/100"? 100 lpm or 50 lpm? If you think of 100 lpm, I´m interested, where do you cite this value from?
Originally Posted by timparkin
For monochrome light with a wavelength of 486 nm (blue, the wavelength most lenses are first of all corrected for) and for a working distance of 100 times the focal length I find a diffraction limit of 75 lpm (f/22) in my photographic chart book (Wunderlich: Tabellenbuch Fotografie, 1984). 486 is somewhere in the the middle of TMax 100´s spectral sensibility response. If Perez / Thalmann used flash or daylight then the diffraction limit at 486 nm could be good value to calculate with. Since they used a working distance of 20 times the focal length if I got them right, the diffraction limit is lower than 75 lpm. From my chart book the diffraction limit drops from 75 at 100 times to 68 at 10 times the focal length working distance. Perez / Thalmann´s working distance (20 times) is in between 100 times and 10 times, where one could use a diffraction limit of roughly interpolated 72 lpm as a value to calculate with. The resulting system´s resolution would be 53 lpm.
I know all of this is very theoretical, but I´m interested how realistic the Perez / Thalmann findings are in absolute terms. This is especially interesting when you want to compare their values with other lpm values for instance for MF or 35mm lenses.
I´m aware of that, but in their comments they try to compare lpm values of LF lenses with lpm values of MF and 35 mm values that they achieved in own testings or did find in publications.
Originally Posted by timparkin
Don´t get me wrong - I appreciate the broad resolution testings, Perez / Thalmann did, very much. Just want to know how sensible it is to compare their lpm values to others that were publicized and compare the results of my own (very small) testings.
Another interesting question regarding this issue: Who also has tested the lpm resolution of LF lenses? Did you find similar values and how did you do your testing?
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I doubt if the formula 1/max system resolution = 1/max resolution film + 1/max resolution is correct. In fact, if the resolution degrading effects of the film (various physical effects) are not statistically correlated with the resolution degrading effects of the lens (diffraction and aberrations) then the correct formula is the following (1/max system resolution)^2 = (1/max resolution film)^2 + (1/max resolution)^2. This formula assumes that resolution is defined as the peak width of an image formed by an infinitely small object and that peak width is defined as the standard deviation of the peak, or in other words as the second moment of a peak relative to mean if the peak is normalized to unit probability. This formula assumes linear response, which is not strictly correct for film.
The above description is true, regardless of the shape of the peak. However, if the peak width is defined in some other way rather than the standard deviation of the peak then the above description may either be true or not true, depending on the functional forms of the peaks.
Sorry for all the fancy talk, but I wanted to say it correctly and unambiguously.
Andreas, years ago Modern Photography magazine published an article that asked whether 100 lp/mm on film was attainable. Short answer, yes, but not consistently or easily.
I've shot USAF 1951 targets with TMX at 1:10 and 1:20 with decent LF and MF lenses. I've never got much better than 50 lp/mm, put the difference between my results and Chris' and Kerry's down to operator error. Mine. Getting the best resolution possible isn't easy. I don't doubt their results even though I haven't been able to match them so far.
I've tested two of the lenses they did, 101/4.5 Ektar and 105/3.7 Ektar. I got the same difference between the two lenses' performance that they did. The 101 is unequivocally sharper across the field.
Thank you for this different formula. The result from with the values I first assumed would be: max system resolution = 1 /(squareroot((1/max resolution film)^2 + (1/max resolution lens)^2))=1/squareroot((1/200)^2+(1/75)^2)=70 lpm. Perez / Thalmann´s results at f/22 are slightly below that for the best lenses. So the "paradox" would be clarified.
Originally Posted by alanrockwood
I looked to find out the "best" approximation of a sytem´s resolution and found in contrary to your formula at the very in depth sites of Norman Koren (http://www.normankoren.com/Tutorials/MTF.html) the following:
Resolution of an imaging system (old definition)— Using the assumption that resolution is a frequency where MTF is 10% or less, the resolution r of a system consisting of n components, each of which has an MTF curve similar to those shown below, can be approximated by the equation, 1/r = 1/r1 + 1/r2 + ... + 1/rn (equivalently, r = 1/(1/r1 + 1/r2 + ... + 1/rn )). This equation is adequate as a first order estimate, but not as accurate as multiplying MTF's. [I verified it with a bit of mathematics, assuming a second order MTF rolloff typical of the curves below. It's not sensitive to the MTF percentage that defines r. The approximation, 1/r2 = 1/r12 + 1/r22 + ..., is not accurate.
This is the formula that I used in the beginning and that led to the contradiction between theory and the test results of Perez / Thalmann.
Bob Atkins cites your "square formula" which is also written in the high res photography bible "Image Clarity" by Williams. Atkins doubt it. He writes here http://www.bobatkins.com/photography/technical/rrs.html :
This relationship is often given as:
1/Rs^2 = 1/Rf^2 + 1/Rl^2
where Rs is the final system resolution, Rf is the film resolution and Rl is the lens resolution. This relationship is quoted in many texts, including publications by Kodak (P315 - Scientific Imaging) and in "Image Clarity" by John Williams. It is certainly a relationship which can give a decent approximation of system resolution under some conditions. However it is not based on any sound theory and can, in fact, be shown to give erroneous results when used improperly. There is no reason why the exponent should be 2. Some studies have shown a better fit with smaller exponents in the region of about 1.5, but even then, it's still empirical - it applies only under the conditions used for the experiment in which it was determined.
I´m still confused but a step farther when I see that the formulae for calculating system´s resolution provide only roughly approximated values if you don´t use the MTF of the sytem´s components. But where do I find a lense´s MTF at spatial frequencies in near of 60 lpm, maybe at 50 cycles?
I´m relieved that I´m not the only one that can not achieve the lens test values of Perez / Thalmann. Theoretically you didn´t have the chance to get absolutely as high as the two since you tested at 1:10 where the diffraction limit is lower than at 1:20 where the two shot.
Originally Posted by Dan Fromm
But the difference with about 10 lpm seems to be larger than the 1:20 and 1:10 effect could produce. So other factors may be to be involved.
I never could produce more than about 40 lpm on film with LF at any aperture. My highest values usually appear with f/22 and for my best lenses sometimes with f/16 or f/11.
I compared many lenses between 210 mm and 300 mm (Apo Gerogon, G-Claron, Symmar-S and some suprisingly sharp oldtimers as for instance a 210 mm Dagor). I used very high resolution Ortho films ORWO FO1, FO5 and ADOX / ROLLEI ORTHO 25. The last is said to resolve a maximum 320 lpm. I developed in Rodinal 1+200 and did not move the tray to much to get edge effects.
The sharpest lenses I tested where the 210 mm Symmar-S over a wide negative´s area and the G-Claron that was surely not as good outside of the center like the Symmar-S. I shot at about 1:80 and did not use USAF chart, but could easily count lines from small details on that I had focused before shooting.
I assume that the most important factor that reduced my resolution were very, very small vibrations, since I did not use flash but daylight and had exposure times between 15 seconds and 2 minutes. My tripod is of wood that should reduce vibrations somehow. Wind could not influence my testing since I shot from a sheltered place.
(The best resolution I ever achieved where about 80 lpm in 35mm with an older (around 1970) 1.4 / 50 mm MF Nikkor in cooperation with Tech Pan developed in Technidol (if I remember the developer´s name correctly). The shooting aperture was f/4 or f/5.6 .)
Actually, the formula is a mathematically rigorous result under the conditions described in my post. It can be derived by a fairly simple derivation involving the moments of a distribution, though I don't recall the details of the derivation at the moment. It even applies to distributions that do not have a finite second moment, such as the Lorentzian function, provided one defines peak width in a slightly different way.
Originally Posted by A49
The only time it does not apply is if the system does not obey the stated conditions, mostly related to linear system response, the absence of statistical correlation between the lens and the film response functions, and the particulars of how one defines peak width or resolution. Other formulas may apply if the conditions are not satisfied, and in a more general case there may be no simple closed form equation, but numerical methods could be used to calculate the quantities in those cases.