[wim]

[quote name='Frank' timestamp='1330333925' post='16211']

Hi Wim:



I can't resist to ask you a question on the optical resolution of a lens. Your replies seem to indicate that best lenses can reach 400-450 lp/mm at MFT-9. Is this resolution averaged over the whole image area?



The reason that I ask this question is that recently I tried to calculate the lens resolution at MTF-50 from the test result at photozone. The purpose was to see the difference between the lens resolution and the system resolution, and the influence of image sensor resolution on the system resolution. I know this is just a crude exercise but I want to get some feelings.



To my surprise, the center optical resolution can easily exeed 450 lp/mm even at MTF-50. Let me take the Nikon 16-35mm f4 lens as an example to show you how I calculated it. At 16mm and f4, the PZ test results on D3x are as follows:



center_res=3536 lw/ph, border_res=2700 lw/ph, corner_res=1278 lw/ph



which translate to lp/mm (divide above numbers by 2*24mm)



center_res=74 lp/mm, border_res=56 lp/mm, corner_res=27 lp/mm



These are system resolutions at MTF-50.



Now, the sensor resolution is 84 lp/mm (=4032/(2*24mm)). Then, using the formula



(1/system_res)=(1/lens_res)+(1/sensor_res)...........(a)



I get the optical resolution of the lens



ceneter_res= 599 lp/mm, border_res= 170 lp/mm, corner_res=39 lp/mm



So, even for a lens that is not the best, I get a center resolution about 600 lp/mm, at MTF-50. If this calculation is correct, the resolution at MTF-9 should be larger. Does my calculation make sense?



I know that for a real system there are more terms on the right-hand-side of equation (a), but those extra terms will lead to even larger optical resolution for a given system resolution (assuming those therms are positive).



I would like to hear your comments very much.



Best regards,

Frank

[/quote]

Hi Frank,



Unfortunately the lw/ih figures provided here on PZ are not usable for photographic resolution calculations, the reason being that these are figures calculated by the software with specific assumptions made which do not reflect photography in itself, but only produce analytical numbers useful for comparison of lenses tested on the same system (i.e., camera).



So, by no means are these system resolution figures, or anything comparable to that. Do also note that some lenses produce "resolutions" higher than the Nyquist frequency (i.e., lp/mm, if you like), which according to the resolution formulas is totally impossible. The system resolution is always lower than the lowest common denominator in the chain, because the formula to calculate the system resolution is



1/system_resolution = 1/lens_resoultion_at_aperture + 1/sensor_resolution



IOW, when lens resolution is infinite, the resulting system resolution is exactly equal to the sensor resolution. BTW, this has been a bone of contention for me with the PZ figures all along, and i have discussed this a few times already. It is also why I suggested quite a while ago to replace the lw/ih figures with just a quality type scale. However, demand was such apparently, that the lw/ih were reintroduced.



If you take into account that because of the diffraction limit, using the Rayleigh criterion, the maximum resolution is 1600/N, and for MTF-50 760/N, where N equals the numerical aperture value, e.g. 4 for F/4, it will become clear that the figures provided in PZ test reviews bear no relationship to anything we see in the photographic image as produced by the camera and lens.



Furthermore, there are only incredibly few normal photographic lenses which are diffraction limited at an aperture wider than F/4, maybe 2 I know of (if the reports are true), and potentially a bunch more around F/4, and most of the best lenses out there at F/5.6. This due to optical aberrations which cannot be entirely eliminated. At F/4 and wider apertures, optical aberrations tend to control the maximum resolution rather than diffraction limits.



These limits are valid for the optical centre, however, there always is fall-off in resolution towards the edges and corners of a lens, although that may not be a nice curve due to lens design, e.g., because of the use of aspherical surfaces or special glass. The fall-off is due to optical projection, effectively, which also causes optical vignetting. Without going into too much detail, in simple terms the same natural forces are at work here which cause vignetting, and on top of that there also is the fact that optical aberrations are stronger towards the edge of the glass, generally speaking.



If you would like to see proper lp/mm system resolution results, I'd suggest you take a look at lenstip. They produce system resolution figures, still at MTF-50 though.



BTW, there is an additional effect limiting system resolution, and that is the AA-filter. I estimate the effect of the AA-filter on average to lower resolution by about 5% to 8%, based on quite a few reviews I charted, but this does vary from system to system, or rather, from camera body to camera body. F.e., D3X system reolution figures are essentially the same as those from a Canon 5D II, which seems to indicate that the AA-filter on the D3X is slightly stronger than that on the 5D II.



I have attached a quick overview of diffraction limits and maximum theoretical system resolutions at different apertures for a few camera, for both Rayleigh criterion and MTF-50.



HTH, kind regards, Wim