Rangefinder

Views on the photographic universe by Erwin Puts

pixel questions

The actual resolution of an imager (image chip) is most often measured in linepairs. This is the logical thing to do as the MTF Graphs that are published (in calculated and measured format) relate contrast to the number of linepairs over the image area. Common knowledge assumed that two pixels are enough to record one linepair (one black and one white pixel). A Leica imager in the M line would have approximately 4000 pixels in the vertical direction of 24 mm height. The theoretical resolution would be 83 lp/mm (1/24/2000). Now the classical studies by Zeiss among others claim that the sensible limit (for silver-halide emulsions and 35 mm film size) is 40 lp/mm. The Leica sensor would be able to double this number and resolve more than 80 lp/mm at the limit. My own comparisons with film and imagers indicate that both perform in the same league (when one compensates for the much higher ISO values of the imager compared to film emulsions). It is not the case that the limiting resolution of 40 lp/mm implies that the optical system is not able to resolve more lp. It is the case however that at this value of lp/mm the contrast drops to a low value of contrast and the fine details cannot be distinguished from each other. A study by Zeiss in 2013 shows that one needs at least four pixels to resolve two linepairs. The Nyquist rule explains why: one needs to double the sampling rate to get a clean record of the frequency. So if the frequency is two lp, one needs a sampling rate of 4 pixels to get a clean record of the signal.
If this is true, then we can say that the current Leica M imagers are capable of resolving just 40 lp/mm. The current Leica lenses are capable of resolving 80 lp/mm with sufficient contrast and are clearly overkill for the actual imagers (but they reduce the moire effects).
A possible future increase of the amount of pixels to let us say 36 million pixels would give 5000 pixels per image height of 24mm and a resolution of 1/24/5000/4) or 50 lp/mm. A hardly impressive increase in performance.