This post will continue looking at the spatial frequency response measured by MTF Mapper off slanted edges in DPReview.com raw captures and relative fits by the ‘sharpness’ model discussed in the last few articles. The model takes the physical parameters of the digital camera and lens as inputs and produces theoretical directional system MTF curves comparable to measured data. As we will see the model seems to be able to simulate these systems well – at least within this limited set of parameters.
The following fits refer to the green channel of a number of interchangeable lens digital camera systems with different lenses, pixel sizes and formats – from the current Medium Format 100MP champ to the 1/2.3″ 18MP sensor size also sometimes found in the best smartphones. Here is the roster with the cameras as set up:
All cameras in this round-up are AAless so they do not have an anti-aliasing filter. The DPReview.com studio scene raw capture used in each test is indicated in the title of the relative plot[1]. The slanted edge below center was fed to MTF Mapper 0.5.8[2] to obtain a measurement of system MTF in the direction of the edge normal. It perchance happens to be the better of the two edges for all of these systems.
The spatial resolution on the x-axis is in cycles per pixel pitch. Measured and Modeled MTF50 values are displayed in lp/ph inside the top box in each graph[3]. The parameters used to generate modeled curves are displayed in the box below it. Keep in mind that though they have known labels they represent a system fit that includes many non-idealities like imperfect edges and longitudinal CA within the passband of a single color channel. So W020 and W040 should be interpreted more as the coefficients of the relative square and fourth power radius of the exit pupil in the model than as absolute lens values.
Note that with the exception of the two Medium Format lenses all focal lengths are more or less equivalent to 85mm Full Frame, although f-numbers appear to have been chosen by DPReview.com for best sharpness as opposed to equivalent aperture. All captures were taken at base ISO.
System MTF Curves and Performance Parameters
Going from largest to smallest sensor, first we have the 101MP Medium Format Phase One XF-IQ3 with a 4.6um pitch mounting a Schneider Kreuznach 80mm LS f/2.8 lens:
Next the 51.4MP Medium Format Panasonic 645Z with a 90mm ED AW SR lens, with a 5.3um pitch:
Then the 36MP Full Frame Nikon D810 with Nikkor AF-S 85mm/1.4G lens from the last article, with a 4.9um pitch:
The 24MP APS-C Sony a6300 with a Zony FE 55mm/1.8ZA lens, with a 3.9um pitch:
The 20.8MP micro Four Thirds Olympus Pen-F mounting a Zuiko 45mm/1.8, with a 3.4um pitch:
A 20.8MP 1″ Nikon J5 with a Nikkor 32mm/1.2, with a 2.4um pitch:
Finally, for fun, the smallest pixel DSC camera I could find, the 18MP Panasonic ZS60 through its built-in lens and a 1.23um pitch:
Note how in the ZS60 diffraction extinction forces the MTF to zero just above Nyquist, which in this case occurs at 
= 0.47 cycles per micron or 0.58 c/p[3]. Truly diffraction limited – definitely no need for an AA here because diffraction performs that job, with the small 1.23um pixel easily oversampling the Airy disc[4].
The other measured curves look fairly similar in shape and that makes sense if you’ve followed this series on hardware ‘sharpness’: the slanted edges are captured with good technique, off the same target near the center of the FOV, the lenses are well corrected primes with approximately circular aperture, the sensors are AAless Bayers with efficient microlenses and effectively squarish pixel apertures. Discrepancy from these ideal shapes would indicate imperfections in the equipment and/or set up.
Checking the Quality of the Fits and the Lenses
The fits are all pretty good, meaning that the model is able to simulate the performance of these systems near the center of the field of view fairly accurately using just the indicated parameters. Defocus and third order Spherical Aberration Optical Path Difference coefficients are contained, which means that good technique was used during capture and these lenses are all fairly well corrected near the center at these relative apertures.
Lord Rayleigh suggested that if the aberrated wavefront lies within a quarter-wave of the Gaussian reference sphere the aberrated image will be of good quality[5]. A useful back-of-the-envelope metric to understand whether a system is properly tuned at the time of capture is therefore the total peak wavefront Optical Path Difference, which is equal to 
when the only aberrations present are Defocus and SA3.
Here is how the various systems fare in this case:
Defocus and SA3 vary with the square and the fourth power of the radius of the exit pupil. Lenses with smaller exit pupil aperture diameters and effective f-numbers should therefore potentially have an advantage unless their size makes them harder to manufacture. And in this test they show it.
Mirror Mirror on the Wall …
It’s interesting to ponder what appears to be the sharpest system of the lot in lp/mm locally, where the edge sits, in the direction of the edge normal. I know I know, resolution in one spot near the center is not necessarily indicative of the overall performance of the lens, and there are many other important factors that we are overlooking. Still, assuming that MTF50 is a good proxy for perceived sharpness[6], the green channel crown goes to – you guessed it – the ZS60 with 135.6 lp/mm. In general, you gotta be better if you are smaller and you aspire to play with the big boys:
Recall that spatial resolution per picture height (lp/ph) is relevant when comparing images displayed at the same size; resolution per mm (lp/mm) is relevant when wishing to know how ‘sharp’ the given system is on the sensing plane in absolute physical units[7].
The MTF value at which each curve meets the Shannon-Nyquist spatial frequency (0.5 c/p) is indicative of the aliasing and moiré inducing energy present in the system. Historically it seems that optical low pass (or anti-aliasing) filters were used to abate the MTF at Nyquist to below about 0.15[8]. From Table 3 above it seems obvious that this no longer seems to be a design goal with the current crop of AAless interchangeable lens digital cameras and their pixel sizes.
A Decent Model for Sharpness in the Center at f/5.6
All in all I am pretty happy with the way the simplified model has performed with this batch of cameras and lenses at f/4-f/8 near the center of the field of view. Until the SA3 portion of the model came into being that was not necessarily the case.
Ignoring a little noise (which presents as undulations superimposed on the main curve) it is able to match the shape of the measured MTF curves quite closely. The aggregate peak wavefront error OPD values obtained seem to be reasonable at 
, although since defocus+SA3 are effectively used as the plug in the model they sweep up all non idealities in the system (e.g. edge length and imperfections, vibration/motion, non circular aperture, axial color, incorrect f-number, pixel shape and size, mean light wavelength, the presence of aberrations other than those accounted for, etc., etc., etc.) so they have more relative than absolute value assuming all else (e.g. edges, shooting distance etc.) is kept the same.
I think with a single raw capture of two orthogonal slanted edges near the center the model fit can tell us a lot about the system that took it: whether the sensor has an AA, whether it is going to be prone to aliasing and moiré, whether the shot was taken with good technique, whether it was in-focus, how good the lens is and whether aberrations other than SA3 are present. Also, though not addressed in this series of posts, how well corrected the lens is for spherochromatism, Chromatic Aberrations and much more.
Now that we know that the model works with these parameters in the f/4-f/8 range it should be easy to simulate a number of scenarios and answer questions related to them. For instance, how would the Phase One perform if it had the pixel size of the 1 incher? Easy.
The next step in the development of the model will be to see how well it works at more challenging f-numbers. But to do that I need to get my hands on a set of slanted edges captured with good technique from f/2 to f/22, like these. Jim has unfortunately erased his. Anyone?[9]
Notes and References
1. DPReview.com Studio Scene raw files can be downloaded from here.
2. Frans van den Bergh’s excellent blog is here; Open source MTF Mapper can be downloaded from here.
3. See here for a discussion of the units used in spatial resolution.
4. The Airy disc diameter is equal to 2.44lambdaN. With 0.53um light and f/4 the diameter is 5.2um.
5. For more on Rayleigh’s Criterion and Strehl ratios see section 5 in this paper by Virendra N. Mahajan.
6. See here for an article discussing whether MTF50 is a good proxy for perceived sharpness.
7. I calculated spatial resolutions based on sensor height, not sensor diagonal; this makes lp/ph values for the Phase One and Olympus look a little better than they should be because of their different form factor. Results in lp/mm should instead be directly comparable for all systems.
8. For the MTF curve of a camera with an Anti Aliasing filter see for instance the Canon 5D mark IV’s plot in Figure 5 of the previous article.
9. See here for a description of the slanted edge method as used in this article and how you can obtain MTF curves for your equipment from it.