Taking the Sharpness Model for a Spin – II

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:

table-1-testing-model
Table 1. The cameras and lenses under test.

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.  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.

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:

xf-iq3-fit
Figure 1. Phase One XF-IQ3 100MP with Schneider Kreuznach 80mm LS f/2.8, green channel MTF curve, MTF50 indicated in the top box, modeled parameters in the lower box.

Next the 51.4MP Medium Format Panasonic 645Z plus a 90mm ED AW SR lens, with a 5.3um pitch:

645z-fit
Figure 2. Panasonic 645Z with 90mm ED AW SR lens, green channel MTF curve, MTF50 indicated in the top box, modeled parameters in the lower box.

Then the 36MP Full Frame Nikon D810 with Nikkor AF-S 85mm/1.4G lens from the last article, with a 4.9um pitch:

d810
Figure 3. Nikon D810 with AF-S 85mm f/1.4G green channel MTF curve, MTF50 indicated in the top box, modeled parameters in the lower box.

The 24MP APS-C Sony a6300 with a Zony FE 55mm/1.8ZA lens, with a 3.9um pitch:

a6300-fit
Figure 4. Sony a6300 with FE 55mm f/1.8ZA green channel MTF curve, MTF50 indicated in the top box, modeled parameters in the lower box.

The 20.8MP micro Four Thirds Olympus Pen-F mounting a Zuiko 45mm/1.8, with a 3.4um pitch:

penf-fit
Figure 5. Olympus Pen-F Zuiko 45mm f/1.8 green channel MTF curve, MTF50 indicated in the top box, modeled parameters in the lower box.

A 20.8MP 1″ Nikon J5 with a Nikkor 32mm/1.2, with a 2.4um pitch:

j5-fit
Figure 6. Nikon J5 Nikkor 32mm f/1.2 green channel MTF curve, MTF50 indicated in the top box, modeled parameters in the lower box.

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:

zs60-fit
Figure 7. Panasonic ZS60 green channel MTF curve, MTF50 indicated in the top box, modeled parameters in the lower box.

Note how in the ZS60 diffraction extinction forces the MTF to zero just above Nyquist, which in this case occurs at \frac{1}{\lambda N} =  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 Differences 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.

In the end a useful metric to understand whether a system is properly tuned at the time of capture is the total peak wavefront Optical  Path Difference (W_{040}+W_{020})\lambda, which should give similar results if only SA3 or Defocus were used as a parameter in the model.  Lord Rayleigh suggested that less than \frac{1}{4}\lambda OPD is a good criterion for an excellently set up lens, although it’s not clear whether he meant peak or rms wavefront OPD.

Here is how the various systems fare in this case:

table-2-testing-model
Table 2. Estimated peak optical path difference for third order spherical aberration and defocus in the green channel of the indicated digital cameras and lenses.

Defocus and SA3 vary with the square and the fourth power of the radius of the exit pupil.  Lenses with smaller exit pupils and effective apertures should therefore potentially have an advantage unless their size makes them harder to manufacture.

Mirror Mirror on the Wall …

It’s interesting to ponder what appears to be the sharpest lens 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[5], 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:

table-3-testing-model
Table 3. Green Channel MTF50 and MTF at Nyquist for the indicated digital cameras and lenses.

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[6].

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 AA) filters were used to abate the MTF at Nyquist to below about 0.15[7].  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.

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 \frac{1}{4} \rightarrow \frac{1}{3}\lambda, although since defocus+SA3 are effectively used as the plug in the model they sweep up all non idealities in the system (e.g. any 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.).

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?[8]

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 radius is equal to 1.22lambdaN. With 0.53um light and f/4 the radius is 2.58um.
5. See here for an article discussing whether MTF50 is a good proxy for perceived sharpness.
6. 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.
7. 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.
8. 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.
9. The slanted edge method produces a directional radial slice of the 2D MTF of the 2D PSF of the imaging system. Its results represent the linear spectral frequency response of the imaging system in the direction of the slice.
10.  Contact me via the form in the About page top right if you would like a copy of the Matlab/Octave scripts used to generate some of the figures in this post.