Thanks, Bart. It turns out that most of the lenses that people are calling "decentered" are actually not, if passing the OOF PSF test is any indication.
Yes, that could be the case.
I think that often the problem is one or more tilted elements, which can cause field tilt that will fail my version of the Siemens Star test, and other effects that will fail both our versions, if they are properly performed.
The Siemens star test is decent at showing asymmetry where symmetry is expected, i.e. in the center of the image with presumed parallel object- and image-planes. An elliptical center star blur can point to tilt issues (maybe even of the sensor itself). Corners show, almost by definition, asymmetrical blurs if astigmatism or coma effects are present, but the blur is reasonably disk shaped on well-corrected lenses, although of lower resolution than the center. But all corners should have similar resolution.
One of the better qualities of these star targets is that focus distance is not critical for the quantification of the limiting resolution, e.g. expressed as % of Nyquist (or pixels or microns if a specific sensor's pitch is used), because that will always produce the same center blur diameter when the shooting distance is not too close. All that changes with distance is the image magnification, but not the resolved limit diameter. Calibration of magnification factor (from focal length and focus distance) is hard, but no longer needed with a star.
But the key phrase in the above is "properly performed". I don't think that Joe Public can reliably focus on each corner. In fact, I can't do that consistently myself, and I have to make many exposures, focusing in between, to get the reliability that I get with my one-focus test.
Yes, it's harder than many think it is. I've been thinking about adding a moiré producing feature as background to the 'star' instead of the medium grey, similar to what I did for my AF micro adjustment target, but the star itself already does make it easier because (in magnified Live-View), one needs to reduce the diameter of the center blur. That's already quite sensitive, and the harder part is often that the focus ring doesn't allow precise enough manual tweaking (most AF lenses have a very short throw). The moiré feature could be a useful tool for achieving plane-parallel orientation.
By the way, I am experimenting with sinusoidal (I actually coded a raised sine wave -- is that what you want?). With a camera with an AA filter it doesn't seem to make much difference:
http://blog.kasson.com/the-last-word/leica-1803-4-apo-telyt-r-on-sony-a9-field-tilt-curvature-astigmatism/
I'll be testing with no-AA cameras, in particular the small micro-lens GFX.
Yes, that's the kind of sinusoidal modulation I use myself. I use a different gamma than in your target so it can be looked at in gamma pre-compensated images, your's are best viewed at linear gamma, although it's not critical if not numerically evaluated for MTF.
The sharper the lens, the more optimal an aperture is chosen for maximum resolution (often around f/4-f/5.6), the smaller the fill-factor, and the larger the photosite pitch, the more you'll avoid excessive aliasing from compromising the analysis if the target produces a well-behaved input signal. It's also more gentle on the demosaicing because it reduces the false color artifacts, thus making e.g. Chromatic Aberration easier to spot.
Your targets use a 60-cycle or 60-sector pairs star, and a 20-cycle or 20-sector pairs stars.
That creates the Nyquist limit blur diameter at an approx. 38.2 pixel, and 12.7 pixel diameter at 100% zoom (2 x cycles / Pi diameter , used as quick estimate).
Cheers,
Bart
