I don't think that's true for slanted edge testing.
Hi Jim,
I was thinking along the lines of
this blog post of yours. Which shows the positive effects of denser sampling at different apertures (levels of diffraction) in the plane of best focus.
When I plot a similar lens scenario for 2 different sampling densities I get the result in the attached graph. The shape is similar (and same amplitude at Nyquist), but the Nyquist frequency and limiting resolution, and the amplitudes (at same cy/mm frequencies), are different.
Maybe we're talking about different things though.
Dropping every other column sample and every row sample (and making the region of interest twice as long to pick up more samples if that's necessary) should produce the same MTF curve, whether the horizontal axis is cy/px or cy/mm. If you don't tell the software that you've dropped those samples, cy/ph will be unaffected as well.
I don't think so, because you've swapped 'area like' samples for sparsely sampled 'point like' (quarter area) samples of the edge. Precision is affected, like in a Nearest Neighbor downsample.
There is one other potentially relevant issue (although I think this is something different from what you mention) that
is addressed in the relevant ISO Standards, but that I almost never see mentioned in e.g. the posts at DPReview by Jack or Frans. Maybe because MTF mapper (using 10 bins per pixel) as a tool already takes care of it, dunno. The ISO states that one should only bin (they use 4 bins, 1/4th of a pixel resolution) "full phase rotations" if I recall their phrasing correctly. Meaning that if e.g. the slope of the slant is ArcTan(1/10) degrees, one should use a multiple of 10 edge pixels for the SFR evaluation. So a cropped Region of Interest (ROI) should have multiples of 10 pixels in dimension in the length. The data is also filtered with (if I recall correctly) a Hamming filter to avoid ripple effects.
I'll try to find a copy that I used to have of the Standards (one for digital camera resolution, and two for scanner resolution) that I used to have, and see if relevant parts can be shared without copyright issues.
So IMHO, dropping rows and columns could disrupt that slightly more robust averaging process at particular slant angles. It may amount to a small difference when many more sparse samples are used (like a Monte Carlo simulation), but still.
The slanted edge method forms a averaged, interpolated edge and examines the characteristics of that edge, but knows nothing about the sampling density (or assumes that it's 100%, if you want to look at it that way).
I agree, but it will influence the sampling accuracy of the interpolation, especially if there is some lens distortion involved, and we need to include the sampling density in cy/mm to see the real differences. The Cy/px metric will show simila shapes, but the spatial frequencies of the projected image are at different detail sizes.
I know this is completely unintuitive, but think about dropping samples out of, say, a 5um grid and you'll see what I'm getting at. Of course, you need enough samples for the slanted edge method to achieve the desired accuracy. You should be able to drop out samples whose location is random with the same effect.
No, not unituitive, but with issues for precision, and no accurate representation of physical resolution (unless recalibrated for the different sampling density).
I do understand the similar curve shape despite the sampling density, but it represents different levels of detail (cy/mm), and thus different amplitudes (as the attached graph shows).
Cheers,
Bart