Diffraction Limit Discussion Continuation

Started Feb 21, 2014 | Discussions thread
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Anders W Forum Pro • Posts: 21,465
Re: Diffraction Limit Discussion Continuation

knickerhawk wrote:

The prior thread on this interesting if somewhat heated discussion maxxed out before I could post some additional information. I'll leave it to others to address the theoretical differences. I want to return to the issue of evidence. What evidence is there to support the proposition that pixel density does or does not affect the optimal aperture setting for a given sensor size? Some (including the calculator at the Cambridge in Colour website) indicate that the effect of diffraction sets in sooner for sensors with smaller (more) pixels than for sensors with larger (fewer) pixels. Others, including such luminaries as Bobn2, Anders, and Great Bustard, say, "no, no, no" pixel size is not a meaningful factor. So we have a pretty clear-cut difference of opinion that should be relatively easy to resolve with objective lens tests performed on same-sized sensors with differing pixel sizes/densities using the same lens tested at various aperture settings. Right?

I noted several times in the prior thread that DXOMark provides those tests. DXOMark is fairly unique in that most of its lens tests are conducted on a range of cameras. The problem is that it's clunky to find the appropriate data points and plot them. I also noted that in every case that I've looked at, the DXOMark data supports the proposition that pixel size is a non-factor. I've looked at over a dozen lenses tested on several dozen cameras and have yet to find contrary examples. However, it's a big database and I'd encourage others to look as well.

One objection that's been raised is that the DXOMark measurements are too coarse because they're only taken at full f/stop settings. The speculation is that the peak acutance might be occurring somewhere between the measured stops and therefore we can't rely on the DXOMark data. Having looked at enough examples, this struck me as pretty preposterous. Surely, the peaks wouldn't always average out exactly to the same major f-stop setting. Putting that aside, I thought that the data points we do have should be sufficient to infer with some degree a certainty exactly where the peaks occur. I'm certainly no math whiz (far from it!) but I can throw data into an Excel chart and see how the trendlines curve. Below are two examples chosen to illustrate the point. One is M43-based because - after all - that's what this forum is all about; and one is based on an extreme case comparing a 12mp camera (the Nikon D3) to a 36mp camera (the D800). Charts below. Fire away...

While I think the DxO data can be used to test whether the peak is independent of sensor resolution, the way I would do it would be the following:

Take a sample of lenses. Record for each where the peak occurs for bodies with different pixel counts along with the pixel count of the body in question. Run a regression with some measure of peak f-stop (e.g., log2((1/f-number)^2) as the dependent variable and some measure of sensor resolution (e.g., the square root of the pixel count) as the independent. If we (you, I, and a whole bunch of others) are right, the relationship should be approximately zero. Ideally, the regression should take the form of so-called multi-level analysis to get the standard errors right.

Not that I'd really find it worth the effort (or I might do it myself). In my view, we already have the evidence to tell which theory is right.

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