Diffraction Limit Discussion Continuation

Started Feb 21, 2014 | Discussions thread
Great Bustard Forum Pro • Posts: 40,847
Re: The error in your analysis is...

knickerhawk wrote:

Great Bustard wrote:

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...

...io assuming that all lenses peak at the same aperture:


Diffraction softening is unavoidable at any aperture, and worsens as the lens is stopped down. However, other factors mask the effects of the increasing diffraction softening: the increasing DOF and the lessening lens aberrations. As the DOF increases, more and more of the photo is rendered "in focus", making the photo appear sharper. In addition, as the aperture narrows, the aberrations in the lens lessen since more of the aperture is masked by the aperture blades. For wide apertures, the increasing DOF and lessening lens aberrations far outweigh the effects of diffraction softening. At small apertures, the reverse is true. In the interim (often, but not always, around a two stop interval), the two effects roughly cancel each other out, and the balance point for the edges typically lags behind the balance point for the center by around a stop (the edges usually suffer greater aberrations than the center). In fact, it is not uncommon for diffraction softening to be dominant right from wide open for lenses slower than f/5.6 equivalent on FF, and thus these lenses are sharpest wide open (for the portions of the scene within the DOF, of course).

In other words, there is absolutely no reason, whatsoever, to expect that an 85 / 1.4G would peak at the same aperture as a 25 / 1.4, regardless of the format or pixel size.

I wasn't comparing the Nikkor to the PanaLeica. They're two separate charts with the comparison in each chart between two cameras with the same sensor size but different pixel sizes/counts.

Apologies for the misinterpretation.

I picked the Nikon comparison because of the significant difference in pixel size between the D3 and the D800 and then picked the Oly comparison because this is an M4/3 site.

That's not the error in my analysis. The error is just plain bad math as Golly and Anders have informed me. That's what I get for trying to waltz with the leftbrains here!

Yeah -- I'm not so sure where I left my brain, but I'll find it, hopefully. 

More seriously, sure, more data points are needed for a more definitive conclusion, but if we assume a smooth curve with at most two inflection points, then your graphs show the difference in peak aperture is certainly no more than a stop (although, as discussed, there is no difference for the peak aperture).

What you would want to do is compare the same lens on different sensors. What you will find is that not only is the peak aperture the same regardless of pixel size, but that the higher pixel count sensor will resolve more at every aperture.

Which is what I tried to show with the vertical blue line in each chart.

In other words, pixel size has no effect on diffraction, but pixel count has a definite effect on resolution, although the resolution advantage of more pixels asymptotically vanishes as you stop the lens down.


Again, apologies for the misinterpretation.

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