Diffraction Limit Discussion Continuation

Started Feb 21, 2014 | Discussions thread
bobn2 Forum Pro • Posts: 57,367
Re: Diffraction Limit Discussion Continuation

Jonny Boyd wrote:

Here's a further thought on practical limitations imposed by diffraction.

If you print a photo, at what point does diffraction reduce the perceived resolution for cameras with different numbers of pixels?

Mathematically of course, diffraction will reduce image quality at the same aperture for every camera. However this will not always produce a perceptible decline in quality so the practical limit may be different to the absolute technical limit.

The following will make use of resolution numbers that are made up for the purposes of illustration to demonstrate the point, rather than to make a declaration about the use of any particular combination of lens, sensor, and printer. This is a demonstration of principle, rather than an examination of any particular set up.

The resolution of a final image, r will be determined by the lens resolution l, the image resolution i, and the printer resolution p. That's somewhat simplifying things, but since the printer resolution will remain constant in this, then we can assume that any other factors affecting resolution can be included in that constant.

r = 1/( 1/(l^2) + 1/(s^2) + 1/(p^2) )^1/2

If we use a subset of the lens and sensor resolutions in my earlier example, and take p = 100, then we get the following results:

Naturally this looks very similar to earlier resolution charts.

Now if we turn to consider the issue of when a difference in quality will be noticable, it would be helpful perhaps to look at relative quality differences instead of absolute, so we'll now look at a chart of printer resolution relative to resolution of a print produced from an image taken at peak aperture (f/4).

Remember this is resolution relative to the resolution at peak aperture, so the lowest res sensor, which is relatively unaffected by diffraction, remains very close to 100% relative resolution at every aperture, but will, in absolute terms, be much worse quality than the highest res sensor which shows the biggest changes in relative resolution.

We now need a cut-off point for when a change in resolution will be noticeable. If we assume that a 5% change in resolution is noticeable i.e. when resolution drops below 95% of peak resolution, a difference is noticeable, then we see that diffraction only starts to limit the perceived quality of a print at smaller apertures for lower res sensors.

s = 1, 3, or 10 are never perceptibly limited by diffraction; s = 30 is limited at f/22; s = 100 at f/11; s = 300, 1000, 3000 at f/8.

Again, this is for a purely theoretical setup

I would not aggrandise it with the word 'theoretical'. There is no theory behind this setup, merely arbitrariness.

so real world examples of sensors, lenses, and printers may have more or less pronounced behaviour, depending on actual resolution. My model also assumes that the percentage drop in relative resolution that becomes noticeable would be the same for every absolute resolution. It may be that at higher absolute resolutions a change in relative resolution would be noticeable at a higher or lower resolution. I'm not sure about that one.

This is a particularly futile exercise. Either do the theory or work the real numbers. Working made-up numbers tells you absolutely nothing. In any case, on what is based your assumption that a 5% change i resolution is noticeable? Do you know even that the noticeability simply scales? Maybe there's a threshold? Maybe it depends on viewing size?

I'm wondering why you feel it necessary to work so hard to find some meaning for 'diffraction limit' without being able to demonstrate that such a definition is even useful. What have you got invested in there being a 'diffraction limit'.

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