Diffraction Limit Discussion Continuation

Started Feb 21, 2014 | Discussions thread
bobn2 Forum Pro • Posts: 56,384
Re: Diffraction Limit Discussion Continuation

Jonny Boyd wrote:

bobn2 wrote:

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.

There's plenty of theory Bob, all explained in thus post and previous posts in this thread. It's just using the equation for determining resolution of a system with multiple components that each have linited resolution themselves.

That isn't 'theory'. The equation you're using is itself a 'rule of thumb', based on the idea that the MTFs . For a start, we don't know what you mean by 'resolution'. Are you taking MTF50, or what?

We're all agreed that it's a good equation

It depends what you mean by a 'good equation' - it's a decent approximation for some purposes.

and as Anders requested, I'm working out the implications. I took a while to carefully explain my methodology, so if you'd like to contribute usefully here you could begin by highlighting where you think my methodology falls flat, rather than pouting off with an unsubstantiated opinion.

Where your methodology falls flat is that the 'experiment' you're performing is fictitious, it's not based on real numbers, nor is it based on the theory.

As for arbitrariness, the numbers I used are quite deliberate. I used lens resolution numbers that give a curve with a shape broadly the same as a standard MTF curve for a lens. Similar real ones have been shown plenty of times in this thread and others. The printer resolution was chosen to be less than the lens, but not so low that it would dominate the final resolution The sensor resolutions were chosen to cover the range of scenarios from sensor limited output, to lens limited, and stuff in between. You'll notice the senaor numbers logarithmically scale for precisely this reason.

In short, your numbers were chosen to get the result that you wanted to demonstrate.

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.

As I said, this is a simple application of an equation we all agree on.

A rule of thumb equation run with made-up numbers.

Working made-up numbers tells you absolutely nothing.

It tells you plenty. You have made a universal claim that diffraction always causes peak sharpness at the same aperture, regardless of pixel count. While I agree that that is mathematically correct, I also believe that a drop in resolution will in some cases only become noticable at a smaller aperture for a low res sensor thanma large one. That's all I'm claiming. If I can find one instance where numbers demonstrate it, then I am correct.

Your numbers do not at all demonstrate that 'that a drop in resolution will in some cases only become noticable at a smaller aperture for a low res sensor thanma large one', since your criterion for what is 'noticeable' was plucked from thin air, as were the numbers that you used.

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 was assuming different viewing sizes because my interest was in the relationship between diffraction effects and pixel count. Introducing another variable would be unhelpful.

You haven't any real variables in any case, just fictitious ones.

Anyway, my point can be demonstrated trivially by looking at the f4 and f22 resoluts for s = 3 and s = 300. For s = 3, there is relative drop in sharpness of 0.1%. For s = 300, the drop is going to be 35.4%. The s = 3 drop is unnoticable.

You haven't even defined 'sharpness' properly, nor do you have any data on what is 'noticeable'.

If the s = 300 drop isn't noticable, then that sensor still has its peak sharpness well after the peak aperture. If the drop is noticable, then it has a peak sharpness at a lower aperture than the s = 3 sensor. Either way, my point is made.

I can't see your point - in every case the peak sharpness is at f/4 because that's where you put it. All that changes is the height of the peak. Not where it is.

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'.

How about we discuss the subject at hand rather than speculating about people's motives?

It's a fair point, you've produced some impressive graphs of fictitious numbers. That must have taken you a fair time and effort, but in the ned they show nothing. However, they are bogusly quantitative, so why is it worth your time and effort to make something bogusly quantitative?

Particularly the second graph is highly bogus, because it shows '100%' at the same level, when the '100%' is of different things.

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