# Diffraction Limit Discussion Continuation

Started Feb 21, 2014 | Discussions thread
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 Re: Diffraction Limit Discussion Continuation In reply to bobn2, Feb 22, 2014

bobn2 wrote:

Jonny Boyd wrote:

bobn2 wrote:

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?

A while ago I was getting the impression that those who think there is no diffraction limit regarded this equation as the golden rule so I was happy to use it. When it produces results you don't like, you want to get rid of it. As far resolution, it would be the number of line pairs that can be distinguished per unit length.

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 which purposes would they be and not be? You're being very vague.

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.

It's working out the implications of the equation Anders is so fond of, as he requested I do. In what way is it inapplicable in this situation?

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.

Rather than merely making an assertion, how about you show your reasoning? What is unrealistic about the shape of the resolution curve? What is wrong with the sensor resolution numbers I picked? As I've already stated, they effectively cover all the possibilities because they range from situations where resolution is sensor limited to situations where it is lens limited.

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.

And again I ask, why is the equation not applicable here and what is wrong with the 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.

Do you deny that there is both a greater absolute and greater relative drop in resolution between peak aperture and lower apertures for higher resolution cameras than lower resolution cameras?

Does it not logically follow from this that all else being equal (printing size, viewing distance, etc.), a sufficiently resolution sensor will show no perceptible difference in quality due to diffraction at apertures where a higher resolution sensor will show a drop (but still retain far greater overall detail)?

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.

So what if they're fictitious examples? It doesn't mean that they're unrealistic.

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'.

I know that the human eye has limits on how well it can perceive changes in sharpness. If both the relative and absolute changes in resolution are sufficiently low when stopping down, then the eye will not perceive them. That's so obvious that I don't know why you're disputing it.

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.

My point is that if you can't see any visible change in sharpness between f/4 and f/22 i.e. they are indistinguishable, then the perceived sharpness will plateau across those apertures, rather than peaking at f/4. So while the s = 300 sensor will show a drop in sharpness between f/4 and f/22 due to diffraction, the s = 3 sensor won't. Diffraction begins to limit sharpness for the s = 300 sensor at f/4, whereas it won't for the s = 3 sensor until f/22 or later.

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?

How are they bogusly quantitative? I clearly and repeatedly said that the numbers were illustrative only and didn't correlate with any particular lenses or sensors. They are however useful and realistic numbers in terms of demonstrating what happens when you change sensor resolution and look to see if there is any visible change in resolution between apertures.

I was quite careful to state all of that so I don't appreciate you constantly suggesting that I'm trying to be deceptive. There's nothing helpful about that attitude.

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

How is it bogus? I clearly explained that it shows the sharpness of the image relative to the peak for that sensor. Hence me saying:

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.

The aim was to show that relative sharpness decreases quicker for a high res sensor than a low res sensor, which shouldn't be remotely controversial because the resolution of an image from a low res sensor is dominated by the sensor's resolution, while the resolution of an image from a high res sensor is dominated by diffraction effects.

Both in relative and absolute terms, diffraction has a greater effect on higher resolution sensors.

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