The whole question of lens sharpness...
Well, you obviously have some expertise, which is why I found it so confusing that some terms and examples I was using seemed unfamiliar to you.
I was unaware of anything in this discussion, to date, which seemed unfamiliar to me, with the exception of the specific theorems about the heat equation. There were instances where I found your language ambiguous, either by the standard ambiguity that happens on forums, or because a term meant something different based on discipline you were coming from. In that case, I asked for a clarification. In some cases, you used somewhat strange (but clear) language. In the example below, "with increasing wavenumber" instead of "at higher frequencies."
Aside from this, can you point to a specific example?
I was looking for some common "language" in which we could communicate.
What's fun about Fourier analysis is that there's at least a half-dozen disciplines which touch on it, each with slightly different language. E.g.:
- Signals and systems (DSP, controls, analog design, image processing, etc.)
- Mathematics (functional analysis)
- Physics (waves, quantum)
And a few others...
You are missing information. That's inevitable. With increasing wavenumber your signal to noise is decreasing, conditional entropy is increasing, hence you are receiving progressively less actual information. (There, that's one of my information entropy arguments).
I'll omit responding point-by-point, since I think this strikes at the heart of our miscommunication:
- Your claim is that, with lens blur, SNR is decreased at higher frequencies, and this can never be improved. This is correct.
- My claim is that the blur can be repaired (without improving SNR at high frequencies), in a typical photographic system, etc.
I think we're mostly just arguing semantics. This is probably the key difference (although we've found a few others).
Your statement is relevant for high-ISO, and mine for low-ISO.
You were about to get to how entropy fit in.... I'm still waiting. So far, the best I've gotten is to use it as a fancy word to mean 'time.'
There was the heat equation example, which you don't seem to follow/acept.
And which didn't hinge on entropy, as far as I could tell.
And one more, but this is already getting too long, so it'll have to wait for later.
I'm looking forward to it At that point, I might also give the argument about why limited DOF and diffraction shouldn't be consider as being caused by the lens.