# The whole question of lens sharpness...

Started Jun 12, 2013 | Discussions thread
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 Re: The whole question of lens sharpness... In reply to olliess, Jun 21, 2013

olliess wrote:

Alphoid wrote:

olliess wrote:

but it is difficult to see how they would apply.

Compare the heat/diffusion kernel to the (model) blur function of a lens.

I don't think those laws say what you think they say. You're using (or occasionally inventing) big words without understanding them.

Look at how a 2-d heat kernel describes the spreading (by heat- or Fickian diffusion) of a point source. Now compare this to the blur kernel (PSF) of a lens.

If you're still not understanding how these are related, then you probably shouldn't go around accusing people of inventing big words.

It's obvious how they're related. They're also not identical. It's a poor way to model the system, and would give bad intuition, and in many cases give incorrect results. There's a difference between math looking kind-of-similar and being identical. The reason I gave a counterexample was so that you could discover how and why they differ for yourself. You have a misconception (several actually), and demonstrating to someone that they have cognitive dissonance is a good forcing function for helping overcome misconceptions.

The more key thing you're missing is what you're missing is what entropy is, how it works, and how and why it is unrelated. I'd encourage you to try to actual write down (in math, not in big words) why you think entropy applies. You'll quickly run into a contradiction. Here, I was trying to drive you to make concrete statements, so I could also force a contradiction. You've been unwilling to do that.

The only bandwidth limit is the Nyquist frequency of your sensor. Limited image extent doesn't matter.

Convolving an image with a PSF means, at least in theory:

1) in the frequency domain, some of the spectrum gets spread beyond the Nyquist limit

This is incorrect.

2) in the spatial domain, some of the image gets spread beyond the edge of the frame

This is correct, but not significant. The PSF is small. This would only matter if the PSF was a substantial portion of the image.

You're trying to improve lens sharpness, not increase DOF.

What you originally said was:

In theory, given a perfect model of the lens, I can completely undo any blur caused by the lens

So are you now saying you are just trying to "unblur" in the plane of focus, and just accept any side effect for all other distances? (For example, if the PSF of the lens has a different shape at other focal distances, you are now inverting for the wrong PSF everywhere else in the image.)

Your goal is to have an image as would come back from an ideal lens. An ideal lens would have a perfectly sharp focal plane, but would still have limited DOF. For any sane optical design, any OOF areas will have a stronger low-pass filter at all frequencies than the areas in the focal plane. Hence, the side-effects at all other distances will not be significant or detrimental (slightly different bokeh).

Noise gets amplified -- I mentioned that -- but it doesn't limit your ability to invert. It's a linear process.

Once you have noise in the problem then it is no longer a linear problem, right?

Incorrect. H(S) is the PSF of the lens. G(S) is the inverse of the PSF. Both are linear. Your input is:

H(image)+noise