Joofa
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Senior Member
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Posts: 2,655

Re: Revisiting Diffraction with an Apodized "Iris"

hjulenissen wrote:

Joofa wrote:

Joofa wrote:

hjulenissen wrote:

Joofa wrote:

In this case it is just the Fourier transform of a (possibly truncated) Gaussian. No need to make it sound more complicated than it is.

So when the image processing people have found favorite kernels to use in their image (down) scaling applications, such as windowed sinc lanczos2/3 or more complex non-separable functions, could those results be used as a guide to the subjectively preferred trade-off between main-lobe width, spatial ringing?

I think Alan R.'s post touches a bit upon lines of main lobe / ringing suppression.

EDIT: Goodman has Figure 6.14 (2nd Edition) to illustrate the effect upon frequency range in the sense of side lobes.

BTW, HJulenissen, your post made me think about the more modern turn signal processing and EE are taking regarding sampling, signal representation, etc. that go far beyond the antiquated frequency spectrum based stuff such as transfer functions based upon frequency response, MTF, PSF, etc., and how Optics will fit in? Some of that is related to compressed sensing also, but not all of it. Outside of Quantum Optics, fundamental Optics (such as Fourier Optics) had traditionally been a derivative to developments in EE and signal processing. But, signal processing and EE have moved on. Optics needs to be upgraded somehow. But, I'm not sure how?

Are you thinking about stuff like encoded/scrambled aperture? ... In the not-so-distant (?) future when megapixels abound and optics are the weakest link in the chain, are there any creative possibilities?

I was specifically talking about Fourier Otpics. The word 'Fourier' over there means that we are dealing with sinusoids - theoretically infinitely long. With them comes notions such as MTF, the holy grail in optics - at least on this forum. MTF is usually narrowly defined as applicable only for sinusoids. A lot of this is due to historic incorporation of ideas regarding the transfer function theory in EE into optics. However, signal representation with high fidelity using sinusoids necessitates high bandwidths and high sampling rates. That is a problem.

Examples:

(1) A piecewise linear signal is not differentiable everywhere, is not bandlimited, and its Fourier transform decays slowly. However, the signal, on the other hand, is described completely by a sequence of signal values at the 'knots' - the points where transition happens. Typically that means is that signal can be described by a smaller rate than what Shannon sampling theorem or Nyquist rate would entail. That points out to other subspace of signal basis that are not sinusoidal as in Fourier analysis, but that when used, possibly in conjunction with sinusoids, could help in describing the essential information in a signal in much more optimized, lower sample rate. BTW, the preceding is the basics of compressed sensing. But, the idea is not restricted to just compressed sensing. In any case the meaning of 'MTF' that so far is only restricted to sinusoids would have to be re-interpreted.

This is just one example, among many, regarding modern direction that signal processing is taking. However, unfortunately, the optics experts on this forum are just blissfully happy with MTF on this forum, as being their bread and butter. Notice I said on this forum. Which brings us to our next example that how woefully inadequate MTF is in some basic practical problems of interest - interest to real photographers not just number crunching geeks.

(2) With all that hoopla surrounding MTF on this forum, and the celebrated status it is awarded in the optics community in general, it failed to answer a simple, practical question asked in the following link that which image is sharper visibly.

https://www.dpreview.com/forums/post/59926461

I'm sure that perhaps some fan of MTF here will come up with a Rube Goldberg Machine contraption to show how to accomplish the above-mentioned tasked in an automated, without human involvement, resolution independent mechanism, but that will be an exception that proves the rule. And, this example is just one of the simplest that can be asked for many practical tasks for which traditionally defined notion of MTF is just not sufficiently capable to provide answers.

(3) Many other examples not provided here.