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I have recently learned about the diffraction limit of telescopes that limit their angular resolution. This YouTube video, "Resolving Power of a Telescope" also provides some good background. I am thinking of this question in terms of the visible spectrum, but thoughts/comments on other frequencies would be helpful in understanding too.

My basic understanding of diffraction is that when a portion of the wave is blocked, the remaining portion of the wave expands into this void. This effect can be reduced by using a waveguide. Essentially a reflective surface that prevents the wave from expanding in unintended directions.

As an engineer that knows just enough physics to be dangerous, I was thinking, could this be applied after the primary objective lens in a telescope to reduce the effects of diffraction? See my rough diagram below. I realize that this would induce other potentially worse issues by picking up off-angle images; but just for the sake of understanding, would this conical waveguide reduce the diffraction impact on the angular resolution of the image?

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ericnutsch
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    The diffraction limit is limited by the largest phase coherent receiving area, here it is the area of the front lens. The diffraction limited resolution is equivalent to the reciprocal of the corresponding antenna directivity. It does not matter what you do after the front lens, the smallest separable point sources in direction space is already lower bounded by the front area, something like $\propto \frac {\lambda^2}{4\pi A}$, that is the "beamwidth". – hyportnex Feb 24 '23 at 02:41
  • @hyportnex, I sure you are correct, but I can't make my brain negotiate this with how I understand diffraction occurring after the slit/lens. Are there other ways of understanding this at-the-lens diameter limitation? Optical interferometric arrays seem to get around this fundamental problem by separating the telescopes by a distance (yet another principle to negotiate in my brain). Perhaps I am drifting off course, but maybe both of these can be looked at in more abstract/fundamentally in terms of data or physical object/distance/wavelength/detector geometry? – ericnutsch Feb 24 '23 at 03:57
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    This may help - Why does light travel in a straight line if the uncertainty principle is true?. There are several good answers, but I think my answer may best fit your question. – mmesser314 Feb 24 '23 at 04:00
  • @mmesser314, Thanks! I read through your answer and others. The thing I can't reconcile in my brain is that, there is no diffraction inside of a wave-guide. Dumbing it down to my level with water; the reflecting walls of a canal apply a back pressure that confines the wave and prevents diffraction at the walls and internally. Light while not exactly the same, fits the analogy well. On that same note, maybe this problem could be dumbed down to detecting two swimmers a certain distance apart across a lake? Would the same angle resolution equation apply? – ericnutsch Feb 24 '23 at 04:38

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A "waveguide" is a homogeneous structure that has its own modes of propagation. As long as the modes do not meet a discontinuity in the waveguide they do not diffract from their being normal modes. Huygens' principle holds all the way through so that the elementary wavelets of the wavefront of the mode whose sum is the mode always add up to be the normal mode until a discontinuity is met at which point they "diffract" and distort the mode.

Free space is also a waveguide whose own modes, those that have all its sources and sinks, the singularities, are at infinity, are the TEM plane waves. Huygens' principle is a superposition principle by which we decompose the TEM modes having singularities at infinity now to be represented as a sum (integral) in which the singularities (sources) are placed here on the wavefront.

The first discontinuity we are speaking of is the front rim of the the cylinder holding the lens at which they diffract. Those diffracted waves are "lost" for anything you can do within the cylinder, they are not in the telescope because they diffracted at the rim to the outside in every possible direction.

Now you may ask if those diffracted wavelets on the outside could be collected and thereby improving the resolution of your telescope. I believe some can be collected but then all you are doing is increasing the effective phase coherent receiving area. But ultimately you will always collect with a finite size that itself will act as the limit to your "diffraction limit".

There are also wavelets that diffract off the rim internally towards the lens but to collect them separately you have to induce more diffracting objects inside and those will also cause diffraction, etc.,

In short, you cannot receive and infinite size wave with a finite size instrument without causing a reconstruction error. This answer is related to your question.

hyportnex
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