# Could an optical waveguide improve the angular resolution of a telescope?

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?

• 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". Feb 24, 2023 at 2:41
• @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? Feb 24, 2023 at 3:57
• 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. Feb 24, 2023 at 4:00
• @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? Feb 24, 2023 at 4:38