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No, even without an atmosphere you have to contend with the diffraction-limited resolving power through an aperture (pupil), which is related to the diameter of the aperture and the wavelength of light.

A diffraction process is, mathematically, a fourier transform. A fundamental mathematical feature of a fourier transform is what's known as the uncertainty principle.

Side note: you've probably heard of the special case of an uncertainty principle encountered in quantum mechanics frequently misattributed to the head of the Nazi nuclear program (Heisenberg), but this mathematical principle was actually well known for centuries beforehand, and the misattribution is mostly because of Nazi propaganda. We see it anywhere a fourier transform is used, from optics to orbital dynamics to quantum particles. This mathematical phenomenon is frequently miscited as quantum "weirdness" even though there's nothing quantum (or all that weird) about it.

The pupil restricts the possible positions of incoming photons. A restriction in position increases the variance of momenta (for a photon, speed never changes, but the momentum vector can still change direction). A smaller pupil is more restrictive and causes the image to be blurrier as the incoming photons from each object you are trying to resolve. If you want to be able to resolve smaller angular sizes (small objects at large distances), you need a large aperture that reduces position restrictions on incoming photons and therefore diffraction-induced blurring due to momentum uncertainties.

Look up Airy diffraction for the special case of a circular aperture (e.g. a pupil or telescope).

this post was submitted on 09 Sep 2024
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