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Reading Yale News' Lighting a path to Planet Nine:

To detect objects that are otherwise undetectable, Rice and Laughlin employ a method called “shifting and stacking.” They “shift” images from a space telescope — like moving a camera while snapping photos — along pre-defined sets of potential orbital paths. Then they “stack” hundreds of these images together in a way that combines their faint light.

They used Transiting Exoplanet Survey Satellite (TESS) data presumably more for it's large number of exposures of a given field than each camera's 10 cm effective aperture.

Apart from mechanical and materials aspects such as (but not limited to) mass, thermal management and radiation and meteorite damage, what optical performance considerations would to into choosing between a refracting and a reflecting space telescope for a given diameter aperture?

A camera lens like TESS' can have many more optical surfaces than a reflecting telescope. The cross-sectional image of TESS' camera shows seven elements and therefore 14 surfaces that can be optimized for near diffraction-limited resolution over a wide field of view, whereas even the Vera C. Rubin Observatory (LSST) has only three reflecting and four refracting surfaces.

Refracting glass surfaces can also be smoother than aluminum on glass surfaces at the nanoscale, reducing haze and scattered light which can impact limiting magnitude especially if there are bright objects nearby.

Question: What are the deciding optical factors between a refractive and reflective space telescope optics in visible light as a function of aperture, apart from mechanical and materials aspects such as (but not limited to) mass, thermal management and radiation and meteorite damage?

Related:

From What causes these cross-shaped artifacts in TESS' first images? (the answer is interesting if you like CCDs)

TESS camera lens cross-section

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    $\begingroup$ But perhaps the optical factors aren't the deciding ones... I mean there's no chance of launching a 6.5m diameter lens. And the TESS image qiuality is awful. $\endgroup$
    – ProfRob
    Commented Oct 28, 2020 at 12:27
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    $\begingroup$ @RobJeffries ya but a practical answer without the exclusions I've put in place wouldn't be very illuminating :-) I didn't know that about TESS. Is it really the optics and not some sensor effect that's awful? Is it consistent with the optical design or is something not working as expected? I could ask a new question to that effect, but the only source I have is your comment. Would you mind if I started such a question with I've recently read that TESS image quality is not necessarily diffraction limited $\endgroup$
    – uhoh
    Commented Oct 28, 2020 at 12:45
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    $\begingroup$ Well yes, the PSF is something horrible like 20 arcseconds cross. That can't be down to the optics. $\endgroup$
    – ProfRob
    Commented Oct 28, 2020 at 15:19
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    $\begingroup$ @B--rian thanks but the question is about equipment that produces and records astronomical images, and not about any one particular system, so yes photography and no tess. Since you are good at tag usage guidance perhaps the tag definition could be updated to include space telescopes? $\endgroup$
    – uhoh
    Commented Mar 23, 2021 at 10:15
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    $\begingroup$ I don’t have a complete answer, as I am unsure why one would choose refracting over reflecting, but what I’ve always have been told is that it is much, much more difficult to make a large refracting telescope than a reflecting one; the comparative difficulty for making a sufficiently good lense vs making a sufficiently good mirror seems to be prohibitive for large apertures $\endgroup$
    – Justin T
    Commented Sep 12, 2022 at 0:06

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