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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

uhoh
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    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. – ProfRob Oct 28 '20 at 12:27
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    @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 – uhoh Oct 28 '20 at 12:45
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    Well yes, the PSF is something horrible like 20 arcseconds cross. That can't be down to the optics. – ProfRob Oct 28 '20 at 15:19
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    @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? – uhoh Mar 23 '21 at 10:15
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    @uhoh True, thanks for undoing it. Just a question: Do I understand you correctly that you are only after optical arguments? I find it a bit hard to distinguish e.g. all the factors: I mean e.g. for near-infrared, temperature is a major factor to decide between the two technologies. I assume it is easier to cool a mirror than a lens. – B--rian Mar 23 '21 at 10:24
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    @B--rian I have "(visible light)" in the title and "space telescope optics in visible light" in the body specifically to keep the scope narrow. One could include near IR and UV, cuts don't have to be exactly at 400 and 700 nm, but answers should be about this wavelength range. Also, cooling is not really about the optics per se. I'm primarily interested in spectral response, multiple reflections, scattered light, diffraction, small-angle scattering and haze from optical surface nano-roughness, chromatic effects... – uhoh Mar 23 '21 at 10:34
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    Thanks for (a) defining your wave-length range, and (b) for the general clarification. It is a bit clearer now, what parameters you are after. I guess you are well aware of https://en.wikipedia.org/wiki/Refracting_telescope#Technical_considerations - I did not consider the bubbles inside lenses a problem, or lense stability in general. – B--rian Mar 23 '21 at 10:43
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    @B--rian note that the question asks for the "Deciding optical factors..." not just catalogue list of all possible factors. In addition to TESS and LRO's laser altimeter telescopes mentioned in the question there's also JunoCam. (See Junocam: Juno’s Outreach Camera and How is JunoCam different from a normal CCD camera?) What were the deciding factors that led to a choice of lenses instead of mirrors in these case? – uhoh Mar 23 '21 at 10:50
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    Would a currated summary of https://skiesandscopes.com/refractor-vs-reflector/ adjusted to space-based telescopes answer your question? – B--rian Mar 25 '21 at 09:52
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    @B--rian I won't go read it but I doubt it. How many of the issues I outlined in the reply to your previous questions here are covered in an authoritative way? Space telescopes expose for long times; minutes to hours and the limiting magnitude is way way lower than looking through a telescope by eye under the Earth's atmosphere, which also has a serious astronomical seeing problem. Since I've asked about the optics of space telescopes, please stick to the optics of space telescopes! – uhoh Mar 25 '21 at 09:59
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    @B--rian any further thoughts? – uhoh Aug 20 '21 at 23:47
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    @uhoh I am busy with other stuff currently, I sadly do not have to much time for astronomy at the moment. – B--rian Aug 25 '21 at 15:11
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    @B--rian I wish you the best, I hope all comes out well. – uhoh Aug 25 '21 at 20:09
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    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 – Justin T Sep 12 '22 at 00:06
  • "A camera lens like TESS' can have many more optical surfaces than a reflecting telescope... that can be optimized for near diffraction-limited resolution" -- This is, I think, a bit confused. In general, fewer optical surfaces are better, because that reduces the opportunities for distortion-inducing errors and minimizes light loss due to absorption. And "diffraction-limited resolution" was not a goal for TESS. – Peter Erwin Sep 12 '22 at 10:31
  • @PeterErwin I do not think I am confused. I welcome an answer post citing factual supporting sources to show otherwise. The light loss of which you worry is really minimal. Modern, engineered multilayer antireflection coatings are engineering wonders with good ones having reflectivity well below 1% across the visible wavelength range. The problems to be concerned about is lens flare due to very bright objects nearby, but those are extended rather than point-like, predictable, and can be handled in processing if absolutely necessary. – uhoh Sep 12 '22 at 20:27
  • @PeterErwin I also maintain that more elements reduces, rather than increases distortion. Any decent, fixed focal length lens for an SLR advertises how numerous the number of elements are, not how few. For projection photolithography where distortion is an absolute killer/show stopper, lenses have well over a dozen elements and two dozen surfaces in order to minimize distortion https://i.stack.imgur.com/ygSZ7.jpg for cameras see https://www.google.com/search?q=nikon+lens+cut+in+half&tbm=isch I stand by my words as written. – uhoh Sep 12 '22 at 20:33
  • @uhoh And light losses due to absorption within the lens itself? In any case, "more optical surfaces = more optimization for diffraction-limited resolution" doesn't make any sense, I'm afraid. Every surface (and transmissive element) is an opportunity for potential errors from manufacturing errors. – Peter Erwin Sep 12 '22 at 20:39
  • @PeterErwin please support your concern with actual numbers and compare to multiple reflection losses in compound reflecting telescopes and associated obstruction losses from the secondary. You might convince me that "I'm confused" with hard numbers from supporting sources, but not with hand-waving prose. Once you work the problem through carefully and completely with all due diligence, I believe that what I wrote will make more sense to you. – uhoh Sep 12 '22 at 20:41
  • "Every surface (and transmissive element) is an opportunity for potential errors from manufacturing errors" and yet the advanced computer chips with a nanometer-level overlay distortion between multiple layer exposures over centimeters of chip area are achieved with lenses with the HIGHEST NUMBER of surfaces! Even DUV scanners (where no lenses are possible) have a dozen mirror surfaces. Optical reality is completely contrary to what you write. – uhoh Sep 12 '22 at 20:48

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