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That's not right about the Hubble repairs,,,They figured it to the accuracy they wanted according to the gizmo used - the problem was an error in producing the gizmo. An incorrectly sized or installed spacer. My recollection is that sizing was the problem. Confusion when the design was moved to actual manufacture. They corrected Hubble eventually by adding something similar to a schmidt camera corrector plate but designed for that specific job. It worked because the main mirror was incredibly accurately out which allowed them to design it to suite.
A parabola is nothing remotely like a sphere and with shorter and shorter focal lengths and increasing diameters the differences get even larger.
There are also various designs of cassegrain type telescopes that use curvatures other than parabolic. This one for instance
Lenses and more mirrors might get added. Null testing is still done the same way - optics in the test kit added to cause it to null when tested just as a spherical mirror does but only for images at it's centre of curvature. At all other distances spherical aberration is added. The curves correct that, This is for the main mirror. There are various ideas on dealing with the others. Other abberations can also be minimised by use of certain curves eg the RC design, Coma is a particular problem.Ritchey–Chrétien telescope - Wikipedia
en.wikipedia.org
The Web is actually a 4 mirror off axis system. All mirror means no chromatic aberration problems. One it seems is flat.
The paper on that page gives more explanations,
I think we all know a parabola and a sphere are different - no idea why you bother to type stuff like that in every post.
You say there are 4 mirrors - well this is one of the more "coo" illustrations: