Are the profiles for reflecting/refracting spherical?

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swampwiz
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Are the profiles of the reflecting/refracting surfaces spherical for the bleeding-edge astronomical instruments?

I realize that because of the paraxial approximation, a "small angle" for a "ray" of light on spherical reflecting & refracting surfaces allows for a clean focus to take place. However, even a very small angle yields some spherical aberration, so I wonder that since astronomical instruments are always focused on infinity (or something so far that the error in presuming infinity is orders of magnitude less than an spherical aberration), the surfaces are tightly designed as a paraboloid - or at least all the surfaces are carefully designed to have the net effect of true focus that is not dependent on the spherical aberration to avoid blur.
 
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swampwiz said:
I see that is the type used for the Hubble. I wonder if the exact calculations of the original, correct design, the error, and the fix to the error are documented somewhere online. I'd be interested in taking at a look at that.
At a purely 'gossip' level, I seem to have read reports that the Hubble mirrors were based on an existing design for Earth surveillance applications. Is that a possibility? Or will you have to kill me once you have told me?