Is it possible to 3D print a mirror to create a high quality telescope? Is it possible to 3D print a mirror with todays available materials?
If so, would there be a reduction in image quality?
 A: The answer is "Yes" but not the way you might expect. It is possible to construct a telescope mirror from rotating liquid metal.Mercury used to be used but something like Gallium is safer and better.
So print a cradle for it, put in the Gallium, raise the equipment past the melting point (about 30 degC), spin gently to get a parabolic surface, and then cool.
A: The highest resolution 3d printers I know of are around 1600dpi, which is a resolution of about 15$\mu m$. Telescope mirrors have to be smooth to fractions of a wavelength of light, so the resolution of current printers is nowhere near good enough.
Whether 3D printers could one day be good enough is a different question, but given that the improvement in resolution required is at least a factor of 1,000 I think it's not likely because 3D printers are designed to address quick manufacture rather than precision manufacture. In any case, making mirrors is a well established procedure. The difficulty is making them large, and it's not obvious how 3D printers would help with this.
A: Can't be done, yet.  But don't expect 3d printing to stand still, it's only recently been born, wait till it starts walking, and running! My hope was that there could be a vacuum process that was usable in just enough vacuum to form a perfect mirror shape over a perfect mirror mold of some kind, then start the vapor deposition on the cheap, lightweight material that was drawn into the perfect mirror mold.  Maybe you could make a lot of them before the mirror was harmed.  Maybe a cousin of mylar. Large cheap mirrors would do wonders for science and astronomy, and people.
