Is it possible to 3D print a mirror with todays available materials?
If so, would there be a reduction in image quality?
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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.
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.
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.
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