The extraordinary precision (under 0.1 microns) is only possible because the surface is close to a sphere; when grinding two surfaces together uniformly in all

The extraordinary precision (under 0.1 microns) is only possible because the surface is close to a sphere; when grinding two surfaces together uniformly in all directions, the result tends towards a sphere (or a flat shape, which is a sphere of infinite radius). If you had to make an arbitrary shape, things would be very different. If there's a bump (a hill) on the surface, it tends to grind out more quickly than the rest because it's jutting out and it's more exposed to pressure from the grit. If there's a hole, it remains untouched while the surface around it is being ground down. This way everything tends towards the ideal shape. By carefully doing a uniform rotation of the pieces during grinding, the resulting shape is symmetrical - spherical or flat. Other shapes are also used in mirrors (revolution surfaces generated by a parabola, hyperbola or ellipse), but they are all basically just small corrections to a sphere (which is a revolution surface generated by a circle). You start with very rough grit to go faster in the beginning and remove most material. Then you just use finer and finer grit as the surface becomes more and more smooth. In the final stages you switch to polishing. It's a different process where the tool is not hard (glass) but soft (pitch), and the grit is replaced with microscopic powders (such as iron oxide or cerium oxide) which work not only through physical mechanisms but also via surface chemistry. Also during polishing you use testing procedures which can show surface errors as small as 0.02 microns. The testing process is steering your polishing techniques; you apply corrections, or choose different polishing strokes to deal with various surface errors. Whereas grinding is mostly automatic (with a few basic checks here and there), during polishing your brain is in the loop, a lot.