Paraboloidal mirror surfaces transform plane wavefronts into spherical ones and vice versa. This allows us to perform an
interferometric measurement of its shape without the need of compensating optics or a CGH. From measurement's point
of view there are good preconditions to manufacture high accuracy paraboloidal surfaces.
On the other hand machining has to deal with the aspherical deviation to the best-fitting sphere. Depending on the
amount of this deviation and the material of the mirror, different machining technologies are applied to bring the surface
into paraboloidal shape. Off-axis paraboloids provide even more challenges in machining. There are two accepted
approaches for manufacturing off-axis precision paraboloids. One way is to figure and polish a rotationally symmetric
part with subsequent separating the off-axis elements from the parent paraboloid. On the other hand you can machine the
single parts right from the start. In this case the surface is a kind of freeform.
In this paper we discuss the manufacturing of on-axis and off-axis paraboloidal mirrors applying various methods.