Reduction of mid-spatial frequency errors on aspheric and freeform optics by circular-random path polishing

Pseudo-random paths are a useful tool to reduce mid-spatial frequency errors created in the processing of optical surfaces by sub-aperture polishing tools. Several types of patterns have been proposed, including hexagonal, square and circular, but prior literature has largely focused on flat and gently curved surfaces. Here, an extension of the circular-random path to strongly curved aspheric and freeform surfaces is proposed. The main feature of the algorithm is to cover the entire surface to be polished with a uniformly distributed tool path. Aspheric condenser lenses are then polished with a regular raster and circular-random path. Analysis of the optical performance shows that the random path can reduce the amplitude of mid-spatial frequency errors and relative intensity of satellite images. These features are particularly desirable in short wavelength applications, such as mirrors for EUV and X-ray.