Power Spectral Density Specification and Analysis of Large Optical Surfaces

The 2-dimensional Power Spectral Density (PSD) can be used to characterize the mid- and the high-spatial frequency components of the surface height errors of an optical surface. We found it necessary to have a complete, easy-to-use approach for specifying and evaluating the PSD characteristics of large optical surfaces, an approach that allows one to specify the surface quality of a large optical surface based on simulated results using a PSD function and to evaluate the measured surface profile data of the same optic in comparison with those predicted by the simulations during the specification-derivation process. This paper provides a complete mathematical description of PSD error, and proposes a new approach in which a 2-dimentional (2D) PSD is converted into a 1-dimentional (1D) one by azimuthally averaging the 2D-PSD. The 1D-PSD calculated this way has the same unit and the same profile as the original PSD function, thus allows one to compare the two with each other directly.