Experimental power spectral density analysis for mid- to high-spatial frequency surface error control

The control of surface errors as a function of spatial frequency is critical during the fabrication of modern optical systems. A large-scale surface figure error is controlled by a guided removal process, such as computer-controlled optical surfacing. Smaller-scale surface errors are controlled by polishing process parameters. Surface errors of only a few millimeters may degrade the performance of an optical system, causing background noise from scattered light and reducing imaging contrast for large optical systems. Conventionally, the microsurface roughness is often given by the root mean square at a high spatial frequency range, with errors within a 0.5×0.5  mm local surface map with 500×500 pixels. This surface specification is not adequate to fully describe the characteristics for advanced optical systems. The process for controlling and minimizing mid- to high-spatial frequency surface errors with periods of up to ∼2-3  mm was investigated for many optical fabrication conditions using the measured surface power spectral density (PSD) of a finished Zerodur optical surface. Then, the surface PSD was systematically related to various fabrication process parameters, such as the grinding methods, polishing interface materials, and polishing compounds. The retraceable experimental polishing conditions and processes used to produce an optimal optical surface PSD are presented.