Effect of Mid- and High-Spatial Frequencies on Optical Performance

In recent years there have been many optical system designs requiring high optical quality (sharp point spread function) as well as low scatter performance on aspheric surfaces. Because of the fabrication differences between the processes of figuring and smoothing on aspheric surfaces, it is important that the optical engineer understand how to trade off these processes during the manufacturing cycle. To describe these processes, the residual wavefront error (departure from the Gaussian reference sphere) is evaluated over a very wide spatial frequency band. From a physical point of view, the spatial frequencies of interest are grouped into three general categories: (1) the classical aberrations, which are low frequency in character and describe what might be called the figuring errors; (2) surface ripple or residual tooling errors, which arise in the fabrication of the optical elements; and (3) microroughness, the very high frequency structure on the surface, generally responsible for surface scattering. In this paper, the methods pioneered by Hopkins for aberration tolerancing and Barakat for random wavefront errors are extended to the discussion of mid- and high-spatial frequency surface errors. Some examples will be given to illustrate some general system properties such as the nature and role of the surface autocorrelation function.