The surface PSD and image degradation due to mid-spatial-frequency errors

Abstract

In the design and specification of precision optical components for advanced imaging applications it is necessary that residual optical fabrication errors be specified and measured over the “entire range of relevant spatial frequencies”. This includes the mid-spatial-frequency surface errors that span the gap between the traditional “figure” and “finish” errors. Since surface scatter is merely a diffraction phenomenon, the linear systems formulation of non-paraxial scalar diffraction theory forms the basis of the GHS surface scatter theory: a linear systems formulation of surface scatter theory valid for smooth or rough surfaces, large or small incident and scattered angles and arbitrary surface PSDs. The resulting surface transfer function can be combined with the conventional OTF which then characterizes image degradation due to diffraction effects, geometrical aberrations, and surface scatter effects. The method of determining the composite surface PSD from the metrology data and the method of predicting the bidirectional scattered distribution function (BSDF) from the surface PSD will be discussed as will the process for deriving the optical fabrication tolerances necessary for satisfying specific image quality requirements.