Understanding Surface Scatter Phenomena: A Linear Systems Formulation deals with surface scatter phenomena that continue to be an important issue in diverse areas of science and engineering in the 21st century. Scattering effects from microtopographic surface roughness are merely non-paraxial diffraction phenomena. After reviewing the historical background of surface scatter theory, this book describes how integrating sound radiometric principles with scalar diffraction theory results in the development of a linear systems formulation of non-paraxial scalar diffraction theory which then becomes the basis of the Generalized Harvey-Shack (GHS) surface scatter theory characterized by a two-parameter family of surface transfer functions. This GHS surface scatter theory produces accurate results for rougher surfaces than the classical Rayleigh-Rice theory and (due to a more general obliquity factor) for larger incident and scattered angles than either the Beckmann-Kirchhoff or Rayleigh-Rice theories. The transfer function characterization of scattering surfaces can be readily incorporated into the traditional linear systems formulation of image formation, thus allowing a systems engineering analysis of image quality as degraded by diffraction effects, geometrical aberrations, surface scatter effects, and a variety of other miscellaneous error sources. This allows us to derive the optical fabrication tolerances necessary to satisfy a specific image quality requirement, which further enables the integration of optical fabrication and metrology into the optical design process.