Fourier optics analysis of scattering from an optically rough surface

The reflection of coherent laser light from an optically rough surface produces a complicated distribution known as a speckle field. Speckle fields are of fundamental theoretical theoretical interest. And speckle fields are of significant practical importance in both mechanical and industrial engineering. It is quite common for example that surface roughness properties of materials are monitored during manufacturing processes. Accordingly detailed theoretical scattering models and industrial metrology techniques have been developed over the years. Nevertheless, Fourier optics based analytical models can still provide useful insights into understanding this engineering problem: Measuring surface profiles. Here we examine the Fourier plane distribution of an optical field that is scattered from a rough surface. We describe the rough surface using a Fourier series expansion and identify properties such as the spatial frequency content and modulation depth and how they relate to industry measurement standards such as root mean square deviation of the surface height using analytical and numerical techniques. We summarize our results and make several conclusions.