Scalar wave solution for the scattering of a partially coherent beam from a statistically rough metallic surface

The scattering of a spatially partially coherent wave from a one-dimensional statistically rough metallic surface is investigated. Assuming a Gaussian Schell-model form for the incident field autocorrelation function, a closedform expression for the scattered field autocorrelation function is derived using the physical optics approximation (Kirchhoff approximation). Two forms of the solution are derived - one applicable to very rough surfaces and the other applicable to moderately rough surfaces. It is shown that for very rough surfaces, the solution, under certain circumstances, remains Gaussian Schell model as has been previously reported. As such, closed-form expressions for the angular coherence radius and angular scattering radius are derived. These expressions are, in general, complicated functions of both the source (size and coherence properties) and surface parameters (surface height standard deviation and correlation length). It is demonstrated that for many scenarios of interest, the angular coherence radius can be safely approximated as a function of just the source parameters and the angular scattering radius can be simplified to a function of just the surface parameters. For the moderately rough surface solution, the scattered field autocorrelation function is, in general, not Gaussian Schell model and it is therefore not possible to derive analytical forms for the angular coherence radius or angular scattering radius. Nonetheless, the form of the autocorrelation function is physically intuitive and is discussed in this work. To verify the presented theoretical analysis, wave optics simulation results are presented and compared to the predictions of the analytical models. This analysis is concluded with a discussion of future work.