Scattering of scalar plane waves from two-dimensional rough surfaces

In a recent paper by Maradudin et al. [1] a method was described for designing a two-dimensional, randomly rough, circularly symmetric, Dirichlet surface, that, when illuminated at normal incidence by a scalar plane wave, produces a prescribed circularly symmetric distribution of the intensity of the scattered light. This method was validated by computer simulation scattering calculations based on the Kirchhoff approximation, also a single-scattering approximation, for the case where the surface acts as a Lambertian diffuser, i.e. produces a distribution of scattered intensity that is proportional to the cosine of the polar scattering angle. This research project involves the development of efficient computational algorithms and methodologies for scattering of scalar plane waves from two-dimensional, rough, circularly symmetric, Dirichlet surfaces. It is based on Green\u27s second integral identity, and exploits the circular symmetry of the surface. Computational algorithms were developed, for application to a wide range of scalar plane wave scattering from two-dimensional rough surfaces, and were tested on specific problems. The rigorous approach and novel algorithms developed facilitated the design of numerous two-dimensional surfaces that scatter light with a prescribed distribution of intensity when illuminated both at normal and non-normal incidence. The applications that follow are numerous, including optical diffusers, atmospheric detectors, radiometers, etc