Coherent Spatially Varying Bidirectional Scattering Distribution Function of Rough Surface

High-resolution synthetic aperture radar (SAR) as an imaging device becomes more and more like a “camera” at the microwave frequency band. How different objects or object surfaces may visually appear in SAR images becomes an interesting research topic. Inspired by the bidirectional reflectance distribution function (BRDF) models employed in computer graphics (CGs), this article proposes the coherent spatially varying bidirectional scattering distribution function (CSVBSDF) for characterizing the electromagnetic scattering and SAR imaging behavior of surfaces. The CSVBSDF establishes a mapping function from observation parameters and surface local parameters to multidimensional measurements. In this article, CSVBSDF of the randomly rough surface is derived via adapting the integral equation method (IEM) to finite-size pixel cells under the plane wave and tapered wave incidence, respectively. It is then validated against the numerical beam simulation method (BSM) in the SAR image domain. A ground-based rail SAR and a 3-D laser scanner are used to measure the SAR image and the corresponding 3-D geometry of a real ground surface. Surface-local parameters, such as the local slope and roughness, are estimated from the measured 3-D geometry and then fed into the CSVBSDF model to produce a synthetic SAR image. Comparison against the real SAR image preliminarily demonstrates the efficacy of the proposed CSVBSDF model.