A Unified Bidirectional Scattering Distribution Function for Convex Quadric Surface

Quadric surfaces are commonly seen geometries in man-made targets. In this article, a unified bidirectional scattering distribution function (BSDF) is analytically derived for general convex quadric surfaces including both the doubly and the singly curved surfaces. Based on physical optics (PO) and stationary phase method (SPM), the BSDFs of the doubly and singly curved surfaces are first deduced separately. Then, the unified form of the two BSDFs is formulated, which can smoothly degenerate to any specific type of canonical curved surfaces by taking the corresponding values of the geometric parameters. Comparison with numerical PO demonstrates the correctness and efficacy of the proposed model. This model can be used to continuously model the bistatic polarimetric scattering behavior of a localized quadric surface patch. It can be used as the prototype for a scattering dictionary for both forward and inverse problems of electromagnetic scattering, which is of great value to radar target recognition and radar image interpretation.