Third-order small-perturbation method for scattering from dielectric rough surfaces

The small-perturbation method (SPM) for rough surface scattering, originally derived by Rice [Commun. Pure Appl. Math.4, 361 (1951)], has been applied extensively to problems in optics, remote sensing, and propagation. Typical uses of the theory involve only the first- or second-order scattered fields in surface height, owing to increasing complexity of the SPM equations as order increases. The SPM equations are solved in a systematic manner that permits third order in surface-height terms to be determined apparently for the first time for scattering from a dielectric surface rough in two directions. Sample results for both periodic and nonperiodic surfaces show that third-order field terms can contribute to fourth-order scattered power and also to a third-order specular-reflection coefficient correction for surfaces with nonvanishing bispectra. The latter case is of particular interest in passive remote sensing of the ocean, since these third-order terms contribute to the first prediction of a first azimuthal harmonic of ocean brightness temperatures.