A study of rough surface scattering effects using the higher-order small slope approximation

Understanding scattering cross sections of randomly rough surfaces is critical for designing terrain and sea surface remote sensing systems. The classical physical optics (PO) and small perturbation methods (SPM) have been applied extensively, but have limitations. Recently developed scattering theories, such as the small slope approximation (SSA) (Voronovich, A. "Wave scattering from rough surfaces", Springer, 1994), attempt to overcome those classical limitations. Although the SSA is formulated as an infinite series, most previous studies examine only the lowest order term. This term, denoted /spl sigma//sup 00/, is second-order in surface "quasi-slope" (Broschat, S.L. and Thorsos, E.I., J. Acoust. Soc. Am., vol.101, p.2615-25, 1997). The second and third terms, /spl sigma//sup 01/ and /spl sigma//sup 11/, respectively, are third and fourth-order corrections in surface "quasi-slope". We present simplified forms for /spl sigma//sup 01/ and /spl sigma//sup 11/ for penetrable surfaces under the assumption of a Gaussian random process surface with an isotropic Gaussian correlation function. These surfaces are, admittedly, simple compared to many natural surfaces, but the Gaussian model is still commonly applied in many studies.