The generalized lommel-seelinger cross section of a foliage environment

In the upper microwave frequency range, the size of leaves is often larger than the operating wavelength. Hence, the scattering from foliage can be studied by approximating the individual leaf as a plane sheet of uniform thickness, random orientation, and arbitrary shape with the same electrical parameters as the leaf itself. The scattering cross section of a foliage environment (i.e., a volume distribution of randomly distributed leaves) can be found from the generalized Lommel-Seelinger bistatic cross section (GLSBS cross section) of the above leaf model. The GLSBS cross section is given here in an integral representation which takes into account the various polarization states of incident and scattered fields, the scattering geometry, the probability distribution of the leaf orientation, and the effect of both singly and doubly scattered radiation. As a part of the formulation, a convenient expression for the "optical depth" (or penetration depth) of the leaf medium is obtained. Numerical results, based on typical leaf parameters are obtained for the back scattering cross section, and show fairly good agreement with measured cross sections of green and desiccated soybeans at frequencies of 2 GHz, 10 GHz, and 35 GHz.