A. K. Fung

Coherent scattering of a spherical wave from an irregular surface

The scattering of a spherical wave from a rough surface using the Kirchhoff approximation is considered. An expression representing the measured coherent scattering coefficient is derived. It is shown that the sphericity of the wavefront and the antenna pattern can become an important factor in the interpretation of ground-based measurements. The condition under which the coherent scattering-coefficient expression reduces to that corresponding to a plane wave incidence is given. The condition under which the result reduces to the standard image solution is also derived. In general, the consideration of antenna pattern and sphericity is unimportant unless the surface-height standard deviation is small, i.e., unless the coherent scattering component is significant. An application of the derived coherent backscattering coefficient together with the existing incoherent scattering coefficient to interpret measurements from concrete and asphalt surfaces is shown.

Backscattering of waves by composite rough surfaces

A general theory of electromagnetic wave scattering is developed using the Stratton-Chu integral as modified by Silver for a gently undulating homogeneous surface on top of which small irregularities are superimposed. It is assumed that the tangent-plane approximation is applicable to the undulating surface so that the local fields can be evaluated by considering a slightly perturbed plane surface. Average powers, both polarized and depolarized, are calculated for the composite surface whose statistical properties are assumed known. Shadowing effects are also included before comparing with experimental results. The comparison between the moon data and the data obtained under laboratory conditions shows very good agreement. The same surface parameters are used for both the polarized and the depolarized returns. Previous theories cannot provide a connection between the parameters used in the polarized return expression and those in the corresponding depolarized expression since only a single-surface model was considered. The results indicate that polarized returns of near vertical incidence are dominated by the large-scale roughnesses, while the depolarized returns are affected by both the large and small roughnesses. As the incident angle increases, the effect of small irregularities becomes increasingly important for both the polarized and the depolarized returns. The cause of depolarization and diffuse scattering, as shown in this theory, is the perturbation of the fields on the surface by the small irregularities.

Multiple scattering and depolarization by a randomly rough Kirchhoff surface

A matrix approach has been developed to compute bistatic scattering coefficients which include shadowing and multiple scattering effects for a randomly rough Kirchhoff surface. The method permits the computation of these coefficients in terms of the existing single-scatter bistatic scattering coefficients. Thus the effects of multiple scattering are readily recognized from the expressions obtained. The bistatic scattering coefficients are shown to satisfy energy conservation to at least two significant figures. It is observed that while polarized backscattering is dominated by the single-scattering process, the depolarized backscattering is due to multiple scattering. Unlike depolarization by slightly rough surfaces or volume scattering, the angular behavior of the depolarized backscattering is similar to that of the polarized backscattering. The transitional behavior of the relative dominance between single and multiple scattering for the polarized and depolarized scattering coefficient as a function of the azimuth angle is illustrated.

A theory of wave scattering from an inhomogeneous layer with an irregular interface

Bistatic wave scattering from a layer of Rayleigh scatterers with an irregular interface is investigated by combining the doubling method in volume scattering with the Kirchhoff method in rough surface scattering. Theoretical results are shown illustrating the effect of the rough interface. It is found that for scattered and incident angles near the vertical, the rough interface causes a substantial increase relative to the plane interface in both the like and cross-scattering coefficients over all azimuth angles. However, for large scattered and incident angles, the reverse is true except for azimuth angles around the specular direction. It is interesting to note that while one dominant peak of the like polarized scattering coefficient occurs along the specular direction, two dominant peaks of the cross-polarized scattering coefficient may appear symmetrically with respect to the specular direction. In backscattering, the surface roughness causes a peak to appear in both the like and cross-scattering coefficients at near vertical incidence and also a decrease of these coefficients at large incidence angles.