The present paper gives a new formulation for rough surface scattering in terms of a stochastic integral equation which can be dealt with by means of stochastic functional approach. The random surface is assumed to be infinite and a homogeneous Gaussian random process. The random wave field is represented in the stochastic Floquet form due to the homogeneity of the surface, and in the non-Rayleigh form consisting of both upward and downward going scattered waves, as well as in the extended Voronovich form based on the consideration of the level-shift invariance. The stochastic integral equations of the first and the second kind are derived for the unknown surface source function which is a functional of the derivative or the increment of the surface profile function. It is also shown that the inhomogeneous term of the stochastic integral equation of the second kind automatically gives the solution of the Kirchhoff approximation for infinite surface.

A generalized surface scattering radar equation for a near-nadir-looking pencil beam radar, which covers both beam-limited and pulse-limited regions, is derived. This equation is a generalization of the commonly used nadir-pointing beam-limited radar equation taking both antenna beam and pulse wave form weighting functions into account, and is convenient for the calculation of radar received power and scattering cross-section of the surface.

A method is presented for reconstructing the surface profile of a perfectly conducting rough surface boundary from the measurements of the scattered far-field. The proposed inversion algorithm is based on the use of the Kirchhoff approximation and in order to determine the surface profile, the Fletcher-Powell optimization procedure is applied. A number of numerical results illustrating the method are presented.

The behavior of TM-wave scattering from a dielectric-loaded semicircular trough in a conducting half-space is investigated. The dielectric loading is made of a circular cylinder which lies in a semi-circular trough in the perfectly conducting plane. The formulation is numerically evaluated to investigate the scattered field pattern for various dielectric loading conditions. It is found that the scattering patterns exhibit the resonant behavior due to both of the concave surface contour and the dielectric loading.