An Analytical Formulation for the Correlation of Surface-Scattered Fields at Two Bistatic Radar Receivers

We present an analytical formulation of the correlation of the electromagnetic fields scattered by a rough or gently undulating surface and measured at two spatially separated points. The latter may be the positions of two different bistatic radar sensors receiving the scattered field at the same time, as in bistatic synthetic aperture radar interferometry, or two positions occupied by a single moving receiver at two slightly different times, as in Global Navigation Satellite System Reflectometry. The scattering surface is modeled as randomly rough, and the Kirchhoff Approximation is employed to compute the scattered field. The obtained closed-form expression of the field correlation is substantially coincident with the one already available in literature for far-from-specular scattering directions; conversely, for close-to-specular directions, the obtained formulation shows that, as the surface correlation length increases, the degree of coherence smoothly increases from the value obtained with the expression available in literature for rough surfaces to a value close to unity for very gently undulating surfaces.