VOLTERRA APPROXIMATION FOR LOW GRAZING ANGLE SHADOWING ON SMOOTH OCEAN-LIKE SURFACES

A new mathematical and numerical technique has been developed for calculating the electromagnetic current on smooth one-dimensional perfectly conducting surfaces for low grazing angles; the surfaces can have large vertical displacements compared with the incident wavelength, resulting in considerable shadowing. The new technique, which is based on approximating the usual Fredholm integral equation for the surface current by a Volterra equation, is highly accurate with the boundary conditions typically satisfied with errors of less than 1% for X-band (3 cm wavelength) at a 5-degree grazing angle.