An efficient approach for computing the geometrical optics field reflected from a numerically specified surface

In the conventional geometrical optical analysis of smooth surfaces it is customary, to search for a specular point on the surface of the scatterer for each given combination of source and observation points. In many situations only a numerical description of the surface is available rather than an analytical expression which lends itself more readily to a determination of the specular point. The numerically prescribed form for the surface may be locally interpolated each time a specular point is to be calculated. An alternative approach is investigated that circumvents the step of deriving the specular point and obtains the scattered field in a more direct manner. Basically, the method begins by computing the reflected rays off the surface at the points where their coordinates, as well as the partial derivatives (or equivalently, the direction of the normal), are numerically specified. Next, a cluster of three adjacent rays are chosen to define a "mean ray" and the divergence factor associated with this mean ray. Finally, the amplitude, phase, and vector direction of the reflected field at a given observation point are derived by associating this point with the nearest mean ray and determining its position relative to such a ray.