Null field approach to scalar diffraction II. Approximate methods

We develop from our generalized null field method a generalization of the Kirchhoff, or physical optics, approach to diffraction theory. Corresponding to each particular null field method there is a corresponding physical optics approximation, which becomes exact when one of the coordinates being used is constant over the surface of the scattering body. We show how to improve these approximations by a computational procedure which is more efficient than those introduced in the previous paper. The reradiations from our physical optics surface sources more nearly satisfy the extinction theorem the deeper they penetrate the interiors of scattering bodies. We find that we have to introduce a new definition of the parts of a body’s surface that are directly illuminated and shadowed, and we suggest that this may be more apposite in general than the usual definition. The computational examples presented herein indicate that useful approximations to surface source densities are obtained in the umbra and penumbra of bodies. These examples also show that our scattered fields are in several particulars superior to those obtained from the conventional Kirchhoff approach. It is important to choose that physical optics approximation most appropriate for the scattering body in question.