Inverse Wave Propagator

In a recent publication, Wolf and Shewell gave a formal solution to the inverse diffraction problem, i.e., to finding the field distribution in the plane z = 0 from the knowledge of the field in an arbitrary plane z = z1 > 0 in the half-space into which the field is propagated. The solution involved the use of a singular kernel. In the present paper the inverse diffraction problem is treated in a rigorous manner. Our method makes use of the representation of the field as an angular spectrum of plane waves and demonstrates the usefulness of this type of representation. It is shown that by the use of a suitable truncation procedure one may avoid the use of a singular kernel or the generalized function theory.