On deducing the form of surfaces from their diffracted echoes

Abstract

Kirchhoff diffraction theory is set up for the echo received back at the source when a spherical outgoing pulse of radiation is reflected from a rough surface. The formulation derived here permits a clear separation between those features of the echo that depend only on the form of the incident pulse, and those involving only the properties of the surface. The surface function depends on the contours of constant distance from the source which can be drawn in the surface; these are the appropriate analogues of Fresnel zone boundaries. Geometrical optics gives the singularities and discontinuities of the surface function. The problem of determining the surface function from echo data which are incomplete in the sense that they do not contain all radiation frequencies is discussed. For the special case of one dimensional roughness, the problem of how far the surface function can be deconvoluted to obtain the shape of the surface is considered.