Geometrical inversion for a scattering curve

Abstract

A space curve S may be determined from measurements of its perpendicular distance from a known space curve Sigma . Such data might be found experimentally using monostatic radar, and S might be the edge of a surface. A unique inversion is possible if Sigma is chosen to lie in the caustic C of S, and a supplementary measurement is made of the orientation of C at some point of Sigma . Explicit algebraic inversion formulae are given for S and its main differential geometric properties. The effect of caustic singularities is considered. Sources of non-uniqueness and ways to overcome them are discussed in detail.