Linear and quadratic inverse scattering for angularly varying circular cylinders

We discuss the problem of determining the class of dielectric profile funct ions that can be reconstructed from scattered electrical field data dependi ng on the model to be inverted. We focus our attention on a cylindrical obj ect with a circular cross section whose permittivity varies only along the angular coordinate. First we examine the linear Born approximation of the r elationship between the permittivity function and the field scattered by th e cylinder. We provide an analytical answer to this problem by singular-val ue decomposition of the relevant operator. We find that only slowly varying profiles can be recovered, both in the single-view and in the multiview ca se. Next we examine a quadratic approximation of the same relationship, whi ch consists in adding a second-order term to the linear term. The effect of changing the model on the class of unknown functions that can be reconstru cted is shown by means of both analytical arguments and numerical simulatio ns. The result is that now the model includes more rapidly varying profiles . (C) 1999 Optical Society of America [S0740-3232(99)00812-1].