Abstract

The inverse problem is particularly important for device and application development. For non-periodic media, approximations can be made which allow estimates of the scattering permittivity distribution to be found. Our own work over the last 15 years [1,2,3] has moved from trying to interpret the most restrictive yet computationally simple of these approximations, the linearizing first Born and Rytov approximations, to the development of techniques which can be applied to both strongly scattering media as well as nonlinear (e.g. χ³) structures. We have also applied these methods to real experimental data as well as simulated cases, as such work has wide ranging uses in fields as diverse as medical and geophyiscal imaging, as well as the design of optical components. Emerging from these studies is a clearer understanding as to how the differential cepstral method (see paper by Morris et al in this volume and [4]) and distorted wave methods can be integrated in order to synthesize structures which are both strongly scattering and which have prescribed optically controllable scattering patterns. The differential cepstral filtering technique processes the function recovered by Fourier inversion of far-field scattering data, recognizing that it represents the product of the permittivity distribution and the total field within the scattering volume. This filtering method can be applied to scattering structures of arbitrarily high permittivity, in principle.

© 1995 Optical Society of America