A High{Order Perturbation Approach to Pro le Reconstruction. I: Perfectly Conducting Gratings

A new method for the reconstruction of two-dimensional periodic structures from scattered fareld data is presented. The approach is based on the recently developed \Methods of Variation of Boundaries" (MVB) for the solution of forward scattering problems. Here, the inverse problem is formulated as that of minimization of an appropriate nonlinear least-squares cost functional. The analytic continuation ideas inherent to MVB are then advanced to enable a global line search at each step of a proposed conjugate gradients algorithm. Through a number of numerical examples it is demonstrated that such globalization may be necessary to overcome the nonconvexity of the cost which, in turn, is shown to persist even when the global minimizer is known to be unique. Department of Mathematics, North Carolina State University, Raleigh, NC 27695{8205 School of Mathematics, University of Minnesota, Minneapolis, MN 55455 0