A two-step algorithm for the reconstruction of perfectly reflecting periodic profiles

We consider the inverse problem of recovering a 2D periodic structure from near-field measurements above the structure. First, following Bruckner et al (2001 Preprint No 682 Weierstrass Institute, Berlin; 2003 Proc. 3rd ISAAC Congress (Berlin, 2001) at press), the inverse problem is reformulated as an optimization problem which consists of two parts: a linear severely ill-posed problem and a nonlinear well-posed one. Then, unlike the work of Bruckner et al, the two problems are solved separately to diminish the computational effort by exploiting their special properties. Numerical results for exact and noisy data demonstrate the practicability of the inversion algorithm