Numerical Method of Profile Reconstruction for a Periodic Transmission Problem from Single-Sided Data (Communications in Computational Physics, 2018)
We are concerned with the profile reconstruction of a penetrable gratingfrom scattered waves measured above the periodic structure. The inverse problem isreformulated as an optimization problem, which consists of two parts: a linear severelyill-posed problem and a nonlinear well-posed problem. A Tikhonov regularizationmethod and a Landweber iteration strategy are applied to the objective function todeal with the ill-posedness and nonlinearity. We propose a self-consistent method torecover a potential function and an approximation of grating function in each iterativestep. Some details for numerical implementation are carefully discussed to reduce thecomputational efforts. Numerical examples for exact and noisy data are included toillustrate the effectiveness and the competitive behavior of the proposed method.