Domain Derivatives in Dielectric Rough Surface Scattering
Interim rept. 1 Nov 2012-30 Sep 2014
AIR FORCE RESEARCH LAB WRIGHT-PATTERSON AFB OH SENSORS DIR
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The inverse scattering solution of shape reconstruction is often posed as a problem in nonlinear minimization of an objective function with respect to N number of unknown model parameters characterizing the scatterer. The minimization procedures are usually iterative, and require the gradient of the objective function in the unknown model parameter vector at each stage of iteration. For large N, finite-differencing becomes numerically intensive, and an efficient alternative is domain differentiation in which the full gradient is obtained by solving a single scattering problem of an auxiliary field using the same scattering operator as that of the forward solution. This report presents the domain derivative calculation of the gradient for a locally perturbed dielectric interface. The method is non-variational, and algebraic in nature in that it evaluates the gradient by directly domain differentiating the scattering equations. The mathematical transformation of the scattering problem into the corresponding problem for the differentiated fields can be visualized explicitly. The formulation of and the motivation behind introducing the auxiliary field are explicitly demonstrated. Closed-form analytic expressions are obtained for the gradients for electromagnetic TETM scattering from dielectric rough surfaces, and for scalar wave scattering from Neumann and Dirichlet rough surfaces.
- Numerical Mathematics