Optimization of radar cross section by a gradient method

Analytical expressions are derived for the derivatives of radar cross sections (RCS) with respect to scatterer shape in two and three dimensions. Using the adjoint formulation, the derivatives of the RCS, with respect to an arbitrary number of design parameters, are found from a single solution of the scattering problem. In two dimensions, gradient-based optimizations converge with a small number of iterations to shapes with strongly reduced RCS in specified angular intervals. The optimal shapes have sharp corners in directions where the RCS is minimized and exhibit corrugations, which can be suppressed by use of penalty functions. The method is also applied to RCS optimization using dielectric and magnetic absorbing materials.