Application of the method of auxiliary sources to a defect-detection inverse problem of optical diffraction microscopy

We propose a method of numerical solution of a type of inverse scattering problem that arises in the optical characterisation/quality control of nanostructures. The underlying global, ill-posed, nonlinear optimisation problem is first localised by best-fit matching of library and measured diffraction efficiency patterns. The inverse problem is then solved using piecewise linear interpolation between the best far-field matches. Finally, the results are refined, on average, by solving an additional local optimisation problem formulated in terms of the method of auxiliary sources. To illustrate the proposed method, we apply it in a concrete quantitative characterisation of a non-periodic, nano-scale grating defect, with numerically simulated measurements. It is shown that the presented procedure can solve the inverse problem with an accuracy usually thought to require rigorous electromagnetic theories.