Computing Gabor Coefficients for a scattering problem:super exponential converging accuracy and a more localized representation

Optical scatterometry is a non-destructive inspection technique to evaluate possible production deformations for integrated circuits. A key component of optical scatterometry is a Maxwell solver to obtain accurate information regarding the electromagnetic scattering from the structures of interest. This Maxwell solver also needs to be capable to quickly adapt the geometrical details of these structures to take various possible deformities into consideration for the fast computation of electromagnetic scattering. A fitting Maxwell solver [1] takes the form of a spatial-spectral domain integral equation such that its computational domain is comparable to the volume of the scattering objects of interest, e.g. parts of an integrated circuit. The spatial-spectral representation in terms of Gabor frames allows to analytically and efficiently incorporate the response of a planarly layered background medium, since the setting of optical scatterometry for integrated circuits is characterized by such a background description. The Gabor frames as in [1] make it possible to describe the electromagnetic fields and scattering objects as weighted sums of shifted and modulated Gaussian window functions, where the so-called Gabor coefficients are the weighting coefficients. We want to make more efficient use of the Gabor frames, which requires the computation of Gabor coefficients, such that the Maxwell solver [1] becomes faster and more suitable for optical scatterometry applications