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Numerical simulation of image formation in near-field optical microscopy

Numerical simulation of image formation in near field optical microscopy is needed to understand a relationship between near field images and actual structure of sample since the image can be differs strongly from real structure. In order to estimate the near field image formation, two different approaches are used, namely numerical solution of integral equations with boundary element method or moment method and analytical solution of light scattering problem obtained by assumption of some hypotheses. The first approach results in reasonably complicated algorithm of calculation and often causes a bed conditioned system of linear equations to be formed. The approach based on an analytical solution of scattering problem is more preferable since allow to reduce the algorithm and increase the calculations speed. A new program of simulation of near field image formation for arbitrary sample shape has been developed. The program is based on the results of analytical calculation of near field light diffraction on sinusoidal diffraction grating of arbitrary corrugation amplitude. The sample shape is presented as a number of sinusoidal gratings of various amplitudes by Fourier transformation, for each of the gratings the light scattering amplitude is calculated and the amplitudes are summarized.