We consider a mathematical problem modelling some characteristics of near field optical microscope. We take a monofrequency line source to illuminate a sample with constant index of refraction and use the scattered field data measured near the sample to reconstruct the shape of it. Mixed reciprocity relation and factorization method are applied to solve our problem. Some numerical examples to show the feasibility of the method are presented.
Helmholtz equation inverse problem mixed reciprocity relation factorization method
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