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IPI

Consider the time-harmonic acoustic scattering of an incident point source inside an inhomogeneous cavity. By constructing an equivalent integral equation, the well-posedness of the direct problem is proved in $L^p$ with using the classical Fredholm theory. Motivated by the previous work [

IPI

This paper is concerned with the inverse problem of recovering a penetrable grating
profile in the TM-polarization case from the scattered field measured

*only above the structure*, corresponding to a countably infinite number of incident quasi-periodic waves. A sampling method is proposed to reconstruct the penetrable grating profile based on a near field linear operator equation in $l^2$. The mathematical justification of the sampling method is established and numerical results are presented to show the validity of the inversion algorithm.## Year of publication

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