IPI
On recovery of an inhomogeneous cavity in inverse acoustic scattering
Fenglong Qu Jiaqing Yang

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 [10], a novel uniqueness result is then established for the inverse problem of recovering the refractive index of piecewise constant function from the wave fields measured on a closed surface inside the cavity.

keywords: Uniqueness inverse scattering refractive index inhomogeneous cavity point source
IPI
Reconstruction of penetrable grating profiles
Jiaqing Yang Bo Zhang Ruming Zhang
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.
keywords: grating profile Sampling method transmission condition quasi-periodic boundary value problem impedance Green's function.

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