Reconstruction of multilayered periodic structures from one-sided acoustic near-field data

Abstract This paper is concerned with the inverse acoustic scattering problem of reconstructing a multilayered periodic structure only by taking the one-sided near-field measurements. A novel integral equation is first proposed for the scattering problem, which plays a key role in uniqueness of inverse problems and inversion algorithms. With this technique, we prove that the periodic structure with a piecewise constant refractive index is uniquely determined. Then, we propose a novel inversion algorithm for reconstructing multilayered interfaces only using one-sided measurements corresponding to single incident wave. The main idea is to reduce the inverse interface problem into reconstructing the discontinuity of the coefficient function within the proposed integral equation, thereby giving a very good initial guess for interfaces. Furthermore, a Newton-type iterative approach is used to refine the inversion results, where a quite simple approach is provided to prove the differentiable analysis of the interfaces. The main advantage of our algorithm lies in its independence from initial values, small amount of data required, and capability to reconstruct three or more interfaces only from one-sided measurements, which is unprecedented in the previous research. Finally, some numerical examples follow to illustrate the effectiveness of our numerical algorithm.