Inverse uniqueness on certain interior heterogeneity in phaseless problem

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Abstract
The wave travels through the heterogeneity, and the wave-form distorts accordingly. We always compare the dynamics between the before and after wave-forms to retrieve the information inside the heterogeneity. Let us see if a layer of known material places outside the heterogeneity could help to find out more information inside. In this paper we consider the inverse scattering problem in one-dimensional setting. The scattering matrix consists of 2 × 2 entries of meromorphic functions, and the analysis focuses on the zeros and poles of the scattering determinant. We consider the dynamic behavior of scattering entries in transition matrix system. We try to derive the inverse uniqueness from the strength/modulus of scattered wave-fields. Given the strength or the modulus of scattered wave-field over the outside region a priori, it is feasible to deduce the information on perturbed potential inside the region with partial information from the exterior layer. The inverse problem is to find certain information on the internal heterogeneity of certain materials and media with knowledge on certain exterior measurement.
Funding Information
  • National Science and Technology Council

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