Identifying of the refractive index for the acoustic equation at fixed frequency

TL;DR

This paper derives a formula to determine the acoustic refractive index from boundary measurements and uses it to identify small perturbations at a fixed frequency, advancing inverse problem techniques in acoustics.

Contribution

It introduces a new formula for calculating the refractive index from the Dirichlet to Neumann map and applies it to detect small volume perturbations at a fixed frequency.

Findings

Derived a formula for the refractive index from boundary data.

Successfully identified locations and values of small perturbations.

Enhanced inverse problem methods for acoustic imaging.

Abstract

In this paper we determine a formula for calculating the refractive index ${\bf n}$ for the acoustic equation from the partial Dirichlet to Neumann map(DN) associated to ${\bf n}$. We apply these results to identify locations and values of small volume perturbations of this refractive index at fixed frequency $\omega$.