Layer stripping approach to reconstruct shape defects in waveguides using locally resonant frequencies

TL;DR

This paper introduces a layer stripping method to reconstruct slowly varying shape defects in 2D waveguides using locally resonant frequencies and one-side measurements, providing a stable and efficient solution validated numerically.

Contribution

It presents a novel layer stripping approach for shape reconstruction in waveguides at resonant frequencies, enabling stable and slice-by-slice recovery of width variations.

Findings

Method accurately reconstructs waveguide width variations.

Approach is stable in the L-infinity norm.

Validated on numerical data with discussion of limits.

Abstract

This article present a new method to reconstruct slowly varying width defects in 2D waveguides using one-side section measurements at locally resonant frequencies. At these frequencies, locally resonant modes propagate in the waveguide up to a "cut-off" position. In this particular point, the local width of the waveguide can be recovered. Given multi-frequency measurements taken on a section of the waveguide, we perform an efficient layer stripping approach to recover shape variations slice by slice. It provides an L infinite-stable method to reconstruct the width of a slowly monotonous varying waveguide. We validate this method on numerical data and discuss its limits.