Determining the twist in an optical fiber

TL;DR

This paper presents a method to determine the twist in a birefringent optical fiber by analyzing measurements at one end, solving an inverse problem with proven stability and a reconstruction algorithm.

Contribution

It introduces a new approach for solving the inverse problem of fiber twist determination with a stability proof and an explicit reconstruction algorithm.

Findings

Proved a stability result for the inverse problem.

Developed a provable reconstruction algorithm.

Demonstrated the method's effectiveness in fiber twist detection.

Abstract

We determine the twist in a birefringent optical fiber from measurements, at one end of the fiber, of the fiber response to an impulsive source at the same end. This is the inverse problem of determining a non-constant coefficient, of a first order hyperbolic system in one space dimension with two speeds of propagation, from measurements at one end of an interval, of the solution of this system corresponding to an impulsive source at the same end. We prove a stability result for this inverse problem and give a provable reconstruction algorithm for this inverse problem.