# Implementation of a Length Gauge Based on Optical Frequency Domain Reflectometry (OFDR)

## TL;DR

This paper shows how to adapt OFDR for precise free-space distance measurements, overcoming challenges like dispersion and calibration.

## Contribution

A new dispersion compensation method and calibration technique for OFDR in free-space environments.

## Key findings

- A dispersion compensation method was developed to maintain trace width at tens of microns over increasing distances.
- Calibration achieved a measurement accuracy of up to 2 μm using an interferometric fringe-counting method.
- The study demonstrated OFDR's feasibility for free-space and complex structured environments.

## Abstract

Optical frequency domain reflectometry (OFDR) is a widely used method for measuring optical lengths to backscattering points in optical fibers and integrated optical chips. However, its application for measuring absolute distances in other media, including free space, remains insufficiently studied. This work aims to solve two main challenges in developing a free-space distance measurement method based on OFDR. The first one is the adaptation of the standard OFDR method to air-based measurements, considering the complex and/or atypical composition of the optical line, including the combination of fiber and air, as well as differing chromatic dispersion. The second task is the calibration of the reflectometer to ensure high measurement accuracy. The article proposes a mathematical framework for eliminating the influence of chromatic dispersion, based on signal transformation and the introduction of an equivalent phase of the reference interferometer. The method was verified experimentally. The experimental setup included an OFDR system, a collimator, and a corner reflector movable along a 2-m rail. An important result is the development and testing of a dispersion compensation method, which eliminated peak broadening in the trace as the distance increased, maintaining its width at a level of tens of microns. Through calibration using an interferometric fringe-counting method, a frequency-to-distance conversion coefficient was determined, ensuring measurement accuracy up to 2 μm. Thus, the study demonstrates the feasibility of adapting OFDR for precise distributed distance measurements in free space and in complex or otherwise non-standard structured environments, significantly expanding the application scope of the technology.