# Impact of Cyclic Error on Absolute Distance Measurement Based on Optical Frequency Combs

## TL;DR

This paper studies how cyclic errors affect distance measurements using optical frequency combs and suggests ways to minimize their impact.

## Contribution

The study quantitatively analyzes cyclic error's impact and provides guidelines for minimizing it in interferometry-based measurements.

## Key findings

- Cyclic error reduces the linearity of OFC-based distance measurements.
- Choosing an optimal reference path length can minimize cyclic error effects.
- Recommendations are given for synthetic wavelength selection to balance NAR and reliability.

## Abstract

Absolute distance measurements based on optical frequency combs (OFCs) have greatly promoted advances in both science and technology, owing to the high precision, large non-ambiguity range (NAR), and a high update rate. However, cyclic error, which is extremely difficult to eliminate, reduces the linearity of measurement results. In this study, we quantitatively investigated the impact of cyclic error on absolute distance measurement using OFCs based on two types of interferometry: synthetic wavelength interferometry and single-wavelength interferometry. The numerical calculations indicate that selecting a suitable reference path length can minimize the impact of cyclic error when combining the two types of interferometry. Recommendations for selecting an appropriate synthetic wavelength to address the tradeoff between achieving a large NAR and minimizing the risk of failure when combining the two methods are provided. The results of this study are applicable not only in absolute distance measurements but also in other applications based on OFCs, such as surface profile, vibration analysis, etc.