Document Type

Article

Journal/Book Title/Conference

Applied Optics

Volume

63

Issue

1

Publisher

Optica

Publication Date

1-2024

Journal Article Version

Version of Record

First Page

1

Last Page

7

Creative Commons License

Creative Commons Attribution-Noncommercial 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License

Abstract

Multiple wavelength phase shifting interferometry is widely used to extend the unambiguous range ( UR ) beyond that of a single wavelength. Towards this end, many algorithms have been developed to calculate the optical path difference (OPD) from the phase measurements of multiple wavelengths. These algorithms fail when phase error exceeds a specific threshold. In this paper, we examine this failure condition. We introduce a “phase-space” view of multi-wavelength algorithms and demonstrate how this view may be used to understand an algorithm’s robustness to phase measurement error. In particular, we show that the robustness of the synthetic wavelength algorithm deteriorates near the edges of its UR . We show that the robustness of de Groot’s extended range algorithm [Appl. Opt. 33, 5948 (1994)] depends on both wavelength and OPD in a non-trivial manner. Further, we demonstrate that the algorithm developed by Houairi & Cassaing (HC) [J. Opt. Soc. Am. 26, 2503 (2009)] results in uniform robustness across the entire UR . Finally, we explore the effect that wavelength error has on the robustness of the HC algorithm.

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