Affiliation:
1. Quantum Sensing & Timing
2. Air Force Research Laboratory
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)APOPAI0003-693510.1364/AO.33.005948] depends on both
wavelength and OPD in a non-trivial manner. Further, we demonstrate
that the algorithm developed by Houairi and Cassaing (HC)
[J. Opt. Soc. Am.
A 26, 2503
(2009)JOAOD60740-323210.1364/JOSAA.26.002503] results in uniform
robustness across the entire UR. Finally, we explore the effect that
wavelength error has on the robustness of the HC algorithm.
Funder
Air Force Office of Scientific
Research
Subject
Atomic and Molecular Physics, and Optics,Engineering (miscellaneous),Electrical and Electronic Engineering