Phase shift estimation from variances of fringe pattern differences

Hongwei Guo; Zhihui Zhang

doi:10.1364/AO.52.006572

Phase shift estimation from variances of fringe pattern differences

Hongwei Guo and Zhihui Zhang

Applied Optics
Vol. 52,
Issue 26,
pp. 6572-6578
(2013)
•https://doi.org/10.1364/AO.52.006572

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Hongwei Guo and Zhihui Zhang, "Phase shift estimation from variances of fringe pattern differences," Appl. Opt. 52, 6572-6578 (2013)

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Related Topics
Table of Contents Category
- Instrumentation, Measurement, and Metrology
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Fringe analysis (100.2650)
- Interferometry (120.3180)
- Phase measurement (120.5050)

About this Article
History
- Original Manuscript: June 26, 2013
- Revised Manuscript: August 14, 2013
- Manuscript Accepted: August 17, 2013
- Published: September 9, 2013

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Abstract

This paper presents a simple algorithm for estimating phase shifts from only three interferograms. In it, the fringe pattern differences are computed first in order to remove the background component, and then the variances and further the standard deviations (SDs) of fringe pattern differences are calculated. The phase shifts are estimated, by using the law of cosines, from a triangle whose lengths of sides are the SDs just calculated. This algorithm offers several advantages over others, e.g., being efficient, easy to implement, accurate, and less sensitive to noise. Numerical simulations and an experiment are performed to demonstrate its validity.

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	No. of Fringes is 1.5			No. of Fringes is 4
SDs of Gaussian Noise	Estimates of $δ_{1}$ (rad)	Estimates of $δ_{2}$ (rad)	Phase RMS Errors (rad)	Estimates of $δ_{1}$ (rad)	Estimates of $δ_{2}$ (rad)	Phase RMS Errors (rad)
0	1.7121	2.9195	0.0115	1.7017	2.9027	0.0016
0.005	1.7124	2.9202	0.0189	1.7017	2.9029	0.0148
0.01	1.7128	2.9212	0.0321	1.7025	2.9045	0.0294
0.02	1.7145	2.9257	0.0609	1.7040	2.9089	0.0589
0.04	1.7184	2.9398	0.1190	1.7114	2.9292	0.1180

	No. of Fringes is 1.5			No. of Fringes is 4
Noise SDs	Estimates of $δ_{1}$ (rad)	Estimates of $δ_{2}$ (rad)	Phase RMS Errors (rad)	Estimates of $δ_{1}$ (rad)	Estimates of $δ_{2}$ (rad)	Phase RMS Errors (rad)
0	1.7121	2.9195	0.0115	1.7017	2.9027	0.0016
0.07	1.7166	2.9335	0.0875	1.7099	2.9236	0.0975
0.1	1.7258	2.9496	0.1235	1.7170	2.9409	0.1390
0.14	1.7317	2.9699	0.1762	1.7351	2.9830	0.1986
0.2	1.7498	3.0226	0.2622	1.7635	3.0506	0.2966

	No. of Fringes is 1.5			No. of Fringes is 4
SDs of Gaussian Noise	Estimates of $δ_{1}$ (rad)	Estimates of $δ_{2}$ (rad)	Phase RMS Errors (rad)	Estimates of $δ_{1}$ (rad)	Estimates of $δ_{2}$ (rad)	Phase RMS Errors (rad)
0	1.7121	2.9195	0.0115	1.7017	2.9027	0.0016
0.005	1.7124	2.9202	0.0189	1.7017	2.9029	0.0148
0.01	1.7128	2.9212	0.0321	1.7025	2.9045	0.0294
0.02	1.7145	2.9257	0.0609	1.7040	2.9089	0.0589
0.04	1.7184	2.9398	0.1190	1.7114	2.9292	0.1180

	No. of Fringes is 1.5			No. of Fringes is 4
Noise SDs	Estimates of $δ_{1}$ (rad)	Estimates of $δ_{2}$ (rad)	Phase RMS Errors (rad)	Estimates of $δ_{1}$ (rad)	Estimates of $δ_{2}$ (rad)	Phase RMS Errors (rad)
0	1.7121	2.9195	0.0115	1.7017	2.9027	0.0016
0.07	1.7166	2.9335	0.0875	1.7099	2.9236	0.0975
0.1	1.7258	2.9496	0.1235	1.7170	2.9409	0.1390
0.14	1.7317	2.9699	0.1762	1.7351	2.9830	0.1986
0.2	1.7498	3.0226	0.2622	1.7635	3.0506	0.2966

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