Iterative algorithm for phase extraction from interferograms with random and spatially nonuniform phase shifts

Jiancheng Xu; Qiao Xu; Liqun Chai

doi:10.1364/AO.47.000480

Iterative algorithm for phase extraction from interferograms with random and spatially nonuniform phase shifts

Jiancheng Xu, Qiao Xu, and Liqun Chai

Applied Optics
Vol. 47,
Issue 3,
pp. 480-485
(2008)
•https://doi.org/10.1364/AO.47.000480

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Jiancheng Xu, Qiao Xu, and Liqun Chai, "Iterative algorithm for phase extraction from interferograms with random and spatially nonuniform phase shifts," Appl. Opt. 47, 480-485 (2008)

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Related Topics
Table of Contents Category
- Interferometry
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
- Phase shift (050.5080)
- Instrumentation, measurement, and metrology (120.0120)
- Fringe analysis (120.2650)
- Interferometry (120.3180)
- Phase measurement (120.5050)

About this Article
History
- Original Manuscript: October 1, 2007
- Manuscript Accepted: November 5, 2007
- Published: January 18, 2008

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Abstract

An advanced iterative algorithm is presented to extract phase distribution from randomly and spatially nonuniform phase-shifted interferograms. The proposed algorithm divides the interferograms into small blocks and retrieves local phase shifts accurately by iterations. Therefore, the phase distribution can be calculated with high precision by eliminating the effect of tilts occurring during phase shifting. Simulated results and experiments demonstrate that the proposed algorithm exhibits high precision and converges faster than previous algorithms even when the tilt errors are up to $27.6 %$ of the normal phase step.

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	Case 1		Case 2		Case 3		Case 4
	Real	Calculated	Real	Calculated	Real	Calculated	Real	Calculated
d ₂	1	1.0185	1.5	1.5169	1.5	1.5122	1.5	1.5396
d ₃	2	2.0514	2	2.0401	2	2.0381	2	2.0738
d ₄	3	3.0857	2.5	2.5669	2.5	2.5672	2.5	2.6106
k _x2	−0.0011	−0.0105	−0.1	−0.0921	−0.2	−0.1818	−0.4	−0.3753
k _x3	0.005	0.0051	0.05	0.0553	0.1	0.1147	0.2	0.2094
k _x4	0.015	0.0156	0.15	0.1553	0.3	0.3141	0.4	0.4205
k _y2	−0.012	−0.0119	−0.1	−0.0968	−0.2	−0.1957	−0.4	−0.3951
k _y3	0.016	0.0162	0.16	0.1681	0.3	0.3143	0.5	0.5049
k _y4	0.002	0.0021	0.02	0.0217	0.1	0.1067	0.2	0.2090
Error	PV	rms	PV	rms	PV	rms	PV	rms
Ours	0.0359	0.0124	0.0760	0.0181	0.1280	0.0229	0.2087	0.0298
Wang and Han	0.0506	0.0128	0.4979	0.0698	1.4333	0.1598	1.8546	0.1780

Errors	Fig. 4(e)	Fig. 4(f)	Fig. 4(g)	Fig. 4(h)	Fig. 4(i)	Fig. 4(j)	Fig. 4(k)	Fig. 4(g)–(h)	Fig. 4(l)
PV	0.2455	0.2907	0.2679	0.2678	0.1107	0.0811	0.0650	0.0841	0.0550
rms	0.0444	0.0535	0.0515	0.0507	0.0963	0.0127	0.0102	0.0168	0.0081

	Case 1		Case 2		Case 3		Case 4
	Real	Calculated	Real	Calculated	Real	Calculated	Real	Calculated
d ₂	1	1.0185	1.5	1.5169	1.5	1.5122	1.5	1.5396
d ₃	2	2.0514	2	2.0401	2	2.0381	2	2.0738
d ₄	3	3.0857	2.5	2.5669	2.5	2.5672	2.5	2.6106
k _x2	−0.0011	−0.0105	−0.1	−0.0921	−0.2	−0.1818	−0.4	−0.3753
k _x3	0.005	0.0051	0.05	0.0553	0.1	0.1147	0.2	0.2094
k _x4	0.015	0.0156	0.15	0.1553	0.3	0.3141	0.4	0.4205
k _y2	−0.012	−0.0119	−0.1	−0.0968	−0.2	−0.1957	−0.4	−0.3951
k _y3	0.016	0.0162	0.16	0.1681	0.3	0.3143	0.5	0.5049
k _y4	0.002	0.0021	0.02	0.0217	0.1	0.1067	0.2	0.2090
Error	PV	rms	PV	rms	PV	rms	PV	rms
Ours	0.0359	0.0124	0.0760	0.0181	0.1280	0.0229	0.2087	0.0298
Wang and Han	0.0506	0.0128	0.4979	0.0698	1.4333	0.1598	1.8546	0.1780

Errors	Fig. 4(e)	Fig. 4(f)	Fig. 4(g)	Fig. 4(h)	Fig. 4(i)	Fig. 4(j)	Fig. 4(k)	Fig. 4(g)–(h)	Fig. 4(l)
PV	0.2455	0.2907	0.2679	0.2678	0.1107	0.0811	0.0650	0.0841	0.0550
rms	0.0444	0.0535	0.0515	0.0507	0.0963	0.0127	0.0102	0.0168	0.0081

Abstract

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