Least-squares method constrained by phase smoothness for correcting illumination fluctuation errors in phase-shifting profilometry

Huijie Zhu; Hongwei Guo

doi:10.1364/AO.505327

Applied Optics
Vol. 62,
Issue 31,
pp. 8451-8461
(2023)
•https://doi.org/10.1364/AO.505327

Least-squares method constrained by phase smoothness for correcting illumination fluctuation errors in phase-shifting profilometry

Huijie Zhu and Hongwei Guo

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Huijie Zhu and Hongwei Guo, "Least-squares method constrained by phase smoothness for correcting illumination fluctuation errors in phase-shifting profilometry," Appl. Opt. 62, 8451-8461 (2023)

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Abstract

Phase-shifting fringe projection profilometry usually suffers from the errors induced by illumination fluctuations. As a result, ripple-like artifacts that have the same periods as fringes appear on the phase map. Because the illumination fluctuations cannot be simply modeled using fringe harmonics, their induced errors are difficult to remove by use of a phase-shifting algorithm. To solve this problem, this paper suggests a least-squares method constrained by phase smoothness. This method calculates fringe phases using the generalized phase-shifting algorithm and estimates coefficients related to illumination fluctuation by use of smoothed phase map. Alternately implementing these two steps enables one to eliminate effects of illumination fluctuations on the measurement results. Experimental results demonstrate that this proposed algorithm is helpful for improving measurement accuracy.

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Corrections

Huijie Zhu and Hongwei Guo, "Least-squares method constrained by phase smoothness for correcting illumination fluctuation errors in phase-shifting profilometry: erratum," Appl. Opt. 62, 9198-9198 (2023)
https://opg.optica.org/ao/abstract.cfm?uri=ao-62-34-9198

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Equations (29)

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Methods	Mean Values	SDs
Generalized phase-shifting algorithm [8,9]	$1.3579 \times 10^{- 3}$	$5.1067 \times 10^{- 3}$
Histogram correction method [22]	$2.6220 \times 10^{- 4}$	$4.6573 \times 10^{- 3}$
Proposed method	$1.6203 \times 10^{- 6}$	$3.3824 \times 10^{- 3}$

Methods	RMS Errors (mm)
Generalized phase-shifting algorithm [8,9]	0.5340
Histogram correction method [22]	0.3675
Proposed method	0.3645

Methods	Mean Values	SDs
Generalized phase-shifting algorithm [8,9]	$- 4.5893 \times 10^{- 3}$	$5.5361 \times 10^{- 3}$
Histogram correction method [22]	$1.2322 \times 10^{- 4}$	$5.2554 \times 10^{- 3}$
Proposed method	$3.0020 \times 10^{- 6}$	$3.7268 \times 10^{- 3}$

Methods	RMS Errors (mm)
Generalized phase-shifting algorithm [8,9]	0.6043
Histogram correction method [22]	0.4307
Proposed method	0.4182

Methods	Mean Values	SDs
Generalized phase-shifting algorithm [8,9]	$- 4.6004 \times 10^{- 3}$	$5.2316 \times 10^{- 3}$
Histogram correction method [22]	$1.2266 \times 10^{- 4}$	$5.0846 \times 10^{- 3}$
Proposed method	$1.4982 \times 10^{- 6}$	$3.4227 \times 10^{- 3}$

Methods	RMS Errors (mm)
Generalized phase-shifting algorithm [8,9]	0.5844
Histogram correction method [22]	0.4201
Proposed method	0.4093

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Applied Optics