Defocused binary fringe phase error modeling and compensation using
depth-discrete Fourier series fitting

Jingcheng Hu; Shaohui Zhang; Yao Hu; Qun Hao

doi:10.1364/AO.440408

Applied Optics
Vol. 60,
Issue 32,
pp. 10047-10054
(2021)
•https://doi.org/10.1364/AO.440408

Defocused binary fringe phase error modeling and compensation using depth-discrete Fourier series fitting

Jingcheng Hu, Shaohui Zhang, Yao Hu, and Qun Hao

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Jingcheng Hu, Shaohui Zhang, Yao Hu, and Qun Hao, "Defocused binary fringe phase error modeling and compensation using depth-discrete Fourier series fitting," Appl. Opt. 60, 10047-10054 (2021)

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Abstract

The binary defocus fringe projection is a widely adopted way to increase the speed of fringe projection profilemotry. However, the projected patterns may deviate from ideal ones at some depths. We propose a theoretical model and a corresponding compensation method to explain and calibrate the phase error of defocus-projected patterns. We first low-pass filter the projected patterns at different depths to obtain corresponding ideal ones. Then, we calibrate the model coefficients based on the errors between the original and ideal fringe patterns. The calibrated phase error model can be used to compensate the phase error at arbitrary depths within the calibration volume. Experiments are conducted to verify the feasibility and performance of the proposed method.

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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 (24)

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	${E R R O R}_{p h a s e} = A_{0} + A_{1} \cos (Ω φ) + B_{1} \sin (Ω φ) + \dots + A_{4} \cos (4 Ω φ) + B_{4} \sin (4 Ω φ)$
$D e p$ $(mm)$	$A_{0} (\times 10^{- 3})$	$A_{1} (\times 10^{- 3})$	$B_{1} (\times 10^{- 3})$	$A_{2} (\times 10^{- 3})$	$B_{2} (\times 10^{- 3})$	$A_{3} (\times 10^{- 3})$	$B_{3} (\times 10^{- 3})$	$A_{4} (\times 10^{- 3})$	$B_{4} (\times 10^{- 3})$	$Ω$
1st 400	6.38	−4.99	−6.57	0.52	−3.96	−1.23	−0.59	−3.72	2.66	4.13
2nd 358	5.06	−4.78	−1.65	4.79	−3.70	0.57	−2.98	−0.98	−2.92	4.07
3rd 336	3.35	3.11	6.58	4.66	6.82	0.04	1.38	−1.00	−1.87	3.97
4th 325	4.92	5.63	15.74	5.45	4.98	−0.83	1.65	−0.75	2.79	3.92
5th 293	5.55	7.38	26.41	3.98	0.04	−1.22	0.95	−2.46	1.17	3.94
6th 272	5.83	9.07	37.96	1.34	−8.97	−0.92	−1.62	−1.46	3.91	4.00
7th 252	7.33	9.78	44.83	−3.07	−13.9	−1.33	−5.31	−4.20	5.21	4.00
8th 238	3.68	13.92	55.55	−9.13	−24.8	−3.34	−6.81	8.31	1.03	4.01
9th 223	3.55	15.03	56.30	−9.15	−24.2	−3.84	−6.21	10.48	1.20	4.01

Theoretical Value	Experiment Value
$A_{n} = 0$	$0.016 > A_{n} > - 0.010$
$Ω = 4$	$4.14 > Ω > 3.91$
$B_{1} > B_{2}$	$B_{1} > B_{2}$

	${E R R O R}_{p h a s e} = A_{0} + A_{1} \cos (Ω φ) + B_{1} \sin (Ω φ) + \dots + A_{4} \cos (4 Ω φ) + B_{4} \sin (4 Ω φ)$
$D e p$ $(mm)$	$A_{0} (\times 10^{- 3})$	$A_{1} (\times 10^{- 3})$	$B_{1} (\times 10^{- 3})$	$A_{2} (\times 10^{- 3})$	$B_{2} (\times 10^{- 3})$	$A_{3} (\times 10^{- 3})$	$B_{3} (\times 10^{- 3})$	$A_{4} (\times 10^{- 3})$	$B_{4} (\times 10^{- 3})$	$Ω$
1st 400	6.38	−4.99	−6.57	0.52	−3.96	−1.23	−0.59	−3.72	2.66	4.13
2nd 358	5.06	−4.78	−1.65	4.79	−3.70	0.57	−2.98	−0.98	−2.92	4.07
3rd 336	3.35	3.11	6.58	4.66	6.82	0.04	1.38	−1.00	−1.87	3.97
4th 325	4.92	5.63	15.74	5.45	4.98	−0.83	1.65	−0.75	2.79	3.92
5th 293	5.55	7.38	26.41	3.98	0.04	−1.22	0.95	−2.46	1.17	3.94
6th 272	5.83	9.07	37.96	1.34	−8.97	−0.92	−1.62	−1.46	3.91	4.00
7th 252	7.33	9.78	44.83	−3.07	−13.9	−1.33	−5.31	−4.20	5.21	4.00
8th 238	3.68	13.92	55.55	−9.13	−24.8	−3.34	−6.81	8.31	1.03	4.01
9th 223	3.55	15.03	56.30	−9.15	−24.2	−3.84	−6.21	10.48	1.20	4.01

Theoretical Value	Experiment Value
$A_{n} = 0$	$0.016 > A_{n} > - 0.010$
$Ω = 4$	$4.14 > Ω > 3.91$
$B_{1} > B_{2}$	$B_{1} > B_{2}$

Abstract

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Tables (4)

Equations (24)

Applied Optics