Optimal frequency selection for accuracy improvement in binary defocusing fringe projection profilometry

Jiangping Zhu; Jiangping Zhu; Jiangping Zhu; Xiaoyi Feng; Xiaoyi Feng; Changhui Zhu; Changhui Zhu; Pei Zhou; Pei Zhou

doi:10.1364/AO.464506

Applied Optics
Vol. 61,
Issue 23,
pp. 6897-6904
(2022)
•https://doi.org/10.1364/AO.464506

Optimal frequency selection for accuracy improvement in binary defocusing fringe projection profilometry

Jiangping Zhu, Xiaoyi Feng, Changhui Zhu, and Pei Zhou

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Jiangping Zhu, Xiaoyi Feng, Changhui Zhu, and Pei Zhou, "Optimal frequency selection for accuracy improvement in binary defocusing fringe projection profilometry," Appl. Opt. 61, 6897-6904 (2022)

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Abstract

The binary defocusing fringe projection profilometry (FPP) technique has demonstrated various advantages for high-speed and high-accuracy three-dimensional (3D) surface measurement. However, higher fringe frequency does not necessarily give better measurements in binary defocusing FPP. To improve the 3D geometry measurement accuracy, this paper proposes an optimal frequency selection approach by analyzing the phase error distribution under different defocusing degrees. The phase error is analyzed theoretically based on the multi-frequency temporal phase unwrapping process, and the associated relationship with fringe frequency, system defocusing degree, noise, and other influencing factors is established. Meanwhile, optimal fringe frequency in a specific system is selected by the theoretical model combined with the validation of simulation experiments. Finally, the measurement accuracy could be effectively enhanced by the generated binary fringe patterns of optimal frequency. Both simulations and experiments verify the effectiveness and robustness of the proposed method.

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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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$σ_{I n}^{2}$	$N$	$σ = 5 / 3$	$σ = 9 / 3$	$σ = 13 / 3$
5	3	$f_{0} < 15.9505$	$f_{0} < 11.8964$	$f_{0} < 9.9008$
5	4	$f_{0} < 16.0888$	$f_{0} < 11.9975$	$f_{0} < 9.9843$
3.5	3	$f_{0} < 16.1212$	$f_{0} < 12.0212$	$f_{0} < 10.0039$
3.5	4	$f_{0} < 16.2536$	$f_{0} < 12.1186$	$f_{0} < 10.0844$

$f_{0}$	Fringe Frequency Ratio	Fringe Period Ratio
4.0	1 : 4 : 16	912 : 228 : 57
5.7	1 : 5.7 : 32.49	912 : 159 : 27
7.0	1 : 7 : 49	912 : 132 : 18
8.0	1 : 8 : 60.8	912 : 114 : 15
9.2	1 : 9.2 : 84.64	912 : 99 : 12

Phase RMSE (rad)	$f_{0} = 4$	$f_{0} = 5.7$	$f_{0} = 7$	$f_{0} = 8$	$f_{0} = 9.2$
$σ \approx 1.66$	0.00245	0.00184	0.00163	0.00159	0.00154
$σ \approx 1.90$	0.00230	0.00180	0.00163	0.00159	0.00156
$σ \approx 2.77$	0.00302	0.00272	0.00266	0.00270	0.00271
$σ \approx 3.29$	0.00322	0.00295	0.00294	0.00300	0.00313
$σ \approx 3.66$	0.00310	0.00281	0.00287	0.00290	0.00308
$σ \approx 4.11$	0.00384	0.00364	0.00368	0.00384	0.00405

	55 cm		57–59 cm
$f_{0}$	Sinusoidal Fringes	Binary Fringes	Sinusoidal Fringes	Binary Fringes
4.0	0.0656	0.1751	0.1388	0.3392
5.7	0.0350	0.0864	0.0718	0.1602
7.0	0.0354	0.0610	0.0621	0.1162
8.0	0.0245	0.0507	0.0500	0.0964
9.2	0.0243	0.0493	0.0466	0.0843

$σ_{I n}^{2}$	$N$	$σ = 5 / 3$	$σ = 9 / 3$	$σ = 13 / 3$
5	3	$f_{0} < 15.9505$	$f_{0} < 11.8964$	$f_{0} < 9.9008$
5	4	$f_{0} < 16.0888$	$f_{0} < 11.9975$	$f_{0} < 9.9843$
3.5	3	$f_{0} < 16.1212$	$f_{0} < 12.0212$	$f_{0} < 10.0039$
3.5	4	$f_{0} < 16.2536$	$f_{0} < 12.1186$	$f_{0} < 10.0844$

Abstract

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Figures (8)

Tables (4)

Equations (16)

Applied Optics