基于相位误差估计的高精度色彩串扰系数标定方法

冯橹源; 梁健; 王湘峻; 赵宗扬; 陈羿帆; 吴斌

doi:10.37188/CO.EN-2025-0041

基于相位误差估计的高精度色彩串扰系数标定方法

冯橹源^{1, 2,},
梁健²,
王湘峻³,
赵宗扬²,
陈羿帆²,
吴斌^2, ,

1.
中国兵器工业导航与控制技术研究所, 北京 100089
2.
天津大学精密测试技术及仪器全国重点实验, 天津 300072
3.
德州市农业科学研究院, 山东 253015

详细信息

中图分类号: TH741
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出版历程
- 收稿日期: 2025-10-16
- 修回日期: 2025-10-27
- 录用日期: 2025-11-06
- 网络出版日期: 2025-12-03

High-precision color crosstalk coefficient calibration method based on phase error estimation

doi: 10.37188/CO.EN-2025-0041

1.
China Ordnance Navigation and Control Technology Research Institute, Beijing 100089, China
2.
State Key Laboratory of Precision Measurement Technology and Instruments, Tianjin University, Tianjin 300072, China
3.
Dezhou Academy of Agricultural Sciences, Shandong 253015, China

Funds: Supported by National Natural Science Foundation of China (No. 62371339).

More Information

Author Bio:
FENG Lu-yuan, male, was born in Tangshan, Hebei Province. He received the Ph.D. degree in Measurement and Control Technology and Instrument from Tianjin University, Tianjin, China, in 2025. His research interests include inertial navigation and vision inspection. E-mail: lyfeng0506@tju.edu.cn

WU Bin, male, was born in Tianjin, China. He received the B.S. and Ph.D. degrees in Tianjin University, in 1997 and 2002, respectively. He is currently a Professor with the Department of Instrumentation Science and Technology, Tianjin University. His main research interests include compute vision, object detection and vision measurement technology. E-mail: wubin@tju.edu.cn

Corresponding author: wubin@tju.edu.cn

摘要

摘要:
彩色编码条纹图案已成为实现条纹投影轮廓术实时三维形貌测量的重要方法。然而，彩色相机中的色彩串扰现象仍然是限制测量精度的主要因素。针对这一问题，本文提出了一种精确的色彩串扰系数标定方法，以实现有效的色彩串扰校正。首先，设计了一种基于正交相位条纹的串扰系数估计器，从理论上推导了色彩串扰系数与相位误差的关系。同时，将设计的彩色正交条纹图案投影至标准平面靶标，实现R、G、B的彩色通道分离图案。最后，基于粒子群优化算法拟合通道串扰相位误差，从而实现高精度色彩串扰系数标定。基于标准双球球板的测量实验验证，两个球体的直径拟合误差分别为0.0191 mm和0.0160 mm，球心间距的计算误差低至0.0120 mm，证明该方法能够有效提高彩色相机在条纹投影技术中的测量精度和适用性。
- 条纹投影轮廓术 /
- 色彩串扰系数 /
- 相位误差 /
- 正交条纹图案
Abstract:
Color-coded fringe patterns have emerged as a key technique for enabling real-time three-dimensional (3D) shape measurement in fringe projection profilometry (FPP). However, color crosstalk inherent in color cameras remains a significant factor limiting measurement accuracy. To mitigate this issue, a high-precision calibration method for color crosstalk coefficients is proposed to enable effective correction in this paper. Specifically, a crosstalk coefficient estimator is developed based on orthogonal phase-shifted fringe patterns, and the theoretical relationship between the crosstalk coefficients and phase error is derived. The color orthogonal fringes are then designed to project onto a standard planar target to acquire separated R, G, and B channel patterns. Finally, a particle swarm optimization (PSO) algorithm is introduced to optimize the crosstalk-induced phase errors and calibrate the crosstalk coefficients with high precision. Experimental validation based on a standard dual-sphere calibration plate shows that the diameter fitting errors of the two spheres are 0.0191 mm and 0.0160 mm, respectively, and the error in the calculated center-to-center distance is as low as 0.0120 mm, which demonstrate that the proposed method can effectively enhance the measurement accuracy and applicability of color cameras in fringe projection technology.
- fringe projection profilometry /
- color crosstalk coefficient /
- phase error /
- orthogonal fringe pattern

HTML全文

Figure 1. Schematic of the color crosstalk. (a) The schematic model of Bayer array; (b) the color crosstalk model

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Figure 2. Wrapped phase error distribution map before compensation

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Figure 3. Wrapped phase error distribution map after compensation

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Figure 4. Procedure of the proposed calibration method

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Figure 5. CFPP system used in our experiments

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Figure 6. Single-channel separated images containing crosstalk coefficients

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Figure 7. Phase error distribution map of the different channels

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Figure 8. Fitting results of the different channels

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Figure 9. Phase error distribution map of different channels

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Figure 10. Phase error distributions before and after crosstalk correction. (a) Crosstalk-induced phase error before correction; (b) phase error along a selected row; (c) residual phase error after correction

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Figure 11. Measurement results of the standard sphere calibration plate

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Table 1. The results of crosstalk coefficients

$ {\kappa }_{st} $	Value	$ {R}^{2} $	$ {\kappa }_{st} $	Value	$ {R}^{2} $
κ_gr	0.0151	0.995	κ_rg	0.0546	0.988
κ_bg	0.1152	0.995	κ_gb	0.0546	0.998
κ_rb	0.0052	0.964	κ_br	0.0614	0.980

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Table 2. Measurement results of the standard sphere calibration plate (mm)

Measurement Index	Diameter d_A	Diameter d_B	Center Distance S_AB
1	31.7284	31.7078	60.0136
2	31.7234	31.7298	60.0148
3	31.7360	31.7283	59.9864
4	31.7527	31.7258	60.0046
5	31.7328	31.7273	59.9989
6	31.7284	31.7404	59.9949
7	31.7288	31.7218	60.0141
8	31.7229	31.7194	60.0179
9	31.7305	31.7127	59.9918
10	31.7340	31.7208	59.9898
Mean Result	31.7318	31.7234	60.0027
MAE	0.0191	0.0160	0.0120
SD	0.0204	0.0179	0.0152

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