High-precision color crosstalk coefficient calibration method based on phase error estimation
doi: 10.37188/CO.EN-2025-0041
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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，从理论上推到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。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.
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图 1 基于FPP的三维测量过程示意图
Figure 1. The schematic of the 3D measurement process based on FPP
图 2 色彩串扰的示意图。 (a) Bayer阵列的结构模型；(b) 色彩串扰数学模型
Figure 2. The schematic of the color crosstalk. (a) the schematic model of Bayer array; (b) the color crosstalk model.
图 7 单通道分离图像（含串扰系数）
Figure 7. Single-channel separated images containing crosstalk coefficients.
图 11 色彩串扰校正前后的相位误差分布。(a)校正前的串扰引起的相位误差；(b)沿选定行的相位误差曲线；(c)校正后的残余相位误差
Figure 11. 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.
图 12 标准球校准板的测量结果图。
Figure 12. Measurement results of the standard sphere calibration plate.
表 1 The Results of Crosstalk Coefficients
Table 1. The Results of Crosstalk Coefficients
$ {\kappa }_{st} $ Value $ {R}^{2} $ $ {\kappa }_{st} $ Value $ {R}^{2} $ κgr 0.0151 0.995 κrg 0.0546 0.988 κbg 0.1152 0.995 κgb 0.0546 0.998 κrb 0.0052 0.964 κbr 0.0614 0.980 
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表 2 Measurement results of the standard sphere calibration plate (mm)
Table 2. Measurement results of the standard sphere calibration plate (mm)
Measurement Index Diameter dA Diameter dB Center Distance SAB 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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