Texture and Crosstalk-Insensitive Orthogonal Self-Equalizing Color Fringe Phase-Shift Method for Fast and High-Precision 3-D Measurement

Phase-shifting profilometry (PSP) is extensively utilized in 3-D measurements. While grayscale-based PSP ensures high measurement accuracy, it suffers from inefficiency. Conversely, color-based PSP enhances efficiency but compromises on accuracy and robustness. To promote both measurement accuracy and efficiency, we propose an orthogonal self-equalizing color fringe PSP (OSCF-PSP) technique. This method employs orthogonal fringes to achieve precise channel decrosstalk while minimizing the condition number of the decrosstalk matrix, thereby improving noise immunity. Moreover, by leveraging the orthogonal nature of fringes, we develop a signal-to-noise ratio (SNR) estimator independent of the measured object's surface shape, texture information, and background illumination. This enables quantitative assessment of the reliability of each channel's computed results and dynamic adaptive weighting of channel outputs, thereby achieving immunity to the object's colored texture. Compared to other color fringe profilometry methods, OSCF-PSP exhibits superior robustness, being insensitive to colored texture variations of the object, cross-channel interference, and projector illumination imbalances. In scenarios where efficiency improves by 30% (three patterns to two patterns) over conventional three-step grayscale PSP, most measurement errors decrease by 32% (0.0717-0.0488 rad, measuring white objects)-50% (0.1242-0.0606 rad, measuring color objects). Even in the worst-case scenario of our algorithm, measurement errors do not exceed those of the classical three-step phase-shifting method. Our proposed approach effectively mitigates the drawbacks of color-based PSP while maintaining its relative efficiency.