Objective  Due to the advantages of high precision, easy recognition and high degree of automation, the three-channel phase measurement profilometry in optical three-dimensional measurement has gained increasing attention in both scientific research and engineering applications. For three-channel phase measurement profilometry, the chromatic aberration between projector channels is the key factor affecting the measurement accuracy. Most of the existing chromatic aberration correction methods of projectors regard projectors as "reverse cameras". Therefore, the accuracy of correction results will be dependent on the imaging quality of the camera. Moreover, the existing chromatic aberration measurement and correction methods still have shortcomings, so it is significant to improve the measurement accuracy of the system. Therefore, this study carries out the research on the projection chromatic aberration modeling and correction of phase target-based phase measurement profilometry.

  Methods  In this paper, the projection chromatic aberration modeling and correction method using the LCD screen with holographic projection film as the phase target is proposed (Fig.3). Firstly, the unfolded phase of LCD display fringes and projector projection fringes are calculated respectively. Next, binary fitting on display phase and projection phase are carried out. The green channel is regarded as an ideal channel, and the ideal pixel values of red and blue channels is calculated. Then the ideal pixel is substituted into the projection equation, and the ideal phases of the red and blue channels are obtained. Thus, the mathematical model of the chromatic aberration of the projector is established. Finally, the pre-compensation of projection fringes is implemented with the established chromatic aberration model(Fig.5). Then, the pre-compensated fringes are projected in three channels, so that the chromatic aberration of the projector is corrected.

  Results and Discussions   The experimental results demonstrated the performance of the proposed method. The average chromatic aberration of the blue and green channels is corrected from 0.325 5 pixel to 0.106 3 pixel. The average chromatic aberration of the red and green channels is corrected from 0.365 1 pixel to 0.111 4 pixel (Fig.10). This method can effectively improve the projection quality for three-channel phase measurement profilometry. The average error of the measured step is reduced from 0.489 mm to 0.038 mm (Tab.2). The experimental results verified the effectiveness of the chromatic aberration modeling and correction method of projector. This method can improve the overall measurement accuracy of three-channel phase measurement profilometry. Compared with the existing methods, the proposed method can be calibrated to avoid the impact of camera errors and effectively shorten the calculation time. Moreover, this method can be applied to the measurement and correction of different projector chromatic aberration.

  Conclusions  A phase-measurement contouring chromatic aberration modeling method using an LCD display as a phase target is designed and calibrated for study. This method eliminated the coupling error of the camera while measuring and calibrating the projector chromatic aberration, and enabled measurement of the projector chromatic aberration at global pixel points, while using mathematical modeling to model the projector chromatic aberration in a chromatic way to shorten the calculation time. By measuring the 3D shape of the actual object for accuracy comparison experiments and comparing the accuracy error before and after correcting the chromatic aberration of CP270 projector and PRO4500 projector, it can be concluded that the projection chromatic aberration modeling and correction study based on phase target proposed in this paper can better improve the projection quality in phase contour measurement and enhance the measurement accuracy of commercial projectors with poor accuracy. For the projectors with low accuracy, the method of correcting chromatic aberration in this paper can greatly improve the measurement accuracy of projectors. For the projectors with high accuracy, the proposed projector chromatic aberration modeling and correction method can further improve the measurement accuracy.