Three-dimensional surface imaging by multi-frequency phase shift profilometry with angle and pattern modeling for system calibration

In this paper, we present a 3D surface imaging system based on the well-known phase shift profilometry. To yield the analytical solutions, four shifted phases and three high carrier frequencies are used to compute the phase map and reduce the noises that are caused by the inherent optical aberrations and external influences, e.g. different illumination light sources, uneven intensity distribution and automatic image processing algorithms. To reduce the system noise, we propose to model the pattern of the calibration grid in a virtual space. To obtain the modeled pattern, we use a plane to intercept the rays that are modeled by the proposed angle modeling method. In the world coordinate system, the angle and the pattern are computed based on the calibration data. A registration method is used to transform the modeled pattern in the virtual space to the ideal pattern in the world coordinate system by computing the least squared errors between the true points in the modeled pattern and the measured points in the practical pattern. The modeled (true) points are used for re-calibration of the 3D imaging system. Experimental results showed that the measurement accuracy increases considerably and the MSE is reduced from 0.95 mm to 0.65 mm (32% average error decrease) after replacing the measured points with the true points for calibration.