Gamma Precorrection and Phase Error Compensation Methods Based on Three-Frequency with Three-Phase Shift

Digital fringe projection measurement technology has been widely used in computer vision and optical three-dimensional (3D) measurement. Considering the phase error caused by the gamma distortion and nonlinear error, the active gamma precorrection and phase error compensation methods based on the three-frequency with three-phase shifts are designed to reversely solve the initial phase and accurately compensate phase error. On the one hand, the gamma coefficient of the measurement system depends on precoding two groups of fringe sequences with different gamma coefficients to calculate the corresponded proportional coefficient of harmonic component. On the other hand, the phase error compensation method is designed to compensate the phase error and improve the accuracy and speed of phase calculation after gamma correction. Experiments show that the proposed precalibration gamma coefficient method can effectively reduce the sinusoidal error in nearly 80 percent which only needs fewer fringe patterns. Compared with the traditional three-frequency with four-phase shift method, the proposed method not only has higher phase accuracy and better noise resistance but also has good robustness and flexibility, which is not limited to the gamma distortion model.