A high-accuracy nonlinear phase error compensation method

Overview: The phase-shifting method uses multiple grating fringe images to solve the phase value pixel by pixel. This method has the advantages of high measurement accuracy and low cost, and is widely used in phase-based 3D topography measurement. Generally, it includes random error and systematic error. The former is usually represented by random noise, while the latter can be divided into phase-shifting error and nonlinear error. Among them, the nonlinear phase error is mainly caused by the nonlinear response in the measurement system, which is inevitable. Therefore, how to quickly and efficiently eliminate the nonlinear error in the system is the key to improve the measurement accuracy. This paper, which takes the three-step phase-shifting method as an example, proposes a phase compensation method based on the accurate mathematical model of phase error. We project a set of large phase shift fringe patterns in the calibration process, and collect all the harmonic components by using a large-step phase-shifting algorithm to measure a reference plane. In the actual measurement, the real phase is calculated by the three-step phase-shifting method, and then the phase compensation can be realized by iteration according to the phase error model and the known amplitude coefficients of all the harmonic components. In order to verify the effectiveness of this algorithm. We project a set of 18-step phase-shifting fringe patterns to obtain the ideal phase distributions and use three of them to get the nonlinear error-inclusive phase distributions. Then we use Pan's method and our method to compensate the phase error of the object respectively, and both methods are quantitatively evaluated by the residual errors. The experimental results show that the standard deviation of the residual errors without compensation is 0.1662 rad, which is reduced to 0.0581 rad by using Pan's method and 0.0193 rad by using our proposed method. The maximum phase error decreased from 0.2676 rad to 0.0807 rad. The original phase error without compensation is mainly 3-fold frequency characteristic, and the residual phase error is mainly 6-fold frequency characteristic after using Pan's method. It means that there are still uncompensated periodic errors, and the residual errors do not have obvious periodic distribution after compensated by our method. The experimental results show that this method is feasible and effective in three-dimensional measurement. The algorithm only needs three sinusoidal fringes to realize high-precision phase error compensation, which has the advantages of high precision and fast speed.