基于通用有理多项式模型的伽马非线性自补偿

Gamma Nonlinear Self-Compensation Based on General Rational Polynomial Model

为减小数字相移条纹投影系统中非线性响应引起的相位误差,提出了一种基于通用有理多项式模型的自补偿方法。该方法首先利用多项式来建模投影仪的未知非线性,然后建立相位误差函数。其次,利用离群检测算法剔除偏离点,并利用优化函数多次迭代求解出误差函数中的相位误差系数。最后,将含有误差的相位代入到相位误差函数中,通过不动点迭代运算对相位误差进行逐点修正。实验结果表明,上述自补偿方法易于实现且不需要预先校准,在无须提前标定数据条件下,可以有效减小数字相移条纹投影过程中的非线性误差,有助于提高系统的测量精度和测量效率。

To reduce the phase error caused by the nonlinear response in the digital phase-shifting fringe projection system,a self-correction method based on the universal rational polynomial model is proposed.The method first uses polynomials to model the unknown nonlinearity of the projector,and then establishes the phase error function.Second,the outlier detection algorithm is used to eliminate the deviation points,and the phase error coefficient in the error function is solved iteratively by using the optimization function.Finally,the phase with error is substituted into the phase error function,and the phase error is corrected point by point through fixed point iteration.The experimental results show that the proposed self-correction method is easy to implement and does not require pre-calibration,and can effectively reduce the nonlinear errors in the digital phase-shifting fringe projection process without the need of data calibration in advance,which is helpful to improve the measurement accuracy and efficiency of the system.