用矩阵条件数求解相移最佳采样方式

应用相移干涉术测量物体相位时,相移量与相移帧数存在着最佳取值问题,即最佳采样方式,它决定着系统抗扰动和降低误差的能力.用系数矩阵的条件数衡量相位测量误差矩阵与强度探测误差矩阵方程的性态,即光强方程组对扰动的敏感程度,经数学推导及论证,得出结论:当系数矩阵为正交矩阵时,相位计算的误差最小,或者说在等间距满周期采样情况下,具有最强的抗噪音能力.在推导出最佳采样方式后,对系数矩阵的条件数与采样方式之间的关系进行了计算机模拟,并给出了模拟曲线.

The Solution of Best Sampling Manner in Phase-shifting Interferometry Based on Matrix Condition Number

This paper searches after what sampling method can get the more accurate phase value when existing experiment error and disturbance in phase-shifting interferometry, namely searches after the best value of phase-shifter and phase-shifting frame. The character of matrix equation of phase measurement error and intensity detection error is scaled in this paper, which is based on condition number of coefficient matrix according to matrix theory. Math demonstration deduced when coefficient matrix is perpendicularity matrix, equal sampling interval within a full cycle brings lest error of phase computation, which is of best noise resistance ability. This sampling method is the best sampling method. The numerical value simulation of coefficient matrix and sampling method relation is carried on, and simulation curve is gived.