基于自调谐相移干涉算法的相移误差分析

Analysis of phase shift error based on a self-tuning phase-shifting interference algorithm

相移干涉技术由于其测量精度高的特点被广泛应用于波面检测干涉仪中。相移误差为测量过程中主要误差来源。基于一种自调谐相移干涉算法,研究在标定误差和随机相移误差下,算法的波前相位还原精度。对于标定误差,算法能精确地求解出实际相移步长,从而极大地提高了相位还原精度。与经典五步Hariharan算法对比,仿真结果表明,该算法的相位还原PV(峰谷)、RMS(均方根)误差响应更低,其PV误差响应远低于10^(-3)λ(λ为光源中心波长),而Hariharan算法在10^(-3)λ量级。基于自调谐算法在标定误差时的相位求解过程,扩展该算法以更适用于随机相移误差。在相同20%随机相移误差范围内,与Hariharan算法计算结果偏差的绝对值接近10^(-9)λ,能达到较高还原精度。将该自调谐算法运用在干涉仪测量光学元件表面形貌实验中,实验结果表明,与Hariharan算法相比,自调谐算法在仅存在标定误差时,能较明显地抑制纹波误差,两者计算面形PV存在偏差。在较小振动环境下,两种算法计算得到的相位面形分布高度一致。

The phase-shifting interferometry technique is widely used in wavefront detection interferometers due to its high measurement accuracy. The phase shift error is the main source of error in measurement process. Based on a self-tuning phase-shifting interference algorithm, the accuracy of wavefront phase restoration is studied under calibration errors and random phase shift errors. For the calibration error, the algorithm can accurately calculate the actual phase shift step size, thus greatly improving the phase restoration accuracy.Compared with the classic five-step Hariharan algorithm, the simulation results show that the phase restoration PV(Peak-Valley)and RMS(Root Mean Square)error response of this algorithm is lower,and its PV error response is much lower than 10^(-3)λ,whereλis the center wavelength of the light source,while the Hariharan algorithm is on the order of 10^(-3)λ.Based on the phase solving process of the self-tuning algorithm in phase shift calibration error,the algorithm is extended to be more suitable for random phase shift error.Within the same 20%random phase shift error range,the absolute value of the deviation from the Hariharan algorithm calculation result is close to 10^(-9)λ,which can achieve high restoration accuracy.The self-tuning algorithm is used in the measurement of the surface topography by the interferometer.The experimental results show that compared with the Hariharan algorithm,the self-tuning algorithm can obviously suppress the ripple error when there is only calibration error.There is a deviation in the surface PV.In a small vibration environment,the phase restored by the two algorithms are highly consistent.