一种小幅度步距相移干涉算法的相移误差分析

Phase Shift Error Analysis of a Phase-shifting Interference Algorithm with Small Phase Step Size

为缩短相移时间,减少实际环境中低频振动的引入,采用极小幅度相移步长如5°、10°、20°替代常用的90°产生5帧相移干涉条纹图进而用相移算法还原相位。同时,基于一种自调谐相移法,提出综合利用3步法和5步法分别求得相移步长与波前相位。仿真分析了相移步长20°时,该算法与Hariharan算法在相移标定、随机误差下的相位还原误差。结果表明,该算法在相移标定误差±10%内,相移步长还原精度达10^(-5)λ,相位还原误差峰谷值低至10^(-6)λ,远低于Hariharan算法误差10^(-3)λ。在5%随机相移误差内,Hariharan算法相位还原精度更高。两种算法的误差峰谷、均方根平均值相差3倍,但该自调谐算法仍具有较高还原精度。同时,取更小相移步长5°、10°对比,结果表明,在标定误差下,两种算法的相位还原精度无明显变化;在随机误差下,两种算法精度均降低。因此,从理论仿真上来说,小相移步长与该自调谐算法结合对标定误差具有突出的抑制作用,在随机相移误差下也能保证一定相位还原精度。

In optical metrology,Phase-Shifting Interferometry(PSI)is used to measure the surface morphology and wavefront phase of optical components,one of the most accurate methods.Phase-shifting interferometers often use piezoelectric ceramics as phase shifters to drive the reference arm to generate phase shift step.The measurement accuracy of the PSI technique is subject to the phase shifter accuracy.If the actual phase shift value deviates from the ideal one,the phase restoration accuracy will be greatly reduced.Considering that the 5-step with step size such as 5°,10°,and 20°phase shift is greatly shortened compared to the 90°stroke,the hysteresis and nonlinearity in the PZT phase-shift curve can be ignored,and higher precision.At the same time,shortening the time can increase the frequency sensitivity to vibration and reduce the introduction of main low-frequency vibration in the actual environment.Therefore,this paper proposes to replace the common 90°with a tiny phase shift step to acquire five frames of interferograms.In order to verify the performance of the tiny phase shift 5-step algorithm,numerical simulation analysis is carried out at the primary error sources of calibration error and random phase shift error.Based on a self-tuning algorithm,restoring the actual phase shift step size by 3-step algorithm before the 5-step Hariharan algorithm is proposed.Under the calibration error,when the fringe phase spatial distribution satisfies the integer fringe number,the actual phase shift can be obtained with high accuracy through the space averaging operation to eliminate phase error as much as possible.While the random phase shift error,the restored phase shift amount will be around to the average value of the intermediate phase shift error by extending the 3-step method to fully utilize the interferograms.The simulation results show that within the±10%calibration error,the restoration accuracy of the phase shift step size increases with a lager calibration error,but as high as 10^(-5)λ.The phase error curve is the same trend as the phase shift amount recovery error curve.The phase restoration error PV and RMS by the self-tuning algorithm remain in the order of 10^(-6)λwhile 10^(-3)λby the classic 5-step Hariharan algorithm,which significantly improves the phase restoration accuracy.Within the 5%random phase shift error,the phase restoration accuracy of the self-tuning algorithm is lower than that of the Hariharan algorithm.The average values of PV and RMS of the two algorithms differ by three times.The maximum PV values are 0.0097λand 0.0029λ,respectively,and the RMS values are 0.004λand 0.0014λ.When the solving phase shift step size is close to the average value,the restoration accuracy is the same as that of the Hariharan algorithm,it may even be higher than that of the Hariharan algorithm.From the results,within 5%of the error margin,the self-tuning algorithm can still ensure high restoration accuracy.At the same time,the results at the smaller phase shift steps of 5°and 10°show that the phase restoration accuracy of the two algorithms does not change significantly under the calibration error;the accuracy of the two algorithms is reduced under the random error,and the selftuning algorithm is difficult to ensure the phase restoration accuracy when the phase shift step is 5°.The 20°phase shift step is a better choice.Due to the tiny phase shift,further sampling of the interferograms can be considered,and the phase error can be eliminated as much as possible by the overlapping average method.Experiments should be carried out to verify the anti-vibration performance of the tiny phase shift algorithm.During the experiment,processes such as CCD sampling and calibration should be considered.