基于主成分分析和VU分解法的两步随机相移算法

Two-step random phase-shifting algorithm based on principal component analysis and VU decomposition method

为了平衡相位计算的精度和速度,大量的两步随机相移算法发展起来。提出了一种基于主成分分析和VU分解法的快速、高精度两步随机相移算法。首先,采用两步主成分分析法对经过滤波的两幅相移干涉图进行计算求出迭代初始相位;然后,利用没有滤波的两幅相移干涉图进行VU分解、迭代求出最终相位。通过模拟和实验结果对比表明:与四种性能良好的两步随机相移算法相比,对于不同的条纹类型、噪声、相移值及条纹数量,提出的算法综合性能最好,其精度最高,有效相移范围和有效条纹数量范围最大,当干涉图像素数为401 pixel×401 pixel时,提出的算法仅比格兰-施密特正交化法和两步主成分分析法多花费0.035 s。在理想情况下,提出的算法可以得到完全正确的结果。如果需要得到较高精度,最好能够提前抑制噪声,同时设置相移值远离0和π,条纹数量大于2。主成分分析和VU分解法无需滤波,花费近似非迭代算法的时间获得迭代算法的精度,其打破了迭代算法花费时间较多的限制,适合高精度光学在线检测,有广泛的发展前景。

Objective The level of optical metrology determines the level of optical manufacturing technology,and the phase-shifting interferometry(PSI)as an easy,high-speed and accurate optical testing tool is usually used during or after optical fabrication.Both accuracy and efficiency are important to PSI.Outstanding phase-shifting algorithms(PSAs)can reduce the requirements for the interferometer hardware and environment,and further improve the accuracy and speed of PSI.Traditional PSAs with known phase shifts are easily affected by the miscalibration of piezo-transducer and environmental errors.In order to save time,many single-step PSAs were developed.Nevertheless,the sign of phase is difficult to judge by only one interferogram.In some high-precision events,accurate phase reconstruction is of interest.Hence,the multi-step PSAs with more than three interferograms were developed.However,it's difficult to reconstruct the phase with high accuracy and efficiency simultaneously.Comparatively,two-step random PSAs can avoid the effect of phase shift error,solve the sign ambiguity problem of the single-step PSAs,and balance the accuracy and speed.However,general two-step random PSAs need pre-filtering or use some complex methods to calculate background,these methods will cost more time.To balance the computational time and accuracy,a fast and high-precision two-step random phaseshifting algorithm based on principal component analysis and VU decomposition method is proposed in this paper.Methods A two-step random phase-shifting algorithm based on principal component analysis and VU decomposition method is proposed in this paper.Firstly,two-step principal component analysis method is used to calculate the initial phase of iteration by two filtered phase-shifting interferograms,and then VU decomposition and iteration of two unfiltered phase-shifting interferograms are used to calculate the final phase.Finally,the proposed method is compared with four good two-step random phase-shifting algorithms for different fringe types,noise,phase shift values and fringe numbers to verify its superior performance in the computational time and accuracy.Results and Discussions Compared with four good two-step random phase-shifting algorithms,the proposed method has the best comprehensive performance for different fringe types,noise,phase shift values and fringe numbers.The proposed method has the highest accuracy.Meanwhile,its effective phase shift range and fringe number range are the largest.When the size of interferograms is 401 pixel×401 pixel,the proposed method takes only 0.035 s more than Gram-Schmidt orthonormalization algorithm and two-step principal component analysis method.Under ideal conditions,the proposed method can get exactly correct result.If high precision is required,it is best to suppress the noise in advance,while setting the phase shift value away from 0 andπ,and the fringe number greater than 2.Conclusions In order to balance the accuracy and speed of phase calculation,a fast and high-precision two-step random phase-shifting algorithm based on principal component analysis and VU decomposition method is proposed in this paper.The method is characterized by high accuracy,high speed and no filtering.It takes approximately the time of non-iterative algorithm to obtain the accuracy of iterative algorithm,and breaks the limit that iterative algorithm costs more time.It is suitable for high-precision optical in-situ measurement and has wide development future.