FFT动态相位重建算法的滤波窗影响分析

Analysis for effect of filter window on fast Fourier transform dynamic phase reconstruction algorithm

为了优化相位重建算法,针对波面干涉图的傅里叶频谱,分析了不同滤波窗口的分布特征和频谱响应,通过计算机仿真和实验测试,确定了FFT动态相位重建算法的最佳滤波窗口类型。其中处理仿真干涉图重建的波面与原始波面的波面峰谷值残差为0.0085λ,波面均方根值残差为0.0001λ;处理实验干涉图获得的波面与移相干涉测量法获得的波面峰谷值残差为0.0093λ,波面均方根值残差为0.0005λ。结果表明:选取Hamming窗进行滤波处理并重建的相位经拟合后得到的波面较参考波面的面形残差最小,相位重建精度优于0.01λ,可进一步应用于大口径光学元件的测量中。

In order to optimize the phase reconstruction algorithm,the distribution characteristics and spectral response of different filtering windows were analyzed for the Fourier spectrum of the wavefront interferogram.The optimal filtering window type of the fast Fourier transform(FFT)dynamic phase reconstruction algorithm was determined by computer simulation and experimental test.The residual error of the wavefront peak-valley value between the reconstructed wavefront by the simulated interferogramand the original wavefront is 0.0085λ,as well as the residual of the wavefront root-mean-square is 0.0001λ,while the residual of the wavefront peak-valley value between the obtained wavefront by the experimental interferogram and by the phase-shifting interferometry is 0.0093λ,as well as the residual of the wavefront root-mean-square is 0.0005λ.The results show that,after fitting the phase filtered and reconstructed by Hamming window,the residual surface error of the wavefront obtained is smaller that the reference wavefront,and the phase reconstruction accuracy is better than 0.01λ,which can be further applied to the measurement of large-caliber optical elements.