二维快速傅里叶变换干涉图相位提取误差分析  

Phase Retrieval Errors Analysis of Interferogram Using Two Dimensional Fast Fourier Transform Method

作　　者：张敏[1,2] 唐锋[1,2] 王向朝[1,2] 戴凤钊[1,2] 

机构地区：[1]中国科学院上海光学精密机械研究所信息光学与光电技术实验室,上海201800 [2]中国科学院大学,北京100049

出　　处：《中国激光》2013年第3期179-184,共6页Chinese Journal of Lasers

基　　金：国家自然科学基金重点项目(60938003;61205102和61275207)资助课题

摘　　要：基于ZYGO干涉仪实测干涉图,利用二维快速傅里叶变换(FFT)法进行相位提取,并与相移干涉相位测量结果进行比对,对影响FFT法相位提取精度的边缘误差、窗函数、滤波器设计、干涉图延拓以及载波条纹数等因素进行了综合分析。结果表明直接二维FFT法干涉图边缘0.05R环形区域的相位提取误差最大,且决定了全局误差的大小。窗函数对边缘误差改善不明显,优化滤波器设计对边缘误差有一定改善。干涉图延拓能有效减小边缘误差,对于连续光学面检测而言是提高二维FFT法相位提取精度的最佳方法。干涉图载波频率为干涉图空间分辨率的1/13～1/3时均能得到较准确的测量结果,相位提取误差峰谷值(PV)可优于λ/20;载波频率越高,细节分辨能力越强。Based on the actual interferogram grabbed by a ZYGO interferometer, the phase is retrieved by twodimensional fast Fourier transform （FFT） method and the factors which impact phase retrieval accuracy of FFT method including edge errors, window function, filter design, interferogram extrapolation and the number of carrier fringes are comprehensively analyzed, by comparing with the phase-shift measurement results. It is found that for the direct 2D FFT method, the edge 0.05R circular area of the interferogram has the biggest phase retrieval errors and decides the value of global errors. Window functions almost have no improvement for edge errors. Optimization of filter design can improve edge errors in some degree. Interferograrn extrapolation can reduce edge errors effectively and it is the best way to enhance phase retrieval accuracy for continuous optical surface test. Accurate measurement results can be achieved when the frequency is 1/13-1/3 of the space resolution of the interferogram with peak-to-walley （PV） value of phase retrieval errors less than ;t/20. The higher the carrier frequency is, the better the detail resolution is.

关 键 词：测量 干涉图 相位提取 二维快速傅里叶变换 边缘误差 干涉图延拓 

分 类 号：O436.1[机械工程—光学工程]