快速傅里叶变换与泽尼克模式拟合的条纹投影面形恢复算法

刘江; 崔穆涵; 高松涛; 隋永新; 杨怀江

doi:doi:10.5768/jao201334.0402004

应用光学, 2013, 34 (4): 614, 网络出版: 2013-10-23

快速傅里叶变换与泽尼克模式拟合的条纹投影面形恢复算法

FFT-Zernike combined algorithm of wavefront reconstruction in measurement of optical surfaces based on projected fringes deflectometry

论文大纲

刘江 ^1,2,*崔穆涵 ^1,2高松涛 ^1,2隋永新 ¹杨怀江 ¹

作者单位

¹ 中国科学院长春光学精密机械与物理研究所应用光学国家重点实验室，吉林长春 130033

² 中国科学院大学，北京 100049

摘要

针对条纹投影偏折法中需要多次迭代进行面形恢复，提出一种结合快速傅里叶变换（FFT）算法与泽尼克（Zernike）模式拟合的算法（FFT-泽尼克）。数值仿真结果表明，直接使用泽尼克模式拟合，需要迭代15次，用时1 min以上，而使用FFT-泽尼克算法，迭代5次已收敛到理想精度。在保证计算精度在纳米量级的情况下，计算时间也缩短了近2/3。

Abstract

The basic principle of projected fringes deflectometry is to measure the point-to-point relations of coordinates among free-form surface, camera and projection screen, and then compute the reconstructed surface with calculated slope data iteratively. In order to reduce the calculating time of the wavefront reconstruction without losing accuracy, a fast Fourier transform(FFT)-Zernike combined algorithm was proposed. The simulated result demonstrates the proposed algorithm can decrease the iterative procedure to 5 times using less than 20 seconds, compared with the traditional Zernike modal algorithm which has 15 iteration times using more than 1 minute. In addition, the calculating time is cut by two-thirds with the accuracy achieving the order of nanometer.

参考文献

[1] MARKUS C K, JURGEN K,GERD H. Phase measuring deflectometry: a new approach to measure specular free-form surfaces[J]. SPIE，2004，5457：366-376.

[2] WANG Jian-feng ,LIU Ke .LI Yan-qiu ,et al. Comparison of wavefront reconstruction with modal method and zonal[J]. SPIE ,2011,8197A:1-10.

[3] RIMMER M P. Method for evaluating lateral shearing interferograms [J] . Appl. Opt., 1974, 13(3):623-629.

[4] CUBALCHINI R. Modal wave-front estimation from phase derivative measurements[J]. J.Opt.Soc.Am.,1979,69(1):972-977.

[5] 谢苏隆. Zernike多项式拟合曲面中拟合精度与采样点数目研究[J] .应用光学, 2010,31(6): 944-949.

XIE Su-long. Sampling point number in curved surface fitting with Zernike polynomials [J].Journal of Applied Optics, 2010, 31(6): 944-949. (in Chinese with an English abstract)

[6] SOUTHWELL W H. Wave-front estimation from wave-front slope measurements[J]. J. Opt. Soc. Am.,1980, 70(8): 998-1006.

[7] KLAUS F, CHRIS L,KOLIOPOU L. Wavefront reconstruction from noisy slope or difference data using the discrete fourier transform[J]. SPIE ,1985, 551: 75-80.

[8] MICHEL G . Method for surface reconstruction from slope or curvature measurements of rectangular areas[J].Applied Optics,1997, 36(20): 4823-4829.

[9] SU Peng ,ROBERT E,PARKS, et al. Software configurable optical test system: a computerized reverse Hartmann test[J]. Applied Optics ,2010, 49(23): 4404-4412.

[10] MALACARA D. Optical shop testing[M].3rd ed. Hoboken:John Wiley&Sons,Inc.,2007.

[11] 王灵杰, 张新, 张建萍, 等. 自由曲面空间光学系统设计研究[J]. 应用光学，2012，33(6): 1041-1046.

WANG Ling-jie, ZHANG Xin, ZHANG Jian-ping, et al. Free-form surface space optical system[J]. Journal of Applied Optics, 2012，33(6): 1041-1046. (in Chinese with an English abstract)

刘江, 崔穆涵, 高松涛, 隋永新, 杨怀江. 快速傅里叶变换与泽尼克模式拟合的条纹投影面形恢复算法[J]. 应用光学, 2013, 34(4): 614. LIU Jiang, CUI Mu-han, GAO Song-tao, SUI Yong-xin, YANG Huai-jiang. FFT-Zernike combined algorithm of wavefront reconstruction in measurement of optical surfaces based on projected fringes deflectometry[J]. Journal of Applied Optics, 2013, 34(4): 614.

快速傅里叶变换与泽尼克模式拟合的条纹投影面形恢复算法

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