基于频域分析的抗振移相干涉测量

刘乾; 王洋; 吉方; 何建国; 张连新

doi:doi:10.3788/ope.20152301.0252

光学精密工程, 2015, 23 (1): 252, 网络出版: 2015-02-15

基于频域分析的抗振移相干涉测量

Vibration-insensitive phase-shifting interferometry based on frequency domain analysis

论文大纲

刘乾 ^*王洋吉方何建国张连新

作者单位

中国工程物理研究院机械制造工艺研究所, 四川绵阳 621900

移相干涉术确定性加工振动频域分析现场测量 phase-shifting interferometry deterministic manufacturing vibration frequency domain analysis on-machine testing

摘要

针对移相干涉测量中振动引起的移相误差和对比度变化, 提出了一种从空间载波干涉图频谱中提取移相和对比度信息的方法。该方法通过分析载波干涉图频谱, 从基带和边带中提取移相和对比度信息, 运用最小二乘法补偿对比度变化并复原波前位相。最后采用构造平滑孔径函数对带有孔径的干涉图进行处理。数值仿真证明: 提出的方法可以高精度检测移相量和对比度变化, 能够有效补偿因对比度变化引起的位相复原误差。在频率为9 Hz、幅度为0.5 μm的简谐振动条件下实验验证了本文方法的实用性。结果显示: 从受振动干扰的干涉图中复原平晶表面时, 其复原误差PV值小于0.015波长。该方法无需硬件改动, 有望为移相干涉测量应用于现场测量提供一种低成本的解决方法。

Abstract

An algorithm was proposed to deal with the phase-shifting error and contrast variation in a Phase-shifting Interferometry (PSI) under vibration. The algorithm detected phase shifts and contrast variation by analyzing the spectra of spatial-carrier interferograms firstly. Then the phase shifts were used as priori information to retrieve the wavefront phase from least-square equation with contrast compensation. To deal with interferograms with non-rectangular aperture, a mask with soft border was constructed and data extrapolation was avoided. The effectiveness of the proposed algorithm was validated by simulations and experiments. The simulation results show the proposed method can detect the phase shifts and contrast variation in high accuracy and can compensate effectively phase retrieval errors caused by contrast variation. The practicability of the algorithm was verified under a simple harmonic vibration with a frequency of 9 Hz and an amplitude of 0.5 μm. The measurement under vibration demonstrates that the retrieval error of a flat surface is less than 0.015 waves (PV value). The algorithm provides a low-cost approach to application of PSI to field measurement under vibration without modification of the hardware of interferometers.

参考文献

[1] 王朋, 陈亚, 宣斌, 等. 大口径光学元件的机械手抛光［J］. 光学精密工程, 2010, 18(5): 1077-1085.

WANG P, CHEN Y, XUAN B, et al.. Polishing large aperture mirrors by manipulator ［J］. Opt. Precision Eng., 2010, 18(5): 1077-1085. (in Chinese)

[2] 王永刚, 崔天刚, 马文生, 等. 弹性球状小磨头加工WolterⅠ型掠入射反射镜的去除函数［J］. 光学精密工程, 2011, 19(1): 10-16.

WANG Y G, CUI T G, MA W SH, et al.. Removal function for fabrication of WolterⅠ grazing mirror by elastic ball tool ［J］. Opt. Precision Eng., 2011, 19(1): 10-16. (in Chinese)

[3] 李娜, 王波, 金会良, 等. 微结构光学元件的大气等离子体数控加工［J］. 光学精密工程, 2013, 21(4): 934-940.

LI N, WANG B, JIN H L, et al.. Numerically controlled atmospheric pressure plasma processing of micro-structured optics ［J］. Opt. Precision Eng., 2013, 21(4): 934-940. (in Chinese)

[4] KINNSTAETTER K, LOHMANN A W, SCHWIDER J, et al.. Accuracy of phase shifting interferometry ［J］. Appl. Opt., 1988, 27(24): 5082-5087.

[5] WINGERDEN J, FRANKENA H, SMORENBURG C. Linear approximation for measurement errors in phase shifting interferometry ［J］. Appl. Opt., 1991, 30(19): 2718-2729.

[6] DECKL. Vibration-resistant phase-shifting interferometry ［J］. Appl. Opt., 1996, 35(34): 6655-6662.

[7] 吴新民. 光干涉测试中的抗振技术研究［D］. 南京: 南京理工大学, 2001.

WU X M. Research on vibration-resistance technology for optical interferometry ［D］. Nanjing: Nanjing University of Science and Technology, 2001. (in Chinese)

[8] HAO Q, ZHU Q D, HU Y. Random phase-shifting interferometry without accurately controlling or calibrating the phase shifts ［J］. Opt. Lett., 2009, 34(8): 1288-1290.

[9] PARK J, KIM S. Vibration-desensitized interferometer by continuousphase shifting with high-speed fringe capturing ［J］. Opt. Lett., 2010, 35(1): 19-21.

[10] 王明, 郝群, 朱秋东, 等. 时频域双重分析法抗干扰移相干涉术［J］. 光学学报, 2011, 31(10): 1112005.

WANG M, HAO Q, ZHU Q D, et al.. Anti-disturbance phase-shifting interferometry method time-and frequency-domain ［J］. Acta Optica Sinica, 2011, 31(10): 1112005. (in Chinese)

[11] XU J CH, XU Q, CHAI L Q. Tilt-shift determination and compensation in phase-shifting interferometry ［J］. J. Opt. A: Pure Appl. Opt., 2008, 10: 075011.

[12] LIU Q, WANG Y, JI F, et al.. Phase- and tilt-shift determinations by analysis of spectra sidebands for phase-shift interferometers ［J］. Appl. Opt., 2013, 52(31): 7654-7659.

[13] LIU Q, WANG Y, HE J G, et al.. Tilt shift determinations with spatial-carrier phase-shift method in temporal phase-shift interferometry ［J］. J. Opt., 2014, 16: 075404.

[14] XU J CH, XU Q, CHAI L Q. Iterative algorithm for phase extraction from interferograms with random and spatially nonuniform phase shifts ［J］. Appl. Opt., 2008, 47(3): 480-485.

[15] 苏志德, 史振广, 苏东奇, 等. 在随机和倾斜移相下光强归一化的迭代移相算法［J］. 光学学报, 2013, 33(1): 0112001.

SU ZH D, SHI ZH G, SU D Q, et al.. Iterative phase shifting algorithm with normalized intensity in the presence of random and tilt phase shifts ［J］. Acta Optica Sinica, 2013, 33(1): 0112001. (in Chinese)

[16] 赵智亮, 夏伯才, 陈立华, 等. 相移干涉测量中相移误差的自修正［J］. 光学精密工程, 2013, 31(5): 1116-1121.

ZHAO ZH L, XIA B C, CHEN L H, et al.. Self-correction of phase step error in phase shifting interferometric measurement ［J］. Opt. Precision Eng., 2013, 31(5): 1116-1121. (in Chinese)

[17] LIU Q, WANG Y, JI F, et al.. A three-step least-squares iterative method for tilt phase-shift interferometry ［J］. Opt. Express, 2013, 21(24): 29505-29515.

[18] 郝群, 朱秋东, 胡摇, 等. 一种在干涉图外圈开辟环形光强监测区的光强修正方法, 中国: CN 101482394 B ［P］. 2010.

HAO Q, ZHU Q D, HU Y, et al.. A light intensity correction method to open annular light intensity monitoring area in the outer interference pattern, China: CN 101482394 B ［P］. 2010.

[19] 马冬梅, 邵晶, 金春水, 等. 一种对移相干涉仪随机误差模态的评估方法, 中国: CN 103047928 A ［P］. 2013.

MA D M, SHAO J, JING CH SH, et al.. A assessment method of random error modal for phase-shift interferometer, China: CN 103047928 A ［P］. 2013.

[20] RODDIER C, RODDIER F. Interferogram analysis using Fourier transform techniques ［J］. Appl. Opt., 1987, 26(9): 1668-1673.

[21] GROOT P D.Measurement of transparent plates with wavelength-tuned phase-shifting interferometry ［J］. Appl. Opt., 2000, 39(16): 2658-2663.

刘乾, 王洋, 吉方, 何建国, 张连新. 基于频域分析的抗振移相干涉测量[J]. 光学精密工程, 2015, 23(1): 252. LIU Qian, WANG Yang, JI Fang, HE Jian-guo, ZHANG Lian-xin. Vibration-insensitive phase-shifting interferometry based on frequency domain analysis[J]. Optics and Precision Engineering, 2015, 23(1): 252.

基于频域分析的抗振移相干涉测量

关于本站 Cookie 的使用提示

全站搜索

基于频域分析的抗振移相干涉测量

相关论文

相关资讯

关于本站 Cookie 的使用提示

全站搜索