用于相移点衍射干涉仪的加权最小二乘相位提取算法

于杰

用于相移点衍射干涉仪的加权最小二乘相位提取算法

于杰

中国科学院长春光学精密机械与物理研究所,吉林长春 130032

基金项目:

国家863高技术研究发展计划资助项目

详细信息

中图分类号: TH744.3; TP391.4
计量
- 文章访问数: 4929
- HTML全文浏览量: 481
- PDF下载量: 1741
- 被引次数: 0
出版历程
- 收稿日期: 2010-05-22
- 修回日期: 2010-07-25
- 刊出日期: 2010-12-20

Weighted least square phase extraction algorithm for phase-shifting point diffraction interferometer

YU Jie

Changchun Institute of Optics,Fine Mechanics and Physics, Chinese Academy of Sciences,Changchun 130033,China

摘要

摘要: 针对现有的相位提取算法只对某些特定的误差不敏感,不能满足高精度光学检测的要求,本文引入一种等间隔多步移相算法权重待定的加权最小二乘算法。通过在最小二乘算法中添加待定的权重,分析移相点衍射干涉仪中多种误差源对算法的影响,获得多组约束方程,从而确定权重和新算法。对新算法和标准四步算法、Hariharan五步算法进行比对分析,验证了新算法对PZT线性和二阶非线性移相不准、光强的一阶二阶波动和光源频率一阶二阶波动等误差抑制能力远远优于标准四步算法和Hariharan五步算法;新算法对CCD的量化误差、光强噪声、频率噪声的抑制能力也具有一定优势,且对CCD的二阶响应非线性完全不敏感。
- 移相干涉技术 /
- 误差分析 /
- 约束方程 /
- 最小二乘法 /
- 相位提取算法
Abstract: Existing phase extraction algorithms are just insensitive to some specifically error sources, which can't satisfy the requirements of optical testing for the high precision. An equal-phase interval multi-step phase-shifting algorithm, weighted least square algorithm with underdetermined weight, was introduced. By introducing undetermined weights to the least square algorithm and by analysing the effect of manifold error sources on the algorithm in phase-shifting point diffraction interferometer, several groups of bound equations were obtained and the undetermined weights and the new phase extraction algorithm were determined by solving these bound equations. The new phase extraction algorithm was compared with standard four-step algorithm and Hariharan five-step algorithm. The results illuminate that the new phase extraction algorithm is much more insensitive to the linearity and nonlinearity of second order of PZT, intensity fluctuation in linearity and nonlinearity of 2nd order, linearity and nonlinearity of 2nd order of frequency of light source fluctuation. The results also illunimate that the new algorithm have advantages over other two algorithms in eliminating the CCD quantization, intensity noise, and the frequency noise. Moreover, the new algorithm is insensitive to the CCD nonlinearity at all.
- phase-shifting interferometry /
- error analysis /
- bound equation /
- least square method /
- phase extraction algorithm

HTML全文

参考文献(1)

[1] BRUNING J H,SCHREIBER H. Optical Shop Testing[M]. 3rd edition. Hoboken:A John Wiley & Sons,2007. [2] BRUNING J H,HERRIOTT D J,BALLAGHER J E,et al.. Digital wavefront measuring interferometer for testing optical surface and lenss[J]. Appl. Opt.,1974,13(11):2693-2703. [3] SOMMARGREN G E. Phase shifting diffraction interferometry for measure extreme ultraviolet optics[J]. OSA Trends Opt. Photonics,1999,4:108-112. [4] NOVAK J. Five-step phase-shifting algorithms with unknown values of phase shift[J]. Optik,2003,2(114):63-68. [5] NOVAK J,NOVAK P,MIKS A. Multi-step phase-shifting algorithms insensitive to linear phase shift errors[J]. Opt. Communications,2008,281:5302-5309. [6] TANG SH H. Generalized algorithm for phase shifting interferometry[J]. SPIE,1996,2860:34-44. [7] CAI L Z,LIU Q,YANG X L. Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps[J]. Opt. Lett.,2003,28(19):1808-1810. [8] CAI L Z,LIU Q,YANG X L. Generalized phase-shifting interferometry with arbitrary unknown phase steps for diffraction objects[J]. Opt. Lett.,2004,29(2):183-185. [9] CREATH K. Error sources in phase-measuring interferometry[J]. SPIE, 1992,1720:428-435. [10] HARIHARAN P,OREB B F,EIJU T. Digital phase-shifting interferometry:a simple error-compensating phase calculation algorithm[J]. Appl. Opt.,1987,26(13):2504-2506. [11] SCHWIDER J,BUROW R,ELSSNER K-E,et al.. Digital wave-front measuring interferometry:some systematic error sources[J]. Appl. Opt.,1983,22(21):3421-3432. [12] 程万杰,赵杰,蔡鹤皋. CCD像素响应非均匀的校正方法[J]. 光学精密工程 ,2008,16(2):314-318. CHENG W J,ZHAO J,CAI H G. Correction method for pixel response nonuniformity of CCD [J]. Opt. Precision Eng.,2008,16(2):314-318.(in Chinese) [13] PHILLION D W. General methods for generating phase-shifting interferometry algorithms[J]. Appl. Opt.,1997,36(31):8098-8115. [14] BROPHY P. Effect of intensity error correlation on the computed phase of phase-shifting interferometry[J]. Opt. Soc. Am. A,1990,7(4):537-541.

施引文献

附加信息(0)

访问统计