多级反射镜阵列Monte Carlo法误差合成与统计分析

吕金光; 梁静秋; 梁中翥

doi:10.7498/aps.61.220701

摘要

本文研究的傅里叶变换红外光谱仪利用两面多级反射镜阵列替代时间调制型傅里叶变换光谱仪中的平面反射镜, 以多级反射镜阵列对干涉图数据进行二维采样, 从而减小系统的体积并增加系统的稳定性.由于多级反射镜阵列在其制作过程中加工精度的限制, 各子反射镜之间会存在厚度偏差ε与角度偏差θ, 这将影响到采样干涉图的光强分布与复原光谱的质量.本文将各子反射镜的 ε与θ 作为随机变量, 利用Monte Carlo方法对傅里叶变换光谱仪中所有子反射镜的误差项进行合成, 并通过对误差合成后光谱误差因子 Q的统计分析来评价子反射镜的各误差项对复原光谱的影响. 统计结果表明, Q的统计均值随着σε 与σθ 的增加表现为一单调递增的曲面, 且与两个偏差之间具有准线性关系. 依据对Q的统计分析, 可以确定多级反射镜阵列各子反射镜ε 与θ 的容限.

关键词:

Abstract

To achieve the miniaturization and the static state of the Fourier transform spectrometer, two stepped mirror arrays are introduced into the time-modulation Fourier transform spectrometer to replace of the plane mirrors. The two stepped mirrors can sample the interferogram data in two-dimensional space, which can reduce the size of the instrument and increase the stability of the system. Due to the precision restriction on the stepped mirrors in the fabrication process, the various sub-mirrors of the stepped mirrors may contain various thickness errors and angle errors, which can affect the distribution of the interferogram and the quality of the spectrum. We regard the thickness error and the angle error of all the sub-mirrors as random variables, and synthesize all the error terms into a Fourier transform integration function using Monte Carlo method. By means of statistic analysis on the spectrum error factor, we can appraise the recovered spectrum affected by the thickness error and the angle error of the sub-mirror. The statistical result indicates that the statistical mean of the spectrum error factor increases with thickness standard deviation and angle standard deviation increasing. According to the statistical analysis on spectrum error factor, the tolerances of the thickness standard deviation and the angle standard deviation of the sub-mirror can be determined in the fabrication process of the stepped mirrors.

Keywords:

作者及机构信息

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, 长春 130033;

2.
中国科学院研究生院, 北京 100049

基金项目: 国家自然科学基金(批准号:61027010, 60977062)、国家高技术研究发展计划(批准号:2009AA04Z315)、吉林省科技发展计划(批准号:201205025)和应用光学国家重点实验室自主基金资助的课题.

Authors and contacts

1.
State Key Laboratory of Applied Optics, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun130033, China;

2.
Graduate University of Chinese Academy of Sciences, Beijing 100049, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61027010, 60977062), the National High Technology Research and Development Program of China (Grant No. 2009AA04Z315), the Jilin Province Science and Technology Development Plan (Grant No. 201205025), and the State Key Lab. of Applied Optics.

参考文献

[1]	Weng S F 2005 Fourier Transform Infrared Spectrometer (Beijing: Chemical Industry Press) p34 (in Chinese) [翁诗甫 2005 傅里叶变换红外光谱仪 (北京: 化学工业出版社) 第34页]
[2]	Zhu L, Chen M X, Fang J, Liu Y, Wang A 2010 Optics and Precision Engineering 18 2537 (in Chinese) [朱灵, 陈明星, 方杰, 刘勇, 王安 2010 光学精密工程 18 2537]
[3]	Zeng L B, Yin B S, He B, Gong D 2006 Optics and Precision Engineering 14 191 (in Chinese) [曾立波, 尹邦胜, 何冰, 龚丹 2006 光学精密工程 14 191]
[4]	Manzardo O 2002 M.S. Dissertation (Switzerland: Neuchatel University)
[5]	Anatoliy M, Henrik A, Goran T, Hans-Erik N 2006 Proc. of SPIE 6395 639504
[6]	Tian E M, Zhang J L, Li X, Zhang Y, Wang Z B 2009 Spectrosc. Spect. Anal. 29 853 (in Chinese) [田二明, 张记龙, 李晓, 张悦, 王志斌 2009 光谱学与光谱分析 29 853]
[7]	Fu J G, Liang Z Z, Liang J Q 2010 Spectrosc. Spect. Anal. 30 3203 (in Chinese) [付建国, 梁中翥, 梁静秋 2010 光谱学与光谱分析 30 3203]
[8]	Lv J G, Liang Z Z, Fu J G, Liang J Q 2011 Spectrosc. Spect. Anal. 31 2865 (in Chinese) [吕金光, 梁中翥, 付建国, 梁静秋2011 光谱学与光谱分析 31 2865]
[9]	Lv J G, Liang J Q, Liang Z Z, Fu J G 2012 Spectrosc. Spect. Anal. 32 259 (in Chinese) [吕金光, 梁静秋, 梁中翥, 付建国 2012 光谱学与光谱分析 32 259]
[10]	Feng C, Liang J Q, Liang Z Z 2011 Appl. Opt. 50 6377
[11]	Feng C, Wang B, Liang Z Z, Liang J Q 2011 J. Opt. Soc. Am. B 28 1
[12]	Fei Y T 2004 Error Theory And Data Processing (Beijing: China Machine Press) p55 (in Chinese) [费业泰 2004 误差理论与数据处理 (北京: 机械工业出版社) 第55页]
[13]	Gao W S, Pan W 2004 Random Mathematics (Beijing: Higher Education Press) p53 (in Chinese) [高文森, 潘伟 2004 随机数学 (北京: 高等教育出版社) 第53页]
[14]	Xiang L B, Yuan Y, Lv Q B 2009 Acta Phys. Sin. 58 5399 (in Chinese) [相里斌, 袁艳, 吕群波 2009 物理学报 58 5399]
[15]	Lv Q B, Yao T, Xiang L B, H M 2010 Spectrosc. Spect. Anal. 30 114 (in Chinese) [吕群波, 姚涛, 相里斌, 黄旻 2010 光谱学与光谱分析 30 114]
[16]	Jian X H, Zhang C M, Zhang L, Zhao B C 2010 Opt. Express 18 5674
[17]	Jian X H, Zhang C M, Zhu B H, Ren W Y 2010 Acta Phys. Sin. 59 6131 (in Chinese) [简小华, 张淳民, 祝宝辉, 任文艺 2010 物理学报 59 6131]
[18]	Zhang C M, Jian X H 2010 Opt. Lett. 35 366
[19]	Zhang C M, Huang W J, Zhao B C 2010 Acta Phys. Sin. 59 5479 (in Chinese) [张淳民, 黄伟健, 赵葆常 2010 物理学报 59 5479]

施引文献

[1]	Weng S F 2005 Fourier Transform Infrared Spectrometer (Beijing: Chemical Industry Press) p34 (in Chinese) [翁诗甫 2005 傅里叶变换红外光谱仪 (北京: 化学工业出版社) 第34页]
[2]	Zhu L, Chen M X, Fang J, Liu Y, Wang A 2010 Optics and Precision Engineering 18 2537 (in Chinese) [朱灵, 陈明星, 方杰, 刘勇, 王安 2010 光学精密工程 18 2537]
[3]	Zeng L B, Yin B S, He B, Gong D 2006 Optics and Precision Engineering 14 191 (in Chinese) [曾立波, 尹邦胜, 何冰, 龚丹 2006 光学精密工程 14 191]
[4]	Manzardo O 2002 M.S. Dissertation (Switzerland: Neuchatel University)
[5]	Anatoliy M, Henrik A, Goran T, Hans-Erik N 2006 Proc. of SPIE 6395 639504
[6]	Tian E M, Zhang J L, Li X, Zhang Y, Wang Z B 2009 Spectrosc. Spect. Anal. 29 853 (in Chinese) [田二明, 张记龙, 李晓, 张悦, 王志斌 2009 光谱学与光谱分析 29 853]
[7]	Fu J G, Liang Z Z, Liang J Q 2010 Spectrosc. Spect. Anal. 30 3203 (in Chinese) [付建国, 梁中翥, 梁静秋 2010 光谱学与光谱分析 30 3203]
[8]	Lv J G, Liang Z Z, Fu J G, Liang J Q 2011 Spectrosc. Spect. Anal. 31 2865 (in Chinese) [吕金光, 梁中翥, 付建国, 梁静秋2011 光谱学与光谱分析 31 2865]
[9]	Lv J G, Liang J Q, Liang Z Z, Fu J G 2012 Spectrosc. Spect. Anal. 32 259 (in Chinese) [吕金光, 梁静秋, 梁中翥, 付建国 2012 光谱学与光谱分析 32 259]
[10]	Feng C, Liang J Q, Liang Z Z 2011 Appl. Opt. 50 6377
[11]	Feng C, Wang B, Liang Z Z, Liang J Q 2011 J. Opt. Soc. Am. B 28 1
[12]	Fei Y T 2004 Error Theory And Data Processing (Beijing: China Machine Press) p55 (in Chinese) [费业泰 2004 误差理论与数据处理 (北京: 机械工业出版社) 第55页]
[13]	Gao W S, Pan W 2004 Random Mathematics (Beijing: Higher Education Press) p53 (in Chinese) [高文森, 潘伟 2004 随机数学 (北京: 高等教育出版社) 第53页]
[14]	Xiang L B, Yuan Y, Lv Q B 2009 Acta Phys. Sin. 58 5399 (in Chinese) [相里斌, 袁艳, 吕群波 2009 物理学报 58 5399]
[15]	Lv Q B, Yao T, Xiang L B, H M 2010 Spectrosc. Spect. Anal. 30 114 (in Chinese) [吕群波, 姚涛, 相里斌, 黄旻 2010 光谱学与光谱分析 30 114]
[16]	Jian X H, Zhang C M, Zhang L, Zhao B C 2010 Opt. Express 18 5674
[17]	Jian X H, Zhang C M, Zhu B H, Ren W Y 2010 Acta Phys. Sin. 59 6131 (in Chinese) [简小华, 张淳民, 祝宝辉, 任文艺 2010 物理学报 59 6131]
[18]	Zhang C M, Jian X H 2010 Opt. Lett. 35 366
[19]	Zhang C M, Huang W J, Zhao B C 2010 Acta Phys. Sin. 59 5479 (in Chinese) [张淳民, 黄伟健, 赵葆常 2010 物理学报 59 5479]

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