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Study on chromatic dispersion of beam splitter in spatially modulated Fourier transform spectrometer

Lü Jin-Guang Liang Jing-Qiu Liang Zhong-Zhu

Study on chromatic dispersion of beam splitter in spatially modulated Fourier transform spectrometer

Lü Jin-Guang, Liang Jing-Qiu, Liang Zhong-Zhu
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  • Due to the chromatic dispersion of beam splitter, the interferogram units from various wavelengths could shift by different offsets, leading to interferogram aliasing in transverse space. Simultaneously, the interferograms of different wavelengths have different offsets of optical path difference, which makes the interferogram aliasing in vertical space. According to geometric optics principles, the transverse aliasing of the interferogram reduces the area of the interferogram unit, and the vertical aliasing of the interferogram leads to a phase-frequency response which could reduce the spectral line intensity. The calculation and the analysis indicate that the transverse aliasing area is only 3.4% of the total area of the interferogram unit in our study, which could be removed in the data processing; and the phase delay from the vertical aliasing of the interferogram is proportional to the thickness difference between the beam splitter and the compensating plate. The maximal thickness difference is provided when the contrast reversion appears in the interference fringe. Finally, we correct the chromatic dispersion from the aliasing interferogram by solving linear equation set, and recover the ideal spectrum.
    • 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), and the Jilin Province Science and Technology Development Plan, China (Grant No. 201205025).
    [1]

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    [2]

    Manzardo O 2002 M.S. Dissertation (Switzerland: Neuchatel University)

    [3]

    Anatoliy M, Henrik A, Goran T, Hans-Erik N 2006 Proc. SPIE 6395 639504

    [4]

    Lin L, Ren Z, Li G 2008 Spectrosc. Spect. Anal. 28 2067 (in Chinese) [林凌, 任钊, 李刚 2008 光谱学与光谱分析 28 2067]

    [5]

    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]

    [6]

    Kong Y M, Liang J Q, Liang Z Z, Wang B, Zhang J 2009 Proc. SPIE 7283 728304

    [7]

    Wang B, Liang Z Z, Kong Y M, Liang J Q, Fu J G, Zheng Y, Zhu W B, Lü J G, Wang W B, Pei S, Zhang J 2010 Acta Phys. Sin. 59 907 (in Chinese) [王波, 梁中翥, 孔延梅, 梁静秋, 付建国, 郑莹, 朱万彬, 吕金光, 王维彪, 裴舒, 张军 2010 物理学报 59 907]

    [8]

    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]

    [9]

    Lü 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]

    [10]

    Jian X H, Zhang C M, Zhao B C 2007 Acta Phys. Sin. 56 824 (in Chinese) [简小华, 张淳民, 赵葆常 2007 物理学报 56 824]

    [11]

    Lü Q B, Yao T, Xiang L B, Huang 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]

    [12]

    Xiang L B, Yuan Y, Lü 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]

    [13]

    Jian X H, Zhang C M, Zhang L, Zhao B C 2010 Opt. Express 18 5674

    [14]

    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]

    [15]

    Zhang C M, Jian X H 2010 Opt. Lett. 35 366

    [16]

    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]

    [17]

    Wu H Y, Zhang C M, Zhao B C, Li Y C 2009 Acta Phys. Sin. 58 1642 (in Chinese) [吴海英, 张淳民, 赵葆常, 李英才 2009 物理学报 58 1642]

    [18]

    Zhang C M, Ren W Y, Mu T K 2010 Chin. Phys. B 19 024202

    [19]

    Wu J F, Zhang C M 2010 Chin. Phys. B 19 034201

    [20]

    Ruan K, Zhang C M, Zhao B C 2008 Acta Phys. Sin. 57 5435 (in Chinese) [阮锴, 张淳民, 赵葆常 2008 物理学报 57 5435]

    [21]

    Zhang C M, Ai J J, Ren W Y 2011 Chin. Phys. B 20 020701

    [22]

    Zhang C M, Zhao J K, Sun Y 2011 Appl. Opt. 50 3497

    [23]

    Mu T K, Zhang C M, Zhang B C 2009 Acta Phys. Sin. 58 3877 (in Chinese) [穆廷魁, 张淳民, 赵葆常 2009 物理学报 58 3877]

  • [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]

    Manzardo O 2002 M.S. Dissertation (Switzerland: Neuchatel University)

    [3]

    Anatoliy M, Henrik A, Goran T, Hans-Erik N 2006 Proc. SPIE 6395 639504

    [4]

    Lin L, Ren Z, Li G 2008 Spectrosc. Spect. Anal. 28 2067 (in Chinese) [林凌, 任钊, 李刚 2008 光谱学与光谱分析 28 2067]

    [5]

    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]

    [6]

    Kong Y M, Liang J Q, Liang Z Z, Wang B, Zhang J 2009 Proc. SPIE 7283 728304

    [7]

    Wang B, Liang Z Z, Kong Y M, Liang J Q, Fu J G, Zheng Y, Zhu W B, Lü J G, Wang W B, Pei S, Zhang J 2010 Acta Phys. Sin. 59 907 (in Chinese) [王波, 梁中翥, 孔延梅, 梁静秋, 付建国, 郑莹, 朱万彬, 吕金光, 王维彪, 裴舒, 张军 2010 物理学报 59 907]

    [8]

    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]

    [9]

    Lü 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]

    [10]

    Jian X H, Zhang C M, Zhao B C 2007 Acta Phys. Sin. 56 824 (in Chinese) [简小华, 张淳民, 赵葆常 2007 物理学报 56 824]

    [11]

    Lü Q B, Yao T, Xiang L B, Huang 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]

    [12]

    Xiang L B, Yuan Y, Lü 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]

    [13]

    Jian X H, Zhang C M, Zhang L, Zhao B C 2010 Opt. Express 18 5674

    [14]

    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]

    [15]

    Zhang C M, Jian X H 2010 Opt. Lett. 35 366

    [16]

    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]

    [17]

    Wu H Y, Zhang C M, Zhao B C, Li Y C 2009 Acta Phys. Sin. 58 1642 (in Chinese) [吴海英, 张淳民, 赵葆常, 李英才 2009 物理学报 58 1642]

    [18]

    Zhang C M, Ren W Y, Mu T K 2010 Chin. Phys. B 19 024202

    [19]

    Wu J F, Zhang C M 2010 Chin. Phys. B 19 034201

    [20]

    Ruan K, Zhang C M, Zhao B C 2008 Acta Phys. Sin. 57 5435 (in Chinese) [阮锴, 张淳民, 赵葆常 2008 物理学报 57 5435]

    [21]

    Zhang C M, Ai J J, Ren W Y 2011 Chin. Phys. B 20 020701

    [22]

    Zhang C M, Zhao J K, Sun Y 2011 Appl. Opt. 50 3497

    [23]

    Mu T K, Zhang C M, Zhang B C 2009 Acta Phys. Sin. 58 3877 (in Chinese) [穆廷魁, 张淳民, 赵葆常 2009 物理学报 58 3877]

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  • Received Date:  30 November 2011
  • Accepted Date:  26 December 2011
  • Published Online:  20 July 2012

Study on chromatic dispersion of beam splitter in spatially modulated Fourier transform spectrometer

  • 1. State Key Laboratory of Applied Optics, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China;
  • 2. Graduate University of Chinese Academy of Sciences, Beijing 100049, China
Fund Project:  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), and the Jilin Province Science and Technology Development Plan, China (Grant No. 201205025).

Abstract: Due to the chromatic dispersion of beam splitter, the interferogram units from various wavelengths could shift by different offsets, leading to interferogram aliasing in transverse space. Simultaneously, the interferograms of different wavelengths have different offsets of optical path difference, which makes the interferogram aliasing in vertical space. According to geometric optics principles, the transverse aliasing of the interferogram reduces the area of the interferogram unit, and the vertical aliasing of the interferogram leads to a phase-frequency response which could reduce the spectral line intensity. The calculation and the analysis indicate that the transverse aliasing area is only 3.4% of the total area of the interferogram unit in our study, which could be removed in the data processing; and the phase delay from the vertical aliasing of the interferogram is proportional to the thickness difference between the beam splitter and the compensating plate. The maximal thickness difference is provided when the contrast reversion appears in the interference fringe. Finally, we correct the chromatic dispersion from the aliasing interferogram by solving linear equation set, and recover the ideal spectrum.

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