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为了详细分析由多个反射镜构成的谐振腔内的闭合光轴(共轭光轴)的特性以及存在条件, 首先从光束传输坐标变换的角度, 分析了由多个平面镜所构成的谐振腔的共轭光轴存在条件, 得出了奇数平面镜谐振腔仅当平面镜间具有高精度的相同垂直度时才存在闭合光轴, 而偶数平面镜谐振腔总是存在闭合光轴的结论, 并给出了腔共轭轴随腔镜方向失调而产生的角度变化关系. 然后从矩阵光学的角度分析包含球面镜的谐振腔的共轭光轴在腔镜间传输时的方向变换问题, 具体分析了由两个平面镜和一个球面镜构成的三角形环形谐振腔的闭合共轭光轴存在的问题. 结果表明, 当不同的镜子出现角度偏差时, 腔内仍然存在闭合的共轭光轴, 并给出了对应的腔轴变化以及新谐振面的位置及方向. 由此表明由于球面镜的加入降低了谐振腔共轭轴存在性对平面镜间高精度平行度的要求, 为基于高品质光学无源腔的光谱测量技术的高精度装调工作提供了理论指导.In order to analyze the characteristic of the close optical axis (conjugate optical axis) and the existence condition of resonator composed of multiple reflective mirrors, the existence condition of conjugate optical axis of the multiple-resonator consisting of many flat mirrors is analyzed and derived from the angle of beam conversion coordinate transformation. The results show that a closed ray axis in resonator with odd number of mirrors can exist only if each mirror is suitably aligned, while a closed ray axis always exists in non-planar resonators with even number of mirrors, and the angle of the cavity conjugate axis direction changes due to the misalignment of different mirrors. Then from the point of view of the optical multi-pass matrix, the incidence direction of the self-conjugate ray of the resonator consisting of spherical mirrors is analyzed. A detailed analysis of conjugated axis of the resonator consisting of two flat mirrors and one spherical mirror is conducted, and the results show that when different mirrors have angle deviations, the closed conjugated optical axis remains in the cavity, the change of resonator axis occurs, and the position and orientation of new resonance surface are given, thereby indicating that in the case of resonator with spherical mirrors there is a self-conjugate ray irrespective of the other flat mirrors positions. All of these will provide theoretical guidance for achieving the high-accuracy alignment and improving the measurement accuracy of spectral measurement technology based on high-quality optical cavity.
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Keywords:
- optical measurement /
- optic axis misalignment /
- mirror misalignment /
- position of self-conjugate ray of resonator
[1] Romanini D, Kachanov A A, Stoeckel E 1997 Chem. Phys. Lett. 270 546
[2] O'Keefe A, Deacon D A 1988 Rev. Sci. Instrum. 59 2544
[3] Chen Y, Yan W B 2007 Proc. SPIE 6756 675607
[4] Fallows E A, Cleary T G, Miller J H 2009 Appl. Opt. 48 695
[5] Rao G N, Karpf A 2010 A Trace Gas Sensor at ppb Sensitivity Based on Multiple Line Integration Spectroscopy Techniques (OSA: Conference on Lasers and Electro-Optics) paper JWA60
[6] Klaassen T, de Jong J, van Exter M, Woerdman J P 2005 Opt. Lett. 30 1959
[7] Dong Y H, Ding Y G, Xiao L 2005 Acta Phys. Sin. 54 5629 (in Chinese) [董玉和, 丁耀根, 肖刘 2005 54 5629]
[8] Yu X D, Long X W, Tang J X 2007 Opt. Precision Eng. 15 1760 (in Chinese) [于旭东, 龙兴武, 汤建勋 2007 光学精密工程 15 1760]
[9] Yi H Y 2006 Chin. J. Lasers 33 399 (in Chinese )[易亨瑜 2006 中国激光 33 399]
[10] Hauck R, Kortz H P, Weber H 1980 Appl. Opt. 19 598
[11] Guo J P, Li Y D, Liu J L 2004 Laser Infrared 34 182 (in Chinese) [郭俊平, 李育德, 刘静伦 2004 激光与红外 34 182]
[12] Al'tshuler G B, Isyanova E D, Karasev V B, Levit A L, Ovchinnikov V M, Sharlai S F 1977 Sov. J. Quantum Electron. 7 857
[13] Sheng S C 1994 Opt. Lett. 19 683
[14] Yuan J, Long X W, Zhang B, Wang F, Zhao H C 2007 Appl. Opt. 46 6314
[15] Yuan J, Chen M X, Li Y Y, Tan Z Q, Wang Z G 2013 Opt. Express 21 2297
[16] Korn G A, Korn T M 1967 Mathematics Handbook for Scientists and Engineers (New York: McGraw-Hill) p267
[17] Tuan H T, Huang S L 2005 J. Opt. Soc. Am. A 22 2476
[18] Maisons G, Gorrotxategi Carbajo P, Carras M, Romanini D 2010 Opt. Lett. 35 3607
[19] Jrmie C, Ajmal Khan M, Daniele R 2010 Opt. Express 18 4845
[20] Tan Z Q, Long X W, Huang Y, Wu S Y 2008 Chin. J. Lasers 35 1563 (in Chinese) [潭中奇, 龙兴武, 黄云, 吴素勇 2008 中国激光 35 1563]
[21] Jun K, Quang-Viet N 2002 Appl. Opt. 41 6360
[22] Kachanov A, Richman B A 2009 US Patent 7 535 573 B2 [2009-05-19]
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[1] Romanini D, Kachanov A A, Stoeckel E 1997 Chem. Phys. Lett. 270 546
[2] O'Keefe A, Deacon D A 1988 Rev. Sci. Instrum. 59 2544
[3] Chen Y, Yan W B 2007 Proc. SPIE 6756 675607
[4] Fallows E A, Cleary T G, Miller J H 2009 Appl. Opt. 48 695
[5] Rao G N, Karpf A 2010 A Trace Gas Sensor at ppb Sensitivity Based on Multiple Line Integration Spectroscopy Techniques (OSA: Conference on Lasers and Electro-Optics) paper JWA60
[6] Klaassen T, de Jong J, van Exter M, Woerdman J P 2005 Opt. Lett. 30 1959
[7] Dong Y H, Ding Y G, Xiao L 2005 Acta Phys. Sin. 54 5629 (in Chinese) [董玉和, 丁耀根, 肖刘 2005 54 5629]
[8] Yu X D, Long X W, Tang J X 2007 Opt. Precision Eng. 15 1760 (in Chinese) [于旭东, 龙兴武, 汤建勋 2007 光学精密工程 15 1760]
[9] Yi H Y 2006 Chin. J. Lasers 33 399 (in Chinese )[易亨瑜 2006 中国激光 33 399]
[10] Hauck R, Kortz H P, Weber H 1980 Appl. Opt. 19 598
[11] Guo J P, Li Y D, Liu J L 2004 Laser Infrared 34 182 (in Chinese) [郭俊平, 李育德, 刘静伦 2004 激光与红外 34 182]
[12] Al'tshuler G B, Isyanova E D, Karasev V B, Levit A L, Ovchinnikov V M, Sharlai S F 1977 Sov. J. Quantum Electron. 7 857
[13] Sheng S C 1994 Opt. Lett. 19 683
[14] Yuan J, Long X W, Zhang B, Wang F, Zhao H C 2007 Appl. Opt. 46 6314
[15] Yuan J, Chen M X, Li Y Y, Tan Z Q, Wang Z G 2013 Opt. Express 21 2297
[16] Korn G A, Korn T M 1967 Mathematics Handbook for Scientists and Engineers (New York: McGraw-Hill) p267
[17] Tuan H T, Huang S L 2005 J. Opt. Soc. Am. A 22 2476
[18] Maisons G, Gorrotxategi Carbajo P, Carras M, Romanini D 2010 Opt. Lett. 35 3607
[19] Jrmie C, Ajmal Khan M, Daniele R 2010 Opt. Express 18 4845
[20] Tan Z Q, Long X W, Huang Y, Wu S Y 2008 Chin. J. Lasers 35 1563 (in Chinese) [潭中奇, 龙兴武, 黄云, 吴素勇 2008 中国激光 35 1563]
[21] Jun K, Quang-Viet N 2002 Appl. Opt. 41 6360
[22] Kachanov A, Richman B A 2009 US Patent 7 535 573 B2 [2009-05-19]
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