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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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