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The influences of atmospheric turbulence and the beam coherence on the average intensity of tilted and off-axis laser beams propagating through a cat-eye optical lens in the turbulence are studied. It is shown that the oscillatory behavior and the skewness of average intensity may appear because there exist apertures and active detection laser beams are tilted or off-axis. The skewness is independent of turbulence, but the oscillatory behavior disappears due to turbulence. For a small positive defocus of a cat-eye optical lens, the on-axis average intensity reaches its maximum. The a positive defocus value becomes small as the focal length of the cat-eye optical lens decreases, but it is independent of atmospheric turbulence and the coherence of active detection laser beams. And the average intensity becomes an off-Gaussian-like profile when the propagation distance is large enough in turbulence. However, less beam spreading may occur with increasing propagation distance for active detection laser beams with less coherence, which is quite different from the behavior of laser beams propagating in free space. The better the coherence of active detection laser beams is, the more the average intensity is affected by the turbulence, but the difference is small. The results obtained in this paper are very useful for the applications is active laser detection.
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Keywords:
- cat-eye optical lens /
- atmospheric turbulence /
- partially coherent beam /
- intensity
[1] Biermann M L, Rabinovich W S, Mahon R, Gilbreah G C 2002 Optical Engineering 41 1655
[2] Xu Z G, Zhang S L, Li Y, Du W H 2005 Opt. Express 13 5565
[3] Lin Y B, Zhang G X, Li Z 2003 Measurement Science and Technology 14 N36
[4] Dimakov S A, Klimentev S L, Khloponina L V 2002 J. of Optical Technology 69 536
[5] Ren D M, Lawton K M, Miller J A 2007 Precision Engineering 31 68
[6] Rabionovich W S, Mahon R, Goetz P G, Swingen L, Murphy J, Ferraro M, Burris H R, Suite M, Moore C L, Gilbreath G C, Binari S, Klotzkin D 2007 Optical Engineering 46 104001
[7] Goetz P G, Rabinovich W S, Binari S C, Mittereder J A 2006 IEEE Photonics Technology Letters 18 2278
[8] Rabinovich W S, Mahon R, Goetz P G, Waluschka E, Katzer D S, Gilbreath G C 2003 IEEE Photonics Technology Letters 15 461
[9] Lecocq C, Deshors G, Lado-Bordowsky O, Meyzonnette J L 2003 Proceedings of SPIE 5086 280
[10] Sun H Y, Zhao Y Z, Tang L M 2007 Proc. 7th International Symposium on Test and Measurement 4 3024
[11] Zhao Y Z, Sun H Y, Song F H, Gu S L 2010 Laser Optoelectronics Progress 47 102802 (in Chinese) [赵延仲, 孙华燕, 宋丰华, 谷锁林 2010 激光与光电子学进展 47 102802]
[12] Zhao Y Z, Sun H Y, Song F H, Tang L M, Wu W W, Zhang X, Guo H C 2008 Acta Physica Sinica 57 2284 (in Chinese) [赵延仲, 孙华燕, 宋丰华, 唐黎明, 吴伟伟, 张曦, 郭惠超 2008 物理学报 57 2284]
[13] Zhao Y Z, Sun H Y, Song F H, Dai D D 2009 Acta Optica Sinica 29 2552 (in Chinese) [赵延仲, 孙华燕, 宋丰华, 戴得德 2009 光学学报 29 2552]
[14] Zhao Y Z, Sun H Y, Yu X Q, Fan M S 2010 Chin. Phys. Lett. 27 034101
[15] Zhao Y Z, Sun H Y, Song F H, Dai D D 2010 Optik 121 2198
[16] Andrews L C, Phillips R L 2005 Laser Beam Propagation through Random Media 2nd ed. (SPIE, Bellingham)
[17] Ricklin J C, Davidson F M 2002 J. Opt. Soc. Am. A 19 1794
[18] Cai Y J, He S L 2006 Appl. Phys. Lett. 89 041117
[19] Dan Y Q, Zhang B 2009 Opt. Lett. 34 563
[20] Luo B, Wu G H, Guo H, Yu S 2010 Opt. Lett. 35 715
[21] Mao H D, Zhao D M 2010 Opt. Express 18 1741
[22] Zhou G Q, Cai Y J, Chu X X 2012 Opt. Express 20 9897
[23] Ji X L, Li X Q, Ji G M 2011 New J. Phys. 13 103006
[24] Tao R M, Si L, Ma Y X, Zhou P, Liu Z J 2012 Appl. Opt. 51 5609
[25] Shao X L, Ji X L 2012 Acta Phys. Sin. 61 164209(in Chinese) [邵晓利, 季小玲 2012 物理学报 61 164209]
[26] Chu X X 2011 Chin. Phys. B 20 014207
[27] Pu J X, Wang T, Lin H C, Li C L 2010 Chin. Phys. B 19 089201
[28] Zhao Y Z, Sun H Y, Song F H 2011 Chin. Phys. B 20 044201
[29] Wang S C H, Plonus M A 1979 J. Opt. Soc. Am. 69 1297
[30] Wen J J, Breazeale M A 1988 J. Acoust. Soc. Am. 83 1752
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[1] Biermann M L, Rabinovich W S, Mahon R, Gilbreah G C 2002 Optical Engineering 41 1655
[2] Xu Z G, Zhang S L, Li Y, Du W H 2005 Opt. Express 13 5565
[3] Lin Y B, Zhang G X, Li Z 2003 Measurement Science and Technology 14 N36
[4] Dimakov S A, Klimentev S L, Khloponina L V 2002 J. of Optical Technology 69 536
[5] Ren D M, Lawton K M, Miller J A 2007 Precision Engineering 31 68
[6] Rabionovich W S, Mahon R, Goetz P G, Swingen L, Murphy J, Ferraro M, Burris H R, Suite M, Moore C L, Gilbreath G C, Binari S, Klotzkin D 2007 Optical Engineering 46 104001
[7] Goetz P G, Rabinovich W S, Binari S C, Mittereder J A 2006 IEEE Photonics Technology Letters 18 2278
[8] Rabinovich W S, Mahon R, Goetz P G, Waluschka E, Katzer D S, Gilbreath G C 2003 IEEE Photonics Technology Letters 15 461
[9] Lecocq C, Deshors G, Lado-Bordowsky O, Meyzonnette J L 2003 Proceedings of SPIE 5086 280
[10] Sun H Y, Zhao Y Z, Tang L M 2007 Proc. 7th International Symposium on Test and Measurement 4 3024
[11] Zhao Y Z, Sun H Y, Song F H, Gu S L 2010 Laser Optoelectronics Progress 47 102802 (in Chinese) [赵延仲, 孙华燕, 宋丰华, 谷锁林 2010 激光与光电子学进展 47 102802]
[12] Zhao Y Z, Sun H Y, Song F H, Tang L M, Wu W W, Zhang X, Guo H C 2008 Acta Physica Sinica 57 2284 (in Chinese) [赵延仲, 孙华燕, 宋丰华, 唐黎明, 吴伟伟, 张曦, 郭惠超 2008 物理学报 57 2284]
[13] Zhao Y Z, Sun H Y, Song F H, Dai D D 2009 Acta Optica Sinica 29 2552 (in Chinese) [赵延仲, 孙华燕, 宋丰华, 戴得德 2009 光学学报 29 2552]
[14] Zhao Y Z, Sun H Y, Yu X Q, Fan M S 2010 Chin. Phys. Lett. 27 034101
[15] Zhao Y Z, Sun H Y, Song F H, Dai D D 2010 Optik 121 2198
[16] Andrews L C, Phillips R L 2005 Laser Beam Propagation through Random Media 2nd ed. (SPIE, Bellingham)
[17] Ricklin J C, Davidson F M 2002 J. Opt. Soc. Am. A 19 1794
[18] Cai Y J, He S L 2006 Appl. Phys. Lett. 89 041117
[19] Dan Y Q, Zhang B 2009 Opt. Lett. 34 563
[20] Luo B, Wu G H, Guo H, Yu S 2010 Opt. Lett. 35 715
[21] Mao H D, Zhao D M 2010 Opt. Express 18 1741
[22] Zhou G Q, Cai Y J, Chu X X 2012 Opt. Express 20 9897
[23] Ji X L, Li X Q, Ji G M 2011 New J. Phys. 13 103006
[24] Tao R M, Si L, Ma Y X, Zhou P, Liu Z J 2012 Appl. Opt. 51 5609
[25] Shao X L, Ji X L 2012 Acta Phys. Sin. 61 164209(in Chinese) [邵晓利, 季小玲 2012 物理学报 61 164209]
[26] Chu X X 2011 Chin. Phys. B 20 014207
[27] Pu J X, Wang T, Lin H C, Li C L 2010 Chin. Phys. B 19 089201
[28] Zhao Y Z, Sun H Y, Song F H 2011 Chin. Phys. B 20 044201
[29] Wang S C H, Plonus M A 1979 J. Opt. Soc. Am. 69 1297
[30] Wen J J, Breazeale M A 1988 J. Acoust. Soc. Am. 83 1752
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