无线光通信系统的影响因素和性能分析
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摘要
无线光通信即自由空间光通信具有保密性好、抗干扰能力强、传输速率高、灵活便捷等优点。在解决“最后一公里”问题、应急通信等方面有着良好的应用前景。大气因素对无线光通信性能影响是各种民用和军用激光通信系统开发和应用中必须首先要研究的关键问题。
激光信号在大气中传输时,会受到各类气溶胶的衰减和大气湍流效应,分析了激光在大气中雨、雾、雪等天气下的衰减和大气湍流的闪烁特性。计算了激光在雨、雾、雪中传输衰减引起的误码率和信噪比,分析了大气湍流引起的误码率与信噪比以及采用多发射机对误码率和信噪比的改进。讨论了弱、强湍流下不同调制技术对误码率的影响,结果表明:副载波BPSK调制在光通信系统应用中较OOK和副载波DPSK调制更具优势。利用部分相干光,结合多发射技术和副载波调制技术对无线光通信系统性能的改善进行了数值分析。采用部分相干光作为激光光源,可以减小系统误码率,提高系统性能。另一方面,多孔径发射可以明显减弱大气闪烁效应,提高通信质量,并对采用多孔径发射和副载波调制相结合,更能提高系统性能。因此,可以通过采用相干参数较大的光源,多孔径发射技术,以及选取合适的调制解调方式来提高光通信系统性能。该研究对于无线光通信系统的开发和应用具有重要的学术和应用价值。
Wireless Optical Communication (Free Space Optical Communication-FSO) has many advantages, such as good security, effective anti-interference, high data transfer rate, flexibility and convenience and so on. So it is an available mean to solve“the last mile problem”and emergence communication. The influence of characteristics of atmospheric on the performance of Wireless Optical Communication systems is currently the key problem for the exploitation of the laser communication systems in civil and military application.
Laser transmitting through the atmosphere, the attenuation characteristics of aerosols, rain, fog and snow and the turbulence scintillation are analyzed. The BER and SNR caused by the laser transmitted attenuation of rain, fog and snow are calculated. The BER and SNR caused by atmosphere turbulence scintillation and improved by more apertures transmitted technique are analyzed. The influences of BER using different modulation techniques in the weak and strong fluctuation regimes on Wireless Optical Communication systems are discussed. The results show that the subcarrier BPSK modulation is superior to the OOK and subcarrier DPSK modulations in Wireless Optical Communication systems applications. The performance of Wireless Optical Communication systems improved by using a partially coherent source beam, more apertures transmitted technique and the subcarrier modulation technique is calculated. The BER can be significantly reduced by means of using a partially coherent source beam, so the performance is improved. On the other hand, more apertures transmitted technique can weaken atmosphere scintillation effects, and improve communication quality. Using more apertures transmitted technique and subcarrier modulation technique can also improve the communication systems performance further. Therefore, the optical communication systems performance in atmosphere optical channels can be improved by means of using a larger correlation parameter partially coherent laser beam source, more apertures transmitted technique, or appropriate modulation and demodulation. These studies have great academic and practical values in the development and application of wireless optical communication systems.
激光信号在大气中传输时,会受到各类气溶胶的衰减和大气湍流效应,分析了激光在大气中雨、雾、雪等天气下的衰减和大气湍流的闪烁特性。计算了激光在雨、雾、雪中传输衰减引起的误码率和信噪比,分析了大气湍流引起的误码率与信噪比以及采用多发射机对误码率和信噪比的改进。讨论了弱、强湍流下不同调制技术对误码率的影响,结果表明:副载波BPSK调制在光通信系统应用中较OOK和副载波DPSK调制更具优势。利用部分相干光,结合多发射技术和副载波调制技术对无线光通信系统性能的改善进行了数值分析。采用部分相干光作为激光光源,可以减小系统误码率,提高系统性能。另一方面,多孔径发射可以明显减弱大气闪烁效应,提高通信质量,并对采用多孔径发射和副载波调制相结合,更能提高系统性能。因此,可以通过采用相干参数较大的光源,多孔径发射技术,以及选取合适的调制解调方式来提高光通信系统性能。该研究对于无线光通信系统的开发和应用具有重要的学术和应用价值。
Wireless Optical Communication (Free Space Optical Communication-FSO) has many advantages, such as good security, effective anti-interference, high data transfer rate, flexibility and convenience and so on. So it is an available mean to solve“the last mile problem”and emergence communication. The influence of characteristics of atmospheric on the performance of Wireless Optical Communication systems is currently the key problem for the exploitation of the laser communication systems in civil and military application.
Laser transmitting through the atmosphere, the attenuation characteristics of aerosols, rain, fog and snow and the turbulence scintillation are analyzed. The BER and SNR caused by the laser transmitted attenuation of rain, fog and snow are calculated. The BER and SNR caused by atmosphere turbulence scintillation and improved by more apertures transmitted technique are analyzed. The influences of BER using different modulation techniques in the weak and strong fluctuation regimes on Wireless Optical Communication systems are discussed. The results show that the subcarrier BPSK modulation is superior to the OOK and subcarrier DPSK modulations in Wireless Optical Communication systems applications. The performance of Wireless Optical Communication systems improved by using a partially coherent source beam, more apertures transmitted technique and the subcarrier modulation technique is calculated. The BER can be significantly reduced by means of using a partially coherent source beam, so the performance is improved. On the other hand, more apertures transmitted technique can weaken atmosphere scintillation effects, and improve communication quality. Using more apertures transmitted technique and subcarrier modulation technique can also improve the communication systems performance further. Therefore, the optical communication systems performance in atmosphere optical channels can be improved by means of using a larger correlation parameter partially coherent laser beam source, more apertures transmitted technique, or appropriate modulation and demodulation. These studies have great academic and practical values in the development and application of wireless optical communication systems.
引文
[1]柯熙政,席晓莉,无线激光通信概论,北京邮电大学出版社, 2004.
[2]王延尧,无线光接入技术进展和应用,科学出版社,2009.
[3] T. Shirai, A. Dogariu, E. Wolf. Mode analysis of spreading of partially coherent beams propagating through atmospheric turbulence. J. Opt. Soc. Am., 2003, 20 (6):1094-1102.
[4]卢文全,光通信概述[J ],光通信技术,1997(3) , 171-180.
[5] H. T. Yura. Physical model for strong optical-amplitude fluctuations in a turbulent medium. Opt.Soc.Am. 1974, 64:59-67.
[6] L. A. Chernov. Wave propagation in a random medium. New York: McGraw-Hill, 1960.
[7] A. Dogariu, S. Amarande. Propagation of partially coherent beams: turbulence-induced degradation. OPTICS LETTERS, 2003, Vol: 28, No.1:10-12.
[8] Frida Str?mqvist Vetelino,Cynthia Young, Larry Andrews.Fade statistics for Gaussian beam waves in moderate-to-strong turbulence. Proc.SPIE Vol. 6399, 639907, 2006.
[9] Ryde J.W., Echo intensity and attenuation due to clouds, rain, hail, sand and duststorms at centimetre wavelengths, Rep.7831, General Electric Co. Research Labs., Wembley, England, Oct. 1941.
[10]黄永平,赵光普,激光通信在大气湍流中的传输,大众科技,2009,39-42.
[11] X. Zhu and J. M. Kahn, Free-space optical communication through atmospheric turbulence channels, IEEE Trans. Commun., 2002, 50: 1293-1300.
[12]莫海涛,雷利娟,王志勇等.天气对大气激光通信信道的影响,信息通信,2009:26-28.
[13] J.Wu, A.D.Boardman. Coherence length of a Gaussian-Schell model beam and atmospheric turbulence. J.Mod.Opt., 1991, 38:1355-1368.
[14]余向东,沈常宇,王育红,影响自由空间光通信的几个重要因素及解决方法[ J ].光通信技术, 2006, 30 (2) : 61263.
[15] Lord Rayleigh, On the scattering of light by small particles, Phil. Mag., 1871, 41, 447~454.
[16]张民,吴振森,张延冬,脉冲波在强起伏湍流介质中的传播特征分析.物理学报,2001,50(6):45-50.
[17]吴健,杨春平,刘建斌,大气中的光传输理论.北京:邮电大学出版社,2005:130-132.
[18]宋正方,应用大气光学基础[M].北京:气象出版社,1990.
[19]万玲玉,气象条件对近地视距光通信链路影响研究.广西大学博士论文,2002年5月.
[20]王一平,肖景明,微波传播[M].人民邮电出版社,1987.
[21]柯熙政,杨利红,马冬冬,激光信号在雨中的传输衰减.红外与激光工程,2008,6(37):1021-1024.
[22] S.Sheikh Muhammad, P.Kohldorfer, E.Leitgeb. Channel Modeling for Terrestrial Free Space Optical Links[A]. IEEE Xplore [C]. 2009, 3:407-409.
[23] KEDAR D, ARNON S. Opt ical w ireless communicaion through fog in the presence of pointing errors [J ]. Applied Op t ics, 2003, 42 (24): 494624954.
[24]马保科,郭立新,雾对无线光通信系统信噪比的影响.西安邮电学院学报,2008,1(13):25-27.
[25] Brian R.Strickland, Michael J.Lavan.Effects of fog on the bit-error rate of a free-space laser communication system. APPLIED OPTICS ,38(3),P.424-430,1999
[26] WANG Rui. Study on the characteristics of laser propagationand attenuation through the fog [D]. Xi′an: Xidian University, 2007: 14-18. (in Chinese)
[27] DONG Qun-feng. Study of transmission effects of pulses atmillimeter wavelengths rain and fog medium [D]. Xi′an:Xidian University,2006 :5-15.(in Chinese)
[28] Vasseur H,Gbbins C J. Prediction of Apparent Extinction for Optical Transmission through Rain.Appl [J]. Opt,1996,35(35): 7144-7150.
[29]张铁英,王红星,朱银兵等.自由空间光通信调制方式研究,无线电通信技术,2006,32(6):13～15.
[30]曾智龙,徐林,杨乾远等.天气因素对大气激光通信质量影响分析,光通信技术,2009,10:54-57.
[31] X Guo liang, Z Xup ing,W Junwei, et al. Influence of atmospheric turbulence on FSO link performance[ J ]. Proc.SP IE, 2004, 5281: 816 - 823.
[32]邓代竹,郭华福,多发设计在大气激光通信中的应用,光学与光电技术,2005,4(3):13-14.
[33]宿伟,齐文宗,大气湍流对激光通信系统影响的数值模拟.激光与红外,2009,8(39): 813-815.
[34] L C Andrews, R L Phillips, C Y Hopen. Laser beam scintillation with app lications [M ]. Bellingham, Washington:SP IE Op tical Engineering Press, 2001.
[35]马东堂,魏急波,庄钊文,大气激光通信中多光束传输性能分析和信道建模[ J ].光学学报, 2004, 24 (8) : 102021024.
[36] OGUCHI T. Eletromagnetic wave propagation and scattering in rain and other hydrometeors[J].Proc IEEE,1983,71(9),1029-1078.
[37] T.Ho, S.Trisno, A.Desai, J.Llorca, S.D.Milner, C.C.Davis,“Performance and analysis of Reconfigurable Hybrid FSO/RF Wireless Networks”, Free-Space Laser Communication Technology XVII , Proc , SPIE, 5712, P.119-130,(2005) .
[38]刘保菊,张长森,大气湍流对复杂路径下光强起伏及误码率的影响[J].光电技术应用, 2007,22(1):14-16.
[39]张辉,曹丽娜.,现代通信原理与技术.西安:西安电子科技大学出版社,2005: 222-224.
[40] M. Uysal, J. Li. Error rate performance of coded free-space optical links over Gamma-Gamme turbulence channels. IEEE International conference on communications, 2004,6:3331～3335.
[41] M. D. Audeh, J. M. Kahn, and J. R. Barry, Performance of Pulse-Position Modulation on Measured Non-Directed Indoor Infrared Channels, IEEE Transactions on Communications,1996, l(6):654-659.
[42]安建梅,肖云波.,大气湍流对无线激光通信误码率的影响,2009,28(3):20-22.
[43] Qingchong Liu, Qi Lu. Subcarrier PSK intensity modulation for optical wireless communications through turbulent atmospheric channel[A]. IEEE Global Telecommunications Conference on Communications[C].2004,3:1872-1875.
[44] J. M. Kahn, and J R.Barry, wireless Infrared communications, Proeeedings of IEEE , 1997, 85(2):265-298.
[45]潘俊俊,贾振红.,Gamma-gamma湍流中副载波大气光通信系统的性能分析..光电子.激光,2007,18(8):953-95.
[46]吴健,多高斯-谢尔光束通过强湍流对光强闪烁的影响..应用光学,2005,1(26): 61-63.
[47] S. F. Cliford, H. T. Yura. Equivalence of two theories of Strong optical scintillation. Opt.Soc.Am.,1974, 64:1641-1644.
[48]刘维慧,激光在大气湍流中传播时光强起伏的初步分析,中国学位论文全文数据库,2004,28-29.
[49] S. C. H. Wang, M. A. Plonus. Optical beam propagation for a partially coherent source in the turbulent atmosphere. J. Opt. Soc. Am., 1979, 69(9):1297-1304.
[50] G. Gbur, E. Wolf. Spreading of partially coherent beams in random media. J.Opt.Soc. Am., 2002, Vol.19:1592-1598.
[51]夏芸,大气湍流对星地光通信的影响及性能分析,浙江大学硕士毕业论文,2007.
[52]杨瑞科,吴振森,赵振维,湍流大气中高斯波束地-空传播闪烁研究,电波科学学报,2005,20(3):306-310.
[53] Ferdinandov E ,Pachedjieva B, Bonev B. Joint influence of heterogeneous stochastic factors on bit error rate of ground to ground free space laser communication systems[J ] . Optics Communiations,2007 ,270 :121 - 127.
[54] X. F. Xiao, D. Voelz. Wave optics simulation approach for partial spatially coherent beams. Optics Express, 2006, 14(16):6986-6992.
[55] X. Ji , Z. Pu. Angular spread of Gaussian Schell-model array beams propagating through atmospheric turbulence. Appl Phys B , 2008, 93: 915-923.
[56]刘维慧,粱敏,李鹏,大气光通信中对光束质量的一种描述方法,山东科技大学学报,2007,26(5):53-56.
[57] Isaac I.Kim, Harel Hakakha. Scintillation reduction using multipletr ansmitters, SHE 2990:Vo1.120-113.
[58] W.G.Kenneth. The Application of Correlation Techniques to Some Acoustic Me as ur em en t s, J .A coust Soc.Am, 1 955, Vo1.27:266-246.
[59]万敏,张卫,向汝建等.激光空间相干性对照明均匀性的影响[J ] .强激光与粒子束,2002 , 14 (1) :41-44. (Wan M , Zhang W, Xiang R J ,et al . Influence of laser spatial coherent on illumination uniformity. Hi gh Power L aser and Particle Beams , 2002 , 14 (1) :41-44.
[60] J. C. Ricklin, F. M. Davidson. Bit error rate in a free-space laser communication system with a partially coherent signal beam. Proceedings of SPIE, 2003, 4884.
[61] Youquan Dan, Bin Zhang, Pingping Pan. Propagation of partially coherent flat-topped beams through a turbulent atmosphere. Optical Society of America, 2008, 2223-2226.
[62]季小玲,黄太星,吕百达.部分相干双曲余弦高斯光束通过湍流大气的光束扩展.物理学报,2006,55(2):978-980. Gori F. Flattened Gaussian beams[J ] . Optics Communications ,1994 ,107 :355 -34.
[2]王延尧,无线光接入技术进展和应用,科学出版社,2009.
[3] T. Shirai, A. Dogariu, E. Wolf. Mode analysis of spreading of partially coherent beams propagating through atmospheric turbulence. J. Opt. Soc. Am., 2003, 20 (6):1094-1102.
[4]卢文全,光通信概述[J ],光通信技术,1997(3) , 171-180.
[5] H. T. Yura. Physical model for strong optical-amplitude fluctuations in a turbulent medium. Opt.Soc.Am. 1974, 64:59-67.
[6] L. A. Chernov. Wave propagation in a random medium. New York: McGraw-Hill, 1960.
[7] A. Dogariu, S. Amarande. Propagation of partially coherent beams: turbulence-induced degradation. OPTICS LETTERS, 2003, Vol: 28, No.1:10-12.
[8] Frida Str?mqvist Vetelino,Cynthia Young, Larry Andrews.Fade statistics for Gaussian beam waves in moderate-to-strong turbulence. Proc.SPIE Vol. 6399, 639907, 2006.
[9] Ryde J.W., Echo intensity and attenuation due to clouds, rain, hail, sand and duststorms at centimetre wavelengths, Rep.7831, General Electric Co. Research Labs., Wembley, England, Oct. 1941.
[10]黄永平,赵光普,激光通信在大气湍流中的传输,大众科技,2009,39-42.
[11] X. Zhu and J. M. Kahn, Free-space optical communication through atmospheric turbulence channels, IEEE Trans. Commun., 2002, 50: 1293-1300.
[12]莫海涛,雷利娟,王志勇等.天气对大气激光通信信道的影响,信息通信,2009:26-28.
[13] J.Wu, A.D.Boardman. Coherence length of a Gaussian-Schell model beam and atmospheric turbulence. J.Mod.Opt., 1991, 38:1355-1368.
[14]余向东,沈常宇,王育红,影响自由空间光通信的几个重要因素及解决方法[ J ].光通信技术, 2006, 30 (2) : 61263.
[15] Lord Rayleigh, On the scattering of light by small particles, Phil. Mag., 1871, 41, 447~454.
[16]张民,吴振森,张延冬,脉冲波在强起伏湍流介质中的传播特征分析.物理学报,2001,50(6):45-50.
[17]吴健,杨春平,刘建斌,大气中的光传输理论.北京:邮电大学出版社,2005:130-132.
[18]宋正方,应用大气光学基础[M].北京:气象出版社,1990.
[19]万玲玉,气象条件对近地视距光通信链路影响研究.广西大学博士论文,2002年5月.
[20]王一平,肖景明,微波传播[M].人民邮电出版社,1987.
[21]柯熙政,杨利红,马冬冬,激光信号在雨中的传输衰减.红外与激光工程,2008,6(37):1021-1024.
[22] S.Sheikh Muhammad, P.Kohldorfer, E.Leitgeb. Channel Modeling for Terrestrial Free Space Optical Links[A]. IEEE Xplore [C]. 2009, 3:407-409.
[23] KEDAR D, ARNON S. Opt ical w ireless communicaion through fog in the presence of pointing errors [J ]. Applied Op t ics, 2003, 42 (24): 494624954.
[24]马保科,郭立新,雾对无线光通信系统信噪比的影响.西安邮电学院学报,2008,1(13):25-27.
[25] Brian R.Strickland, Michael J.Lavan.Effects of fog on the bit-error rate of a free-space laser communication system. APPLIED OPTICS ,38(3),P.424-430,1999
[26] WANG Rui. Study on the characteristics of laser propagationand attenuation through the fog [D]. Xi′an: Xidian University, 2007: 14-18. (in Chinese)
[27] DONG Qun-feng. Study of transmission effects of pulses atmillimeter wavelengths rain and fog medium [D]. Xi′an:Xidian University,2006 :5-15.(in Chinese)
[28] Vasseur H,Gbbins C J. Prediction of Apparent Extinction for Optical Transmission through Rain.Appl [J]. Opt,1996,35(35): 7144-7150.
[29]张铁英,王红星,朱银兵等.自由空间光通信调制方式研究,无线电通信技术,2006,32(6):13～15.
[30]曾智龙,徐林,杨乾远等.天气因素对大气激光通信质量影响分析,光通信技术,2009,10:54-57.
[31] X Guo liang, Z Xup ing,W Junwei, et al. Influence of atmospheric turbulence on FSO link performance[ J ]. Proc.SP IE, 2004, 5281: 816 - 823.
[32]邓代竹,郭华福,多发设计在大气激光通信中的应用,光学与光电技术,2005,4(3):13-14.
[33]宿伟,齐文宗,大气湍流对激光通信系统影响的数值模拟.激光与红外,2009,8(39): 813-815.
[34] L C Andrews, R L Phillips, C Y Hopen. Laser beam scintillation with app lications [M ]. Bellingham, Washington:SP IE Op tical Engineering Press, 2001.
[35]马东堂,魏急波,庄钊文,大气激光通信中多光束传输性能分析和信道建模[ J ].光学学报, 2004, 24 (8) : 102021024.
[36] OGUCHI T. Eletromagnetic wave propagation and scattering in rain and other hydrometeors[J].Proc IEEE,1983,71(9),1029-1078.
[37] T.Ho, S.Trisno, A.Desai, J.Llorca, S.D.Milner, C.C.Davis,“Performance and analysis of Reconfigurable Hybrid FSO/RF Wireless Networks”, Free-Space Laser Communication Technology XVII , Proc , SPIE, 5712, P.119-130,(2005) .
[38]刘保菊,张长森,大气湍流对复杂路径下光强起伏及误码率的影响[J].光电技术应用, 2007,22(1):14-16.
[39]张辉,曹丽娜.,现代通信原理与技术.西安:西安电子科技大学出版社,2005: 222-224.
[40] M. Uysal, J. Li. Error rate performance of coded free-space optical links over Gamma-Gamme turbulence channels. IEEE International conference on communications, 2004,6:3331～3335.
[41] M. D. Audeh, J. M. Kahn, and J. R. Barry, Performance of Pulse-Position Modulation on Measured Non-Directed Indoor Infrared Channels, IEEE Transactions on Communications,1996, l(6):654-659.
[42]安建梅,肖云波.,大气湍流对无线激光通信误码率的影响,2009,28(3):20-22.
[43] Qingchong Liu, Qi Lu. Subcarrier PSK intensity modulation for optical wireless communications through turbulent atmospheric channel[A]. IEEE Global Telecommunications Conference on Communications[C].2004,3:1872-1875.
[44] J. M. Kahn, and J R.Barry, wireless Infrared communications, Proeeedings of IEEE , 1997, 85(2):265-298.
[45]潘俊俊,贾振红.,Gamma-gamma湍流中副载波大气光通信系统的性能分析..光电子.激光,2007,18(8):953-95.
[46]吴健,多高斯-谢尔光束通过强湍流对光强闪烁的影响..应用光学,2005,1(26): 61-63.
[47] S. F. Cliford, H. T. Yura. Equivalence of two theories of Strong optical scintillation. Opt.Soc.Am.,1974, 64:1641-1644.
[48]刘维慧,激光在大气湍流中传播时光强起伏的初步分析,中国学位论文全文数据库,2004,28-29.
[49] S. C. H. Wang, M. A. Plonus. Optical beam propagation for a partially coherent source in the turbulent atmosphere. J. Opt. Soc. Am., 1979, 69(9):1297-1304.
[50] G. Gbur, E. Wolf. Spreading of partially coherent beams in random media. J.Opt.Soc. Am., 2002, Vol.19:1592-1598.
[51]夏芸,大气湍流对星地光通信的影响及性能分析,浙江大学硕士毕业论文,2007.
[52]杨瑞科,吴振森,赵振维,湍流大气中高斯波束地-空传播闪烁研究,电波科学学报,2005,20(3):306-310.
[53] Ferdinandov E ,Pachedjieva B, Bonev B. Joint influence of heterogeneous stochastic factors on bit error rate of ground to ground free space laser communication systems[J ] . Optics Communiations,2007 ,270 :121 - 127.
[54] X. F. Xiao, D. Voelz. Wave optics simulation approach for partial spatially coherent beams. Optics Express, 2006, 14(16):6986-6992.
[55] X. Ji , Z. Pu. Angular spread of Gaussian Schell-model array beams propagating through atmospheric turbulence. Appl Phys B , 2008, 93: 915-923.
[56]刘维慧,粱敏,李鹏,大气光通信中对光束质量的一种描述方法,山东科技大学学报,2007,26(5):53-56.
[57] Isaac I.Kim, Harel Hakakha. Scintillation reduction using multipletr ansmitters, SHE 2990:Vo1.120-113.
[58] W.G.Kenneth. The Application of Correlation Techniques to Some Acoustic Me as ur em en t s, J .A coust Soc.Am, 1 955, Vo1.27:266-246.
[59]万敏,张卫,向汝建等.激光空间相干性对照明均匀性的影响[J ] .强激光与粒子束,2002 , 14 (1) :41-44. (Wan M , Zhang W, Xiang R J ,et al . Influence of laser spatial coherent on illumination uniformity. Hi gh Power L aser and Particle Beams , 2002 , 14 (1) :41-44.
[60] J. C. Ricklin, F. M. Davidson. Bit error rate in a free-space laser communication system with a partially coherent signal beam. Proceedings of SPIE, 2003, 4884.
[61] Youquan Dan, Bin Zhang, Pingping Pan. Propagation of partially coherent flat-topped beams through a turbulent atmosphere. Optical Society of America, 2008, 2223-2226.
[62]季小玲,黄太星,吕百达.部分相干双曲余弦高斯光束通过湍流大气的光束扩展.物理学报,2006,55(2):978-980. Gori F. Flattened Gaussian beams[J ] . Optics Communications ,1994 ,107 :355 -34.