钠信标光斑大小及回光数研究
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摘要
钠信标已经成为地基大口径望远镜自适应光学系统的必要组成部分。钠信标光斑大小和回光数是影响自适应光学系统性能的关键因素,从发射角度考虑,主要由激光到达钠层时功率密度分布和耦合效率共同决定。为了准确估计钠信标光斑大小和回光数,首先建立了激光在大气中传输的模型,通过分析激光发射望远镜口径和上行路径大气湍流对激光到达钠层功率密度分布的影响,得出优化激光发射望远镜口径的普适方法;然后根据激光通过发射望远镜后到达钠层的功率密度与耦合效率的关系,计算钠信标光斑大小和回光数;最后利用探测误差和时域误差作为评价指标,计算了系统的最优采样频率。研究结果表明,针对丽江高美古天文台大气条件(大气相干长度(r0@550 nm)中值为7～9 cm),激光发射望远镜口径最佳值为300 mm,此时产生的光斑最优;当r0为9 cm,激光器采用中国科学院理化技术研究所20 W级百微秒脉冲激光器并利用D2a+D2b双峰泵浦激发钠原子时,产生的钠信标回光数为1.3×10~7 photons·s~(-1)·m~(-2),光斑大小为0.6″,最优的采样频率为900 Hz。
The sodium laser guide star facility has become one of the most important subsystems of adaptive optics system for large ground-based telescope. Spot size and photon return of the sodium laser guide star are the main factors that affect the performance of an adaptive optics system, both of which depend strongly on the laser power density distribution at the sodium layer and the coupling efficiency of the laser. In order to accurately estimate the photon return and spot size, a model was established for laser propagation in atmosphere and the effect of laser launch telescope′ s diameter and turbulence in the uplink path on the power density distribution was analyzed. A general technique to optimize the laser launch telescope′s design was devised. Then the spot size and photon return according to the relationship between the power density and the coupling efficiency were calculated. By minimizing measurement error and temporal error, an optimal sampling frequency was obtained. The researching results show that, for atmosphere condition at Gaomeigu Lijiang(median value of Fried parameter(r0) is 7 to 9 cm at a wavelength of 550 nm), the minimum spot size occurs when the diameter of the laser launch telescope is300 mm. For an r0 value of 9 cm and at a laser power of 20 W with D2a+D2bre-pumping, the photon return of the sodium laser guide star is expected to be 1.3×10~7 photons·s~(-1)·m~(-2) and the spot size is 0.6 ″. The optimal sampling frequency is around 900 Hz.
The sodium laser guide star facility has become one of the most important subsystems of adaptive optics system for large ground-based telescope. Spot size and photon return of the sodium laser guide star are the main factors that affect the performance of an adaptive optics system, both of which depend strongly on the laser power density distribution at the sodium layer and the coupling efficiency of the laser. In order to accurately estimate the photon return and spot size, a model was established for laser propagation in atmosphere and the effect of laser launch telescope′ s diameter and turbulence in the uplink path on the power density distribution was analyzed. A general technique to optimize the laser launch telescope′s design was devised. Then the spot size and photon return according to the relationship between the power density and the coupling efficiency were calculated. By minimizing measurement error and temporal error, an optimal sampling frequency was obtained. The researching results show that, for atmosphere condition at Gaomeigu Lijiang(median value of Fried parameter(r0) is 7 to 9 cm at a wavelength of 550 nm), the minimum spot size occurs when the diameter of the laser launch telescope is300 mm. For an r0 value of 9 cm and at a laser power of 20 W with D2a+D2bre-pumping, the photon return of the sodium laser guide star is expected to be 1.3×10~7 photons·s~(-1)·m~(-2) and the spot size is 0.6 ″. The optimal sampling frequency is around 900 Hz.
引文
[1] Hardy J W. Adaptive Optics for Astronomical Telescopes[M]. Oxford:Oxford University, 1998.
[2] Mccullough P R, Fugate R Q, Christou J C, et al.Photoevaporating stellar envelopes observed with Rayleigh beacon adaptive optics[J]. The Astrophysical Journal, 1995, 438(1):394-403.
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[4] Allen J Tracy, Allen K Hankla, Camilo Lopez, et al.High-power solid-state sodium laser guidestar for the Gemini North Observatory[C]//SPIE, 2004, 5490:998-1009.
[5] Holzlhner R, Calia D B, Bello D, et al. Comparison between observation and simulation of sodium LGS return flux with a 20 W CW laser on Tenerife[C]//SPIE,2016, 9909:99095E.
[6] Jason C Y Chin, Peter Wizinowich, Ed Wetherell, et al.Keck II laser guide star AO system and performance with the TOPTICA/MPBC laser[C]//SPIE, 2016, 9909:99090S.
[7] Yutaka Hayano, Masayuki Akiyama, Takashi Hattori, et al. Ultimate-Subaru:project status[C]//SPIE, 2014,9148:91482S.
[8] Boyer C, Ellerbroek B. Adaptive optics program update at TMT[C]//SPIE, 2016, 9909:990908.
[9] Michael Hart, Stuart M Jefferies, Neil Murphy. Daylight operation of a sodium laser guide star for adaptive optics wavefront sensing[J]. J Astron Telesc Instrum Syst, 2016, 2(4):040501.
[10] C d″Orgeville, Bauman B, Jim Catone. Gemini north and south laser guide star systems requirements and preliminary designs[C]//SPIE, 2002, 4494:302-316.
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[12] Hugues Guillet de Chatellus, Jean-Paul Pique, Ioana Cristina Moldovan. Return flux budget of polychromatic laser guide stars[J]. J Opt Soc Am A,2008, 25(2):400-415.
[13] Marc F, Hugues Guillet de Chatellus, Jean Paul Pique.Effects of laser beam propagation and saturation on the spatial shape of sodium laser guide stars[J]. Opt Exp,2009, 17(7):4920-4931.
[14] Liu Xiangyuan, Li Yujie, Qian Xianmei, et al.Numerical simulation and analysis of beam wander and spot radium for sodium laser beacon[J]. Journal of Atmospheric and Environmental Optics, 2015, 10(5):357-367.(in Chinese)刘向远,李玉杰,钱仙妹,等.激光钠信标光斑漂移和光斑半径的数值模拟与分析[J].大气与环境光学学报, 2015,10(5):357-367.
[15] Liu Xiangyuan, Qian Xianmei, Cui Chaolong, et al.Numerical simulation of return photons number of sodium laser beacon in the atmospheric turbulecne[J].Acta Optica Sinica, 2013, 33(2):0201001.刘向远,钱仙妹,崔朝龙,等.大气湍流中激光钠信标回波光子数的数值模拟[J].光学学报, 2013, 33(2):0201001.
[16] Wei Kai, Li Min, Chen S Q, et al. First light for the sodium laser guide star adaptive optics system on Lijiang 1.8-meter telescope[J]. Research in Astronomy and Astrophysics, 2016, 16(12):41-45.
[17] Jin K, Wei K, Feng L, et al. Photon return on-sky test of pulsed sodium laser guide star with D2b repumping[J]. Publ Astron Soc Pac, 2015, 127:749-756.
[18] Feng Lu, Kibblewhite E, Jin Kai, et al. A Monte Carlo simulation for predicting photon return from sodium laser guide star[C]//SPIE, 2015, 9678:96781B.
[19] Liu Xiangyuan, Qian Xianmei, Zhang Suimeng, et al.Numerical calculation and discussion on the return photon number of sodium laser beacon excited by a macro-micro pulse laser[J]. Acta Phys Sin, 2015, 64(9):094206.(in Chinese)刘向远,钱仙妹,张穗萌,等.宏-微脉冲激光激发钠信标回波光子数的数值计算与探讨[J].物理学报, 2015, 64(9):094206.
[20] Morris T J, Wilson R W, Myers R M, et al.Performance predictions of the GLAS Rayleigh laser guide star adaptive optics system for the 4.2-m William Herschel Telescope[C]//SPIE, 2006, 6272:627237.
[21] Ronald R Parenti, Richard J Sasiela. Laser-guide-star systems for astronomical applications[J]. J Opt Soc Am A, 1994, 11(1):288-309.
[22] Noll R. Zernicke polynomials and atmospheric turbulence[J]. J Opt Soc Am, 1976, 66(3):207-211.
[23] Fried D L. Statistics of a geometric representation of wavefront distortion[J]. J Opt Soc Am, 1965, 55(11):1427-1435.
[24] Yura H T. Short-term average optical-beam spread in a turbulent medium[J]. J Opt Soc Am, 1973, 63(5):567-572.
[25] Holzlhner R, Rochester S M, Calia D B, et al.Optimization of cw sodium laser guide star efficiency[J]. Astronomy&Astrophysics, 2010, 510:A20.
[26] Conan R, Correia C. Object-oriented Matlab adaptive optics toolbox[C]//SPIE, 2014, 9148:91486C.
[27] Jin Kai, Wei Kai, Li Min, et al. Theoretical and experimental study on photometry of a sodium laser guide star[J]. Infrared and Laser Engineering, 2018,47(1):0106005.(in Chinese)晋凯,魏凯,李敏,等.钠信标测光理论与实验研究[J].红外与激光工程, 2018, 47(1):0106005.
[28] Richard Dekany. Optimal LGS pointing with faint tiptilt NGS[C]//SPIE, 2010, 7736:773625.
[2] Mccullough P R, Fugate R Q, Christou J C, et al.Photoevaporating stellar envelopes observed with Rayleigh beacon adaptive optics[J]. The Astrophysical Journal, 1995, 438(1):394-403.
[3] Xu Zuyan, Bo Yong, Peng Qinjun, et al. Progress on sodium laser guide star[J]. Infrared and Laser Engineering, 2016, 45(1):0101001.(in Chinese)许祖彦,薄勇,彭钦军,等.激光钠导引星技术研究进展[J].红外与激光工程, 2016, 45(1):0101001.
[4] Allen J Tracy, Allen K Hankla, Camilo Lopez, et al.High-power solid-state sodium laser guidestar for the Gemini North Observatory[C]//SPIE, 2004, 5490:998-1009.
[5] Holzlhner R, Calia D B, Bello D, et al. Comparison between observation and simulation of sodium LGS return flux with a 20 W CW laser on Tenerife[C]//SPIE,2016, 9909:99095E.
[6] Jason C Y Chin, Peter Wizinowich, Ed Wetherell, et al.Keck II laser guide star AO system and performance with the TOPTICA/MPBC laser[C]//SPIE, 2016, 9909:99090S.
[7] Yutaka Hayano, Masayuki Akiyama, Takashi Hattori, et al. Ultimate-Subaru:project status[C]//SPIE, 2014,9148:91482S.
[8] Boyer C, Ellerbroek B. Adaptive optics program update at TMT[C]//SPIE, 2016, 9909:990908.
[9] Michael Hart, Stuart M Jefferies, Neil Murphy. Daylight operation of a sodium laser guide star for adaptive optics wavefront sensing[J]. J Astron Telesc Instrum Syst, 2016, 2(4):040501.
[10] C d″Orgeville, Bauman B, Jim Catone. Gemini north and south laser guide star systems requirements and preliminary designs[C]//SPIE, 2002, 4494:302-316.
[11] Holzlhner R, Calia D B, Hackenberg W. Physical optics modeling and optimization of laser guide star propagation[C]//SPIE, 2008, 7015:701521.
[12] Hugues Guillet de Chatellus, Jean-Paul Pique, Ioana Cristina Moldovan. Return flux budget of polychromatic laser guide stars[J]. J Opt Soc Am A,2008, 25(2):400-415.
[13] Marc F, Hugues Guillet de Chatellus, Jean Paul Pique.Effects of laser beam propagation and saturation on the spatial shape of sodium laser guide stars[J]. Opt Exp,2009, 17(7):4920-4931.
[14] Liu Xiangyuan, Li Yujie, Qian Xianmei, et al.Numerical simulation and analysis of beam wander and spot radium for sodium laser beacon[J]. Journal of Atmospheric and Environmental Optics, 2015, 10(5):357-367.(in Chinese)刘向远,李玉杰,钱仙妹,等.激光钠信标光斑漂移和光斑半径的数值模拟与分析[J].大气与环境光学学报, 2015,10(5):357-367.
[15] Liu Xiangyuan, Qian Xianmei, Cui Chaolong, et al.Numerical simulation of return photons number of sodium laser beacon in the atmospheric turbulecne[J].Acta Optica Sinica, 2013, 33(2):0201001.刘向远,钱仙妹,崔朝龙,等.大气湍流中激光钠信标回波光子数的数值模拟[J].光学学报, 2013, 33(2):0201001.
[16] Wei Kai, Li Min, Chen S Q, et al. First light for the sodium laser guide star adaptive optics system on Lijiang 1.8-meter telescope[J]. Research in Astronomy and Astrophysics, 2016, 16(12):41-45.
[17] Jin K, Wei K, Feng L, et al. Photon return on-sky test of pulsed sodium laser guide star with D2b repumping[J]. Publ Astron Soc Pac, 2015, 127:749-756.
[18] Feng Lu, Kibblewhite E, Jin Kai, et al. A Monte Carlo simulation for predicting photon return from sodium laser guide star[C]//SPIE, 2015, 9678:96781B.
[19] Liu Xiangyuan, Qian Xianmei, Zhang Suimeng, et al.Numerical calculation and discussion on the return photon number of sodium laser beacon excited by a macro-micro pulse laser[J]. Acta Phys Sin, 2015, 64(9):094206.(in Chinese)刘向远,钱仙妹,张穗萌,等.宏-微脉冲激光激发钠信标回波光子数的数值计算与探讨[J].物理学报, 2015, 64(9):094206.
[20] Morris T J, Wilson R W, Myers R M, et al.Performance predictions of the GLAS Rayleigh laser guide star adaptive optics system for the 4.2-m William Herschel Telescope[C]//SPIE, 2006, 6272:627237.
[21] Ronald R Parenti, Richard J Sasiela. Laser-guide-star systems for astronomical applications[J]. J Opt Soc Am A, 1994, 11(1):288-309.
[22] Noll R. Zernicke polynomials and atmospheric turbulence[J]. J Opt Soc Am, 1976, 66(3):207-211.
[23] Fried D L. Statistics of a geometric representation of wavefront distortion[J]. J Opt Soc Am, 1965, 55(11):1427-1435.
[24] Yura H T. Short-term average optical-beam spread in a turbulent medium[J]. J Opt Soc Am, 1973, 63(5):567-572.
[25] Holzlhner R, Rochester S M, Calia D B, et al.Optimization of cw sodium laser guide star efficiency[J]. Astronomy&Astrophysics, 2010, 510:A20.
[26] Conan R, Correia C. Object-oriented Matlab adaptive optics toolbox[C]//SPIE, 2014, 9148:91486C.
[27] Jin Kai, Wei Kai, Li Min, et al. Theoretical and experimental study on photometry of a sodium laser guide star[J]. Infrared and Laser Engineering, 2018,47(1):0106005.(in Chinese)晋凯,魏凯,李敏,等.钠信标测光理论与实验研究[J].红外与激光工程, 2018, 47(1):0106005.
[28] Richard Dekany. Optimal LGS pointing with faint tiptilt NGS[C]//SPIE, 2010, 7736:773625.