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To understand the characteristics of the anisoplanatic error resulting from different return-light experiences between the sodium beacon with a greater angular offset and the science object through atmospheric turbulence, the angular anisoplanatism for sodium beacon is investigated experimentally based on the technique of synchronized range gating. The return-light spot arrays through turbulent atmosphere from the natural star and the sodium beacon with 50 rad angular offsets are synchronously collected by using a single Hartmann wavefront sensor, consequently the synchronous turbulence-induced wavefront distortion sequences are recovered for the on-axis natural star and the off-axis sodium beacon. According to the experimental data, the temporal correlations of the wavefront distributions and decomposed Zernike modes between the on-axis natural star and the off-axis sodium beacon are discussed. By comparing the off-axis sodium beacon with the on-axis natural star, we analyse the statistics of the acquired angular anisoplanatism error and its associated Zernike-modal variances for the off-axis sodium beacon, and derive the Zernike-modal relative anisoplanatic errors as well. Furthermore, the influence of the acquired angular anisoplanatism error on the quality of imaging point spread function (PSF) is studied. The experimental results show that the existence of 50 rad angular deviation between the sodium beacon and the natural star causes that there are a certain correlation between just low-order Zernike modes of these two types of wavefronts (e.g. from the 3rd order to the 9th order), but the correlations between other high-order Zernike modes of these two types of wavefronts are severely degenerated and even these modes are de-correlated, resulting from the improper turbulence probing with off-axis sodium beacon off the ray path from the natural star to the telescope aperture. The angular anisoplanatism error has a great influence on the quality of imaging PSF, which leads to a degradation of Strehl ratio of 0.31-0.22 and beam quality factor of 2.70-3.35. Therefore, the influence may not to be ignored. At the end of this paper, according to the derived experimental turbulence coherence length and the generalized Hufnagel-Valley model, we calculate the theoretical anisoplanatic phase variance for the sodium beacon with 50 rad angular offsets, which is in good accordance with the measured anisoplanatic phase variance. This investigation is useful in promoting our knowledge of sodium beacon angular anisoplanatism effect on turbulence probing.
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Keywords:
- adaptive optics /
- sodium beacon /
- angular anisoplanatism /
- anisoplanatic error
[1] Foy R, Labeyrie A 1991 Nature 353 144
[2] Fugate R Q, Fried D L, Ameer G A, Boeke B R, Browne S L, Roberts P H, Ruane R E, Tyler G A, Wopat L M 1991 Nature 353 144
[3] Humphreys R A, Primmerman C A, Bradley L C, Herrmann J 1991 Opt. Lett. 16 1367
[4] Humphreys R A, Bradley L C, Herrmann J 1992 Lincoln. Lab. J. 5 45
[5] Xu Z Y, Bo Y, Peng Q J, Zhang Y D, Wei K, Xue S J, Feng L 2016 Infrared Laser Eng. 45 0101001 (in Chinese) [许祖彦, 薄勇, 彭钦军, 张雨东, 魏凯, 薛随建, 冯麓 2016 红外与激光工程 45 0101001]
[6] Sasiela R J 2007 Electromagnetic Wave Propagation in TurbulenceEvaluation and Application of Mellin Transforms (2nd Ed.) (Bellingham: SPIE Press) p69
[7] Molodij G, Rousset G 1997 J. Opt. Soc. Am. A 14 1949
[8] Shen F, Jiang W H 2003 Acta Opt. Sin. 23 348 (in Chinese) [沈锋, 姜文汉 2003 光学学报 23 348]
[9] Wan M, Su Y, Xiang R J 2001 High Power Laser Part Beams 13 282 (in Chinese) [万敏, 苏毅, 向汝建 2001 强激光与粒子束 13 282]
[10] Yan H X, Wu H L, Li S S, Chen S 2005 Proceedings of SPIE Anstronomical Adaptive Optics Systems and Applications Ⅱ San Diego, California, USA, August 3-4, 2005 p59030U
[11] Luo X, Li X Y, Shao L, Hu S J, Huang K 2014 Proceedings of SPIE XX International Symposium on High-Power Laser Systems and Applications Chengdu, China, August 25-29, 2014 p92553A
[12] Luo X, Li X Y 2014 Chin. J. Lasers 41 0612002 (in Chinese) [罗曦, 李新阳 2014 中国激光 41 0612002]
[13] Luo X, Li X Y, Shao L, Huang K, Wang X Y 2014 Chin. J. Lasers 41 0612003 (in Chinese) [罗曦, 李新阳, 邵力, 黄奎, 王晓云 2014 中国激光 41 0612003]
[14] Dam M A V, Sasiela R J, Bouchez A H, Mignant D L, Campbell R D, Chin J C Y, Hartman S K, Johansson E M, Lafon R E, Stomski P J, Summers D M, Wizinowich P L 2006 Proceedings of SPIE Advances in Adaptive Optics Ⅱ Orlando, Florida, USA, May 24, 2006 p627231
[15] Zhou W C, Hu X Y, Yun Y, Tian X Q, Huang D Q 2014 Infrared Laser Eng. 43 1943 (in Chinese) [周文超, 胡晓阳, 云宇, 田小强, 黄德权 2014 红外与激光工程 43 1943]
[16] Chen T J, Zhou W C, Wang F, Huang D Q, Lu Y H, Zhang J Z 2015 Acta Phys. Sin. 64 134207 (in Chinese) [陈天江, 周文超, 王锋, 黄德权, 鲁燕华, 张建柱 2015 物理学报 64 134207]
[17] Hardy J W 1998 Adaptive Optics for Astronomical Telescopes (Oxford, New York USA: Oxford University Press) p85
[18] Sasiela R J 2007 Electromagnetic Wave Propagation in TurbulenceEvaluation and Application of Mellin Transforms (2nd Ed.) (Bellingham, Washington USA: SPIE Press) p62
[19] Li X Y, Wang C H, Xian H, Li M, Li M Q, Ren S H, Zhou L C, Wang X Y 2005 China Patent CN1570570A (in Chinsese) [李新阳, 王春鸿, 鲜浩, 李梅, 李明全, 任绍恒, 周璐春, 王晓云 2005 中国发明专利 CN1570570A]
[20] Du X W 1997 Chin. J. Lasers 24 327 (in Chinese) [杜祥琬 1997 中国激光 24 327]
[21] Du X W 2010 High Power Laser Part Beams 22 945 (in Chinese) [杜祥琬 2010 强激光与粒子束 22 945]
[22] Li X Y, Luo X, Shao L, Huang K, Hu S J, Tian Y, Li M 2013 China Patent CN103335950A (in Chinese) [李新阳, 罗曦, 邵力, 黄奎, 胡诗杰, 田雨, 李敏 2013 中国发明专利 CN103335950A]
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[1] Foy R, Labeyrie A 1991 Nature 353 144
[2] Fugate R Q, Fried D L, Ameer G A, Boeke B R, Browne S L, Roberts P H, Ruane R E, Tyler G A, Wopat L M 1991 Nature 353 144
[3] Humphreys R A, Primmerman C A, Bradley L C, Herrmann J 1991 Opt. Lett. 16 1367
[4] Humphreys R A, Bradley L C, Herrmann J 1992 Lincoln. Lab. J. 5 45
[5] Xu Z Y, Bo Y, Peng Q J, Zhang Y D, Wei K, Xue S J, Feng L 2016 Infrared Laser Eng. 45 0101001 (in Chinese) [许祖彦, 薄勇, 彭钦军, 张雨东, 魏凯, 薛随建, 冯麓 2016 红外与激光工程 45 0101001]
[6] Sasiela R J 2007 Electromagnetic Wave Propagation in TurbulenceEvaluation and Application of Mellin Transforms (2nd Ed.) (Bellingham: SPIE Press) p69
[7] Molodij G, Rousset G 1997 J. Opt. Soc. Am. A 14 1949
[8] Shen F, Jiang W H 2003 Acta Opt. Sin. 23 348 (in Chinese) [沈锋, 姜文汉 2003 光学学报 23 348]
[9] Wan M, Su Y, Xiang R J 2001 High Power Laser Part Beams 13 282 (in Chinese) [万敏, 苏毅, 向汝建 2001 强激光与粒子束 13 282]
[10] Yan H X, Wu H L, Li S S, Chen S 2005 Proceedings of SPIE Anstronomical Adaptive Optics Systems and Applications Ⅱ San Diego, California, USA, August 3-4, 2005 p59030U
[11] Luo X, Li X Y, Shao L, Hu S J, Huang K 2014 Proceedings of SPIE XX International Symposium on High-Power Laser Systems and Applications Chengdu, China, August 25-29, 2014 p92553A
[12] Luo X, Li X Y 2014 Chin. J. Lasers 41 0612002 (in Chinese) [罗曦, 李新阳 2014 中国激光 41 0612002]
[13] Luo X, Li X Y, Shao L, Huang K, Wang X Y 2014 Chin. J. Lasers 41 0612003 (in Chinese) [罗曦, 李新阳, 邵力, 黄奎, 王晓云 2014 中国激光 41 0612003]
[14] Dam M A V, Sasiela R J, Bouchez A H, Mignant D L, Campbell R D, Chin J C Y, Hartman S K, Johansson E M, Lafon R E, Stomski P J, Summers D M, Wizinowich P L 2006 Proceedings of SPIE Advances in Adaptive Optics Ⅱ Orlando, Florida, USA, May 24, 2006 p627231
[15] Zhou W C, Hu X Y, Yun Y, Tian X Q, Huang D Q 2014 Infrared Laser Eng. 43 1943 (in Chinese) [周文超, 胡晓阳, 云宇, 田小强, 黄德权 2014 红外与激光工程 43 1943]
[16] Chen T J, Zhou W C, Wang F, Huang D Q, Lu Y H, Zhang J Z 2015 Acta Phys. Sin. 64 134207 (in Chinese) [陈天江, 周文超, 王锋, 黄德权, 鲁燕华, 张建柱 2015 物理学报 64 134207]
[17] Hardy J W 1998 Adaptive Optics for Astronomical Telescopes (Oxford, New York USA: Oxford University Press) p85
[18] Sasiela R J 2007 Electromagnetic Wave Propagation in TurbulenceEvaluation and Application of Mellin Transforms (2nd Ed.) (Bellingham, Washington USA: SPIE Press) p62
[19] Li X Y, Wang C H, Xian H, Li M, Li M Q, Ren S H, Zhou L C, Wang X Y 2005 China Patent CN1570570A (in Chinsese) [李新阳, 王春鸿, 鲜浩, 李梅, 李明全, 任绍恒, 周璐春, 王晓云 2005 中国发明专利 CN1570570A]
[20] Du X W 1997 Chin. J. Lasers 24 327 (in Chinese) [杜祥琬 1997 中国激光 24 327]
[21] Du X W 2010 High Power Laser Part Beams 22 945 (in Chinese) [杜祥琬 2010 强激光与粒子束 22 945]
[22] Li X Y, Luo X, Shao L, Huang K, Hu S J, Tian Y, Li M 2013 China Patent CN103335950A (in Chinese) [李新阳, 罗曦, 邵力, 黄奎, 胡诗杰, 田雨, 李敏 2013 中国发明专利 CN103335950A]
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