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Optimizing the location of multiple laser guide stars in ground layer adaptive optical systems
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摘要:
对地面层自适应光学系统而言，多采用呈正多边形排列的多颗激光导引星星座作为参考来测量大气湍流对系统的影响。针对多颗激光导引星应当如何排布的问题，本文采用简化的地面层自适应光学几何模型作为系统性能评价函数，通过遗传算法优化获得不同湍流廓线下导引星的最优分布。同时，采用多进程、Numba库和多线程提高海量大气湍流廓线下对整个系统性能的估计速度。利用上述方法，以一个视场为14'的地面层自适应光学系统为例，用实测的大气湍流廓线数据分析了不同天文观测台址下湍流廓线与最优位置分布的关系。研究结果表明，同一台址下不同数目导引星的最优位置分布差异不大，其统计最优位置均呈中心一颗或角半径接近视场边缘的正多边形分布；不同台址下的导引星最优位置分布差异明显；大气湍流廓线测量的空间分辨率直接影响系统性能评价结果：其测量结果中的等效层数越多，导引星位置分布越接近规则的多边形。
Abstract:At present, the ground layer adaptive optical systems are using multiple laser guide stars arranged in regular polygons as reference targets to measure the effects of atmospheric turbulence. Obtaining the optimal position of laser guide stars becomes an interesting problem to analyze. This paper proposes a method to obtain the optimal position of laser guide stars by using a genetic algorithm as the optimization algorithm and a simplified geometry model of the ground layer adaptive optic system as the evaluation function. Furthermore, multi-process, Numba library, and multi-thread techniques methods are used to accelerate calculation speed. Based on these methods, real atmospheric turbulence profiles are used to analyze the relationship between the optimal position of laser guide stars with different numbers and the different atmospheric turbulence profiles from the same site, through an example of a ground layer adaptive optics system with 14 arcmin field of view. The results show that the optimal position of laser guide stars in the same site is almost the same and their statistically optimal positions are all regular polygon. Besides, we also find that the spatial resolution of turbulence profiles has strong effects to positions of laser guide stars, showing that the more equivalent layers in the measurement results, the closer the position distribution of laser guide stars is to the regular polygon.
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Overview: The ground layer adaptive optic system (GLAO) uses wavefront sensors to measure wavefront errors from several different field of views and corrects the 'mean' wavefront errors from these measurements with a deformable mirror, which could slightly increase image quality in a wide field of view. The GLAO is particular useful for multi object observations, such as multi-object spectroscopic observations and wide field astrometry or photometry. The GLAO system normally assumes that there is a ground layer atmosphere turbulence in a fixed height, and thus it uses several laser-guide stars with fixed positions in the field of view to measure wavefront errors from that layer. However, the atmospheric turbulence is a stochastic medium and the height and strength of the ground layer will change continuously in real applications. Does there still exist optimal positions for these laser guide stars? Calculating the performance of the GLAO system with different configurations under different turbulence profiles is a straight forward method to obtain the optimal position of laser guide stars, but it will cost a very long time. In this paper, a simplified geometric model is proposed to evaluate the performance of the GLAO system. The genetic algorithm is used to obtain optimal positions of laser guide stars for different turbulence profiles from real measurements of different sites. Because there is a huge amount of atmospheric turbulence profiles, multi-processing, Numba library, and multi-thread techniques are used to further accelerate the computation speed up 3240 times that of the ordinary method. Based on the aforementioned methods, we have evaluated the GLAO performance with laser guide stars of different locations under different turbulence profiles from Paranal and Mauna Kea. We assume the turbulence profiles as random variables of independent and identically distributed and random sample a small batch (2000 turbulence profiles from different sites) to estimate the optimal position of laser guide stars. We have found that the optimal position of laser guide stars in the same site is almost the same and their statistically optimal positions are all regular polygon. However, we have also found that the spatial resolution of atmospheric turbulence profile measurements has strong impacts to the performance evaluation, showing that higher spatial resolution can lead to a more concentrated distribution of the laser guide stars. It indicates that it is necessary to obtain enough high-resolution turbulence profile data to better evaluate site conditions for China future large telescopes with GLAO systems.
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图 1 地面层自适应光学系统简化几何模型图
Figure 1. Geometric model for ground layer adaptive optics systems
图 6 一条湍流廓线数据下5次激光导引星位置结果。(a)~(e)分别为5次相同条件下的导引星位置结果；(f) 5次位置的统计结果
Figure 6. The position results of the laser guiding star for five measurements with single turbulent profile data. (a)~(e) The results of guiding star positions under the same condition for five measurements respectively; (f) Total positional results of five measurements
图 7 另一条湍流廓线数据下3次激光导引星位置结果。(a)~(c)分别为3次相同条件下的导引星位置结果
Figure 7. The position results of the laser guiding star for three measurements with another turbulent profile data. (a)~(c) The results of guiding star positions under the same condition for three measurements respectively
图 9 不同观测台址下激光导引星的位置分布图。(a) 帕拉纳尔下的位置分布；(b) 莫纳克亚山下的位置分布
Figure 9. Location distribution of laser guiding stars at different observation stations. (a) Paranal; (b) Mauna Kea
图 10 帕拉纳尔下 3 颗和 4 颗激光导引星的位置分布。(a) 3 颗星的位置分布；(b) 4 颗星的位置分布
Figure 10. The position distribution of three and four laser guiding stars in Paranal. (a) Three stars; (b) Four stars
图 11 莫纳克亚山下 3 颗和 4 颗激光导引星的位置分布。(a) 3 颗星的位置分布；(b) 4 颗星的位置分布
Figure 11. The position distribution of three and four laser guiding stars in Mauna Kea. (a) Three stars; (b) Four stars
表 1 大气湍流数据情况
Table 1. Atmospheric turbulence data
台址 测量方法 数据量 等效层数 智利帕拉纳尔 Stereo-SCIDAR 7563 100 夏威夷莫纳克亚山 MASS 163208 6 
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表 2 帕拉纳尔台址下的湍流数据格式
Table 2. Turbulence data format in paranal
高度/m 大气折射率结构常Cn2/m^(1/3) 风速/(m/s) 风方向/(°) 0 2.247E-14 11.474 347.4 250 2.068E-14 10.345 332.9 ... ... ... ...
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表 3 莫纳克亚山台址下的湍流数据格式
Table 3. Turbulence data format in Mauna Kea
L 3 0.5 7.99E-14 5.9 1.47E-14 9.9 4.28E-14 X 6 0.5 6.97E-14 1.0 8.89E-22 2.0 1.09E-20 4.0 3.49E-15 8.0 4.90E-14 16.0 6.63E-15 ...
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表 4 地面层自适应光学系统的参数
Table 4. Parameters of the ground layer adaptive optical system
参数 数值 望远镜口径/m 10 激光导引星数目 5 激光导引星高度/km 90 视场角/(') 14 大气相干长度r0/m 0.1 外尺度L0/m 10
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表 5 不同加速方案的运行时间结果对比
Table 5. Comparison of running time with different acceleration schemes
s 加速方案 子种群数目 1 10 15 20 30 40 50 100 几何模型：多进程+Numba 3.5 33.5 48 65 96 128 164 321 几何模型：多进程+Numba遗传算法：多线程 3.2 32.5 47 64 97.5 129 164 320 几何模型：多线程+Numba遗传算法：多进程 15 15 18 21 25 38 43 78
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