Atmospheric Optical Turbulence Profile Model Fitting Based on Improved Particle Swarm Algorithm

Ketao Feng; Xiaoyi Li; Xuan Qian; Lehua Wu; He Zheng; Mou Chen; Mengru Li; Bo Liu

doi:10.3788/LOP202259.0501002

Laser & Optoelectronics Progress, Volume. 59, Issue 5, 0501002(2022)

Atmospheric Optical Turbulence Profile Model Fitting Based on Improved Particle Swarm Algorithm

Ketao Feng¹, Xiaoyi Li^1、*, Xuan Qian², Lehua Wu¹, He Zheng¹, Mou Chen¹, Mengru Li¹, and Bo Liu³

Author Affiliations

¹Communication Sergeant School, Army Engineering University of PLA, Chongqing 400035, China

²National Astronomical Observatory, Chinese Academy of Sciences, Beijing 100101, China

³Unit 78092 of PLA, Chengdu , Sichuan 610036, China

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Abstract Get PDF(in Chinese)

Figures & Tables(16)

Fig. 1. Particle position update method

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$Curves of fitting formula for refractive index structure constant$

Fig. 2. Curves of fitting formula for refractive index structure constant

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Fig. 3. Flowchart of the improved PSO algorithm

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Fig. 4. Comparison of the fitted profiles and the statistical average profiles of $C_{n}^{2}$ for different periods in Ali. (a) In the morning; (b) in the evening

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Fig. 5. E_BIAS between the profile of $C_{n}^{2}$ fitting model and the statistical average profiles in the morning and evening of Ali. (a) In the morning; (b) in the evening

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Fig. 6. [in Chinese]

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Fig. 7. E_BIAS between the profile of $C_{n}^{2}$ fitting model and the statistical average profiles for different seasons of Ali. (a) In the spring; (b) in the summer; (c) in the autumn; (d) in the winter

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Fig. 8. Comparison of turbulence profile model optimization curves in autumn

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Table 0. R² of four seasons turbulence profile models
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Table 0. R² of four seasons turbulence profile models
Method Spring Summer Autumn Winter
SPGD 0.9989 0.9895 0.9918 0.9989
Our method 0.9995 0.9977 0.9992 0.9996

Table 1. Turbulence profile model constants in the morning and evening
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Table 1. Turbulence profile model constants in the morning and evening
Time a₁ a₂ a₃ b₁ b₂ b₃ c₀ h_T
Morning 4.435×10^-20 1.302×10^-17 8.629×10^-16 2.064 3.061 0.032 3.881 5.3
Evening 7.453×10^-20 2.456×10^-18 1.162×10^-16 1.978 5.195 0.028 3.743 5.1

Table 2. Turbulence profile model coefficients in the morning and evening
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Table 2. Turbulence profile model coefficients in the morning and evening
Time β₀ β₁ β₂ β₃ β₄ β₅ β₆ β₇
Morning -16.66 -1.479 1.416 -0.569 0.1023 -0.00692 0 0
Evening -18.46 2.167 -2.289 1.034 -0.1997 0.01376 0 0

Table 3. R² of turbulence profile model in the morning and evening
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Table 3. R² of turbulence profile model in the morning and evening
Method Morning Evening
SPGD 0.9983 0.9707
Our method 0.9997 0.9976

Table 4. Model constants of turbulent profiles in four seasons

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Table 4. Model constants of turbulent profiles in four seasons

Season	a₁	a₂	a₃	b₁	b₂	b₃	c₀	h_T
Spring	1.702×10^-20	4.013×10^-18	3.812×10^-16	1.376	5.964	0.030	5.385	10.4
Summer	9.587×10^-29	6.411×10^-18	1.772×10^-16	0.813	4.727	0.0207	15.399	10.3
Autumn	3.571×10^-21	5.081×10^-18	2.423×10^-16	1.402	5.102	0.0293	5.967	5.0
Winter	3.701×10^-21	7.590×10^-18	6.098×10^-16	1.391	4.994	0.0329	6.014	9.8

Table 5. Model coefficients of turbulent profiles in four seasons

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Table 5. Model coefficients of turbulent profiles in four seasons

Season	β₀	β₁	β₂	β₃	β₄	β₅	β₆	β₇
Spring	-17.3625	-0.7477	0.779	-0.30482	0.05486	-0.004568	0.0001425	0
Summer	-17.39	-0.2824	0.3231	-0.0981	0.011	-0.000421	0	0
Autumn	-15.607	-10.598	18.91	-15.95	7.145	-1.74	0.2176	-0.010954
Winter	-16.799	-1.47205	1.25	-0.4465	0.07668	-0.006254	0.0001944	0

Table 7. Convergence accuracy results

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Table 7. Convergence accuracy results

Time	Method in Ref.［36］	Method in Ref.［41］	Method in Ref.［42］	Our method
Morning	1.4808	1.4808	1.4796	1.4795
Evening	0.9471	0.9468	0.9469	0.9465
Spring	1.2292	1.2296	1.2286	1.2277
Summer	1.4931	1.4945	1.4921	1.4916
Autumn	1.6139	1.6143	1.6131	1.6122
Winter	1.7725	1.7725	1.7725	1.7725

Table 8. Convergence rate results
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Table 8. Convergence rate results
Time Method in Ref.［36］ Method in Ref.［41］ Method in Ref.［42］ Our method
Morning 89 196 203 57
Evening 184 209 202 186
Spring 109 201 202 103
Summer 62 206 201 103
Autumn 206 220 209 65
Winter 132 198 219 55

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Ketao Feng, Xiaoyi Li, Xuan Qian, Lehua Wu, He Zheng, Mou Chen, Mengru Li, Bo Liu. Atmospheric Optical Turbulence Profile Model Fitting Based on Improved Particle Swarm Algorithm[J]. Laser & Optoelectronics Progress, 2022, 59(5): 0501002

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