Inversion Calculation of Atmospheric Refractive Index Structure Constant Based on Atmospheric Coherence Length and Isoplanatic Angle Measured in Nanshan, Xinjiang

Yuxi Cao; Haifeng Yao; Heng Zhang; Lei Zhang; Shuai Chang; Shoufeng Tong; Xiaoke Tao

doi:10.3788/LOP222937

Laser & Optoelectronics Progress, Volume. 60, Issue 21, 2101003(2023)

Inversion Calculation of Atmospheric Refractive Index Structure Constant Based on Atmospheric Coherence Length and Isoplanatic Angle Measured in Nanshan, Xinjiang

Yuxi Cao¹, Haifeng Yao^2、**, Heng Zhang¹, Lei Zhang^1、*, Shuai Chang³, Shoufeng Tong^3、***, and Xiaoke Tao⁴

Author Affiliations

¹School of Optoelectronic Engineering, Changchun University of Science and Technology, Changchun 130022, Jilin , China

²School of Optics and Photonics, Beijing Institute of Technology, Beijing 100081, China

³National and Local Engineering Research Center of Space Optoelectronic Technology, Changchun University of Science and Technology, Changchun 130022, Jilin , China

⁴Army of32215

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Figures & Tables(13)

Fig. 1. Flow chart of specific calculation method

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Fig. 2. Three-ring apodizing mirror. (a) Physical picture; (b) structural drawing

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Fig. 3. Structure diagram of optical receiving system

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Fig. 6. Trend change of $R_{x y}$

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Table 1. Bright ring size of three-ring apodizing mirror
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Table 1. Bright ring size of three-ring apodizing mirror
Type of ring Inner/Outer radius /mm
Inner 37.389/43.840
Middle 62.890/69.240
Outer 81.940/101.600

Table 2. Values of HV model parameters, $r_{0}$ , and $θ_{0}$

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Table 2. Values of HV model parameters, $r_{0}$ , and $θ_{0}$

Model	a₁	c	b₁	a₂	b₂	a₃	b₃	r₀ /cm	θ₀ /μrad
HV-5/7	3.59 $\times$ 10^-53	10	1000	2.7 $\times$ 10^-16	1500	1.7 $\times$ 10^-14	100	4.9607	6.9032
HV-10/10	2 $\times$ 10^-53	10	1000	9 $\times$ 10^-17	1500	4.5 $\times$ 10^-15	100	10.3366	10.1686
HV-15/12	1.54 $\times$ 10^-53	10	1000	7 $\times$ 10^-17	1500	2 $\times$ 10^-15	100	14.8158	11.8978

Table 3. Parameters of common HV model, Xianghe model, and Xinglong model

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Table 3. Parameters of common HV model, Xianghe model, and Xinglong model

Parameter	a₁	c	b₁	a₂	b₂	a₃	b₃	Model
Value	2.3×10^-52	10	1000	4.1×10^-16	2300	1×10^-17	520	Xianghe
	9.68×10^-52	10	990.1	8.1×10^-18	2800	3×10^-15	812	Xinglong
	3.59×10^-53	10	1000	2.7×10^-16	1500	1.7×10^-14	100	HV-5/7
	2×10^-53	10	1000	9×10^-17	1500	4.5×10^-15	100	HV-10/10
	1.54×10^-53	10	1000	7×10^-17	1500	2×10^-15	100	HV-15/12

Table 4. Value range of parameters
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Table 4. Value range of parameters
Parameter a₁ c b₁ a₂ b₂ a₃ b₃
Value range ［10^-53，10^-51］［8，12］［800，1200］［10^-17，10^-15］［1800，3000］［10^-18，10^-15］［300，1000］

Table 5. Relevant parameters of $C_{n}^{2}$ profile simulation

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Table 5. Relevant parameters of $C_{n}^{2}$ profile simulation

Parameter	Range	Parameter	Range/Value
a₁	［10^-53， 10^-51］	b₂	［1500， 3000］
c	［8， 12］	a₃	［10^-17， 10^-14］
b₁	［800， 1200］	b₃	［200， 800］
a₂	［10^-18， 10^-15］	G	0.0001
M（Average）	［0.41625， 0.41630］	R /cm（Average）	6.3313
M（2020-12-12）	［0.45440， 0.45450］	R /cm（2020-12-12）	4.9984
M（2020-12-14）	［0.45740， 0.45780］	R /cm（2020-12-14）	6.5638
M（2020-12-17）	［0.46970， 0.46980］	R /cm（2020-12-17）	6.9843

Table 6. Results of parameter simulation

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Table 6. Results of parameter simulation

Parameter	a₁	c	b₁	a₂	b₂	a₃	b₃	Model
Value	7.10 $\times$ 10^-52	10	900.00	2.61 $\times$ 10^-16	2500.00	1.10 $\times$ 10^-15	250.00	Average
	6.73 $\times$ 10^-52	10	933.33	3.74 $\times$ 10^-16	2200.00	1.64 $\times$ 10^-15	350.00	2020-12-12
	4.68 $\times$ 10^-52	10	943.51	1.83 $\times$ 10^-16	2131.10	1.02 $\times$ 10^-15	414.14	2020-12-14
	1.30 $\times$ 10^-52	10	1000.00	1.41 $\times$ 10^-16	2700.00	1.21 $\times$ 10^-15	340.00	2020-12-17

Table 7. Calculated values of $R_{x y}$

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Table 7. Calculated values of $R_{x y}$

Date	$R_{x y}$	Date	$R_{x y}$	Date	$R_{x y}$	Date	$R_{x y}$
2020-12-12	0.8380	2020-12-16	0.8033	2020-12-23	0.8260	2021-01-04	0.8108
2020-12-13	0.8156	2020-12-17	0.8128	2020-12-24	0.8017	2021-01-05	0.8299
2020-12-14	0.8708	2020-12-18	0.8051	2020-12-30	0.8087	2021-01-06	0.8234
2020-12-15	0.8129	2020-12-19	0.8150	2021-01-01	0.8132	2021-01-07	0.8247

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Yuxi Cao, Haifeng Yao, Heng Zhang, Lei Zhang, Shuai Chang, Shoufeng Tong, Xiaoke Tao. Inversion Calculation of Atmospheric Refractive Index Structure Constant Based on Atmospheric Coherence Length and Isoplanatic Angle Measured in Nanshan, Xinjiang[J]. Laser & Optoelectronics Progress, 2023, 60(21): 2101003

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