Path-averaged Cn2 estimation using a laser-and-corner-cube system

Walter P. Cole; Michael A. Marciniak

doi:10.1364/AO.48.004256

Path-averaged $C_{n}^{2}$ estimation using a laser-and-corner-cube system

Walter P. Cole and Michael A. Marciniak

Applied Optics
Vol. 48,
Issue 21,
pp. 4256-4262
(2009)
•https://doi.org/10.1364/AO.48.004256

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Walter P. Cole and Michael A. Marciniak, "Path-averaged C_n² estimation using a laser-and-corner-cube system," Appl. Opt. 48, 4256-4262 (2009)

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Related Topics
Table of Contents Category
- Atmospheric and Oceanic Optics
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Atmospheric propagation (010.1300)
- Atmospheric turbulence (010.1330)
- Laser beam transmission (010.3310)

About this Article
History
- Original Manuscript: April 2, 2009
- Revised Manuscript: June 16, 2009
- Manuscript Accepted: June 24, 2009
- Published: July 17, 2009

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Abstract

As a finite cross-section laser beam propagates through the atmosphere, the beam spreads due to both diffraction and atmospheric turbulence effects. Using turbulence theory valid in both weak and strong optical turbulence regimes, a relationship between atmospheric beam spread and the resulting return power for an optical system and the refractive-index structure parameter or $C_{n}^{2}$ can be established. A technique for estimating the path-averaged $C_{n}^{2}$ using a laser-and-corner-cube system based on this relationship is described. Experimental results using near-infrared laser wavelengths show good agreement between theoretical predictions and scintillometer-measured $C_{n}^{2}$ values for near-ground line-of-sight propagation paths.

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Parameter	Value	Uncertainty	Relative Uncertainty
Laser power	$22 - 62 mW$	$0.75 - 1.25 mW$	0.02
Full-angle divergence	$1.45 mrad$	$0.1 mrad$	0.07
Range to target	$504 m$	$5 m$	0.01
Corner-cube OCS	$1.82 \times 10^{5} m^{2} / sr$	$0.11 \times 10^{5} m^{2} / sr$	0.06
Atmospheric transmission	0.927–0.975	$\pm 0.03$	0.03

Parameter	Value	Uncertainty	Relative Uncertainty
Laser power	$185 - 280 mW$	$5 - 6 mW$	0.02
Full-angle divergence	$1.7 mrad$	$0.1 mrad$	0.06
Range to target	$773 m$	$5 m$	0.01
Corner-cube OCS	$1.35 \times 10^{5} m^{2} / sr$	$0.067 \times 10^{5} m^{2} / sr$	0.05
Atmospheric transmission	0.927–0.975	0.03	0.03

Date	Local Time	Return Power ( $μW$ )	Uncertainty Mean ( $μW$ )	BLS-900 Measured $C_{n}^{2}$ ( $m^{- 2 / 3}$ )	Calculated $C_{n}^{2}$ ( $m^{- 2 / 3}$ )	Rytov Variance	% Difference
27-7-07	16:22	14.70	0.14	$3.19 \times 10^{- 14}$	$4.60 \times 10^{- 14}$	0.36	44.20
10-8-07	15:30	12.43	0.14	$2.07 \times 10^{- 13}$	$2.09 \times 10^{- 13}$	2.33	0.97
10-8-07	15:31	17.75	0.13	$1.32 \times 10^{- 13}$	$1.45 \times 10^{- 13}$	1.49	9.85
10-8-07	15:32	22.49	0.12	$8.14 \times 10^{- 14}$	$1.10 \times 10^{- 13}$	0.92	35.14
10-8-07	15:34	22.19	0.14	$6.54 \times 10^{- 14}$	$1.12 \times 10^{- 13}$	0.74	71.25
10-8-07	15:36	22.20	0.13	$8.82 \times 10^{- 14}$	$1.12 \times 10^{- 13}$	0.99	26.98
10-8-07	15:37	13.97	0.15	$1.91 \times 10^{- 13}$	$1.86 \times 10^{- 13}$	2.15	2.62
10-8-07	15:42	13.22	0.12	$1.78 \times 10^{- 13}$	$1.97 \times 10^{- 13}$	2.01	10.67
14-8-07	16:19	9.22	0.13	$2.74 \times 10^{- 13}$	$2.86 \times 10^{- 13}$	3.09	4.38
14-8-07	16:23	8.23	0.13	$3.28 \times 10^{- 13}$	$3.18 \times 10^{- 13}$	3.70	3.05
14-8-07	16:33	9.64	0.12	$2.80 \times 10^{- 13}$	$2.74 \times 10^{- 13}$	3.16	2.14
14-2-08	13:58	10.44	0.15	$1.07 \times 10^{- 13}$	$1.07 \times 10^{- 13}$	2.06	0.06
14-2-08	14:03	12.34	0.19	$9.14 \times 10^{- 14}$	$8.94 \times 10^{- 14}$	1.76	2.19
14-2-08	14:06	12.20	0.17	$1.12 \times 10^{- 13}$	$9.11 \times 10^{- 14}$	2.16	18.66
14-2-08	14:10	12.73	0.17	$8.94 \times 10^{- 14}$	$8.83 \times 10^{- 14}$	1.72	1.23
14-2-08	14:15	13.51	0.20	$9.02 \times 10^{- 14}$	$8.08 \times 10^{- 14}$	1.74	10.42
14-2-08	14:20	13.93	0.20	$7.52 \times 10^{- 14}$	$7.83 \times 10^{- 14}$	1.45	4.12
14-2-08	14:24	13.36	0.19	$8.87 \times 10^{- 14}$	$8.20 \times 10^{- 14}$	1.71	7.55
14-2-08	14:28	12.58	0.18	$1.04 \times 10^{- 13}$	$8.72 \times 10^{- 14}$	2.00	16.15
14-2-08	14:33	14.29	0.21	$7.74 \times 10^{- 14}$	$7.61 \times 10^{- 14}$	1.49	1.68
28-2-08	09:37	9.03	0.18	$8.60 \times 10^{- 14}$	$8.09 \times 10^{- 14}$	1.66	5.93
28-2-08	09:50	8.96	0.17	$7.74 \times 10^{- 14}$	$8.15 \times 10^{- 14}$	1.49	5.30
28-2-08	10:54	8.61	0.17	$7.14 \times 10^{- 14}$	$8.52 \times 10^{- 14}$	1.38	19.33
28-2-08	11:00	8.30	0.16	$9.71 \times 10^{- 14}$	$8.88 \times 10^{- 14}$	1.87	8.55

Parameter	Value	Uncertainty	Relative Uncertainty
Laser power	$22 - 62 mW$	$0.75 - 1.25 mW$	0.02
Full-angle divergence	$1.45 mrad$	$0.1 mrad$	0.07
Range to target	$504 m$	$5 m$	0.01
Corner-cube OCS	$1.82 \times 10^{5} m^{2} / sr$	$0.11 \times 10^{5} m^{2} / sr$	0.06
Atmospheric transmission	0.927–0.975	$\pm 0.03$	0.03

Parameter	Value	Uncertainty	Relative Uncertainty
Laser power	$185 - 280 mW$	$5 - 6 mW$	0.02
Full-angle divergence	$1.7 mrad$	$0.1 mrad$	0.06
Range to target	$773 m$	$5 m$	0.01
Corner-cube OCS	$1.35 \times 10^{5} m^{2} / sr$	$0.067 \times 10^{5} m^{2} / sr$	0.05
Atmospheric transmission	0.927–0.975	0.03	0.03

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