Interferometric Study of Phase Fluctuations of a Laser Beam Through the Turbulent Atmosphere

M. Bertolotti; M. Carnevale; L. Muzii; D. Sette

doi:10.1364/AO.7.002246

Applied Optics
Vol. 7,
Issue 11,
pp. 2246-2251
(1968)
•https://doi.org/10.1364/AO.7.002246

Interferometric Study of Phase Fluctuations of a Laser Beam Through the Turbulent Atmosphere

M. Bertolotti, M. Carnevale, L. Muzii, and D. Sette

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M. Bertolotti, M. Carnevale, L. Muzii, and D. Sette, "Interferometric Study of Phase Fluctuations of a Laser Beam Through the Turbulent Atmosphere," Appl. Opt. 7, 2246-2251 (1968)

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Abstract

Phase fluctuations of a laser beam propagating through a turbulent atmosphere are studied as a function of the distance in a cross section of the beam. An interferometer is described that allows simultaneous measurements of phase fluctuations for pairs of rays that travel in the beam at different distances between each other. Experiments with this method have been performed in an urban center at a distance of 3.5 km and 0.5 km from the source (a helium–neon laser). The results of these measurements are described, and the behavior of the mean square fluctuation of the phase difference is studied. The values of the structure constant C_n are calculated.

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Runs	Values of M_i²				C_n $(m^{- \frac{1}{3}})$	Observations	Path travelled (km)

	M₁²/4π²	M₂²/4π²	M₃²/4π²	M₄²/4π²
A	0.0432	0.0825	0.1085	0.1327	2.9 × 10⁻⁸		3.5
B	0.0463	0.0784	0.1041	0.1218	2.9 × 10⁻⁸	Measurement performed 30 min later than A.	3.5
D	0.0076	0.0104	0.0141	0.0157	3.4 × 10⁻⁸	Measurement C was performed 30 min later. During the interval a fire was lighted in the path of the laser beam.	0.5
C	0.0162	0.0397	0.0526	0.0587	5 × 10⁻⁸		0.5
E	0.0085	0.0138	0.0338	0.0400	4 × 10⁻⁸		0.5
F	0.0112	0.0200	0.0300	0.0360	4.2 × 10⁻⁸	Measurement performed 30 min later than E.
G	0.1027	0.2060	0.2509	0.2785	8.4 × 10⁻⁸		3.5

τ₁₂ =	5/16 sec
τ₁₃ =	15/16 sec
τ₁₄ =	33/16 sec
τ₂₃ =	10/16 sec
τ₂₄ =	28/16 sec
τ₃₄ =	18/16 sec

Runs	Values of M_i²				C_n $(m^{- \frac{1}{3}})$	Observations	Path travelled (km)

	M₁²/4π²	M₂²/4π²	M₃²/4π²	M₄²/4π²
A	0.0432	0.0825	0.1085	0.1327	2.9 × 10⁻⁸		3.5
B	0.0463	0.0784	0.1041	0.1218	2.9 × 10⁻⁸	Measurement performed 30 min later than A.	3.5
D	0.0076	0.0104	0.0141	0.0157	3.4 × 10⁻⁸	Measurement C was performed 30 min later. During the interval a fire was lighted in the path of the laser beam.	0.5
C	0.0162	0.0397	0.0526	0.0587	5 × 10⁻⁸		0.5
E	0.0085	0.0138	0.0338	0.0400	4 × 10⁻⁸		0.5
F	0.0112	0.0200	0.0300	0.0360	4.2 × 10⁻⁸	Measurement performed 30 min later than E.
G	0.1027	0.2060	0.2509	0.2785	8.4 × 10⁻⁸		3.5

τ₁₂ =	5/16 sec
τ₁₃ =	15/16 sec
τ₁₄ =	33/16 sec
τ₂₃ =	10/16 sec
τ₂₄ =	28/16 sec
τ₃₄ =	18/16 sec

Abstract

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Equations (13)

Applied Optics