Effect of turbulence on a focused laser beam and its application to a time-of-flight velocimeter

R. F. Kelley; L. S. Hsu; C. Y. She

doi:10.1364/JOSAA.1.000579

Journal of the Optical Society of America A
Vol. 1,
Issue 6,
pp. 579-584
(1984)
•https://doi.org/10.1364/JOSAA.1.000579

Effect of turbulence on a focused laser beam and its application to a time-of-flight velocimeter

R. F. Kelley, L. S. Hsu, and C. Y. She

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R. F. Kelley, L. S. Hsu, and C. Y. She, "Effect of turbulence on a focused laser beam and its application to a time-of-flight velocimeter," J. Opt. Soc. Am. A 1, 579-584 (1984)

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Abstract

The effect of atmospheric turbulence on a focused laser beam has been evaluated experimentally using a diode array. A proposed model for the calculation of the turbulence-induced beam radius is compared with other available models and is found to yield better agreement with the measured beam radii at different ranges. The turbulence-induced beam radius is then used in the scaling law of a laser time-of-flight velocimeter for performance evaluation. Although the different turbulence models have little effect on the aerosol distribution constant β, which is determined from the scaling law, the proposed model predicts a signal particle arrival rate comparable with the experimental values at a range of 500 m, suggesting that practical long-range (500–1000-m) wind-speed measurements using a cw visible laser are feasible.

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Beam Radius ρ^b	Aerosol Distribution Constants^a

	β	c₀ (av)	c₀ (max)	c₀ (min)
r_G	3.55 ± 0.21	1.48 × 10⁻¹⁰	2.72 × 10⁻⁹	7.99 × 10⁻¹²
r_TA	3.47 ± 0.20	5.04 × 10⁻¹⁰	8.22 × 10⁻⁹	3.06 × 10⁻¹¹
r_TC	3.25 ± 0.18	1.60 × 10⁻⁸	1.90 × 10⁻⁷	1.34 × 10⁻⁹
r_TD	3.19 ± 0.17	2.83 × 10⁻⁸	3.03 × 10⁻⁷	2.62 × 10⁻⁹

			Predicted F and r_s for Radius ρ^a

			ρ = r_G		ρ = r_TA		ρ = r_TC		ρ = r_TD

Experiment	N^b	F_m^c (number/sec)	r_s (μm)	F (number/sec)	r_s (μm)	F (number/sec)	r_s (μm)	F (number/sec)	r_s (μm)	F (number/sec)
7-20-1	12.65	1.0 × 10⁻²	555	2.85 × 10⁻⁴	222	9.12 × 10⁻³	528	3.77 × 10⁻²	503	4.67 × 10⁻²
7-20-2	13.0	5.25 × 10⁻²	174	3.80 × 10⁻³	144	1.52 × 10⁻²	319	4.84 × 10⁻²	308	5.73 × 10⁻²
10-6-1	13.25	3.0 × 10⁻³	155	1.17 × 10⁻³	195	1.49 × 10⁻³	555	2.26 × 10⁻³	532	2.80 × 10⁻³
11-29-1	12.75	1.67 × 10⁻³	61.0	4.80 × 10⁻³	97.9	3.96 × 10⁻³	449	2.84 × 10⁻³	427	3.50 × 10⁻³

Beam Radius ρ^b	Aerosol Distribution Constants^a

	β	c₀ (av)	c₀ (max)	c₀ (min)
r_G	3.55 ± 0.21	1.48 × 10⁻¹⁰	2.72 × 10⁻⁹	7.99 × 10⁻¹²
r_TA	3.47 ± 0.20	5.04 × 10⁻¹⁰	8.22 × 10⁻⁹	3.06 × 10⁻¹¹
r_TC	3.25 ± 0.18	1.60 × 10⁻⁸	1.90 × 10⁻⁷	1.34 × 10⁻⁹
r_TD	3.19 ± 0.17	2.83 × 10⁻⁸	3.03 × 10⁻⁷	2.62 × 10⁻⁹

			Predicted F and r_s for Radius ρ^a

			ρ = r_G		ρ = r_TA		ρ = r_TC		ρ = r_TD

Experiment	N^b	F_m^c (number/sec)	r_s (μm)	F (number/sec)	r_s (μm)	F (number/sec)	r_s (μm)	F (number/sec)	r_s (μm)	F (number/sec)
7-20-1	12.65	1.0 × 10⁻²	555	2.85 × 10⁻⁴	222	9.12 × 10⁻³	528	3.77 × 10⁻²	503	4.67 × 10⁻²
7-20-2	13.0	5.25 × 10⁻²	174	3.80 × 10⁻³	144	1.52 × 10⁻²	319	4.84 × 10⁻²	308	5.73 × 10⁻²
10-6-1	13.25	3.0 × 10⁻³	155	1.17 × 10⁻³	195	1.49 × 10⁻³	555	2.26 × 10⁻³	532	2.80 × 10⁻³
11-29-1	12.75	1.67 × 10⁻³	61.0	4.80 × 10⁻³	97.9	3.96 × 10⁻³	449	2.84 × 10⁻³	427	3.50 × 10⁻³

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Journal of the Optical Society of America A