Scaling law and photon-count distribution of a laser time-of-flight velocimeter

C. Y. She; R. F. Kelley

doi:10.1364/JOSA.72.000365

Journal of the Optical Society of America
Vol. 72,
Issue 3,
pp. 365-371
(1982)
•https://doi.org/10.1364/JOSA.72.000365

Scaling law and photon-count distribution of a laser time-of-flight velocimeter

C. Y. She and R. F. Kelley

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C. Y. She and R. F. Kelley, "Scaling law and photon-count distribution of a laser time-of-flight velocimeter," J. Opt. Soc. Am. 72, 365-371 (1982)

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Abstract

The equations for performance evaluation of the laser time-of-flight velocimeter (LTV) for atmospheric wind-speed measurement with single-particle digital-correlation analysis have been derived theoretically. Using an inverse power law for aerosol-size distribution and a simple expression for backscatter-differential cross section, the minimum-detectable number of signal photon counts, the photon-count distribution of signal particles, and the scaling law for LTV measurement rate are expressed in terms of correlator settings and parameters of a Gaussian laser beam. It is shown, both theoretically and experimentally, that these equations can be used to evaluate the system performance and assess the potential usefulness of the single-particle LTV.

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(dn/dt)τ₀	κ	m	T_c (msec)	ρ/vτ₀	n_s	E_n(T_c)
0.02	2	1	10	1.936	7.28	1.31 × 10⁻³
0.02	3	1	10	1.936	9.71	6.56 × 10⁻⁶
0.02	4	1	10	1.936	12.1	2.60 × 10⁻⁸
0.005	1	2	10	1.936	5.55	1.25 × 10⁻²
0.005	2	1	10	1.936	7.28	2.08 × 10⁻⁵
0.005	3	1	10	1.936	9.71	2.90 × 10⁻⁸

P₀ (W)	q	κ	m	n_s	E_n(T_c)	E_n(T)	q_a	F	d $\bar{n}$ /dt
1	150853	4	1	12.2	3.00 × 10⁻⁷	4.50 × 10⁻²	1840	1.22	3253
0.5	196353	3	1	9.7	4.71 × 10⁻⁶	9.06 × 10⁻¹	1206	6.14 × 10⁻¹	1829
0.25	327427	3	1	9.7	2.33 × 10⁻⁷	7.37 × 10⁻²	492	1.50 × 10⁻¹	859
0.10	498537	2	1	7.3	6.83 × 10⁻⁶	3.17	266	5.34 × 10⁻²	337
0.05	655112	2	1	7.3	1.04 × 10⁻⁶	4.78 × 10⁻²	178	2.72 × 10⁻²	175

P₀ (W)	n_s	n_s (at 1 W)	q_a (1350 sec)	∑N(n)
1	12.2	12.2	1647	1756 (n ≥ 12)
				1532 (n ≥ 13)
0.5	9.7	19.4	829	800 (n ≥ 19)
				705 (n ≥ 20)
0.25	9.7	38.8	203	170 (n ≥ 38)
				161 (n ≥ 39)
0.10	7.3	73.1	72	94 (n ≥ 47)
0.05	7.3	146	37	94 (n ≥ 47)

(dn/dt)τ₀	κ	m	T_c (msec)	ρ/vτ₀	n_s	E_n(T_c)
0.02	2	1	10	1.936	7.28	1.31 × 10⁻³
0.02	3	1	10	1.936	9.71	6.56 × 10⁻⁶
0.02	4	1	10	1.936	12.1	2.60 × 10⁻⁸
0.005	1	2	10	1.936	5.55	1.25 × 10⁻²
0.005	2	1	10	1.936	7.28	2.08 × 10⁻⁵
0.005	3	1	10	1.936	9.71	2.90 × 10⁻⁸

P₀ (W)	q	κ	m	n_s	E_n(T_c)	E_n(T)	q_a	F	d $\bar{n}$ /dt
1	150853	4	1	12.2	3.00 × 10⁻⁷	4.50 × 10⁻²	1840	1.22	3253
0.5	196353	3	1	9.7	4.71 × 10⁻⁶	9.06 × 10⁻¹	1206	6.14 × 10⁻¹	1829
0.25	327427	3	1	9.7	2.33 × 10⁻⁷	7.37 × 10⁻²	492	1.50 × 10⁻¹	859
0.10	498537	2	1	7.3	6.83 × 10⁻⁶	3.17	266	5.34 × 10⁻²	337
0.05	655112	2	1	7.3	1.04 × 10⁻⁶	4.78 × 10⁻²	178	2.72 × 10⁻²	175

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Equations (17)

Journal of the Optical Society of America