With a focused continuous-wave CO2 Doppler lidar at 9.1-µm wavelength, the superposition of backscatter from two ∼14.12-µm-diameter silicone oil droplets in the lidar beam produced interference that resulted in a single backscatter pulse from the two droplets with a distinct periodic structure. This interference is caused by the phase difference in backscatter from the two droplets while they are traversing the lidar beam at different speeds, and thus the droplet separation is not constant. The complete cycle of interference, with periodicity 2π, gives excellent agreement between measurements and lidar theory.

© 1999 Optical Society of America

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    [Crossref] [PubMed]
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1996 (3)

1986 (1)

1983 (1)

1971 (1)

Bowdle, D. A.

Briers, J. D.

Chambers, D. M.

Dean, C. E.

Fuller, K. A.

Horrigan, F. A.

Jarzembski, M. A.

Jones, W. D.

Kattawar, G. W.

Rothermel, J.

Sonnenschein, C. M.

Srivastava, V.

Wang, R. T.

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Figures (4)

Fig. 1
Fig. 1

Time-resolved signal pulse measurements with a high-speed transient LeCroy oscilloscope from single silicone oil droplets as well as from two closely spaced droplets that show a structure of constructive and destructive interference. A time scan for the signal fed into an amplitude demodulator circuit is also shown for each figure. For all figures, the time scale is 50 µs/division, whereas the amplitude scale is 1 V/division.

Fig. 2
Fig. 2

Schematic showing the condition for interference of backscatter from two droplets moving at different speeds traversing the lidar beam.

Fig. 3
Fig. 3

Calculation of the function [cos(ϕ) + cos(ϕ + δ)] for δ = 0.0226ϕ as a function of ϕ for (a) 11 periods and (b) 1 period with higher resolution, where the number of wavelengths contained within one period can be distinguished. Calculation of the same function modulated by exp[-2(ϕ/K)2] for (c) δ = 0.0226ϕ and K = 1248 to compare with Fig. 1(a) for 1 µs ≈ 21.35 rad, (d) δ = 0.0121ϕ and K = 1246 to compare with Fig. 1(b) for 1 µs ≈ 21.32 rad, (e) δ = 0.0094ϕ and K = 1250 to compare with Fig. 1(c) for 1 µs ≈ 21.38 rad.

Fig. 4
Fig. 4

Vector addition of the harmonic wave functions i s1 and i s2 for each droplet and the resultant harmonic wave function i s [relation (3)] for the case shown in Fig. 1(a) for an arbitrary initial condition of ϕ = ϕ0 with (a) δ = 0.0π (totally constructive interference), (b) δ = 0.226π (nearly constructive interference), (c) δ = 0.904π (nearly destructive interference).

Tables (1)

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Table 1 Calculated Interference Parameters for Figs. 1(a)1(c)

Equations (4)

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is  exp-2πRrλL2cosϕ,
ϕ=2kL+fDt-φR+2φ+2 tan-1πR2λL1-LF,
is  cosϕ+cosϕ+δ.