Abstract

The results of experiments to measure the delay, temporal stretching, attenuation, and spatial spreading of optical pulses in scale model clouds are reported. The model clouds consisted of diiodomethane/water or paraffin oil/water emulsions maintained in a rotating scattering cell to prevent settling of the droplets. The optical pulses were 532-nm, 25-psec duration pulses generated by a frequency-doubled passively mode-locked Nd:YAG laser and were detected with a 10-psec resolution streak camera. The measurements of the delay in the mean arrival time of the pulses due to multiple scattering are the first measured directly.

© 1983 Optical Society of America

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References

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  4. G. R. Hostetter, “Downlink Laser Cloud Experiment, Final Report,” GTE/Sylvania contract N00014-78-C-0716 (Feb.1980).
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1983 (1)

1982 (2)

1981 (3)

1980 (3)

1979 (2)

1978 (3)

1977 (1)

A. Ishimaru, Proc. IEEE 65, 1030 (1977).
[CrossRef]

1976 (1)

1973 (2)

Bradley, R. G.

Bucher, E. A.

Carswell, A. I.

Cheung, R. L. -T.

Ciero, A. P.

A. P. Ciero, “Multiple Scattering in Clouds,” Pacific Sierra Research Corp., Report 923, contract N00014-78-C0751 (Sept.1979).

Furutsu, K.

Geller, M.

Gupta, H. M.

H. M. Gupta, Opt. Quantum Electron. 12, 499 (1980).
[CrossRef]

Hostetter, G. R.

G. R. Hostetter, “Downlink Laser Cloud Experiment, Final Report,” GTE/Sylvania contract N00014-78-C-0716 (Feb.1980).

Ishimaru, A.

Ito, S.

Krautwald, R. A.

Kuga, Y.

Lerner, R. M.

Matter, J. C.

Mooradian, G. C.

Pal, S. R.

Ryan, J. S.

Shimizu, K.

Stephens, D. H.

Stotts, L. B.

Tam, W. G.

Zardecki, A.

Appl. Opt. (9)

J. Opt. Soc. Am. (6)

Opt. Eng. (1)

A. Ishimaru, Opt. Eng. 20, 63 (1981).
[CrossRef]

Opt. Quantum Electron. (1)

H. M. Gupta, Opt. Quantum Electron. 12, 499 (1980).
[CrossRef]

Proc. IEEE (1)

A. Ishimaru, Proc. IEEE 65, 1030 (1977).
[CrossRef]

Other (2)

A. P. Ciero, “Multiple Scattering in Clouds,” Pacific Sierra Research Corp., Report 923, contract N00014-78-C0751 (Sept.1979).

G. R. Hostetter, “Downlink Laser Cloud Experiment, Final Report,” GTE/Sylvania contract N00014-78-C-0716 (Feb.1980).

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Figures (16)

Fig. 1
Fig. 1

Apparatus for separating large and small buoyant droplets in, e.g., an oil/water emulsion. A thin stainless steel shutter may be drawn across the column to isolate the top 1/9 of the volume from the bottom 8/9. For diiodomethane/water or other emulsions with droplets more dense than the bulk medium the column is inverted with the shutter located near the bottom.

Fig. 2
Fig. 2

Size distribution histogram for emulsion Code F. The dashed line is the theoretical distribution according to Eq. (16). The measured mean diameter and standard deviation are 9.39 and 1.69 μm compared to the predicted values of 9.32 and 1.30 μm, respectively. A total of 802 droplet diameters was measured on 400× micrographs of samples of the emulsion.

Fig. 3
Fig. 3

Scattering cell. The cylinder rotates at a constant speed of 1 rpm to prevent the emulsion droplets from collecting at the top or bottom. The distance between the entrance and exit windows is variable between 0.2 and 11.7 cm. All interior surfaces are flat black to reduce reflection of escaping radiation back into the scattering medium.

Fig. 4
Fig. 4

Schematic layout of the optical system.

Fig. 5
Fig. 5

Typical intensity vs time streak camera record. The left-hand pulse is the reference, and the right-hand is the pulse which has passed through the scattering medium. Optical thickness τ = 9, emulsion Code A.

Fig. 6
Fig. 6

The same as Fig. 5 except τ = 63.

Fig. 7
Fig. 7

Delay in the mean arrival time due to multiple scattering vs optical thickness for diiodomethane emulsions. Measured delay times have been normalized by multiplying by cb−1g−0.94/0.62: □, Code A; ○, Code B; ◊, Code C; and △, Code D. The line is τ1.94.

Fig. 8
Fig. 8

Same as Fig. 7 but for paraffin oil emulsions: □, Code E;○, code F; ◊, Code G; and △, Code G with restricted field of view (16°) detector.

Fig. 9
Fig. 9

Pulse stretching normalized by multiplication by cb−1g−0.81/1.28 vs optical thickness for diiodomethane emulsions: □, Code A; ○, Code B; ◊, Code C; and △, Code D. The line is τ1.81.

Fig. 10
Fig. 10

Same as Fig. 9 but for paraffin oil emulsions. □, Code E; ○, Code F; ◊, Code G; and △, Code G with restricted field of view (16°) detector.

Fig. 11
Fig. 11

Logarithm of the relative integrated intensity of scattered pulses vs optical thickness times the asymmetry factor for diiodomethane emulsions: □, Code A; ○, Code B; ◊, Code C; and △, Code D.

Fig. 12
Fig. 12

Same as Fig. 11 but for paraffin oil emulsions: □, Code E; ○, Code F; ◊, Code G; and △, Code G with restricted field of view (16°) detector.

Fig. 13
Fig. 13

Profiles of the irradiance at the exit window of the scattering cell for the optical thicknesses indicated on the curves. Paraffin oil emulsion Code G.

Fig. 14
Fig. 14

Beam radius vs optical thickness as measured from the half-power points on the profiles displayed in Fig. 13. The line is r = 0.78bg−7τ0.93.

Fig. 15
Fig. 15

Least squares fit of two-gamma distribution functional form to pulse scattered by 167 optical thicknesses of diiodomethane emulsion Code A:– – –, 0.94t exp(−1.94t) + 0.27t exp(−0.60t), t in nanoseconds.

Fig. 16
Fig. 16

Same as Fig. 15 but for a pulse scattered by 107 optical thicknesses of paraffin oil emulsion Code G:– – –, 3.28t exp(−2.78t) + 0.34t exp(−0.77t), t in nanoseconds.

Tables (12)

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Table I Physical Properties of Emulsified Liquids

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Table II Emulsion Characteristics

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Table III Scattering Parameters

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Table IV Measured Scattered Pulse Parameters, Emulsion Code A

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Table V Measured Scattered Pulse Parameters. Emulsion Code B

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Table VI Measured Scattered Pulse Parameters, Emulsion Code C

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Table VII Measured Scattered Pulse Parameters, Emulsion Code D

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Table VIII Measured Scattered Pulse Parameters Emulsion Code E

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Table IX Measured Scattered Pulse Parameters, Emulsion Code F

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Table X Measured Scattered Pulse Parameters, Emulsion Code G

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Table XI Scattered Pulse Parameters Measured with 16°-FOV Detector, Emulsion Code G

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Table XII Spatial Spreading of Scattered Beam

Equations (17)

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g = 1 cos θ = 1 2 π σ s 1 0 π P ( θ ) cos θ sin θ d θ ,
b = ( N σ s ) 1 = [ 2 π N 0 π P ( θ ) sin θ d θ ] 1 ,
τ = Z / b ,
l = 0.62 b g 0.94 τ 1.94 ,
σ l = ( l l ) 2 = 0.64 b g 0.81 τ 1.81 ,
r c = 0.78 b g 0.07 τ 0.93 ,
I τ / I 0 = 1.69 ( g τ + 1.42 ) 1 .
Δ t = l / c = 0.62 c 1 b g 0.94 τ 1.94 ,
σ t = σ l / c = 0.64 c 1 b g 0.81 τ 1.81 ,
I ( t ) = A t exp ( α t ) ,
I ( t ) = A 1 t exp ( α 1 t ) + A 2 t exp ( α 2 t ) .
V ( d ) = G d 2 ( ρ 0 ρ ) / ( 18 η ) ,
T c = ( 72 8 ) / V ( d c ) = 1152 η / ( G | ρ 0 ρ | d c 2 ) ,
N L ( d ) = N 0 ( d ) [ 1 ( d / d c ) 2 ] ; d < d c = 0 ; d d c ,
N s ( d ) = 1 / 9 N 0 ( d ) [ 1 + 8 ( d / d c ) 2 ] ; d < d c = N 0 ( d ) ; d d c ,
N 1 ( d ) = N 0 9 4 [ 1 + 8 ( d / 10 ) 2 ] 4 ; d < 10 = N 0 ; d 10
N 2 ( d ) = N 1 ( d ) [ 1 ( d / 12 ) 2 ] = N 0 9 4 [ 1 + 8 ( d / 10 ) 2 ] 4 [ 1 ( d / 12 ) 2 ] ; d < 10 = N 0 [ 1 ( d / 12 ) 2 ] ; 10 d < 12 = 0 ; d 12 .

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