Abstract

Measurements were made of the angular distribution of power scattered from a diffuse reflector illuminated by a laser beam directed normal to the surface of the reflector. Experiments were performed on dry, wet, and ice-covered planar targets. They revealed that the diffuse component of scattered power from a wet or ice-covered target is reduced by an amount proportional to the inverse of the square of the index of refraction of the layer, which is consistent with simple theory. Backscattered radiation from a water- or ice-covered target was found to be enhanced compared with that from a dry target in the region about a cone centered on the line normal to the target. The half-angles of the cones for dry, water-covered, and ice-covered targets were 2.5, 12.5, and 30°, respectively. The large half-angles of the covered targets may be due to multiple reflections within the layer. Small air bubbles in the ice and the roughness of the ice surface may be responsible for the particularly large increase in half-angle of the ice-covered target.

© 1987 Optical Society of America

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References

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  1. J. Y. Wang, P. A. Pruit, “Laboratory Target Reflectance Measurements for Coherent Laser Radar Applications,” Appl. Opt. 23, 2559 (1983).
    [CrossRef]
  2. Y. Kuga, A. Ishimaru, “Retroreflectance from a Dense Distribution of Spherical Particles,” J. Opt. Soc. Am. A 1, 831 (1984).
    [CrossRef]
  3. W. G. Egan, T. Hilgeman, “Retroreflectance Measurements of Photometric Standards and Coatings,” Appl. Opt. 15, 1845 (1976).
    [CrossRef] [PubMed]
  4. E. A. Milne, “Thermodynamics of the Stars,” in Handbuch der Astrophysics, Vol. 3/1, G. Eberhard, A. Kohlschutter, H. Ludendorff, Eds. (Springer-Verlag, Berlin, 1930), pp. 65–255.
    [CrossRef]
  5. S. G. Warren, “Optical Constants of Ice from the Ultraviolet to the Microwave,” Appl. Opt. 23, 1206 (1984).
    [CrossRef] [PubMed]
  6. L. Tsang, A. Ishimaru, “Backscattering Enhancement of Random Discrete Scatterers,” J. Opt. Soc. Am. A 1, 836 (1984).
    [CrossRef]
  7. S. A. Twomey, C. F. Bohren, J. L. Mergenthaler, “Reflectance and Albedo Differences Between Wet and Dry Surfaces,” Appl. Opt. 25, 431 (1985).
    [CrossRef]

1985 (1)

1984 (3)

1983 (1)

1976 (1)

Bohren, C. F.

Egan, W. G.

Hilgeman, T.

Ishimaru, A.

Kuga, Y.

Mergenthaler, J. L.

Milne, E. A.

E. A. Milne, “Thermodynamics of the Stars,” in Handbuch der Astrophysics, Vol. 3/1, G. Eberhard, A. Kohlschutter, H. Ludendorff, Eds. (Springer-Verlag, Berlin, 1930), pp. 65–255.
[CrossRef]

Pruit, P. A.

Tsang, L.

Twomey, S. A.

Wang, J. Y.

Warren, S. G.

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Figures (8)

Fig. 1
Fig. 1

Apparatus used to collect data. The laser is mounted ∼1 m above the target plane. The photodetector mounted on the radial arm inclines around the target.

Fig. 2
Fig. 2

Measured signal strength as a function of detector inclination angle (solid circles) for (a) barium sulfate stanard, (b) brown, and (c) green targets. The solid line in (a) was fitted to the data by multiplying Eq. (2) by the responsivity of the photodetector. The responsivity was varied for best fit to the data. The solid lines in (b) and (c) were calculated using Eq. (2), the measured reflection coefficients (see Fig. 3), and the responsivity of the photodetector as determined from (a).

Fig. 3
Fig. 3

Probability density functions for near-normal incidence and detection for each paint. The power reflection coefficient, computed by taking the ratio of the signal level of the target ST to the signal level of the standard SS, is 0.068 green; 0.077 brown.

Fig. 4
Fig. 4

Probability density function collected solely over the wet portion of the target.

Fig. 5
Fig. 5

Measured signal strength as a function of detector inclination angle for the wet target (solid circles). The solid line was computed using Eq. (7).

Fig. 6
Fig. 6

Schematic illustrating the effect of dielectric layer covering diffuse target.

Fig. 7
Fig. 7

Ice layers on top of target: (a) fine-grained ice; (b) coarsegrained ice.

Fig. 8
Fig. 8

Measured signal strength as a function of detector inclination angle for (a) fine-grained ice layer; (b) coarse-grained ice layer (solid circles). The solid lines were computed using Eq. (7).

Equations (7)

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P R = P T G T A e α ρ f ( r ) ,
P R = P T A ρ cos θ π R 2 ,
VO = P R R e = P T A b A d ρ R e ,
Total power = 0 2 π θ θ + P T ρ τ cos θ sin θ L 2 π L 2 d θ d ϕ ,
A R = 0 2 π θ θ + R 2 sin θ d θ d ϕ ,
σ = ρ P T τ 2 π R 2 n 2 cos θ + + cos θ 2 .
P R = A σ .

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