The multiple scattering of laser beams is usually described within the framework of small-angle scattering theory. The validity of this approximation as well as improvements due to the incorporation of diffusion theory in the calculations were studied

Elliott, N. E.

Gerstl, S. A. W.

Stokes, G. H.

Stupin, D. M.

Unruh, W. P.

Weinman, J. A.

Zardecki, A.

English

NASA Technical Reports Server

N87-10316
MULTIPLE SCATTERING OF LASER BEAMS
IN DENSE HYDROSOLS
A. Zardecki, S.A.W. Gerstl, Theoretical Division
Wesley P. Unruh, International Technology Division
Grant H. Stokes, David M. Stupin and Norman E.
Elliott, Materials Science Technology Division
Los Alamos National Laboratory, Los Alamos, NM
87545, USA and J.A. Weinman, Dept. of Meteorology,
University of Wisconsin, Madison, WI 53706, USA.
The multiple scattering of laser beams is usually
described within the framework of small-angle scattering
theory. The purpose of this investigation is to study the
validity of this approximation as well as improvements due
to the incorporation of diffusion theory in the calculations.
We measured the intensity (power per unit area within
the detector's field of view) of scattered laser light from
an optically dense hydrosol and compared the measured intensi-
ties to those calculated from a multiple scattering theory.
The nonabsorbing hydrosol was composed of 2.26+ 0.07 _m
diameter polystyrene spheres suspended in essentially scatter-
free water. We injected a HeNe laser beam perpendicular
to and at the center of one face of a 10xl0xl0 cm tank contain-
ing this suspension. The intensity of the scattered light
at the exit face of the tank was measured to a relative
accuracy of 1% with a photomultiplier tube (Fig. i). The
axis of the photomultiplier was parallel to the incident
beam and the half-angle field of view (FOV) was either 0.357
deg or approximately 90 deg. In both cases the diameter
of the detector aperture was 500 _m. We measured the intensity
at the exit face of the tank in 100 _m steps from the center
of the emerging laser beam to a radial distance of 4 cm.
We also recorded the shapes of the intensity distributions
from both the exit face and side of the tank with a densito-
metric television camera (Fig. 2) and displayed them on a
false-color image analyzer. An intensity distribution from
the side of the tank is shown in Fig. 3, in which the laser
beam enters from the left. Each color band, shown here in
black and white, represents an equal range in the logarithm
of the intensity.
An example of the comparison of the calculated and
measured irradiances from the exit face of the tank is shown
in Fig. 4 for the 90 deg half angle For detector and an
optical depth of 5.02, as a function of radial distance from
the beam center. In the figure both the measured irradiance
and the calculated total scattering are normalized to unity
at the beam center. The contributions to the total scattering
from the attenuated laser beam, small-angle approximation
and diffusion theory are separately displayed. They are
labelled, respectively, unscattered, scattered and diffuse.
The experimental data are shown by the open symbols which
are considerably larger than the 1% errors in the measurement.
143
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I Fig. 3. Intensity contours measured from the side of the scattering tank. 
~ 
Equal ranges in the logarithm of the scattering intensity are plotted. 
The laser beam enters from the left in t h e  figure. 
POLYSTYRENE PARTICLE COLLIMATED BEAM 
BEAM SPOT= .04CM FOV= SOODEC 
h 
(A 
5 
e 
lo-' 
- -  
E '  
I - '  
Optical Depth= 5.02 
0 = Experimental 
- - - Unscattered 
Scattered 
Diffuse 
To ta 1 
- - -  
-.-.- 
0.0 02 0.4 0.6 0.8 1.0 1.2 L4 1.6 
r (cm) 
Fig. 4 .  A comparison between measured and calculated irradiances for the open 
FOV detector. The separate contributions to the calculated results 
are discussed 2n t h e  text. 
145 


Multiple scattering of laser beams in dense hydrosols

Multiple scattering of laser beams in dense hydrosols

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