NASA TECHNICAL
NOTE
NASA
e.
TN
-
D-5458
_-
THE SCATTERING
OF
POLARIZED
LIGHT BY POLYDISPERSE SYSTEMS
OF
IRREGULAR PARTICLES
by
Alfred
CI
Holland
Electronics Research Center
Cam bridge,
M
assI
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON,
D.
C.
NOVEMBER
1969
I
19.
Security Classif. (of this report)
Unclassified
.
TECH
LIBRARY
KAFB,
NM
20.
Security Classif. (of this page)
Unclassified
. .
-
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1111
0132107
1.
Rwort No.
2.
Government Accession No.
NASA
TN
D-5438
I
4. Title and Subtitle
'he Scatterinq of Polarized Light by
'olydisperse Systems of Irregular
-
'articles
7.
Authods)
Jfred
C.
Holland
:lectronics Research Center
lambridge, Mass.
9.
Performing Orgonizotion Name and Address
2.
Sponsoring Agency Name and Address
rational Aeronautics and Space
idmini
s
tr at ion
Vashington,
D .
C
.
20546
5.
Supplementary
Notes
I
3.
Recipient's Catalog No.
5.
Report Date
-
November
1969
6.
Performing Organizotion Code
0.
Performing Orgonizotion Roport No.
c-97
129-02-06-08
IO.
Work Unit No.
11. Contract or Grant No.
13.
Type
of Report and Period Covorod
Technical Note
14. Sponsoring Agency Code
6.
Abstract
The elements of the Mueller matrix for polydisperse
;ystems of irregular, randomly oriented particles have
ieen measured in absolute terms as a function of scat-
zering angle for one wavelength. These results have been
:ompared to the matrix elements that were calculated for
issemblies of spherical particles that fit the same
)article size distribution function and have the same
(real) refractive index. Correlations between the
ieasured and calculated matrix elements are discussed.
17. Key
Words
.
Mueller Matrix
.
Polydisperse Systems
.
Spherical Particles
.
Refractive Index
___
18.
Distribution Statement
Unclassified
-
Unlimited
THE SCATTERING
OF
POLARIZED LIGHT BY
POLYDISPERSE SYSTEMS
OF
IRREGULAR PARTICLES
By Alfred
C.
Holland
Electronics Research Center
SUMMARY
The elements of the Mueller matrix for polydisperse systems
of irregular, randomly oriented particles have been measured in
absolute terms as a function of scattering angle for one wave-
length. These results have been compared to the matrix elements
that were calculated for assemblies of spherical particles that
fit the same particle size distribution function and have the
same (real) refractive index. Correlations between the measured
and calculated matrix elements are discussed.
I.-
INTRODUCTION
The atmospheric aerosols exert a profound influence
on
the
optical properties of the earth's atmosphere. Despite their low
concentration relative to the molecular constituents, the aerosol's
effect on atmospheric scattering can never be completely ignored,
particularly when polarization phenomena are considered. The
atmospheric aerosol is composed of particles of many different
shapes, sizes, and materials. Most of the aerosol particles
(dusts, smokes, snow, and ice crystals) are known to have non-
spherical shapes.
Before a complete description of light scattering by the
atmosphere can be made, one must know the detailed scattering
behavior of such nonspherical particles: specifically, how the
scattering matrix of the atmospheric aerosol depends on the
particle composition, size distribution, shape, and, finally, on
the wavelength of the incident light. However, except for
spherical. particles, and within certain limits, ellipsoids and
cylinders, no rigorous theoretical description of particulate
scattering is known.
The practical importance
of
the problem can hardly be over-
estimated. Beyond the case of atmospheric optics and the effect
of the atmosphere on solar insolation and, hence, climatology,
there is the possibility of using light beams to probe the
atmosphere. Determining the properties of an unknown medium by
examining the behavior
of
its scattering-matrix with scattering
angle and wavelength has many potential applications.
At the present time, most investigators (for lack
of
any
better practical model) assume that their scattering particles
are spheres. The scattering properties of spheres can be
calculated exactly with a large digital computer.
Deirmendjian (ref.
1)
for example, has calculated scattering
matrix elements for models of haze and fog and found his results
to be in excellent agreement with the measurements of Pritchard
and Elliott on natural fog (ref.
2).
There has been some experimental evidence that the scattering
behavior of assemblies of irregular but randomly-oriented
particles is similar
to
the scattering behavior of assemblies
of spherical particles. Hodkinson (ref.
3)
showed that the angular
distribution of light scattered in the forward direction by
samples of quartz, flint, and diamond dusts was similar to the
light distribution predicted on the basis of geometric optics.
Holland and Draper (ref.
4)
showed reasonably good agreement
between the unpolarized scattering coefficient for polydisperse
samples of talc and that calculated for spherical particles
fitting the same size distribution.
The experiments reported here have two main objectives.
The first objective is to investigate possible correlations
between the scattering matrix elements of irregular
oriented) particles and the matrix elements calculated for
spherical particles having the same size distribution and
refractive index. The second objective is to compile sufficient
data on the scattering properties of irregular particles of known
size distribution and physical properties to aid in the develop-
ment or testing of the necessary theoretical models.
(but randomly
Considering the second objective, this work can be viewed
as a preliminary step in a program aimed at developing methods
for describing the scattering of light by real media.
11.-
THEORETICAL CONSIDERATIONS
The scattering
of
a polarized beam of
light by an optically
thin volume element of
a
scattering medium can be described
efficiently by the Mueller calculus. The scattering event is
described as a linear transformation; the Stokes vector of the
incident light beam is transformed into the Stokes vector of the
scattered beam by the Mueller or scattering matrix:
(Ti}
=
const
[sij]{rj}
.
The Stokes vectors of both incident and scattered beams depend
only on the characteristics of the two beams,
while the scattering
matrix depends only on the characteristics of the scattering
medium.
2
The Stokes parameters and the Mueller matrix have been
discussed fully by many authors including Perrin (ref.
5),
Van
De Hulst (ref.
6),
Rozenberg (ref.
7),
and Parke (ref.
8)
and
will not be described in detail here. In brief, if one chooses
as the reference plane the scattering plane, defined by the
directions of the incident and the scattered beams, then the
complex electric vector
of
either beam can be decomposed into
components perpendicular and parallel to the reference plane.
With this convention, the Stokes parameters are defined as:
The subscripts
R
and r denote components parallel and perpendic-
ular to the reference plane; the brackets denote time averages
of
the noted quantities, and the asterisks denote complex con-
jugates.
The Stokes parameters all have the dimensions of intensity
and satisfy the following inequality:
12>Q2+U2+V 2
.
-
The equality holds only for completely polarized light. It can
be shown (ref.
9)
that this characterization of a light beam is
unique and that two beams of light with identical Stokes para-
meters cannot be distinquished by optical analysis.
The four Stokes parameters can be considered as components
of a four-vector and
3
scatterin
multiplication:
I
event described as a matrix
In general, the scattering matrix has sixteen independent
coefficients; however, Perrin has shown that if the scattering
3