JOURNAL OF THE OPTICAL SOCIETY OF AMERICA
Method for the determination of the index of refraction of particles
suspended in the ocean*
J. Ronald V. Zaneveld and Hasong Pak
Department of Oceanography, Oregon State University, Corvallis, Oregon 97331
(Received 18 May 1972)
It is shown that the complex index of refraction of a given particle-size distribution may be calculated if
the particle extinction coefficient and the particle absorption coefficient are known. If the particles are
assumed to be nonabsorbing, a real index of refraction may be calculated from the ratio of light scattering
at 45' from the forward for two wavelengths. Application of the method to two stations off Ecuador
indicates that the particle index of refraction can be determined with sufficient accuracy to become an
important parameter in the study of the oceans.
Index Headings: Oceanography; Refractive index; Scattering.
The index of refraction of suspended particles in the
ocean is a most interesting but elusive parameter. The
index of refraction of suspended particles has not been
measured directly. Nevertheless, many calculations of
volume scattering functions using the Mie theory have
been carried out using estimated indices of refraction.
The index of refraction can also be a useful oceanic
parameter describing the origin of particles. Pavlov and
Grechushnikovl have estimated that the relative index
of refraction of minerals in the sea is 1.17, whereas the
relative index of refraction of living matter in the sea is
probably closer to unity. Pak et al.A have characterized
the suspensoids in the ocean by means of "light-
scattering vectors." These vectors use the average size of
a suspended particle in a sample and the average
scattering at 45°. The method could probably be im-
proved by using the particulate index of refraction
rather than the average scattering.
The only method currently available for the calcula-
tion of a weighted average index of refraction is that of
Gordon and Brown.
3 Using the theory developed by
Mie
4 to calculate a number of volume scattering func-
tions, they found the closest fit to experimental data.
The corresponding index of refraction is that of the
scattering sample.
This method, although accurate, is not deterministic.
In this paper, a theory will be developed that will give
an index of refraction directly from the particle-size
distribution and the inherent optical properties (light
attenuation and scattering).
Caution must be exercised when the term index of
refraction is used for a collection of particles. The
average index of refraction such as determined by
Gordon and Brown
3 and by ourselves is really the value
of the index of refraction that reproduces the bulk
scattering properties of the particles. The individual
indices of refraction are weighted by the scattering
cross sections of the particles and then averaged. This
process tends to favor the larger particles, as the
scattering cross section is related to the cross-sectional
area of the particles. In order to distinguish it from a
true average index of refraction, the term significant
index of refraction will be applied to the value of the
index of refraction that will reproduce the bulk optical
properties of the particle distribution.
GENERAL CONSIDERATIONS
The ocean will be considered to be a collection of
spherical particles suspended in pure water. The index
of refraction of water (real) will be given by mr, and the
(complex) significant index of refraction of the particles
will be given
by mr,= n,-inj', following
Van de
Hulst's
5
notation.
The particles will further be characterized by a
particle-size distribution f(D)dD, giving the number of
particles with diameters between D and D+dD. Mie4
theory permits us to calculate extinction, scattering, and
absorption cross sections for suspended spherical parti-
cles if the indices of refraction of the particles and the
suspending medium are known. The expressions for the
cross sections may be greatly simplified if the index of
refraction of the particles is close to that of the sus-
pending medium
IlM-ll<l,
where n =m /mrn.
This implies
both I n/mn- 13(<1 and
n,'/mn<<«l.
In
the ocean, the assumption rm-1i<<1 is reasonable.
Van de Hulst5 has derived approximate formulas for the
extinction (Qert) and absorption efficiencies (Qabs) de-
rived from Mie theory for the case rm-1j<<1. The
efficiencies are obtained by dividing the cross sections
for the extinction or absorption by the geometrical
cross section of the particle. Burt' has presented a useful
scattering diagram that shows the efficiency
factor as a
function of size, wavelength, and relative refractive
index. The relations are
cost
Qext= 2 -4e-p tanft sinf(p-
p
fcosf3\ 2 /cos/3 2
-4eP tan\ c ) cos(p-21)+4 -) cos2i3
(1)
321
VOLUMNE 63, NUMBER 3MARCH 1973
