AEROSOL OPTICS
Short Course Module, March 2012
Rudolf B. Husar, rhusar@wustl.edu
Energy, Environmental and Chemical Engineering
Washington University, St Louis
================== Administrative ==================
The Aerosol Optics Module will consist of
4 sessions, 1.5 hours each. Two homeworks. Quiz at the end of module.
Session 1: Radiation and scattering fundamentals
Session 2: Scattering calculations for aerosol systems
Session 3: Application to measurements, in situ, remote sensing
Session 4: Applications for atmospheric aerosols, visibility, climate
Goals of the module:
 To explain the physical principles of aerosol interaction with light
 Show the relevant computational procedures and tools
 Demonstrate their application to aerosol measurements and characterization
======================Table of Contents========================
AEROSOL OPTICS ................................................................................................................... 1
Short Course Module, March 2012 ........................................................................................ 1
Introduction ............................................................................................................................ 2
Radiation ................................................................................................................................ 2
The Physics of Radiation .................................................................................................... 2
The Electromagnetic Spectrum (EM)................................................................................. 3
Gaseous Absorption ........................................................................................................... 5
Reflectance ......................................................................................................................... 6
Aerosol Scattering and Absorption ........................................................................................ 7
Scattering and Absorption by Single Spherical Particles: Mie Scattering ......................... 8
Role of Particle Size ........................................................................................................... 8
Cross Section and Efficiency ............................................................................................. 9
Efficiency per Unit Mass .................................................................................................. 10
Albedo for Single Scatter ................................................................................................. 10
Scattering Diagram and Phase Function, Asymmetry Factor .......................................... 11
Diffraction, Refraction, and Reflection ............................................................................ 14
Role of Diffraction ........................................................................................................... 14
Refraction ......................................................................................................................... 15
Refractive Index ................................................................................................................... 18
Refractive Index for Shortwave Radiation ....................................................................... 18
Refractive Index for IR Radiation .................................................................................... 21
1
Introduction
Aerosol optics is concerned with the interaction of visible or near visible
electromagnetic radiation aerosol clouds and with the processes associated with
radiative transfer. From the point of view of radiation, the aerosol system consists
of randomly suspended discrete mass centers, which interacts with the radiation by
absorption and scattering.
Radiation
The Physics of Radiation
Radiant energy may be alternatively envisioned as being transported either by
electromagnetic waves or by photons. Neither point of view completely describes
the nature of observed phenomena. Nevertheless, these separate concepts have
considerable utility. For example, the scattering from a single particle within a
radiation wave front may be predicted through use of electromagnetic theory,
whereas quantum theory and discrete approach is utilized to determine the
properties of gaseous absorption or multiple scattering in turbid media.
Figure 1. Simplified visualization of scattering of an incident electromagnetic wave by a
particle.
Radiation travels at the speed of light. Thus, from the viewpoint of electromagnetic
theory, the waves travel at this speed. Alternatively, from a quantum point of view,
energy is transported by photons, all of which travel at the speed of light. (This
differs from molecular transport in that all the photons have the same speed.) There
2
is, however, a distribution of energy among the photons. The energy associated
with each photon is hν, where h is Planck’s constant and ν is the frequency of the
radiation. Each photon also possesses a momentum hν/c, where c is the velocity of
light within the medium through which the radiation travels.
Three parameters may be employed in characterizing radiation: The frequency ν,
the wavelength λ, and the wave or photon speed c. Of these, only two are
independent, since they are related by c = λν. The choice as to whether to
employ ν or λ as a characteristic parameter is somewhat arbitrary, although ν has
the advantage in that it does not change when radiation travels from one medium to
another. The speed of light c within a given medium is related to that in a vacuum,
co, by
c = co/m
where m is the index of refraction. In vacuum, the index of refraction is unity while
in gases it is also approximately one. For common liquids and solids it is between
1.3 and 3.
The Electromagnetic Spectrum (EM)
The EM spectrum spans over 14 orders of magnitudes, from radio waves with
wavelengths of hundreds of meters, to gamma rays of which wavelength is a small
fraction of a nanometer. The wavelength range of interest to aerosol optics is the
visible and the near-visible part of the spectrum, ranging between 0.3 < λ < 1.0 um.
The various radiation sub ranges are illustrated in Fig. 2.
3
The
The Electromagnetic
Electromagnetic Spectrum
Spectrum
 Remote sensing uses the radiant energy that is reflected and emitted from
Earth at various “wavelengths” of the electromagnetic spectrum
 Our eyes are only sensitive to the “visible light” portion of the EM
spectrum
 Why do we use nonvisible wavelengths?
Michael D. King, EOS Senior Project Scientist
1
August 25, 2002
Figure 2. The electro magnetic spectrum
4
Figure 3. Spectral characteristics of sensors
Gaseous Absorption
Atmospheric
Atmospheric Absorption
Absorption in
in the
the
Wavelength
Wavelength Range
Range from
from 0-15
0-15 µm
µm
Michael D. King, EOS Senior Project Scientist
4
August 25, 2002
Figure 4. Atmospheric absorption by gases
5
Reflectance
Typical
Typical Spectral
Spectral Reflectance
Reflectance Curves
Curves for
for
Vegetation,
Vegetation, Soil,
Soil, and
and Water
Water
Michael D. King, EOS Senior Project Scientist
3
August 25, 2002
Figure 5. Angular and spectral reflectance of surfaces
6
Aerosol Scattering and Absorption
When a particle is irradiated with light of a given wavelength, two different
physical processes will occur. The incoming radiation can be transformed into
other forms of energy, such as heat, energy of chemical reactions, or radiation at a
different wavelength. In such a case the energy transformation is called absorption.
The absorption of radiation is associated with transitions of the energy levels of the
atoms or molecules that constitute the aerosol. Absorption terminates the path of a
photon. In visible range very few gases, such as NO 2, have spectral absorption
bands. The most important gaseous absorption bands are in the ultraviolet (e.g.
ozone) and in infrared regions (water vapor, CO2).
Particles may also scatter photons. Scattering is defined as any change in the
direction of propagation of the photons. This process is physically due to local inhomogeneities within the medium, e.g. suspended solid particles or liquid droplets
within the gas. Light scattering is produced by the gas molecules. When radiant
energy is scattered with no change in frequency, the scattering is referred to as
coherent scattering.
If the scattering of radiation within a gas is strictly molecular scattering (i.e., there
are no foreign particle present), it is designated as Rayleigh scattering. The
Rayleigh theory predicts that the spectral intensity of the scattered radiation will
vary as the fourth power of the frequency; that is, the scattering is predominantly at
the shorter wavelengths. This accounts for the fact that the sky appears blue, for the
preferential scattering in the atmosphere involves the short wavelength blue light.
This is also the reason why sunsets are red, for the long wavelength red light suffers
less attenuation in traversing the large atmospheric path length. Although Rayleigh
scattering is an important mechanism in global atmospheric phenomena, it is
usually unimportant for microclimatological applications due to the short path
lengths involved in the latter.
Scattering can, however, play an important role in radiation energy transfer when
foreign particles are present. Typical examples include clouds, fogs, and air
pollution particulates. In these cases scattering may encompass the combined and
interactive effects of reflection, refraction, and diffraction. A theory that is pertinent
to such situations is Mie scattering, which is concerned with electromagnetic
scattering from spherical particles with sizes on the order of the wavelength of the
incoming radiation.
The foregoing was a discussion of the physics of absorption and scattering.
Attention will now be turned to the formulation of the processes of absorption and
scattering in terms of defined radiation properties.
7
Scattering and Absorption by Single Spherical Particles: Mie Scattering
In this section we shall consider the scattering characteristics of single particles and
provide the information required for the calculation of radiative transfer and
visibility in the hazy atmosphere. The objective is to relate the properties of the
scattering particles, shape, size and refractive index, to the intensity and angular
distribution of the redirected light.
It is of interest to note that scattering is not restricted to the visible part of the
electromagnetic radiation spectrum. The scattering of radio waves by satellites, the
scattering of microwaves by raindrops, scattering of thermal radiation by cloud
droplets, scattering of light by small particles, and electron scattering by molecules
are all similar phenomena, since in each case the wavelength is of the same
magnitude as that of the scattering object. Thus, as a natural scaling fact or for
scattering is the wavelength of the incoming radiation and it is used in the
dimensionless parameter, called the optical size parameter, α.
α= 2  r/ λ =  D/ λ
where r or D is characteristic particle size; in the case of a sphere it is the radius. In
the following discussion, the incident radiation will be assumed to be
monochromatic.
Role of Particle Size
The primary role of particle size is that it determines the regime of interaction with
radiation. For particles much smaller than the wavelength α<< 1, the presence of
the particle does not perturb the wavefront of the electromagnetic radiation. The
physical process of scattering in such a regime is described by dipole interaction
with electromagnetic radiation and it is also referred to as Rayleigh scattering.
8
Figure 6. Rayleigh scattering by air (bRg) is proportional to (wavelength)4 Reduced air
density at higher altitudes causes a reduction of bRg. The NO2 absorption band
peaks at 0.4 m but vanishes in the red portion of the spectrum
When the particle size becomes comparable to the wavelength, then the wavefront
suffers a substantial distraction in the vicinity of the particle. Waves scattered by a
particle will tend to interfere positively and negatively with the surrounding
radiation wavefront, which leads to a peculiar interference pattern in the vicinity
range and this particle - radiation is called Mie scattering.
For particles with diameter at least ten times the wavelength, the interaction with
the wavefront again becomes relatively simple. Such a particle will reflect, refract
(the lens effect), and diffract certain amounts of radiation. These particles fall in the
regime of geometrical optics scattering.
Cross Section and Efficiency
When the electromagnetic wavefront passes a particle, the radiation in the vicinity
of the particle will be abstracted from its original path, by scattering and absorption.
This fraction of incoming radiation is extinct from the original beam. Hence, the
extinction cross section of a particle, Cext, is the area in the particle where all the
incoming radiation changes directions or gets absorbed. The scattering cross section
Cscat and the absorption cross section, Cabs, are defined analogously and follow the
relation:
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Cext = Cscat + Cabs
Intuitively, the extinction cross section is the cross sectional area of the particle, A
=  r2 i.e. the ‘efficiency’ of extinction is unity. In other words, the amount of
energy impinging upon the particle cross sectional area is extinct with unit
efficiency factor. However, in reality this efficiency factor Q ext, can be significantly
higher than or in cases less than unity depending on wavelengthand the refractive
index m.
Cext = Qext  r2
The efficiency factors for scattering, Qscat, and absorption, Qabs, are defined in a
similar manner. In analogy of the cross sections, it also holds that
Qext = Qscat + Qabs
One would expect that for very large spheres, certainly for large absorbing spheres,
the extinction cross section would approach the physical cross section i.e. Q ext ~ 1.
Paradoxically, this is not so. A large scattering sphere extincts twice its geometrical
cross section. The cause for this discrepancy is explained by the "diffraction
paradox."
Efficiency per Unit Mass
It is often desirable to define and compute the efficiency of extinction per unit mass
of aerosol. The mass extinction efficiency Mext is defined for spherical particles as
The mass scattering and absorption efficiency factors are defined analogously and
satisfy the relationship
Mext = Mscat + Mabs
The utility of the mass efficiency factors lies in that they are identically potency
functions .
Albedo for Single Scatter
In the general case, the photons may be scattered and absorbed by the particles, thus
only a fraction of the incident photons will be leaving the particle. The albedo for
10
single scatter, ω, is defined as the fraction of light lost from the incident light due to
scattering, while ( 1 – ω ) represents the absorbed fraction of the energy. Thus, the
albedo ω is defined as
ω = Cscat / Cext = Qscat / Qext = Mscat/ Mext
The single scatter albedo is particularly useful in multiple scattering calculations.
Scattering Diagram and Phase Function, Asymmetry Factor
The scattered wave of any point in the distant field has the character of a spherical
wave in which energy flows outward from the particle. The direction of scattering
is characterized by the scattering angle θ and azimuth angle  .
The most important property of the incident and scattered wave is the intensity, I.
The intensity of electromagnetic radiation is the rate of energy flow across a unit
area (erg/cm2sec) perpendicular to the direction of propagation. In optics this is also
called irradiance. The intensity is occasionally also referred to as illuminance, i.e.
luminous flux per unit area (lumens/m2 = lux). Both the incident and scattered
waves are unidirectional, i.e. each confined to a narrow solid angle. The term I is
the total energy flux in this narrow solid angle dω.
The waves are also assumed to be monochromatics, i.e. confined to a narrow
frequency interval. Here we should recall that it is advantageous to use frequency
rather than wavelength, since ν is independent of the refractive index of the medium.
However, for practical reasons, the intensity is commonly defined in terms of
wavelength increment dλ.
If Io and I are the intensities of incident and scattered light respectively, and R is the
distance from the particle, then I must be proportional to I o and R –2, and we may
write
11
Figure 7. Schematics of the angular distribution of the scattered light
The total amount of incident energy that changes direction of propagation is the
amount confined to the scattering cross-section, Cscat. The same energy is now
distributed in all directions as given by the dimensionless angular function called
the scattering diagram, F (θ,  ). From conservation of energy, we get
Wave number k = 2 / λ
where dω = sin θ d θ d is the infinitesimal solid angle and the integral is taken
over all directions, 0 < θ <  ; 0 <  < 2 .
The scattering diagram, when divided by Cscat k2 yields the phase function P (θ, ):
P (θ, ) = F (θ, ) / Cscat k2
which is the fraction of the total amount of light scattered into direction θ and  .
The integral of P (θ, ) over all directions is unity.
Hence the phase function represents the probability of scattering in any given
direction. The probabilistic interpretation of P (θ,  ) is useful for the photon
tracing in multiple scattering problems. Clearly, shape value of the phase function P
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(θ,  ) depends on the size parameter, and the refractive index m. For spherical
particles in natural nonpolarized light, the light scattering phase function has
circular symmetry coinciding with the axis of incident beam propagation such that
P(θ, ) = P(θ)
Generally, the forward scattering dominates the backscattering and this asymmetry
is quantified by the asymmetry parameter cos θ, defined as
The asymmetry factor increases with increasing particle size.
Scalar waves, like sound, are fully described by the intensity. However, neither the
incident light nor the scattered light is completely characterized by intensity. The
transverse nature of light waves allows the phenomenon of polarization to occur.
The additional parameters required for the full description
are polarization and phase.
Light consists of many simple waves with frequency 1014 sec –1 and with the
duration of coherent wave trains 10 –8 sec. The simple waves are all monochromatic
and completely (elliptically) polarized. Light that is commonly measured is the net
effect of many simple waves and in general it is partially polarized. Natural light,
such as direct sunlight, is a mixture of uncorraleted simple waves. Over a time
period of usual measurements ( t > 10 –8 sec) the electric vector exhibits no
preferential vibration i.e. it is unpolarized.
An arbitrary beam of light, of intensity I, consists of an unpolarized part and a
totally polarized part.
I = Iunpol + I pol
The degree of polarization is defined as Ipol / I. The polarized part of the beam is in
general elliptically polarized, and it can be further separated into a linearly
polarized part, Ilp, and a circularly polarized part, Icp, where Ipol = ( Ilp2 + Icp2 ) (1/2).
The scattered radiation is in general polarized. For the present discussion it will
suffice to say that the scattered intensity will have components vibrating
perpendicularly (i1) and parallel (i2) to the plane through the directions of
propagation of the incident and scattered beams.
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Degree of polarization is = (i1 – i2)/(i1 + i2).
The wave phenomena involved in light scattering are illustrated schematically in
Fig. 8.
Figure 8. Schematics of the spherical wave of linearly polarized light leaving the particle.
Much of the light scattering theory is concerned with the understanding of the
intricate interference relationship between the scattered (diffracted, refracted, and
reflected) and the incident light. In the next section, consideration is given to the
basic physical processes, which cause light scattering to occur.
Diffraction, Refraction, and Reflection
The combined and mutually interfering effects of diffraction, refraction, and
reflection can describe the physics of light scattering by small particles. Reflection
is a well known phenomenon and generally contributes < 5% of the scattering.
Therefore, no further consideration will be given to its role at this point.
Role of Diffraction
Diffraction is an edge effect. It arises from the incompleteness of the wavefront
passing the sphere.
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Figure 9. Diffraction
A fraction of the radiation near the edge of the particle is bent towards the particle
to "fill its shadow." On rigorous physical grounds it can be shown that the amount
of radiation diffracted is precisely the cross sectional area of the particle. This holds
for any shape particle. Hence, the extinction cross section of a large sphere consists
of the refracted (or absorbed) cross section,  r2, and of the diffracted cross section,
which is also  r2. This explains the "diffraction paradox" that Qext = 2 (Van de
Hulst, 1957) for large particles, and the polarization of diffracted light is the same
as that of the incident light.
Refraction
The refractive index plays three major roles in extinction: 1) phase shift, due to
difference of speed of wave propagation inside and outside the particle, 2) bending
of the wavefront direction (the lens effect), 3) dissipation (absorption).
The speed of a wavefront entering the particle with n > 1 is reduced by the amount
c = co /m, where co is the speed of light in a vacuum. Since the frequency remains
constant, this leads to reduction of the wavelength within the particle. Consequently
a phase shift develops between the wave within and outside the particle. Hence, the
wave leaving the particle (i.e. center of the particle) may be in or out of the phase
with its surroundings. This then may lead to positive or negative interference. We
shall note later that it should also be stressed that phase shift is a necessary
condition for scattering to occur, i.e. the refractive index difference at the particle
interface needs to be large.
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Figure 10. Phase shift.
The refraction index is also responsible for bending the arriving wavefront in a
similar manner as observed in the well known convex lens effect. For small
refractive index, the bending is weak, while at high n, the dispersion is strong as
illustrated schematically in Fig. 11. The refracted light from a particle contributes
most of the polarization.
Figure 11. The "lens effect" of refractive index
For absorbing media such as metal oxides and elemental carbon, the refractive
index, m, is complex. The refracted wave now becomes inhomogeneous, with
decaying intensity (amplitude) as it penetrates the particle, Fig. 12.
16
Figure 12. Absorption
The refractive index, m, is now expressed as a complex number
m = n – in’
where n and n’ are the real and imaginary parts of m. The radiation intensity in the
particle decreases by exp (-2α n’), and the amplitude by exp (-2α n’).
In summary, the basic interactions between light and atmospheric particles are
illustrated in Figure 13. For spherical particles of sizes similar to the wavelength of
visible light (0.1 to 1 μm), the scattering and absorption of individual particles can
be calculated through use of the “Mie” equations (Mie, 1908).
Figure 13. Light scattering by ‘Mie Particles’ is the combined effect of diffraction and
refraction. A) Diffraction is an edge effect whereby the radiation is bent to "fill the
shadow" behind the particle. B) The speed of a wavefront entering a particle with
refractive index n >1 (for water n = 1.33) is reduced. This leads to a reduction of the
wavelength within the particle. Consequently a phase shift develops between the
wave within and outside the particle leading to positive and negative interferences. C)
Refraction also produces the "lens effect." The angular dispersion by bending of
incoming rays increases with n. D) For absorbing media, the refracted wave intensity
decays within the particle. When the particle size is comparable to the wavelength of
17
light (0.1 - 1 m), these interactions (a-d) are complex and enhanced. For particles of
this size and larger, most of the light is scattered in the forward hemisphere, or away
form the light source.
Figure 14. Single Particle Scattering and Absorption. For a single particle of typical
composition the scattering per volume has a strong peak at particle diameter of 0.5
m (m = 1.5 - 0.05i; wavelength: 0.55m). The absorption per aerosol volume
however is onlly weakly dependent on particle size. Thus the light extinction by
particles with diameter less than 0.1 m is primrily due to absorption (Charlson et al.
1978). Scattering for such particles is very low. A black plume of soot from an oil
burner is a practical example.
Refractive Index
Refractive Index for Shortwave Radiation
The value of the refractive index for dry atmospheric aerosol particles ranges from
1.4 < n < 1.6. For water, the value is 1.33. For a hygroscopic or deliquescent
particle, the refractive index will approach that of water as the particle grows at
high humidities. Since the growths of particles with humidity is only known for a
few pure substances, the RH dependence of refractive index of atmospheric
aerosols is not predictable on theoretical grounds.
Barnhardt & Strate (1970) quote an empirical formula
N = 1.54 + 0.03 ln (1-RH/100).
Hanel (1971) proposed a linear interpolation between the dry particle refractive
index and water, based on the volume fraction of the dissolved matter.
The refractive indices of crystalline aerosol materials have been compiled by
Bullrich (1964) and are shown in Table 1. These crystalline compounds have 1.48 <
18
n < 1.64 in dry state and all f them are transparent in the visible window (i.e. the
imaginary part of their refractive index is negligible).
The imaginary part of the refractive index is responsible for the absorption
(heating) of particles, but its value for atmospheric aerosols is not well established.
For urban aerosols it is considered to range between 0.005 to 0.03.
Absorption in the visible region may be due to organic aerosols or metal (ferrous)
oxide, but is believed to be dominated by carbon (soot) particles emitted from
combustion sources. Twetty & Weinman (1971) have reviewed the real and
imaginary refractive indices of graphites, soot, coals, etc., and gave an average
value of m=1.8-0.5 i. Bergstrom (1972) proposed 0.63 < n' < 0.69 in the visible
window, but he also stressed the wavelength dependence of both n and n'.
Bergstrom's n, n' values for the 0.3-3 m range are given in Table 2.
Figure 15. Real (nr) and imaginary (ni) parts of the refractive index of quartz (silica).
(After Conel, 1969).
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Figure 16. Refractive index for propane soot, chimney soot, soot from precipitation dust,
coarse dust, and fine dust ( Volz,1972)
Particle
Refractive
Index
Particle
Refractive
Index
NH4Cl
1.64
CaSO4
1.57
NH4NO3
1.60
KCl
1.49
(NH4)2SO4
1.52
Na2SO4
1.48
MgCl2
1.54
SiO2
1.49
NaNO4
1.59
K2SO4
1.49
Table 1. The refractive index of atmospheric aerosol materials which have a crystalline
structure (Bullrich, 1964).
20
The calculation of the effective refractive index of a mixture of particles such as the
atmospheric aerosol, is possible if the size, chemical composition distribution
function is known. In that case, the average real and imaginary refractive indices
may be extracted from properly calculated scattering and extinction coefficients.
The real and imaginary parts of the refractive index of atmospheric aerosols have
been examined by a variety of experimental techniques, some requiring aerosol
deposition on filter. In other methods, n and n’ were inferred from in situ optical
measurements. Table 3 summarizes n and n’ data for soot, fly ash, atmospheric
aerosol, and dry dust. Prudent users of such tables will carefully compare their own
application with the conditions that the above data were taken.
Refractive Index for IR Radiation
In the wavelength range 0.7 < λ< 14 m, the real and imaginary refractive indices
of materials cannot be taken as constant. Most materials exhibit absorption bands
particularly in the 1-10 m region, in which n’ will vary drastically. If this variation
of n’ occurs in the "transparency window" of the atmosphere (8-14 m) the analysis
needs to be with care (in spectral bonds).
The extinction is generally dominated by particle sizes comparable to the
wavelength of radiation. Hence, for the transparency window, the particle sizes 814 m are of particular importance, which is dominated by earth’s crust materials:
silicates and metal oxides. Conel (1969) reviewed the optical properties of silicates
and gave n and n’ (Fig. 15) from measurements of Spitzer & Kleinman (1961).
The imaginary part of refractive index for propane soot, chimney soot, soot from
precipitation dust, coarse dust, and fine dust, has been measured (Fig. 16) by Volz
(1972) over a 2-30 m wavelength range. While soot is an efficient absorber, dust
has been shown to be quite absorbing (n’ ~ 0.1) in the 8-14 m band. Further
discussion on the subject is given by Paltridge and Platt (1976, pp 287).
21
Table 2. Indices of refraction ( m = n2 - ik2) for carbon and nickel at various
wavelengths. The actual index of refraction of quartz in the solar spectrum is about =
1.52--0.0 I (Peterson and Weinman, 1969); however, the value of 1.50 was used to be
consistent with that comomnly employed for the natural aerosol (Quenzel, 1970;
Yamamoto and Tanaka, 1969; and others).
 ( m)
n2
k2
0.3
1.84
0.70
0.4
1.88
0.69
0.5
1.94
0.66
0.6
1.99
0.64
0.7
2.03
0.63
0.8
2.07
0.61
0.9
2.09
0.60
1.0
2.12
0.59
1.5
2.14
0.65
2.0
2.17
0.75
2.5
2.21
0.86
3.0
2.26
0.98
0.42
1.41
2.53
0.589
1.79
3.33
0.75
2.19
4.36
1.0
2.63
5.26
2.25
3.95
9.20
(a) Carbon
(b) Nickel
22
Table 3. Values of the real (nr) and imaginary (ni) parts of the refractive index of
atmospheric particles for the short-wave region observed from various experimental
measurements. (Paltridge and Pratt, 1976).
ni
nr
Type
Twitty and Weinman
(1971)
1.8
0.5
soot and coal
dust
Grams et al. (1972)
1.55
0.044
fly ash
0.01
atmospheric
aerosol
0.005
atmospheric
aerosol
0.01
atmospheric
aerosol
Fischer (1970)
Ivley and Popova
(1973)
Lin et al. (1973)
1.65
23