Optical properties and mass concentration of
carbonaceous smokes
Petr Chylek, V. Ramaswamy, R. Cheng, and R. G. Pinnick
Absorption or extinction measurements at wavelengths of 0.5145and 10.6Atmlead to determination of the
mass concentration of carbonaceous smokes with an accuracy of -20%. The results do not depend on the
details of the particle size distribution or on particulate to void ratio.
I.
Introduction
of their formation. For example, particles produced in
Carbonaceous smokes are produced by a variety of
combustion sources such as chimney stack furnaces,
industrial flames, aircraft and rocket engines, all motor
vehicles, and especially diesel engines.
The soot for-
mation results from incomplete combustion of fuels
containing carbon. The carbonaceous particles contribute to local air pollution of densely populated urban
and industrial areas as well as to global pollution. Even
though their mass concentration is small compared with
other atmospheric particles, carbon particles are highly
absorbing at visible and IR wavelengths, and consequently they may affect the earth's climate.
For these reasons there is a need to measure and
eventually routinely monitor the mass concentration
of these pollutants released into the atmosphere. In
this paper we propose a method based on the extinction
or absorption measurement at two wavelengths to determine the mass concentration of carbonaceous
smokes.
II.
Index of Refraction
The extinction caused by soot particles depends on
their number concentration, size, shape, and refractive
index. Although the number concentration varies
widely from a few particles/cm3 to perhaps 106 particles/cm3 , sizes are predominantly within the 0.0050.15-,m range.1-4 Soot particles can have markedly
different shapes depending on the way and the source
combustion of oil have a corallike structure with an
overall spherical shape (Fig. 1), whereas particles of coal
origin consist of spheres within spheres (Fig. 2). Consequently, if we model a soot particle by an effective
homogeneous particle we cannot expect its effective
refractive index to be equal to that of graphitic or
amorphous carbon. But what refractive index should
be used for particles that contain a significant volume
fraction of void?
The principal method used to measure the refractive
index of soot is based on reflectivity of soot compressed
into pellets. The results reported by different investigators are not in good agreement. In general the refractive index depends upon the molecular structure,
the hydrogen-to-carbon (H/C) ratio, and the ratio of
a particulate phase in agglomerated soot particles. It
has been recognized5 that the effect of molecular
structure is almost negligible. Dalzell and Sarafim 6
measured indices of refraction of acetylene soot with an
H/C ratio equal to 0.068 and of propane soot with an
H/C ratio of 0.217. Although the H/C ratio between the
two measured kinds of soot varied by more than a factor
of 3, they found no detectable difference between refractive indices at visible wavelengths. Differences
were less than 7% from a common mean in IR around
the wavelength of 4 um,and within about 20% from the
mean value at 10 Azm. Consequently, we suspect that
the strongest influence on the value of the refractive
index of carbonaceous smokes is exercised by the vol-
ume fraction of a particulate phase of agglomerated
soot particles.
To investigate the dependence of the refractive index
of soot particles on the particulate fraction
a prescription
R. G. Pinnick is with U.S. Army Atmospheric Sciences Laboratory,
White Sands Missile Range, New Mexico 88002; the other authors
are with State University of New York, Atmospheric Sciences Research Center, Albany, New York 12222.
Received 3 April 1981.
2980
APPLIED OPTICS/ Vol. 20, No. 17 / 1 September 1981
we need
for a refractive index n of a soot as a
function of an index of refraction n of a carbon and of
the particulate volume fraction .
The simplest and commonly used prescription for a
refractive index7 - 9 n of a two-phase composite particle
is
work we adapt the approximation given by the set of
Eqs. (1). Later we discuss the effect of using a different
rule. In the case of soot particles composed of carbon
and voids, we obtain
nS = 1 + O(n.
k =
where mc = nc
-
-
1),
(4)
kc,
(5)
ikc is the refractive index of pure
carbon, and m =ns - ik8 is the refractive index of a
soot particle with particulate fraction s.
For numerical calculations we adopt for the refractive
index of carbon in the visible part of the spectrum the
value 5 mc = 2.0 - i. In the IR we use the values of mp
= 5.0 - 4.Oi at X = 10.6 Aim. The IR values 6 were ob-
tained by reflectivity measurement of soot particles
compressed into a pellet, and it has been suggested 5 that
Fig. 1.
compressed pellets were not all carbon by volume and
that they still contained about 33%of air by volume (0
Soot particle from an oil-fired power plant.
= 0.67). Denoting the refractive index of a pellet by mp
= np - ikp, the refractive index of a soot particle with
the particulate fraction P at 10.6 ,gm can be obtained
from the equations
(6)
0.67
k = O0 kp.
0.67
III.
Fig. 2.
Soot particle from a coal-fired power plant.
n = n + (1 -
O)nZ,
k = k + (1 - )k2,
(1)
where m1 = n - ik, and m 2 = n2- ik2 are refractive
indices of the individual components and k is a volume
fraction of the component having refractive index ml.
It seems that the relation (1) is a purely empirical relationship with no derivation given in the published literature.
A slightly modified version of the same empirical rule
combines the real parts and the ratio of imaginary to
real part of refractive indices1 0 according to
n = On, + (1-
k/n = kk/n2 + (1 - k)k2/n2. (2)
k)n2,
A similar empirical rule has been proposed for the
dielectric constant
=
(7)
Extinction and Absorption in the Visible Region
Using the above specified optical constants we have
calculated the specific extinction and absorption (extinction and absorption per unit mass) of carbonaceous
smokes assuming a surface log-normal distribution of
soot particles, with standard deviation ag equal to 1.5,
2.0, and 2.5, and the mean geometric radius rg in the
10-3 -10-pm region. The results for ag = 2.0 and various values of 0 at the argon laser wavelength X = 0.5145
,um are shown in Fig. 3.
l0
r'
E
I-
bw
bi
100
2
m instead of the refractive index
n. Thus,
e = kes+ (1 -
)e2.
(3)
Other frequently used refractive-index mixing rules
are the Maxwell-Garnettl approximation, the effective
medium approximation,12 and the Lorentz-Lorenz
rule,13 to name a few.
The accuracy and regions of applicability of listed
approximations and empirical rules are not well established. Only the first two of the approximations
consider complex values of refractive indices. For our
0
'-
[
10-3
10-2
lo-,
100
l0
rg(m)
Fig. 3. Specific extinction UEXT/M and absorption OTABS/M at the
wavelength X = 0.5145 Am is relatively insensitive to changes of the
particulate fraction
of a soot particle. Especially in the region of
0, between 0.25 and 0.50 (where most carbonaceous smokes seem to
be), the specific extinction changes only by ±10% for the mean geometric radius rg 0.1 ,um.
1 September 1981 / Vol. 20, No. 17 / APPLIED OPTICS
2981
I
As stated before,1 4 most soot particles have radii
smaller than 0.15 gim. If we require that not more than
5% of the total volume of particle size distribution may
be attributed to particles with radii larger than 0.15, gim
I
I
12.0
I
I
X =0.5145 Im
10.0
ABs/M-12.48-0.0690-_
7
for g = 2.0 the geometric mean radius rg ' 0.045 gim.
8.0
Thus, for almost all practical cases of carbonaceous
I
smokes we take rg < 0.05 gim.
6.0
We notice (Fig. 3) that the specific extinction and
In
by~
specific absorption in the range of rg • 0.05 gimis not
a very sensitive function of X,the fraction of particulate
phase in soot particles. With 0 varying between 25 and
x rg=Q00pm
o r =0.05pm
2.0
100%the specific extinction and absorption vary only
by a factor of 2. Although numerical results are shown
only for the standard deviation ag = 2.0, the same is true
for ag = 1.5 and 2.5, which covers the whole range of size
distribution of interest.
From the above it followsthat from the extinction or
absorption measurement at some visible or near IR
wavelength (index of refraction of carbon remains essentially the same within the 0.40 gim< X < 1.10-gim
4.0 -
A
0
Fig. 4.
I
I
I
I
20
40
60
80
I
100
4 (%)
Specific absorption at X = 0.5145 Am can be approximated
by a linear function of 4 for all rg < 0.05 jim.
region) the mass concentration of carbonaceous smokes
can be determined within a factor of 2. We show later
that the accuracy can be substantially improved by
combining extinction and/or absorption measurement
in visible with extinction and/or absorption measurement in the IR region around X= 10 gim.
We notice (Fig. 4) that the specific absorption for a
OC
E
range of rg < 0.05 gum
can be accurately approximated
by a linear function of particulate volume fraction 0.
_q
We write
b
2M = A -Bo,
(8)
where A = 12.5 and B = 6.9 for 0.1 < 0 < 1.0.
Similarly, the specific extinction can be approximated
(although with not so good accuracy) by
aE!T
= A' -
Blot,
l21
l0o
10-3,
(9)
M
where A' = 13.0 and B' = 5.9. The values of constants
A, B and A', B' are valid only for the considered wavelength X = 0.5145 gim. If different X is used, new values
100
10
rg (pm)
Fig. 5. Specific extinction
GExT/M
and absorption
GrABs/M at
the
wavelength X = 10.6 ,jm is a sensitive function of a particulate fraction
0 of a soot particle. With the change of 0 between 0.25 and 0.50 the
specific extinction changes by a factor of 4.
of these constants have to be determined by numerical
calculations or experimentally.
(At X = 1.06 gim we
obtained A' = 6.2 and B' = 3.0.)
Jennings and Pinnick'4 using a method suggested by
Chylek' 5 obtained an expression for specific absorption
(7.2 M2 g'l) and extinction (10.2 m2 g'l) of carbon
We notice that the specific extinction and/or absorption changes by a factor of 30 (compared with a
particles (4 = 1.0) valid for particles with radius S0.11
gim. Although they were able to explain the measured
absorption and extinction in the visible part of the
spectrum, the same approach fails completely when
applied to IR measurements. On the other hand, the
method suggested in the present paper is consistent
with measurements in the visible and IR regions.
factor of 2 at visible wavelengths) with the change of the
IV.
IR Extinction
Specific extinction and absorption at the wavelength
X = 10.6 gimare shown in Figs. 5 and 6. Results shown
0
are again for the standard deviation ag
= 2.0. However,
all curves remain essentially unchanged for all 1.5 • 0g
< 2.5 as long as rg < 0.05 gim.
2982
APPLIED OPTICS/ Vol. 20, No. 17 / 1 September 1981
particulate volume function between 4 = 25 and 100%.
Consequently, the absorption or extinction measurement in the IR region is not a convenient way to determine the mass concentration, since the fraction is
generally unknown.
Specific extinction or absorption at the wavelength
X = 10.6 gimcan be well approximated
M = C(1004,)-D,
by
(10)
where C = 491,D = 1.98, and 0.2 < 0 < 1.0. Since at X
= 10.6 gimthe extinction is dominated by absorption,
the same relation is valid for specific absorption.
Table I.
Relation Between the ParticulateVolume Fraction 4 and the
AVSS/ TRatio Calculated From Eq. (11) with A =12.5, B = 6.9, C =
491, andD = 1.98.a
1.4
0
1.0
0'
NE>
0.8
b
0.6
0.4
0
20
40
60
80
100
Table II.
4, (%)
Relation Between the ParticulateVolume Fraction and the
= 5.9, C
Calculated from Eq. (13) with A
491, and D = 1.98a.
EXT/ EXT Ratio
Fig. 6. Specific extinction at the 10.6 Aimwavelength can be approximated by an exponential function for all rg ' 0.05 jm.
vis
4,
Mass Concentration
V.
EXT
2.29
8.53
17.86
29.48
42.61
56.48
70.30
83.35
94.83
104.02
a Values of these constants are determined by the wavelengths
(0.5145 and 10.6 m) and the refractive-index mixing rule (1) used.
0.2
0
CABS
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.0
.2
and Particulate
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.0
Volume
Fraction
The absorption and/or extinction measurements of
carbonaceous smokes in the visible and IR regions can
be combined to determine more accurately the mass
concentration M and the volume fraction 0.
The most accurate results can be obtained by combining the absorption measurement at visible and extinction (or absorption) in IR. From Eqs. (8) and (10)
UEXT/EXT
IR
2.41
9.07
19.23
32.21
47.32
63.91
81.31
98.87
115.94
131.88
aValues of these constants depend on the wavelengths and refractive-index mixing rule used.
we obtain
A- -B
C
BS
IR
(100)D
(11)
The left-hand side of this equation is known from the
measurements. Thus, this relation can be used to determine the particulate volume fraction 0. For the
values of constants A, B, C, and D appropriate for the
wavelengths X = 0.5145 and 10.6 gim, Table I gives the
volume fraction 0 for given OaXVS/0-11T
ratios. Once
is determined the mass concentration M follows from
Eq. (8) in the form
M
kBss
,
12.5 - 6.90
(12)
where M is in g/m 3 ,
NIS in m-1, and 0.2 <
< 1.0.
If instead of absorption only extinction at visible
wavelength is known, Eq. (11) has to be replaced by
UVXT
EXT
A' - B,
cTEXT
(100p)D.
(13)
C
Values of 0 for a given vETkEsxTare given in Table II.
The mass concentration is then
vis
M=
TEXT
13.0 - 5.90
(14)
In principle either of the OAVBs
or oEXT can be used for
is more accurate than the one for
TEisT/M
[Eq. (9)], the
absorption measurement leads to more accurate results.
Also, one could use Eqs. (8) and (9) to determine 4
from the oABSS/ExTratio. However, since both AXBLs
and
vis
sol ayn
)
e
fTEXT are only a slowly varying function of , such determination of 0 would be very inaccurate and useless
for practical purposes.
VI.
Effect of Nonsphericity
Although the photograph of a soot particle (Fig. 1)
shows basically spherical character, it is necessary to
assume that in many cases of interest the carbonaceous
smoke particles will be nonspherical. In this case the
Mie scattering formulation cannot be used, and the
question arises whether the proposed method of determination of the mass concentration still remains
valid.
To determine at least the direction of an error caused
by nonsphericity on the mass determination, we have.
calculated extinction in the visible and IR regions of
nonspherical particles described by the equation
r = ro[l + eT2(0)],
(15)
the determination of the 4 and the mass concentration
where T2 is the second-order Chebyshev polynomial.
M.
The value of e was taken to be 0.2. Numerical results
However, since the parameter Eq. (8) for o'b~s/M
1 September 1981 / Vol. 20, No. 17 / APPLIED OPTICS
2983
I
3.0
I
I
I
I
X=0.5145Am
I
I
8
of 4ErXT
anda&T byRoesslerandFaxvog1are
TableIll. Measurements
from
Eq.
(13)
and
the Particulate
VolumeFraction
usedto Determine
M fromEq. (14).a
the MassConcentration
I
-
IEXT
m=2.0-1.Oi
0.525
1.16
1.59
2.0
Sphere
t
~ ~
/--
~
~~~
n
0
0.2
0.051
0.126
0.148
0.21
0.20
0.22
0.045
0.098
0.136
M(g- 3)
0.052
0.120
0.165
Accuracy
15%
18%
18%
P.
The error of measurement of ai and M is -10%.
T2 }
T-I2IIel
0.2
extinction will be a general feature of all nonspherical
/
I~~1.
M(g-3)
a Results are compared with the measured18 mass concentration
W
CY
4
cIR
1
~~~
1
1
0.4
0.6
0.8
1
1.0
1.2
1.4
1.6
1.8
20
XEV
Fig. 7. There is almost no difference between the extinction efficiency UEXT of nonspherical T2 particles and extinction efficiency
of equal volume spheres at X = 0.5145 jim. Size parameter XEV=
1
(6ir 2 V)' 3 X,where V is a volume of the considered particle.
particles regardless of their shape. If this is so, the
nonsphericity of smoke particles will lead to a systematic underestimate of the mass concentration as given
by Eqs. (12) and (14).
VII.
Comparison with Measurements
To verify the validity of the proposed method for the
determination of the mass concentration of carbonaceous smokes we used the extinction and mass measurements of Roessler and Faxvog' 0 on acetylene smoke.
Unfortunately, their measurements of visible and IR
extinction were not made simultaneously on the same
0.03
aerosol. We therefore picked from their data the visible
and IR measurements that correspond to nearly the
same measured mass content and used our relation (14)
to determine the mass concentration M. The particwas determined from the
ulate volume fraction
cTE/0JRXT using Table II. The results summarized in
Table III show agreement of calculated and measured
mass concentration to within 18%. Since both extinction and the experimentally measured mass concen-
0.02
a
0.01
tration are determined
with 110% accuracy, we con-
clude that the mass concentration calculated using Eq.
(14) is in agreement with the measured mass concentration. Roessler and Faxvogl8 did not measure par0
ticulate volume fraction 4 so no comparison of predicted
0
0.01 0.02 0.03
0.04 0.05 0.06
0.07
0.08 0.09
010
XEV
Fig. 8. Extinction efficiency of nonspherical T' particles are up to
20% higher than the extinction efficiency of an equal volume sphere
2
at X = 10.6 jim. Size parameter XEV= (67r V)/3 X,where V is a volume of the considered particle.
values with measurements is possible. The fact that the
mass concentration values obtained from Eq. (14) are
consistently below the measured value by 15-18% might
suggest that a systematic error may be caused by the use
of a specific refractive-index mixing rule or by the
nonsphericity of smoke particles. The use of a different
mixing rule leads to the same expressions for the mass
concentration M [Eqs. (12) and (14)] and for the particulate fraction 0 [Eqs. (11) and (13)]. Only the values
(Figs. 7 and 8) were obtained using the extended
boundary condition method.' 6 In the visible region
there is a very little difference between the extinction
of a sphere and the extinction of considered randomly
oriented nonspherical particles of the same volume. On
the other hand, at the 10.6-gm wavelength we observe
differences up to 20%between a sphere and randomly
oriented nonspherical particles of the same volume.
We notice that both the Tj and T- particles show a
systematically higher extinction than an equal volume
sphere. Since the particles are strongly absorbing, and
since their projected area is always larger than that of
spheres of equal volume,'7 we suggest that the higher
2984
APPLIED OPTICS / Vol. 20, No. 17 / 1 September 1981
of the constants A, B, A', B', C, and D would be slightly
different.
We conclude that the measurement of extinction or
absorption at two different wavelengths leads to a reasonably accurate (we estimate the accuracy to be better
than ±20%) determination of the mass concentration
of carbonaceous smokes, regardless of the particle size
distribution (as long as rg • 0.05 gm and 1.5 ' ag < 2.5)
and regardless of the particulate fraction 0 of soot
particles. Since such measurements are relatively
simple, we believe that the proposed method may serve
as a basis for routine measurements and monitoring of
mass concentration of carbonaceous smokes.
The first author named is also associated with the
Atmospheric Science Section of the Physics Department at Tufts U. The reported research was supported
in part by the National Science Foundation grant
1. J. E. McDonald, J. Appl. Meteorol. 1, 391 (1962).
2. H. G. Wolfhard and W. G. Parker, Proc. Phys. Soc. London Sect.
B 62, 523 (1949).
3. R. C. Millikan, J. Opt. Soc. Am. 51, 535 (1961).
4. J. Cartwright, G. Nagelschmidt, and J. W. Skidmore, Q. J. R.
Meteorol. Soc. 82, 82 (1959).
5. J. Janzen, J. Colloid Interface Sci. 69, 436 (1979).
6. W. H. Dalzell and A. F. Sarafim, J. Heat Transfer 91, 100
(1969).
7. S. C. Graham, Combust. Sci. Technol. 9,159 (1974).
8. W. G. Egan and T. Hilgeman, Appl. Opt. 19, 3724 (1980).
9. S. G. Jennings, submitted to J. Opt. Soc. Am. xx, 000 (1981).
10. A. I. Medalia and L. W. Richards, J. Colloid Interface Sci. 40,233
(1972).
11. J. C. M. Garnett, Philos. Trans. R. Soc. London 203, 385
(1904).
12. J. B. Smith, J. Phys. D: 10, L39 (1977); G. B. Smith, Appl. Phys.
Lett. 35,668 (1979); W. Lamb, D. M. Wood, and N. W. Ashcroft,
Phys. Rev. B: 21, 2248 (1980).
13. H. A. Lorentz, The Theory of Electrons (Leipzig, 1909; Dover,
New York, 1952).
14. S. G. Jennings and R. G. Pinnick, Atmos. Environ. 14, 1123
(1980).
15. P. Chylek, J. Atmos. Sci. 35, 296 (1978).
16. P. Barber and C. Yeh, Appl. Opt. 14, 2864 (1975).
17. P. Chylek, J. Opt. Soc. Am. 67, 1348 (1977).
18. D. M. Roessler and F. R. Faxvog, J. Opt. Soc. Am. 69, 1699 (1979);
70, 230 (1980).
Books continuedfrompage2968
certwining a certain amount of the philosophy of inverse scattering
ATM-8007443 and by the U.S. Army Research Office
grant DAAG29-80-C-0108. Part of this work was done
while the first author named was a Visiting Professor
in the Department of Civil Engineering at the Massachusetts Institute of Technology.
References
nations." The structural determination referred to in the title is the
problem
of determining
the inhomogeneity
of a medium from
into the text.
Chapter 3, "Photon-Counting Statistics of Optical Scintillation,"
knowledge of the spatial distribution of radiation scattered by the
by E. Jakeman and P. N. Pusey, concentrates on strong scattering
medium, usually under the assumption that the source of the radiation
is known. Both random and what are referred to as deterministic (or
by random media. The problem addressed in this chapter is not
stationary nonrandom) media are treated.
of treating the statistical properties of the optical field from photon
This contribution is
somewhat deceiving in its importance. The solutions presented to
the problems posed in this chapter in most instances are incomplete,
at best. However, the properties of the scattered fields, shown to be
present in all inverse scattering problems as a direct result of the re-
quirement that the scattered field satisfy the wave equation, are of
fundamental importance. They represent information typically ignored in dealing with inverse scattering problems. Among other
results, the authors show that all solutions to the vector Helmholtz
equation governing the propagation of the fields are entire functions
of the exponential type. They also show that, for problems of finite
extent, these functions are always of the first order on a complex
surface with a curvature that depends on the distance from the scatterer. They demonstrate the link between this mathematical result
and information theory.
An extensive investigation is made into the
relationship between the zeros of the field and the properties of the
source term in the wave equation (either the medium properties or
the properties of the source). The effects of noise on the location and
properties of these zeros are also considered. By itself, this chapter
would be an interesting contribution; it represents a potentially exciting area for research. However, apparently since the publication
of this book, the authors have carried this highly mathematical de-
velopment to an extremely practical and important conclusion.'
They recently demonstrated how to obtain the amplitude and phase
of a scattered optical field from a simple measurement that can be
made with extreme accuracy. Oversimplifying, they accomplish this
by putting the scattered field through a simple optical processor which
permits a true map of the complex plane representation of the field
to be obtained. Determination of the field is as simple as measuring
positions of the minima (the zeros) of this map on a Cartesian grid
with a ruler. This makes it possible to obtain for optical inverse
scattering measurements the same data that are readily available in
lower frequency electromagnetic and acoustic measurements. It also
permits the techniques developed for these lower frequency regimes
to be applied to solving the inverse scattering problem in optics.
Reading Chap. 2 gives an excellent insight into how the authors were
led to this most important result. It also provides a new and original
way of thinking about inverse scattering problems which quite
probably will lead to other discoveries of importance in this field. The
authors have added to the pleasure of reading this chapter by in-
usually considered in discussions of inverse scattering.
The problem
counting experiments is considered, including the effects of statistics,
instrumental effects, and their relation to photon correlation spectroscopy. The determination of the properties of the scatterer in
terms of a statistical moment description is then looked at. Discussion of the theory is limited to the strong scattering case, and this
distinguishes it from a large body of literature treating weak scattering
and its relation to scintillation. K distributions and distributions
derived from the random walk problem are discussed. Experimental
results derived from scattering by nematic liquid crystals, hot air
phase screens, and measurements in the presence of extended atmospheric turbulence, are reviewed. This chapter is an interesting
if somewhat narrow review. Its appeal to workers in the inverse
scattering field is likely to be less broad than other chapters in the
book.
"Microscopic Models of Photodetection" by A. Selloni is Chap.
4. Again this chapter deals with a subject that many would not think
of as inverse scattering. The problem considered is that of deter-
mining the statistical properties of stochastic radiation fields by
means of photoelectric counting detectors.
The chapter begins with
the definition of the detection problem and a comparison between
ideal and real photodetection processes. A brief review of several
models for ideal detection is given. "Open system" detection schemes
are discussed, including some recent results employing a zero-temperature heat bath. An open system detector employs some mechanism to withdraw the electrons excited by the photons being detected
from the detecting system and then repopulating the lower states.
This is done in such a manner that the upper states of the detector
do not become appreciably populated, avoiding emission back into
the field. Disturbing effects to photodetection are reviewed, including
dark current and noise, dead-time effects, and effects of coherence
in sampling. The effects of temperature are discussed, including a
treatment of the connection between atomic and field dynamics. This
chapter, which ends with a summary of statistical methods for pho-
todetection and a statistical description of the open photodetection
system, is probably of most value to those concerned with the design
and construction of optimum photodetectors. It is probably of little
value to those engaged in developing and applying inverse scattering
theories per se, for such theories usually begin with an implicit ascontinuedonpage3026
1 September 1981 / Vol. 20, No. 17 / APPLIED OPTICS
2985