EPA-650/2-74-031-b
April 1974
Environmental Protection Technology Series
1
jfe*jij:^p:iJK*Sii
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EPA-650/2-74-031-b
APPLICATION OF HOLOGRAPHIC
METHODS TO THE MEASUREMENT
OF FLAMES AND PARTICULATE,
VOLUME II
by
B.J. Matthews and C.W. Lear
TRW Systems Group
One Space Park
Redondo Beach, California 90278
Contract No. 68-02-0603
ROAP No. 21ADG-51
Program Element No. 1AB014
Project Officer: William B. Kuykendal
Control Systems'Laboratory
National Environmental Research Center
Research Triangle Park, N. C. 27711
Prepared for
OFFICE OF RESEARCH AND DEVELOPMENT
ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
April 1974
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This report has been reviewed by the Environmental Protection Agency
and approved for publication. Approval does not signify that the
contents necessarily reflect the views and policies of the Agency,
nor does mention of trade names or commercial products constitute
endorsement or recommendation for use.
ii
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TRW REPORT NO. 23523-6001-TU-00
APPLICATION OF HOLOGRAPHIC METHODS
TO THE
MEASUREMENT OF FLAMES AND PARTICIPATE
VOLUME II
Prepared for
OFFICE OF RESEARCH AND DEVELOPMENT
ENVIRONMENTAL PROTECTION AGENCY
Washington, D.C. 20460
iii
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ABSTRACT
The report gives results of an investigation to determine the feasi-
bility of applying pulsed ruby laser holographic techniques to the measure-
ment of particulate in the 1-micron and sub-micron size range. The investi-
gation included the design and evaluation of a scattered light holocamera,
and evaluation of the effects of four basic variables on scattered light
methods. The variables were: particle size, angular illumination of the
particle (scattering angle), particle number density, and incident laser
beam diameter. The program included an analysis of the mathematical and
physical models from which the transformation can be made from a scattered
light distribution to a particle size distribution. The experimental por-
tion of the program was conducted to assess the advantages and limitations
of certain promising scattered light holographic methods. This report was
submitted in fulfillment of TRW Project No. 23523 and Contract No. 68-02-0603
by TRW Systems Group under the sponsorship of the Environmental Protection
Agency. Work was completed as of November 1973.
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CONTENTS
Page
1. OBJECTIVE AND SCOPE 1
2. PROBLEM ANALYSIS '. 3
2.1 General Formalism 4
2.2 Linearization and the "Inverse Problem" 7
2.3 The Scattering Gain Matrix 10
2.4 The Log Normal Distribution 20
2.5 Estimation of Distribution Parameters for a
Sub-Micron Particulate 24
2.6 Discrimination Between Two Types of Particulate ....- 30
3. EXPERIMENTAL PROGRAM 33
3.1 Experimental Objectives 34
3.2 Test Apparatus 39
3.3 Experimental Procedures 60
3.4 Results 71
4. CONCLUSIONS AND RECOMMENDATIONS 100
REFERENCES 101
APPENDICES
A THE IMAGINARY PART OF THE INDEX OF REFRACTION 103
B COMPUTER PROGRAM FOR FORWARD DIFFRACTION
SCATTERING 105
vii
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ILLUSTRATIONS
Page
2-1 Angular Gain at e = 90 Degrees for Totally
Reflecting Spheres 15
2-2 Angular Gain at 6= 60 Degrees for Totally
Reflecting Spheres 15
2-3 Angular Gain at 6 = 120 Degrees for Totally
Ref1ecti ng Spheres 16
2-4 Position and Value of the First Maximum of the
Angular Gain Function for Totally Reflecting Spheres 17
2-5 Position and Value of the First Minimum of the Angular
Gain Function for Totally Reflecting Spheres 18
2-6 Angular Gain at 6 = 10 Degrees for Totally
Ref1ecti ng Spheres 21
2-7 Scattering Diagram for Totally Reflecting Spheres in Each
Polarization Mode 21
2-8 A Plot of the Function E (<*,£), Showing the Sensitive
Dependence on o- and a 25
2-9 Scattering Diagram for Very Small Totally Reflecting
Spheres 26
2-10 The Scattered Light Distribution for Particulate with
Xg = 1.0 and o-g = 1.7 29
3-1 Schematic Diagrams of Focused Ground Glass Holocamera
Arrangements to Record Bright Field (Lower Diagram) and
Dark Field (Upper Diagram) Scattered Light Holograms 41
3-2 Photograph of Breadboard Scattered Light Holographic
Arrangement Shown in Figure 3-1 44
3-3 The Garrett Two-Beam Scattered Light Holocamera in its
Compl eted Form 45
3-4 Three-Beam Breadboard Holocamera Used to Test Linearity
and Sensitivity of the Holographic Process 46
3-5 Perspective Sketch of Wide Angle Double Reference Beam
Holographic Arrangement 48
3-6 Layout Drawing of Wide Angle Double Reference Beam Bread-
board Holocamera 49
viii
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ILLUSTRATIONS (Continued)
Page
3-7 Aerosol Sol ution Feed System 54
3-8 Voice Coil and Aerosol Generator Orifice Mount 55
3-9 Breadboard Three-Beam Wide Angle Scattered Light
Holocamera With Monodisperse Aerosol Generating
System 56
3-10 Geometry of Internally Scattered Light From a Liquid
Aerosol Droplet of Di ameter a 58
3-11 Nonlinear Diffraction Equations for Light Internally
Reflected From a Sphere and the Two Branches of Their
Solution 58
3-12 TRW Q-Switched Ruby Laser Illuminator 59
3-13 Ruby Laser Illuminator With Cover Removed to Show
Location of Major Components 59
3-14 Schematic Diagram of Compact Ruby Laser Illuminator 61
3-15 Photograph of TRW Pulsed Ruby Laser Power Supply
Consoles and Tektronix 535A Oscilloscope 62
3-16 The Optical Arrangement by Which Light Intensity From
a Small Volume Element of the Reconstructed Real Image
of a Hologram is Imaged Onto a Power Sensitive Detector ... 66
3-17 Photomicrographs of Sample "Micro-Balloons" 72
3-18 High Magnification Photomicrographs of Sample
"Micro-balloons" 73
3-19 Photographs of the Reconstruction of Two Different
Hoi ograms 75
3-20 Photographs of the Reconstruction of Same Scattered
Light Hologram of Glass Micro-Balloons of 30-Micron
Typical Size 76
3-21 Photographs of the Reconstruction of the Same Hologram
of Phenolic Micro-Balloons Recorded in the Dark Field
Scattered Light Holocamera Shown in Figure 3-1 77
3-22 Sensiometric Curves of Emulsions Used In Holography 83
3-23 Primary Laser Beam Flux to Record Scattered Light
Holograms of Individual Particles on Agfa 8E75 Plate 85
ix
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ILLUSTRATIONS (Continued)
Page
3-24 Schematic Diagram of Scattered Light Three-Beam
Transmission Holocamera Test Setup 86
3-25 Reconstruction Photographs of Holograms 9A and 98,
Showing Forward and Side Scattering 88
3-26 Reconstruction of Hologram 12A, Showing Forward Scattered
Light From Tobacco Smoke 90
3-27 Reconstruction Photos of Hologram 16A at 30 Degrees
Scattering Angle, and Hologram 16C at 150 Degrees
Scattering Angle 91
3-28 Observed and Calculated Scattered Light Intensity
Distribution from Tobacco Smoke 92
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TABLES
Page
2-1 A Matrix of Angular Scattering Gain Coefficients
for Totally Reflecting Spheres,x< 2 18
2-2 The First Five Angular Scattering Gain Coefficients
for the Diffraction Approximation to Forward
Scatteri ng 19
40
2-3 A Comparison of the Rayleigh Coefficients, C , for
Polarization in the Scattering Plane 26
2-4 Components of the H Matrix for Xg 1 and erg = 1.7,
and Components of the Resulting A Matrix Using the
Forward Scattering Model of Equation (2-20). Components
are normalized to n = 1 28
3-1 Reference and Scene Beam Intensities in Terms of Photo-
cell Output 79
3-2 Transmission of Filters at 0.6328 Micron 80
3-3 Experimental Results 81
3-4 Maximum Velocity for Q-Switch Ruby Laser Forward-
Scattered Hologram With Particle Moving Parallel to
Hoiogram 98
3-5 Maximum Velocity for Q-Switched Ruby Laser for Different
Ranges and for Particle Moving Parallel to Hologram and
Viewing Along All Angles Perpendicular to Motion 98
3-6 Maximum Velocity for Q-Switched Ruby Laser Forward Scat-
tered Hologram When Particle Moves Toward or Away from
the Hologram 99
XI
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ACKNOWLEDGMENTS
We are indebted to Dr. R. F. Wuerker and Dr. L. 0. Heflinger of the
TRW Systems Group Research Staff for valuable technical assistance, and
direct contribution to the work done on the Garrett holocamera and the
holographic linearity and sensitivity tests. Thanks are also due to
Mr. H. W. Reim and Mr. R. A. Briones for technical support of the holography.
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NOMENCLATURE
a Particle diameter - microns
A - Matrix relating 50. to 80^
s Area of intensity observing lens or telescope, cm2
B - Effective hologram diameter, cm
- Angular parts of the scattering gain function
d - Effective scattering diameter, cm
D - Orifice or aperture diameter - cm
E(a,p) - Exp [ao- (2/z+acr]: Normalization factor for log-normal
distribution moment of order a.
f(p,M) - Log-normal particle size distribution
g.(x) - Particulate distribution dependent parts of scattering
gain function
G 4/x (S*:.S), the scattering gain function
/a
dx n-j(p.a) x 5. ; augmented particulate distribution
u ~ vector
ra
H - / dx (9n/2q)x3+2: particulate distribution matrix
Jo
2
IQ - Incident beam intensity, watts/cm
3
J_ Light intensity distribution watts/sterad-cm
k - T/A, cm"
K Ratio of scene beam to reference beam intensity
L - Fluid instability wavelength, cm
m - Complex index of refraction of particulate
2
n - Particle number density functions, particles/cm
p - Particulate distribution parameters
P - Power, watts
xiii
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- Re-indexed vector of particulate distribution parameters
2
" 4E sea/*3 ' scattering efficiency
r - Vector from scattering source to center of AQ
R - Volumetric flow rate - cm /sec
S - Amplitude scattering matrix
u - £n x, log-normal distribution variable
u.. - Mean value of u under f-(p,u)
v - Velocity, cm/sec
3
V$ - Volume containing scattering particulate, cm
x - eu, geometric mean particle size
y - Focal length, cm
Z - Hologram-to-image distance, cm
Nomenclature - Greek
a - q + 2, distribution moment index
0 - Angle of incidence
0 - Angle of refraction
Y - an nQ, a log-normal distribution parameter
6 - Signifies increment
A - Optical path length
2
ES - Emulsion sensitivity, joules/cm
e - Scattering angle or its complement, degrees
X - Light wave length, microns
v - Frequency - sec~
xiv
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a - Standard deviation of log-normal distribution
c - e0, geometric standard deviation of particle distribution
2
£*.,.=, - Total scattering cross section, cm
sea
T - Pulse time - sec
- Angle between r and the normal to s
n - Solid angle - steradians
X ka
xv
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Metric System Conversion Table
SYMBOL
in.
ft
yd
Ib
°F
psi
WHEN YOU KNOW
inches
feet
yards
pounds
Fahrenhei t
temperature
pounds per
square inch
MULTIPLY BY
TO FIND
SYMBOL
25.4
0.3048
0.9144
0.453592
5/9 (after
millimeters
meters
meters
kilograms
Celsius
mm
m
m
kg
°c
subtracting 32)
51.71
temperature
torr
torr
mm
m
m
kg
°c
torr
millimeters
meters
meters
kilograms
Celsius
temperature
torr
0.03937
3.28084
1.09361
2.20462
9/5 (then
add 32)
0.01933
inches
feet
yards
pounds
Fahrenheit
temperature
pounds per
square inch
in.
ft
yd
Ib
°F
psi
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1. OBJECTIVE AND SCOPE
The holography of particulate using scattered light techniques is con-
cerned with demonstrating the feasibility of recording and identifying par-
ticulate in the one-micron and sub-micron size range. Development of such
methods would provide new diagnostic tools in the form of various types of
laser instrumentation which could be used in situ, and without disturbing
the process being observed.
The work described herein is an extension of previous EPA holography
1 2
studies. ' These and other similar studies have already demonstrated the
ability to holographically record micron size aerosols. Further, quantita-
tive estimates of particle number densities as a function of scattered light
intensity have been accomplished. The methodology thus far has been based
on a simple model in which scattered light intensity is a function of a
single parameter, usually the average product of number density and scatter-
ing cross section. The optical scattering cross section is assumed to be
equal to the geometrical cross section multiplied by an optical factor de-
pending only on scattering angle. The method is incapable of distinguishing
between number density and mean particulate size, and some assumption must
be made about one or the other in order to obtain useful information. The
uncertainties, therefore, center on the problem of estimating particle size
or size distribution from recorded or measured data on scattered light in-
tensity, or by other means.
It would seem to be a fairly straightforward task to holographically
record the laser light scattered from a particulate for all (or nearly all)
scattering angles so that the scattered light angular distribution can be
studied at leisure. It is an objective of the present study to demonstrate
the feasibility of doing so. The second objective of the study is concerned
with what useful information can be obtained about the particulate size
distribution once such a scattered light distribution function is available.
In particular, is there a way to extract both mean particle size and number
density independently from the data? Can information also be obtained about
the particulate size range? If a scattered light intensity as a continuous
function of angle is given, is it possible to extract from it a continuous
particulate size distribution function? And if two particulate distribu-
tions are present is it possible to distinguish between them? The answer
1
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to all these questions is a conditional "yes" based on the results of this
study. In theory, at least, conditions can be found for which all of the
desired information is contained in an angular distribution of scattered
light. In practice, however, these conditions may not be so easy to estab-
lish.
The scope of this work includes an analysis of the mathematical and
physical models by which the transformation can be made from a scattered
light distribution to a particle size distribution. Also included is an
experimental program designed to assess the advantages and limitations of
certain promising scattered light holographic methods. The program includes
the design and evaluation of a scattered light holocamera, and an evaluation
of the effects of four basic variables on the scattered light methods.
These four variables are: (1) particle size, (2) angular illumination of
the particle (scattering angle), (3) particle number density, and (4) inci-
dent laser beam diameter.
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2. PROBLEM ANALYSIS
In this section, a physical and mathematical formalism suitable for the
study of light scattering by small particulate is presented. Existing for-
malism shows how to obtain a scattered light intensity distribution as a
function of scattering angle, given a particle size distribution function.
Conditions necessary to the solution of the "inverse problem" are derived;
that is, given the scattered light distribution, find a unique particle size
distribution. A possible numerical method of solution emerges from a study
of these necessary conditions. Using a polynomial approximation for the
scattering matrix and assuming a log normal type of particle distribution,
we then determine the feasibility of estimating distribution parameters for
a sub-micron particulate, and'of differentiating between the number densi-
ties of a sub-micron and a 10-micron particulate size distribution both
present in the same volume.
In the mathematical formalism which follows, vector quantities will be
represented by a straight bar underlining the character. For example, J_
will be presented as a scattered light intensity vector having two components.
Matrices and higher order tensors will be represented by a curved bar under-
lining the character. For example, the 2 by 2 scattering matrix is represen-
ted by a curved bar underlining the character. For example, che 2 by 2
scattering matrix is represented by £. The components of a vector or tensor
will be represented by subscripts or superscripts, depending on whether the
index property is contravariant or covariant. For practical purposes, con-
travariant indices will here represent the components of a column vector,
and covariant indices represent the'components of a row vector. When vector
superscripts are used, they will be indicated as such; otherwise, a power
function may be assumed. Because of an extensive use of subscripts and
superscripts throughout this text, the same characters will sometimes appear
as representing a variable and an index. The value of an index is entirely
independent of the value of any variable bearing the same notation.
In writing vector inner products, summation notation over repeated
indices will be assumed. Thus, an inner product
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assumes sum over all n. Direct products of the form
A = g. £ = q1 Ck = A^
will also be employed to form higher order tensors.
Complex conjugates will be denoted with an asterisk where variables
have both real and imaginary parts. In the case of tensor quantities, the
asterisk denotes a conjugate transposition of the tensor indices.
2.1 GENERAL FORMALISM
We first present a mathematical method by which an angular distribu-
tion of scattered light intensity can be obtained when particle number den-
sity is known as a function of particle size. The physical conditions
under which this method is valid are discussed.
Let Jn(0)6Vs6J2 be the light intensity scattered out of a small, incre-
mental unit of volume 6V containing particulate and into an incremental
unit of solid angle 6fi, oriented at an angle 8 from the forward path of the
incident beam. The index n is a vector superscript taking the value n=l if
the light is polarized in the scattering plane or n=2 if polarized at right
angles to it. The units of Jn will be watts/steradian~cm when the units
3 -
of avs are cm. ihis notation is chosen to be consistent with that of
Van de Hulst.3
Suppose the observing telescope used to make scattered light intensity
measurements has an objective of area SQ, at a distance r from the source,
and at an angle 0 to the vector r from source to center of the objective.
2 ~~
We assume sQ/r is sufficiently small to approximate the solid angle. Then,
the total power measured is:
P = Z Jn(6) 6Vs<5n (2-1)
2
n s
6fi = SQ cos0/r
2
Let IQ be the incident beam intensity in watts/cm, into the volume
increment <5Vg. Suppose 6Vg has one particle, spherical, with diameter a
and complex index of refraction m. Let k=7r/X be the wave number of the
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incident wave amplitude into the scattered wave amplitude is a 2 by 2 non-
singular matrix denoted by S(ka,0,m). The matrix is dimensionless and com-
plex. The scattered light intensity from the particle is now represented
as follows.
* (2~2)
The two components of I and J represent simple linear combinations of
~"~O ~~~
four independent variables, called Stokes parameters, which completely
describe the intensity and polarization of monochromatic light. Thus, the
complete transformation matrix of Equation (2-2) would be a 4 by 4. In
restricting ourselves to plane polarized light, we have effectively dropped
the two Stokes parameters which describe the ellipticity and orientation of
the polarization. The remaining two equations become decoupled from the set
describing J_, and only the two equations in Equation (2-2) need be con-
sidered.
The next step is to fill 6VS with parti cul ate having a range of dia-
meters a, and sum or integrate an equation of the form (2-2) over all
particle sizes. In doing this, we make three simplifying assumptions.
First, we assume that the parti cul ate is not optically dense, so that mul-
tiple scattering of photons 'does not occur. If multiple scattering should
occur, Equation (2-2) becomes considerably more complicated to solve. The
light will be depolarized, and the matrix will have off-oiagonal terms
which will depend on integrals of particle number density. Secondly, it is
assumed that the particulate is small enough to avoid depolarization effects
from higher order electromagnetic modes. This implies ka<10. de may then
assume that £ is a diagonal matrix, and the equations are further simplified.
Finally, we assume that the particulate number density distribution is
spatially uniform.
With these restrictions established, we define a particulate number
density distribution n(£,a)cm , so' that n(p_,a)da is the number of particles
per cm having diameters between a and a+da, and
/»oo o
Jn(p,d)da = n_ particles/em (2-3)
•v* — Q
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The p vector is a set of parameters for the distribution which fix, among
other things perhaps, the value of nQ, the mean size of the distribution,
and the standard deviation.
Suppose further that there are several different particle species in
the volume 6VS, and that each has a separate distribution function n^^-.a)
associated with it. Then, the n.. can be treated as the components of a
vector, and pkl- is a matrix. Each of the n^ has a different scattering
matrix S^1 associated with it, so S becomes a third order tensor. The scat-
tered light intensity coming from these particulate distributions may now
be written as follows:
j"(,> = ly Jfda n.(p.,a) £» ^ (k..,)
or, J(0) = ~ /°°da n(p,a) - S*: S(ka,0) • I
£. ~
There are a few notational simplifications which will put Equation (2-4)
in its final form. In order to simplify the integration, we will change to
a variable X.
X = ka (2-5)
In rewriting n(p,x) the scale factor k then becomes a part of the parameter
matrix £. We then define a tensor quantity G(x,0) which we shall call the
"scattering gain."3
_*in <.m _ 1 2 pih
Sm Si j ~ T * Gj (2-6)
or, S*: S(ka,0) = 1 X2 G(X,0)
The function G is defined such that
o
where Qc/_ = 424?/.a/7ra is the total scattering efficiency.
4?/.a
5 Ca
Finally, suppose there are a number of specific values of 0, denoted
em, at which data are available. We now remove the variable 6 and replace
it with index notation, thus:
i"(*m) - Jfi ; •}" (x>6m) - G^" (x) (2.7)
and so on, where applicable.
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Equations (2-5) through (2-7) into (2-4) can now be substituted, and the
final form of the scattering equation be obtained.
Io X (2-8)
Tl\ -
The indices n and j of G in this equation correspond to the indices
of the original scattering matrix £. The index i denumerates the particu-
late species, and the index m denumerates scattering angle. The matrix
fil' for a given m and i is a positive definite diagonal matrix, which means
"I n
that the equation for J is decoupled from that for J . It is convenient
to rewrite Equation (2-8) in partial index form which emphasizes the de-
coupling.
l"--!y'/to „,(,,.*) -g'-to} 'I0X2
4kz -b i -i o
•3
We have renormalized the n. so that the units are cm and
noi particles/cm3 (2_g)
Equation (2-8) is a representation of the "normal" scattering problem,
in which a gain tensor G is given, and a particulate distribution n.^. ,x)
along with its parameters is given, and the unknown to calculate is the
scattered light intensity distribution on the left side of the equation.
The J.n vectors may be looked upon as nonlinear functions of the distri-
bution parameters p.
2.2 LINEARIZATION AND THE "INVERSE PROBLEM"
In the last section, we posed ithe problem of obtaining a scattered
light density distribution off of a known particulate size distribution.
We shall now formulate conditions necessary to solve the "inverse problem";
that is, given a scattered light intensity distribution, what is the
particle distribution?
A number of previous investigators have defined and solved the inverse
problem under various conditions and assumptions on the nature of the
scattered light and particulate size distributions. Their work deserves
some comment and reference here. A good overview of the problem has been
given by Kerker4, who has also reviewed previous investigations in some
detail.
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Among the methods more closely related to the one discussed in this
report is one by Kerker, et al.5 which makes use of the angular dependence
of the ratio J1(0)/J2(0). The method is similar to the present method in
that it makes use of data matching at various scattering angles, and uses
a parameter adjustment on a known mathematical model for the parti cul ate
distribution. Another widely used method involves the use of turbidity
measurements, and Wallach and Heller have shown the feasibility of using
turbidity spectra of visible light at various scattering angles.
789
A number of techniques have been proposed ' ' which are based upon
the angular variation of the intensity of forward scattered light at very
small angles and at a single wavelength. These deserve comparison with the
analysis in this report. They involve integral transforms of scattered
light distribution functions, and lead directly to a nonparametri c distri-
bution function n(a) without any a priori assumption of its form.
In Equation (2-8) we assume there is a mathematical model for the dis-
tributions n.(p,x) which is sufficiently general that any desired degree of
agreement can be achieved with the actual distributions by choosing the
parameters p to fit the data. The more elements there are in the matrix,
the more degrees of freedom are available to achieve the data match. In
theory, an infinite number of p.. would be required to fit a real distri-
bution exactly. In practice, just a few will give a good approximation if
the functional dependence n_(p,x) is chosen wisely.
The inverse problem can then be stated in terms of finding a solution
to Equation (2-8) when the vector J° is known and the parameter matrix p
is a matrix of unknown quantities which must be solved for.
The necessary and sufficient conditions that a unique solution p exists
are that £n be an analytically continuous, single valued function of p and
that the values used for j" lie within the solution space of Equation (2-8).
Suppose now there are measurements of the function J' taken at
angles 0m. The data should correspond to the components of the Jn vector
m An m ,
and may be represented by Jffl. Suppose a p is found such that the following
increment is small.
= 3; - jjj(p) (2-10)
8
-------
We now perform a linearization of Equation (2-8) by using a first order
Taylor series expansion.
The parameter p^. is the k'th parameter for the i'th distribution.
Equation (2-11) is a set of linear equations in the unknown variables p, ..
It is convenient to simplify the notation by rearranging the components of
Pki into a single vector £, which has every parameter for each distribution.
q« = Pn (2-12)
Then define a matrix An such that
ki
= An
The superscript n may be considered as fixed, and it determines also
which of the two components of IQ is selected. The indices j and m vary in
such a way as to make of An a second rank tensor — that is, a matrix.
The necessary and sufficient conditions that there be a unique solution
vector, 6q_, to Equation (2-13) may then be simply stated. The matrix An
must be square and nonsingular. It may be proven that these are also
necessary and sufficient conditions' that there be a locally unique solution
matrix to the nonlinear inverse problem posed by Equation (2-8), and that
they are also necessary conditions (but not sufficient) that there be a
globally unique solution matrix. .
The requirement that An = A^J be a square matrix dictates that the
range of the index j equals that of the index m. This simply means that the
number of angles @m at which there are data equals the number of parameters
q. for which we are solving. Every degree of freedom in o^ requires a data
point to fix it. If j>m there are more variables than equations, and the
data are not sufficient to uniquely determine a solution to Equation (2-13).
-------
In this case, there are an infinite number of solutions to the equations,
all lying within a continuous (j-m)-dimensional subspace of the vector space
having the same dimension as the range of j. If on the other hand j
-------
with respect to the index m. In this section we discuss some conditions foi
the nonsingularity of G, We then investigate some properties of the gain
matrices for totally reflecting spheres, and for small angle scattering of
diffracted light, with the aim of establishing nonsingularity for a special
case.
We begin with the assumption that the gain function can be written in
the following series form, where q is the summation index of the series.
GJn (x,0) = gk (x) cn (e) (2-14)
Thus, each term of the series is separable in X and Q. The indices i
and k refer to particle species, and g\ is non-zero only for i=k. The n
qK
and j indices refer, as before, to the state of polarization of the incoming
and outgoing light. The series (2-14) may be infinite, in which case
q=0,l,2,... , co. The functions gQ(X) and Cq(0) may be taken as complete
sets of orthonormal functions, in which case Equation (2-14) will describe
any desired gain function, either calculated from theory or measured from
experimental data. If we now choose 0=0m, where scattering data are avail-
able, we recover the originally defined gain tensor.
G(X) = g(x): C (2
pi" tv\ - n1 (y\ cqkn
Gmj (X) - 9qkW Cmj
Using this form for G, we can now rewrite the basic elements of the
linearized equations from Equations (2-8) and (2-13).
. a
J" = -V f/dXn(p,X) • g(x)x2] : £n-I.0 (2
4k^ L o ~ J
An = -V Tpx (an/aq) ' g(x) X2]: Cn-I^
4IC L ° ~ J
In index notation,
C %
n
-------
In each of these equations, the quantity in brackets is an integral
tensor of second or third order, computed entirely from functions of X and
the parameters, p. All of the angular dependence is contained in the
tensors C11-^. These tensors are also third order. For a given value of
the index k, corresponding to a given particulate species, the elements of
£ 'Io form a matn"x- Should only one species be present, this matrix
must then be shown to be nonsingular with respect to the index m. If
several species are present, then it is a linear superposition of these
matrices which must be shown to be of full rank.
A particular case of interest arises when the index q has only one
value. Then the gain matrix is a direct product of a function of x and a
function of Q. Such is the case, for example, for small particulate
Rayleigh scattering (X«l) or large particulate isotropic scattering (x»l).
It is convenient to drop the index q in Equation (2-16). Suppose also there
is only one particulate distribution, and drop the index i. Suppose I has
only one non-zero component, and drop the index p. Then the matrix expres-
sion is greatly simplified.
rt ~ x
n/aq) g(x)x2] Cn
~ J
This is the direct product of two vectors, one of which is the column vector
£n. This means that every column vector of An is a multiple of C_n, and An
has rank one. Thus, An is nonsingular only if it is a scalar. Only one
value of q can be estimated from light scattering data.
Reintroducing the index q only, we can replace g(x) with a vector g (x)
and the vector Cn with a matrix C'n. Then, Equation (2-16) gives
An = -| [px (9n/9q) g(x) X2] - Cn (2-17)
z L° " ~ J
In this equation, the matrix Cn must be nonsingular with respect to the
index m, which means that the range of q must be at least as great as the
range of m. This establishes a condition on the number of non-zero terms
in the series of Equation (2-15). There must be at least as many terms as
the number of parameters to be estimated.
12
-------
Among the various sets of orthonormal functions which can be used for
g(x) in Equation (2-17), are several polynomials. Of these, the associated
Legendre polynomials, for example, have a density function of unity. It is
reasonable to expect, then, that with a suitable choice of the coefficient
matrix £, we can choose a form
9q(x) ~ xl
and obtain the gain function dependence on x to any desired degree of
accuracy. This is in fact the case. Much of the existing theoretical work
on the description of the scattering gain function is expressed in terms of
infinite converging series in the variable X.
There is good motivation for this choice of g(x), since for some den-
sity functions the integral in Equation (2-17) can then be evaluated direct-
ly. Accordingly, we define a matrix ft and simplify Equation (2-17) once
more.
I
(2-18)
or
or'
A"
nj
to
_ o
2 urn
•W
= Jo
4k2
H
Hq
. cn
t+*t
C
where HJ = JdX (8n/9q.) xq+2
.TO J
In the remainder of this section, we will discuss some possible choices
o
for a particular matrix, C , for licjht polarized parallel to the plane of
reflection. In Section 2.1, we referred to the fact that £, and then 6, is
a function of the particulate index of refraction, m. Thus far we have
not made use of that dependence. As we now begin to discuss some particular
gain matrices, however, we must make some assumptions about the optical
properties of the scattering particulate. These include properties of light
absorption, refraction and reflection, all of which are implied by a given
complex index of refraction (see Appendix A). As we calculate a polynomial
fit to a particular gain matrix, the scattering gain coefficients C will
•-x1 ***
then depend on the chosen index of refraction.
13
-------
In general, gain function dependence on angle and particle size is
very complex, exhibiting multiple lobe structure and ripple structure. One
way to picture them is as a multimode superposition of complex harmonic
functions. These are difficult to model analytically, since they generally
require many terms of an infinite series expansion to obtain sufficient
convergence to describe the function over the complete range of interest.
One case which is at least conceptually less complex is the gain
function for totally reflecting spheres. The index of refraction for total
reflection is real and infinite. The resulting lobe structure varies more
smoothly and regularly, and does not exhibit any significant secondary
A
ripple structure such as is characteristic of normal dielectrics. Kerker
gives calculated values for gain functions for totally reflecting spheres
in the size range 0
-------
0 123456789 10
Figure 2-1. Angular Gain at 6 = 90 Degrees for Totally
Reflecting Spheres
0 1 2 3 4 5 6 7 8 9 10 11 12 13 1415
Figure 2-2. Angular Gain at e = 60 Degrees for Totally
Reflecting Spheres
15
-------
8 10
Figure 2-3. Angular Gain at 6 = 120 Degrees for Totally
Reflecting Spheres
Even in the limited range of x, the gain functions require many more
terms than three to give an adequate convergence. In order to obtain a
good fit with just the three coefficients of Equation (2-19), they were
chosen to match the position and value of the first maximum, and to pass
through the point at the first minimum of the theoretical curves. Figure
2-4 shows the interpolated values for the position and height of the first
maximum of G (x), and Figure 2-5 shows the interpolated values for the
first minimum. The resulting fit is a fair approximation to most portions
of the first peak.
Table 2-1 shows the resulting coefficient matrix, computed for three
different scattering angles, 30, 90 and 150 degrees, corresponding to
forward, side, and back scattering. These angles were chosen to fit the
experimental geometry of the scattered light holocamera described in Section
3.2. A calculation of the determinant of the matrix shows that it is non-
singular and fairly well conditioned for numerical inversion.
A second approach to the scattering gain matrix calculation was investi-
gated, which makes use of some simple and more general properties of forward
scattered light.
16
-------
TOO
MAX
10
\
•MAX
\
\
1
10
Figure 2-4.
9 (DEGREES)
100
Position and Value of the First Maximum of
the Angular Gain Function for Totally Reflect-
ing Spheres
17
-------
Figure 2-5.
\7
\
10
100
6 (DEGREES)
Position and Value of the First Minimum of
the Angular Gain Function for Totally Reflect-
ing Spheres
Table 2-1.
0
e
e
30°
90°
150°
A Matrix of Angular Scattering Gain
Coefficients for Totally Reflecting
Spheres, X< 2.
C42
0.05391
1.220
3.229
C62
-0.002309
-0.3519
-2.646
,82
0.00002163
0.02408
0.4873
Determinant: 0.00462
The forward lobe of the scattered light intensity distribution is due
primarily to Fraunhofer diffraction, and arises predominantly from light
passing near the particle, rather than from rays which undergo refraction
and reflection. It is thus independent of the index of refraction of the
18
-------
scattering medium. The angular gain function for diffraction scattering
is given by
- 9
6\ (2-20)
which is valid for both n=l and n=2. J1 here indicates the first order
Bessel function. This approximation is good for forward scattering angles
up to about 30 degrees over a wide range of X(0
-------
Figure 2-6 shows the angular gain function for totally reflecting
spheres at 0=10 degrees, following Kerker . At this angle, there is con-
siderable contribution from diffraction scattering. A comparison of this
figure with Figures 2-1 through 2-3 will indicate that a given order poly-
nomial approximation will be valid over a broader range of x for smaller
scattering angles.
Van de Hulst has shown a comparison of angular gain functions versus
scattering angle, between Mie theory for totally reflecting spheres and the
diffraction theory of Equation (2-20). This comparison is presented in
Figure 2-7 for a value of X=3.
2.4 THE LOG NORMAL DISTRIBUTION
If we maintain the assumption that 1^ has only one component, out
return to the assumption that there is a multi-species particulate distri-
bution, we have now obtained the following particular form for the linear-
ized equations, last expressed in Equation (2-16).
,n o . in
J = —5- h • • C
4k^ 1 ~
hqi = JT dx n. (p.x) Xq+2
An - J° H • r1n
n r\ "• \f
Hai • /" dx K'/aqJ) *q+2 (2-22)
H
Here, the index i corresponds to the particulate species, and may be dropped
if there is only one species, to obtain a similar equation to Equation (2-18).
The £ln are 2nd order tensors (matrices), consisting of the coefficients of
polynomials chosen to fit the gain function at various angles. The computa-
i2
tion of C was discussed in the last section for two special cases. The
h_ vector is of the same general form as the H matrix, and can be considered
as an augmented column vector.
20
-------
Figure 2-6. Angular Gain at 6 = 10 Degrees for Totally Reflect-
ing Spheres. Points designated by spuare are cal-
culated according to diffraction Equation (2-20).
'IS1/X
FRAUNHOFER DIFFRACTION
2
1 1/2
1
1/2
30 60 90 120 150 180
9 (DEC)
Figure 2-7. Scattering Diagram for Totally Reflecting Spheres
in Each Polarization Mode. The comparison graph
is as calculated from Equation (2-20).
21
-------
The next task is to investigate some properties of the particulate dis-
tribution matrix [H, hJ . A large number of naturally occurring polydisperse
particulates are adequately described by the log normal distribution. This
may be defined as follows:
n(p,x) dx = f(p_,u) du
u = J8n X
f(p,u) = _P- exp [- (u-u)2/2cr2] (2-23)
The commonly-referred-to geometric mean size and geometric standard
deviation are given by:
Xg = exp (u)
-------
p = (r,u,a)
p' = (r,u + a
-------
increasing functions of (q+2)2 and cr4. Thus, a moderate increase in the
size range o- of a parti cul ate distribution may mean many more terms are
needed to obtain a good series approximation. Values of this function are
shown plotted for comparison in Figure 2-8.
2.5 ESTIMATION OF DISTRIBUTION PARAMETERS
FOR A SUB-MICRON PARTICULATE
In the last two sections, we have examined the C and H matrices of
* »"W <"fc*
Equation (2-22) for some particular assumptions. Both matrices were found
to carry full rank for the conditions investigated, and were thus non-
slngular. We have, in a limited sense, proven the feasibility of solving
the inverse problem for a sub-micron particulate by proving that the neces-
sary conditions are met for a unique solution to exist. This is of course
subject also to the validity of the conditions and approximations we made
in showing that the matrices were nonsingular.
In setting out to choose these conditions and approximations, one is
naturally influenced by the choice of data available. In the experimental
portion of this program, the sub-micron particulate studied was tobacco
smoke, which is known to have a distribution between approximately 0.01
and 1 micron, with a 0.1 -micron geometric mean. This leads to values of
X between approximately 0.05 and 5.
The three-coefficient scattering matrix derived in Section 2.3 for
totally reflecting spheres is good only for values of X less than about
2.0. This model was therefore not successful in describing the experimental
data. The latter corresponded more to the shape of the gain curve forx=3,
shown in Figure 2-7. The three-coefficient model seemed successful only in
describing small-particle scattering, for X<1, and then only moderately so.
The conclusion to be drawn is that more than three or four terms are needed
in the power series expansion to be able to successfully extend it to values
of X of one or larger.
Ay
The leading coefficients in the power series expansion, the C , cor-
respond to the Rayleigh scattering coefficients. For small, totally re-
flecting spheres the Rayleigh scattering gain functions are given by
6](e) = 4x4(l - I cose)2
G2(0) = 4x4(cos - I)2 (2-27)
24
-------
PO
-3
-1
0 ]
LOGE(a,P)
Figure 2-8. A Plot of the Function E (a,p_), Showing the Sensitive
Dependence on
-------
The scattering diagram correspond-
ing to Equation (2-27) is shown in
Figure 2-9. The predominant back-
scattering for this configuration is
clearly evident. The backscatter
gain is nine times the forward scat-
tering gain. The theoretical values
of the C42 are just the coefficients
of G2 in Equation '(2-27), for the
various angles — for example, 30,
90 and 150 degrees. These values,
calculated from Equation (2-27), are
shown in Table 2-3, where they are
compared with the approximations of Section 2.3 [Table 2-1, Equation (2-19)].
Figure 2-9. Scattering Diagram for
Very Small Totally Reflecting
Spheres. The scattering is pre-
dominantly back to the source.
Table 2-3. A Comparison of the Rayleigh Coefficients, C
For Polarization in the Scattering Plane
42
A —
fl — •
0 =
30°
90°
150°
Equation (2-9)
0.05391
1.220
3.229
Equation (2-27)
0.536
1.00
7.48
Equation (2-28)
2.99
0
2.99
Equations (2-27) include the effects of both electric and magnetic
dipole scattering. Classical Rayleigh scattering is derived assuming only
an electric dipole contribution, when the dielectric medium is not strongly
absorbing. The resulting gain function is
G](e) =
G2(0) •
ra2-!
m2-!
m
2
COS 0
(2-28)
26
-------
If we assume a very large index of refraction again in this equation, the
result is as follows
G](e) - 4x4
G2(0) 4x^ cos2e
The effect of assuming this form is also shown for comparison in Table 2-3.
If one is constrained to assume a Rayleigh-type distribution, then only
one gain coefficient is available, only one element of the £ matrix need be
computed, and only one distribution parameter can be estimated. Consequen-
tially, only one data point is needed to estimate the chosen parameter. As
a rule, however, sufficient data will be taken to verify the presence of
Rayleigh scattering, and perhaps to be used in a least-squares estimation.
A Rayleigh scattering model can be used in conjunction with a log-normal
distribution model to estimate any of the components of £ given in Equation
(2-25), provided the remaining two are known or can be estimated from other
sources. An alternative is to renormalize the H matrix of Equation (2-18)
in terms of an unknown geometric mean, x . Under these circumstances, the
log-normal distribution has
u - u = 4nx - inx = in (x/x ) u'
and has an effective logarithmic mean of zero. In Equation (2-18), q=4 for
Rayleigh scattering. The distribution and its moments remain integrable,
and the coefficient n.a_ may be estimated in place of n . This is in sharp
° a 2
contrast to the estimation of n a for the large sphere isotropic scatter-
ing model.
Somewhat more successful results were obtained by applying the five-
coefficient forward scattering model discussed in Section 2.3. With this
model we were able to fit the data obtained from light scattering from
tobacco smoke (Section 3.4). If the five-coefficient model of Table 2-2
is used to calculate the forward scattering gain function for x=3, the
results agree with Equation (2-20) within 0.2 percent for all angles up to
30 degrees. A plot of the gain function is shown in Figure 2-7.
27
-------
This model was used to obtain the linearized Equations (2-22) for
he result for X =3 and ffg=l.l was found to
several values of X and aq.
agree closely with the shape of Figure 2-7. The results were convergent
for values of x_ up to 10 and values of a_ up to 2.0.
These calculations were made with a small computer program written in
the BASIC language. This program is illustrated in Appendix B. Table 2-4
shows the results of such calculations for a geometric mean x of 1, and a
geometric standard deviation a of 1.7. The columns of H and A correspond
to the parameter components of p. The rows of H are labeled according to
coefficient powers of X, and rows of A are labeled according to scattering
angle.
The first column of the A matrix in Table 2-4, corresponding to the nQ
or x parameter, is the same numerically as the non-dimensional scattered
light intensity distribution. This is evident from Equation (2-26). These
values were computed for several scattering angles between zero and thirty
degrees, for the same parameters, x =1 and
-------
3.7
3.5
3.0
FIVE TERM DIFFRACTION MODEL
J(6) - _h-C
2.5
0
10
20
6 (DEGREES)
Figure 2-10. The Scattered Light Distribution for Particulate
with Xg - 1.0 and
-------
2.6 DISCRIMINATION BETWEEN TWO TYPES OF PARTICIPATE
It is possible under certain limited conditions to distinguish between
two different types of particulate in the same scattering medium. An
example of how this may be done will now be derived.
The presence of multiple scattering species corresponds to the use of
multiple values of the index i in Equation (2-22). Then each of the dis-
tribution functions and parameter vectors described by Equations (2-23) and
(2-24) need also to be indexed. In the example chosen here, we start with
two values of i in Equation (2-22), the value i=l corresponding to a small
particle Rayleigh scatterer, and the value i=2 corresponding to a large
particle isotropic scatterer. We will then choose two different scattering
angles 0^, with k=l,2, and from these see if it is possible to estimate
the two number densities n0,-» or alternatively the two number density loga-
rithms y.. Log-normal particulate distributions will be assumed for both
species, and in each case we will have to assume some a priori knowledge of
average particulate size and distribution spread. If the An matrix of
Equation (2-22) is nonsingular, then a separate identification is possible.
We first write down the values of the scattering gain coefficients to
be used. For the first species, there is a coefficient only of X , and we
can obtain it from Equation (2-28).
412
= 4
= 4
m2-!
m2 + 2
m2-!
2
cos 0,
(2-29)
m2 + 2
For the second species, we assume an isotropic scatterer with a total scat-
tering efficiency of unity. This is often a good model for particulate
with large X and back scattered light. The normalization criterion of
Equation (2-6) shows that
(f-,.0
(2-30)
This is the coefficient of x to the zero power, all other coefficients
vanishing.
30
-------
Next we compute the components of the H matrix according to Equation
(2-22). In this case, the components of the complete parameter vector £
are simply the two number density logarithms y., for i=l a(nd i=2. Then the
integrand of the H matrix has the partial derivative matrix (an^/ay.), which
is non-zero only for i=j. In this case.
Hqi "
(2-30)
= n0i E(q+2,£.)
all other components of H"" . are vanishing. Furthermore, only the values
My
for q=0 and q=4 are needed since these are the only non-vanishing coeffi-
cients in the Cn matrix.
The vector ]i.j, which gives the light intensity distribution, is the
same as the first column vector of Hj. Performing the required sums over
particulate species i and over powers of xq, and considering only light
o
polarized in the scattering plane, we first obtain the Jf vector.
4k
4n
0]
m2-!
m2+2
E(2
»P2>]
(2-32)
Because of the term in cos 0k, the intensity is maximum for back scattering,
and is a minimum but non-zero at 0=90 degrees. The model is not generally
valid for forward scattering, since we have neglected diffraction effects
of the large particulate.
With the matrix product H:£, again summed over i and q, we now obtain
the A2 matrix of Equation (2-22).
4n
°1
4n
°1
nf-1
mS-2
m
n02 E(2,p2)
E(6,p2) cos292 n02 E(2,p2)
(2-33)
31
-------
Clearly, two scattering angles e-i and B^ may be found such that Equa-
tion (2-33) is nonsingular, and4a distinction between n0-j and no? may be
made. It is clear also from Equation (2-29) that if the / vector were
measured, light being polarized normal to the plane of reflection, Equation
(2-33) would be singular, and no such distinction would be possible. Then
for Equation (2-32) we would have a uniform J_ distribution.
32
-------
3. EXPERIMENTAL PROGRAM
The experimental objectives of the Task II program may be summarized
as follows. A determination is to be made of the feasibility of hologra-
phically recording the scattered light signatures of airborne pairticulate
down to 1-micron diameter in size. Either individual particles or an aggre-
gate cloud of particulate are of interest. The feasibility of extending
scattered light holography into the sub-micron size range is of interest.
Finally, a determination of our ability to subsequently identify the parti-
culate from the reconstructed holographic images is to be made. These
objectives will be discussed in some detail in Section'3.1.
In Section 3.2, we will describe basic features of the test apparatus
which was used. There were three basic test systems used. The first was
a two-beam scattered light holocamera, hereinafter referred to as the
12 14
Garrett holocamera, ' which was developed on another program for the
purpose of making holographic recordings of the flow field of an experi-
mental fan turbine. This holocamera has a maximum included viewing angle
of about 30 degrees, and effectively records light which is transmitted or
scattered in the forward direction. It is easily adjustable to permit
either bright field or dark field holography of a given scene. The second
test system was a simple three-beam holographic apparatus using a point
source scene, for the purpose of testing linearity and sensitivity of the
holographic process. The third test system was a breadboard three-oeam
scattered light holocamera system with a three-plate holder designed to
record light scattering over most of the range from 0 to 180 degrees scat-
tering angle. This system included simple particulate generation devices
for smoke and for water droplets.
Actual test procedures differed somewhat from those planned for reasons
discussed in Section 3.3. Among the influencing factors were the avail-
ability for demonstration of the Garrett holocamera design and the desire
to make a controlled test of two-beam and three-beam holographic process
sensitivity. Progress with the three-beam scattered light holocamera was
hampered by development difficulties related to the reference beam scatter-
balls.
Finally, in Section 3.4 we summarize and discuss the major results.
These are briefly as follows.
33
-------
With the Garrett holocamera, detection of particulate sizes down to 1
micron by forward scattering was demonstrated. It was visually apparent
that some differentiation between particulate distributions was possible,
at least in an unmixed state, by studying variation of light intensity with
scattering angle. Although nothing basically new was learned, the method
did demonstrate a consistently higher sensitivity by virtue of a lower
noise-to-signal ratio than has previously been obtained.
The sensitivity of the holographic process was explored directly in
terms of the ratio of scene light intensity to reference light intensity.
This was found to be a significant parameter. A limiting value for this
ratio of about 3xlO"7 was found. Surprisingly, the second reference beam
was not found to contribute significantly to the sensitivity.
The three-beam scattered light holocamera was therefore found to have
merit only insofar as the third beam could be used as an intensity reference.
A number of configurational changes were explored in order to try to use
the holocamera to its best advantage in this mode. It was finally concluded
that the best configuration to facilitate reconstruction and maintain
linearity was one in which the reference beams were point sources at great
enough distance from the holographic plate to provide a uniform intensity
incident wave front.
Three-beam scattered light holograms were made of 30- and 50-micron
water droplets obtained from a monodisperse droplet generator. Holograms
were also obtained of a sub-micron tobacco smoke, and of mixtures of these
two particulates. The two types of particulate were easily different!'able
visually, and also from scattered light angular variation considerations.
With the particular polarization mode chosen, the holocamera configuration
was not sensitive enough to study side scattered light from sub-micron par-
ticulate. The forward scattered light, however, was found to be amenable
to a size distribution analysis and was of sufficiently high intensity to
seem preferable from sensitivity considerations.
3.1 EXPERIMENTAL OBJECTIVES
Experiments at TRW had previously verified our ability to make holo-
graphic recordings of small particulate by light scattering. Both indivi-
dual particles (>15 to 20 microns) and clouds of micron-size particulate
34
-------
aerosols have been successfully recorded using this technique. Further,
it was verified that particle number densities could be estimated from such
recordings. To date, the limits of the scattered light holography tech-
niques have not been fully established. The essential objective of the
Task II program was to explore these limits. A brief summary statement of
the objectives is as follows.
t Determine the feasibility of hologra'phically recording the
scattered light signature of airborne particulate down to
1-microrf diameter in size. Either individual particles
or an aggregate cloud of particulate are of interest.
• Determine the feasibility of extending scattered light
holography into the sub-micron size range.
0 Determine the feasibility of subsequently identifying the
particulate from the reconstructed holographic images.
In pursuit of these objectives, and following the contractual work
statement, the holographic process was studied with regard to the various
effects of the following parameters and configurations.
Particle Size
This is perhaps the fundamental parameter of the whole study. The
smaller the particle size, the more difficult it is to detect, and possibly
less and less information about the particle is available from scattered
light. The question of a lower useful size limit must be explored. Exper-
ience seems to indicate that, as a rule of thumb, anything that is photo-
graphically recordable is also holographically recordable. A comparison
of techniques of scattered light holography for sub-micron particulate and
for large particulate is of interest in order to see which problems are
universal and which are a function of size. We therefore endeavored to
make holographic measurements in each of four size ranges: (1) sub-micron,
(2) 1 micron, (3) 10 micron and (4) 100 micron. Monodisperse particulate
distributions were sought, and in one case used (30 to 50 micron water
droplets).
Particle Number Density
Larger particle concentrations may be desirable since they will scat-
ter proportionally more light intensity, and this is advantageous from a
35
-------
detection standpoint. Small particle size may be compensated for by large
number density. On the other hand, large concentrations lead to increased
liklihood of multiple scattering with consequent difficulties in modeling
and interpretation. The program objective in this regard was to measure at
least two number densities and evaluate their effacts on light scattering.
Scattering Angle
The objective here was to measure as much as possible of the full range
of forward, side and back scattering illumination of the particulate. This
was achieved with some success using the three-beam scattered light holo-
camera, which simultaneously exposed three holographic plates at different
orientations with respect to the scattered light. In this regard, forward
scattered light has the property of being more intense and more easily
recordable. Further, for relatively large particles, the forward scatter-
ing is primarily diffraction scattering and is independent of optical proper-
ties of the scattering medium. Under these conditions forward scattering is
useful for obtaining size distributions for particulates with unknown index
of refraction.
Side scatter is most sensitive to the internal structure of the scat-
tering particles. However, net scattered light is also lowest in this
direction. Side scatter holography is worthy of consideration for two
reasons. One reason is that for certain applications, physical restrictions
limit one to side scatter techniques. Secondly, side scatter illumination
of complex particles may offer the most sensitive means of detection and
identification of particulates with complex optical structure and scatter-
ing properties. A possible example of this was given in Reference 1, where
flyash from pulverized coal-fired combustion was found to consist partly of
hollow spheres containing smaller internal particles.
Incident Beam Diameter
The tradeoff between the aerosol volume which can be holographically
recorded and the particle size and number density has been studied. To
state this problem in simple terms, the scattered light intensity falling
on a film plate is an increasing function of each of these three parameters -
scene volume, particle size, and number density. The recordable scene light
intensity depends on film sensitivity and on the ratio of scene light to
36
-------
reference light intensity. It was originally intended to study this aspect
of the problem by; using several (at least two) different incident laser beam
* i
diameters to probe the test aerosol. However?, the same information was
obtained and the intent of the work statement: was satisfied by a study of
the effects of emulsion sensitivity and scene to reference light intensity
ratio.
Particle Velocity
In typical applications, particle velocities might range from very low
values (1 to 2 ft/sec) up to perhaps 100 ft/sec, depending ppon the duct or
*
stack design and flow conditions. Hence, particle velocity is still another
variable of interest. One must consider the velocity of the particles with
respect to the stability of the holographic interference pattern for various
holographic arrangements (i.e., forward, side and back scatter recordings).
The worst case is the back scatter. Here, the limiting particle velocity
is
b 2 T
where \ is the wavelength of the probing laser beam (~0.7ju) and T is the
duration of the laser pulse. As indicated in Section 3.2, 2-nanosecond
laser pulses have been achieved at TRW Systems. With a ruby laser pulse
of this duration, the limiting particle velocity for the back scatter con
dition is
vk 1 °'7/10n 0.0175xl09 microns/sec
b 2(2xlO-9)
i
vb < 1750 cm/sec (~60 ft/sec)
In other words, recording back scatter holograms of particles moving at
velocities approaching 100 ft/sec is feasible provided a very short duration
laser pulse is used.
The effect of particle velocity on holographic techniques is conveniently
assessed by analytical means. The objective of the present study was to make
this assessment while using a conventional 50-nanosecond laser to determine
37
-------
the limitation of the holographic technique with respect to the other vari-
ables discussed previously. Thus, only low velocity particles were studied.
Velocity measurements were made, and the effect was determined to be minimal.
Three-Beam Holography
One of the objectives of this program was to explore the potentialities
of this relatively new holographic test configuration. The name "three-beam
holography" is derived from the presence of a scene beam and two reference
beams. The two reference beams may be used interchangeably as reconstruction
reference beams, if the configuration is properly chosen. The advantages
were expected to be twofold.
In the first place, if one reference beam were chosen for reconstruc-
tion purposes, then the other would be available as a point source light
intensity reference. Its intensity can be measured and compared to that of
the incident scene light in the holocamera before any holograms are made.
Then in the reconstructed hologram the ratio of reference light intensity
to incident scene light intensity can be taken as the previously determined
constant. In this way, a direct calibration is achieved for the ratio of
scattered light to incident light intensity.
scattered light _ scattered light reference light
incident light ~ reference light incident light
The first intensity ratio on the right is measured from the hologram. The
second is measured directly in the holocamera.
The second reference beam was also expected to result in an increase
in the sensitivity of the holographic process. Preliminary investigation
of this effect seemed to show that the fringe pattern obtained from the
two reference beams had the effect of increasing sensitivity in recording
p
scene light. When the scene consists of weakly scattered light, it is
desirable to reduce the reference light intensity correspondingly, dimin-
ished light intensity at the hologram would result in adverse non-linear
effects at the low end of the film emulsion characteristic curves. The
presence of a second reference beam was intended to raise the exposure into
the linear portion of the film characteristic. Outside of a tendency to
reduce background light scattering from the hologram during reconstruction,
no real effect of this sort was found during this program.
38
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Two-Color Holography
This technique was considered as a possible approach to the program
objectives, but time did not permit its use. In two-color holography, the
output of the ruby laser is directed through a crystal of potassium dihydro-
gen phosphate (KDP). This crystal acts as a frequency doubler, and converts
as much as 20 percent of the incident beam into light of half the wavelength.
The output of the combination of the ruby laser and KDP crystal consists of
both the primary red ruby radiation at 0.6943 micron, and the doubled ultra-
violet radiation at 0.3471 micron. Either or both may be used to record a
hologram of scattered light. The technique has been used to double the
10
sensitivity of holographic interferometry.
Since the size and intensity of the forward scattered light cone is
sensitive to both particle size and incident wavelength, the two-color tech-
nique should make differentiation of particles of different size ranges
easier. The use of two separate wavelengths gives each particle size "a"
two different values of the parameter x=ka. (See Section 2.) Analysis is
then possible over a large range of "a" while considering only a restricted
range of x. Reconstructions of both the primary and secondary images can
be obtained with a 0.6328-micron He-Ne laser, since the angular separation
is great enough to view the two separately.
3.2 TEST APPARATUS
In the introductory remarks for this section we outlined three basic
test systems which make up most of the experimental apparatus. In order
of use, these were the Garrett scattered light holocamera, a three-beam
sensitivity test breadboard holocamera, and a three-beam scattered light
holocamera. Auxiliary units included the pulsed ruby laser system used for
recording holograms of airborne particulate, and a monodisperse droplet
generator which was used in conjunction with the three-beam scattered light
holocamera.
Garrett Holocamera
The Garrett holocamera was developed at TRW for studying the flow
Although the work subsequently described with the Garrett holocamera was
not accomplished under this contract, it does constitute directly related
technology. See Reference 14.
39
-------
fields around the rotating blade rows of an aircraft fan turbine compressor.
The holocamera is actually two separate holographic arrangements on a single
frame, permitting the recording of bright field single and double exposure
holograms (i.e., holographic interferograms), and dark field forward-
scattered light holograms. The two arrangements use much the same optics.
The holocamera can be changed from one type of recording to the other by
simple interchange of a few optical elements. Schematics of the two arrange-
ments are shown in Figure 3-1. The lower diagram in Figure 3-1 shows the
optical arrangement for recording bright field holograms (principally double
exposure holographic interferograms). It is basically a "path-matched
focused ground glass holocamera," similar to the ones first built to record
holograms of liquid rocket fuel combustion. > The principles behind the
design of this type of holocamera have already been elucidated.
Of interest to the present EPA work is the scattered light holographic
arrangement developed to record particulate in the flow field of the
AiResearch fan turbine. The upper diagram in Figure 3-1 shows the scat-
tered light arrangement in detail. Light from a pulsed ruby laser illumina-
tor (typically 50-nanoseconds duration) is deflected into the holocamera by
a prism reflector mounted below the tubular framework. The light is deflec-
ted vertically onto a glass wedge beam splitter which divides it into scene
and reference beam components. The reference beam is the small (~4 percent)
portion reflected from the first surface of the wedge. The scene component
is the principal amount of light transmitted through the wedge (~92 percent).
The beam is then incident on a second right angle prism reflector which
directs it onto a third larger prism reflector. This then reflects the
light toward the hologram. The prism is mounted for path adjusting reasons.
The scene light is next focused through a pin hole aperture. Focusing of
the pulsed laser beam with a positive lens was, in itself, a special develop-
*
ment. The pin hole blocked all light scattered by and from surfaces of the
optics behind it; namely, the reflecting prisms, beam splitter, lenses, etc.
Focusing of-a Q-switched ruby laser beam with a positive lens leads to a
phenomenon known as "air breakdown." The plasma formed at the focus of a
lens is opaque to the laser beam. To prevent breakdown, a weak cylinder
lens (0.5 diopter) was placed before the pair of focusing lenses. The
combination produced an astigmatic pencil which reduced the electric fields
below the breakdown threshold.
40
-------
-------
The result is the creation of a single point source of light before the
pair of 14-inch-diameter intermediate focusing lenses.
The intermediate focusing lenses refocused the light just before the
hologram. A stop was mounted at the conjugate image point to absorb all
of this light. Thus, the hologram received only light scattered from the
surfaces of the intermediate focusing lenses (i.e., dirt) or from any other
objects in the converging scene beam.
Particulate matter in this region scatters light in the forward direc-
tion, the arrangement for the most efficient scattering of light.
This scattering arrangement differs from earlier ones used by the
writer in that light is convergent over a far wider solid angle. That is
to say, the intermediate focusing lenses give a large scene volume for light
scattering.
The reference beam, as noted earlier, is reflected from the first sur-
face of the wedge beam splitter onto a wedge and prfsm reflector mounted in
the base of the framework. These two elements direct the reference beam
parallel to the framework, through a positive lens and second aperture,*
onto a mirror which reflects the reference light onto the hologram. The
reference beam is incident on the hologram at an angle of 45 degrees rela-
tive to the axis of the intermediate focusing lenses.
The beam splitter, two scene beam prism reflectors, the astigmatic
focusing lens, and pinhole aperture were mounted on a platform, supported
kinematically on horizontal rails. Also mounted on the same platform was
the beam splitter diverging lens (a single plano-concave lens), prism
plates, and ground glass diffuser of the bright field holographic arrange-
ment. Sliding the plate sidewards converts the holocamera from the one
type of recording to the other. A pneumatic cylinder was added for this
purpose.
The two holographic arrangements were "breadboarded" before final
construction. This was particularly important in the case of the scattered
light configuration, where proper performance had to be verified by actual
*
An astigmatic lens combination is not needed in the reference beam leg
since the intensity is below the breakdown threshold.
42
-------
test. The bright field arrangement was also tested since it was a further
simplification of the earlier focused ground glass holocameras.15
A photograph of the scattered light holographic breadboard is shown in
Figure 3-2. Figure 3-3 shows a photograph of the completed holocamera.
Breadboard Sensitivity Tests
A three-beam breadboard holocamera was set up to test both the linearity
and sensitivity of the holographic process. It is shown schematically in
Figure 3-4. The optical components were placed on a large (242 by 152 by
21 cm) granite table\(2 megagrams) mounted on vibration-isolation pads. A
15-milliwatt Spectra Physics Model 124 helium-neon laser was used as the
illuminating source. Reference to Figure 3-4 shows that the laser beam is
reflected from a mirror onto'the first of two variable beam splitters (a
Jodon VBA-200)*. Light reflected from this beam splitter is reflected from
the two mirrors, which directs the resulting beam through a stack of atten-
uators and through a microscope objective. This beam, variable in intensity,
is the scene beam. The objective spreads the scene beam across the hologram.
The portion of the initial laser beam which passes through the first
variable beam splitter is next incident on a second identical variable beam
splitter. Light reflected from this component is then reflected by a mirror
which directs it through a Spectra Physics spatial filter. This element
spreads the beam, uniformly illuminating the hologram. For the present dis-
cussion, this beam is the "first reference beam."
The component of light which passes through the second variable beam
splitter is the "second reference beam." Like the first reference beam, it
is reflected from a mirror and passed through a spatial filter (identical)
to the one used for the first reference beam).
The two reference beams and the scene beam were set up so that their
axes passed through one another at the hologram at angles of 30 and 45
degrees, respectively. That is to say, the first and second reference beams'
axes were at an angle of 30 degrees. The first reference beam and scene
beams' axes were at angles of 45 degrees. The angles were arbitrarily
Rotation of the Jodon beam splitter about its axis allows one to contin-
uously vary the intensity of the reflected and transmitted components.
43
-------
Figure 3-2. Photograph of Breadboard Scattered Light Holographic
Arrangement Shown in Figure 3-1. Hologram is on far
right, behind the model of a portion of the turbine
fan. Before the fan is a nebulizer used to thrust
larger particles in the scene volume.
-------
\
Figure 3-3. The Garrett Two-Beam Scattered Light Holocamera in its
Completed Form. The scene volume is to the right of
the large condensing lenses. To the right of that is
the kinematic plate holder mounting. The beam form-
ing optics are in the housing to the left. The beam
enters from the underside. The whole camera sits on
a water-filled ballast platform to provide stability.
45
-------
Figure 3-4. Three-beam Breadboard Holocamera Used to Test Linearity
and Sensitivity of the Holographic Process
-------
chosen, not to be too large and such that the conjugate image reference
beam (on reconstruction) did not appear close to the scene beam). Also,
the second order reconstructed images did not appear near the reconstructed
image of the scene beam.
The photographic plate or hologram was oriented relative to the three
incoming beams so that the portions of the two reference beams reflected
from its surface did not illuminate the front portion microscope objective
which formed the scene beam, creating extraneous light signals. A little
experimenting showed that this was possible with the surface of the holo-
gram oriented at an angle of 45 degrees with respect to the axis of the
second reference beam.
Black paper was placed between both the spatial filter, and the micro-
scope objective and all of the other optical components. The paper barrier
blocked the light scattered from the beam-forming components. As a result,
the hologram "saw" (or was illuminated by) only three point sources of
light — the two reference point sources and the scene, also a single point
source.
Inspection of Figure 3-4 shows that by interchanging the microscope
.objective with the first reference beam, a three-beam arrangement with a
weak scene beam between two strong reference beams is quickly created.
This arrangement was tested after completion of tests with two reference
beams proximate to one another. A telescope with a photomultiplier tube
at the focal point was used to measure intensities.
Three-Beam Scattered Light Holocamera
A breadboard three-beam scattered light holocamera was designed with
a three-plate holder designed to record light scattering over most of the
range from about 5 to 175 degrees scattering angle. A perspective view of
the holocamera is shown in Figure 3-5, and Figure 3-6 shows a layout draw-
ing of the holocamera design.
The holocamera shown in Figure 3-5 utilizes a double reference beam
and is designed to record ruby laser particulate light scattering over wide
angles. Wide angle recording of the scattering is achieved by simultaneous-
ly exposing the three adjacent holograms. Each pair of adjacent holograms
are positioned at an included angle of 120 degrees to each other.
47
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LASER
(Q SWITCHED RUBY)
INPUT LASER BEAM
REFERENCE BEAM SPLITTERS
REFERENCE MIRROR (2ND BEAM)
FIRST SCATTER BALL
SECOND SCATTER BALL
- SCATTERING PARTICLES
REFLECTOR (FOR 2ND REF. BEAM)
LASER
SCENE
BEAM
Figure 3-5. Perspective Sketch of Wide Angle Double Reference Beam
Holographic Arrangement for Recording Scattered Light
Holograms of Small Particles with Q-Switched Ruby Laser
-------
RCF&t£NC£ BEAM
T SCATTERING BAU.
"
ft£F£ECTQR KM F/KST
•SR/SM REFLECTORS
-SCTAT SEAM
•SPUTTERS
^.ftZFLKTO*
-SCfiTTER/NG &LL.
(SPCOfll)
SIDE VIEW
LOCATION FOR
SALL
Figure 3-6. Layout Drawing of Wide Angle Double Reference
Beam Breadboard Holocamera
-------
O1
o
MOST iSCATTfAIMG BALL
^REFERENCE B&M
TOP VIEW
Figure 3-6. Layout Drawing of Wide Angle Double Reference
Beam Breadboard Holocamera (Continued)
-------
/A/tT/AL
WffTUAL SOURCE LOCATtQN
FRONT VIEW
Figure 3-6. Layout Drawing of Wide Angle Double Reference
Beam Breadboard Holocamera (Continued)
51
-------
The output of the pulsed ruby laser passes through a pair of wedge beam
splitters. Reflected light from the beam splitters forms the two reference
beams. Scene light transmitted through the glass wedges is directed into the
scene volume with the aid of three .prism reflectors. The incident scene
light is not incident on any of the three holograms. The beam is directed
past the edges of the two outside film plates.
Reference beams are derived from light reflected by the two glass wedges
arranged in series. The first reference beam is formed at an elevation above
the film plates using two first surface mirrors and a polished steel or
coated glass scattering ball. The latter simultaneously illuminates the
three holograms with reference light. The second reference beam is simi-
larly formed except that the beam forming optics are arranged on a plane
below the three holograms. The optical paths of the scene and reference
beams are matched.
Figure 3-6 shows two alternate locations for the scatterballs. The
preferred, first location is with the balls symmetrically located on either
side of the film holder. The second location has both scatterballs on the
same side of the film holder, as shown also in Figure 3-5. 3oth arrangements
were tried during the experimental program. An additional configuration was
tried which was similar to the first, only with the balls in closer to the
center plane of the film holder and some distance out from it. This was to
try and bring the scatterballs and the scattering parti oil ate into the same
field of view. Both polished steel, and gold- and silver-coated spherical
glass lenses were tried for the scatterballs. The steel balls were 12.7-
miHimeter-diameter spheres. The glass lenses used were 10 millimeters in
diameter, with a 10-millimeter focal length. A 15-millimeter diameter scene
beam was used, and 15-millimeter reference beams were incident on each scat-
terball. In the final configuration, the path matching needed 18 centimeters
from each scatterball to the center of each plate, and 12 centimeters from
the scene to the center of each plate.
These variations in experimental procedure will be discussed further
in Section 3.4.
The holocamera was originally intended to be oriented so that the scat-
terballs would be located above or below the film holder, on a vertical line,
as indicated in Figure 3-5. In the final configuration the film holder and
52
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apparatus was rotated 90 degrees, for reasons of mounting convenience. The
scatterballs were then both mounted below the film holder, on a horizontal
line perpendicular to its center plane and the particulate stream was injec-
ted from left to right underneath the film holder.
The principal reconstruction angles chosen for the holograms were 30,
90 and 150 degrees, since these corresponded to the normals to the three
plates.
Monodisperse Aerosol Generator
A vibrating orifice device for generating monodisperse aerosols, of the
type described by Berglund and Liu,16 was designed and fabricated and used
in conjunction with the three-beam wide angle scattered light holocamera.
Its use was directed toward determining our ability to discriminate between
particulates of different size ranges. The basic components of the gener-
ator are an aerosol solution feed system, a 70-watt voice coil, and a 6.4-
millimeter-long hollow stainless steel needle.
The vibrating orifice is the hollow needle, which has an ID of about
0.005 inch or 100 microns. The needle has a Luerlok fitting serving as an
attachment to the feed system. A feed pressure of 520 to 750 torr (10 to 15
psi) produces a steady flow of aerosol solution to the orifice. The aerosol
solution used was electronic grade isopropyl alcohol containing about 1 per-
cent nonvolatile impurities (mostly water). The orifice is driven longitu-
dinally with the 70-watt voice coil. The longitudinal vibration creates an
instability in the fluid flow which causes the emerging liquid jet to break
up into small, uniformly-sized droplets. The initial size of these droplets
depends somewhat on the driving frequency, but more strongly on the orifice
diameter.
The feed system is diagrammed in Figure 3-7. A 300-milliliter glass
flask with a stopper and a tube insert serves as a reservoir for the aero-
sol solution. The flask is pressurized to 520 torr (10 psi) from air pres-
sure reduced by a regulator and a pair of bleed valves.
The aerosol solution is forced through a feed line and through the
hollow stainless steel needle by means of the 520 torr pressurization. The
needle, or tube, has a 0.203-millimeter OD and a 0.127-millimeter ID (approx-
imately 100 microns ID). The resulting aerosol flow is governed predominantly
by the flow impedance of the needle. It was experimentally determined to be
53
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HOUSE
AIR
PRESSURE REDUCER
VALVE
A A 1
* 0
DOME ><
REGULATOR 0-60
0-200 PSIG PS'G
(0- 10,300 TORR) (0-3100TORR)
BLEED VALVE
V
A
FILTER
. TTL
r? i p
STOPPER ||
J\
/ \
/T\
__ TO ROOM AIR.
OR SMOKE GENERATOR
TO
ORIFICE
ALCOHOL
FLASK
Figure 3-7. Aerosol Solution Feed System
0.02 ml/sec at 520 torr feed pressure to within about 10 percent. Variations
in flow rate are mostly due to dirt clogging the needle. This was alleviated
by inserting a 10-micron Teflon Millipore filter in the feed line between
the needle and the reservoir.
The method of mounting the needle orifice is illustrated in Figure 3-8.
A conical stainless steel insert stiffens the voice coil and provides mass.
The orifice is supported at the apex of a triangle formed of two stiff wires
with the cone at its base. The orifice is held so that the driving force
supplied by the speaker is longitudinal. The voice coil is driven by a
Hewlett Packard signal generator with a 10-volt output and a 60-ohm internal
resistance. Its output is amplified by a Macintosh audio amplifier. The
optimum frequency for the 100-micron orifice size is 3 kilocycles. The
power input to the voice coil at this frequency is not critical, and was not
measured, but it is known to be in the neighborhood of 20 watts.
The liquid aerosol generator was operated in conjunction with a simple
forced air smoke generator, consisting of a cigarette holder and a duct to
direct the smoke upstream. The air flow through the burning cigarette was
obtained directly off the droplet generator pressure manifold, as shown in
Figure 3-7.
54
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SOLDER
NEEDLE
0.127 MM I.D.
0.203 MM O. D. X 6.35 MM
LONG
50.8X0.8128 MM DIA.
S.S. TUBE
0.381 MM DIA. I.D.
LUERLOK
FITTING
VOICE COIL
SPEAKER
DIAPHRAGM
SUPPORT PANEL
Figure 3-8. Voice Coil and Aerosol Generator Orifice Mount
55
-------
Figure 3-9 shows the droplet generator mounted in conjunction with the
three-beam wide angle breadboard holocamera. In the picture are seen the
voice coil, the aerosol liquid flask and filter, the pressure plenum, the
Macintosh amplifier, the three-plate film holder and the reversing prisms.
VOICE
COIL
FILTER
Figure 3-9. Breadboard Three-Beam Wide Angle Scattered
Light Holocamera With Monodisperse Aerosol
Generating System (101119-73)
The droplet generator operates at frequencies around an optimum fre-
The wavelength
quency given by the flow velocity divided by a wavelength.
is found experimentally to be
=4.5080
(3-1)
Here, D is the jet diameter and may be taken as the same as the orifice
ID, 100 microns. The optimum wavelength has also been calculated theoretic-
ally. The results were similar to Equation (3-1). The flow velocity is '
related to volumetric flow rate, Q, by
(3-2)
56
-------
The droplet diameter at the optimum frequency is then given by
(3-3)
A rather wide variation in frequency around the optimum for a given
flow rate is possible. Droplets of uniform size were formed, for example,
at a frequency as high as 9 kc. The droplet formation instability mechanism
is ineffective too far above or below the optimum frequency.
The above equations give a flow velocity of 158 cm/sec for a flow rate
of 0.02 cc/sec. The diameter of the droplets thus formed, before any eva-
poration occurs, is 240 microns. This diameter is found to be independent
of flow velocity at the optimum frequency, since both v and a have a factor
,.of v which cancels out in Equation (3-3). Droplet diameter thus depends
mainly on orifice diameter, and can be varied only insofar as the frequency
can be tuned away from the optimum.
Once the droplets were formed, the alcohol in the aerosol solution
evaporated very radidly, leaving only water droplets. Complete evaporation
of the alcohol should leave a water droplet of a diameter reduced by a fac-
tor of the cube root of the original water concentration. This is a factor
of about 0.22, and the predicted water droplet diameter is thus 53 microns.
The aerosol thus formed was illuminated with a 15-milliwatt beam from
a He-Ne laser. Interference rings of diffracted light were observed, the
outer maximum of which occurred at an angle of about 35 degrees from the
incoming laser beam. The interference fringes are caused by internally
reflected light from the droplets, following an optical path illustrated in
Figure 3-10. For a given fringe angle 0, there exist two incident light
paths corresponding to two different values of ft. Light from these paths
interferes either constructively or destructively. Interference fringes
were located at values of tane of 0.7, corresponding to the 35-degree outer
fringe, and then at 0.660 and 0.642. Analysis of the fringe spacing gave
the droplet diameter. The value obtained was 50 microns. The nonlinear
equations and their solution are illustrated in Figure 3-11.
Pulsed Ruby Laser Illuminator
The source of illumination for the holocameras was a pulsed ruby laser
system designed and built at TRW Systems Group. Photographs of this solid-
57
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I
—INCOMING LIGHT
RAY
•-REFERENCE PATH
.60
.75
.70
.65
.60
OUTGOING
LIGHT RAY
Figure 3-10. Geometry of Internally Scattered Light From
a Liquid Aerosol Droplet of Diameter a
1. H^= «. =1.36
SIN"'
2. 8 - 4o' - 2o
3- — mCOS»'*SINn + SIN « SIN >s^ ^V
x>^
"x
\^
X^
2.54
2.S6
2.58 2-60
a/o = PATH LENGTH « DROPLET DIAMETER
2.62
Figure 3-11. Nonlinear Diffraction Equations for Light
Internally Reflected From a Sphere and the
Two Branches of Their Solution
58
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;
Figure 3-12. TRW Q-Switched Ruby Laser Illuminator
RUBY
AMPLIFIER
AUTOCOLLIMATOR
Figure 3-13.
Ruby Laser Illuminator With Cover Removed to
Show Location of Major Components
59
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state ruby laser are shown in Figures 3-12 and 3-13. The laser emits 1 to
3 joules of 0.6943 micron wavelength (red light) in pulses of 30 to 50 nano-
seconds duration. The temporal coherence of the laser is about 5 centimeters.
A schematic diagram, Figure 3-14, shows a plan view of the components
in the ruby laser. Included in the package are a "folded" arrangement of
the osciliator-amplifier Q-switched ruby laser, a monitor diode, a dark-
field alignment autocollimator and a helium-neon directional pointing gas
laser. Switching of the optical path among these components is accomplished
by an arrangement of reflectors operated by the small round knobs on top of
the laser cabinet (Figure 3-12). Keference to Figure 3-14, and the photo-
graph of Figure 3-13 illustrates the internal optical path of the laser and
the various components of the system.
The laser power supply and control electronics are housed in separate
consoles as seen in Figure 3-15. The right-hand console contains two igni-
tron-fired 0 to 5 kv, 375 jiF capacitor banks used to energize the helical
Xenon flash lamps in the ruby oscillator and amplifier assemblies of the
laser. The comparison console contains the independent high voltage supply
and control circuits for the Kerr cell Q-switch, Also shown in Figure 3-15
is a Tektronix Type 535A oscilloscope used to record the ruby oscillator
output energy monitored by the integrating photodiode.
3.3 EXPERIMENTAL PROCEDURES
Test methods and analytical methods were chosen which would accomplish
all the objectives set forth in Section 3.1 as expeditiously as possible.
The choice of methods was also governed by the need to make best use of
currently available facilities.
When the Garrett holocamera was under development on a separate con-
tract,^ it became available for test work which was directly related to
this program. This afforded a good opportunity to test an optimum, two-
beam scattered light holocamera design in the sensitive forward scattering
regime. The scattering angles which could be visualized were between 0
and 15 degrees.
In order to test the effects of the particulate size variable and
variable optical properties, three different types of particulate were
used. These were phenolic and glass micro-ballons, and incense smoke. The
effects of these three size ranges will be discussed further in Section 3.4.
60
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HcKIt LASER
COILIMATING
LENS
W PLANE OF
ILARIZATION
OSCILLATOR
OUTPUT PORT
RESONANT MIRROR
ADJ. KNOBS
99% DIELECTRIC
REFLECTOR
OUTPUT
RESONANT
REFLECTOR
Figure 3-14. Schematic Diagram of Compact Ruby Laser Illuminator
-------
Figure 3-15. Photograph of TRW Pulsed Ruby Laser Power Supply
Consoles and Tektronix 535A Oscilloscope
62
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The glass micro-balloons were in the 30 to 50 micron size range. The
phenolic particles were slightly larger, but more important was their tend-
ency to agglomerate into macro-particles of several hundred microns diam-
eter. The incense smoke was in the 1 to 3 micron size range.
The micro-balloon particulate was thrust into the scene volume with a
forced air nebulizer. The incense smoke was wafted into the scene volume
by convection. In neither case were velocity measurements made, but the
velocities
-------
Particulate scattering in the Garrett holocamera (forward scattering)
was recorded with an expanded beam, with a diameter of order one meter.
The three-beam wide angle breadboard holocamera used an unexpended beam of
approximately a diameter of 1.5 centimeters. These two-beam diameters
afforded some information on our ability to study spatial variations. How-
ever, a more definitive study of the effects of aerosol size, density, etc.,
on scattered light intensity and our ability to record it was made with
the three-beam apparatus set up specifically for that purpose. Studies
were made of the effects of film sensitivity, and of the use of both single
and double reference beams. A lower limit for the required ratio of scene
light to reference light intensity was found, and this limitation was then
translated into minimum incident beam intensity needed to record particu-
late of various diameters. As well as testing holographic sensitivity and
linearity of the emulsion exposure process, this technique also afforded
a test on the value of a second reference beam as an intensity calibration
device.
The design of the three-beam wide angle scattered light holocamera was
accomplished early in the program, and was followed shortly by the fabrica-
tion of the three-plate film holder. Actual testing with the holocamera
was not accomplished until later in the program, however, when the holo-
camera layout was breadboarded.
The parameter studies done with this holocamera included a particulate
sizing. Two size ranges were studied. The first was a monodisperse water
droplet distribution of size ranges 30 and 50 microns. The droplet size
was calculated directly from the aerosol generator characteristics, and
was also measured indirectly from the coherent light fringe pattern it
produced. (See Section 3.2.) The two sizes thus obtained agreed to with-
in 10 percent. The second size range was from submicron cigarette tobacco
smoke. The size distribution of this smoke was not monodisperse. It was
estimated directly from the forward scattered light intensity distribution
as obtained both from holographic and direct observation. The measurements
showed the smoke to be in the 0.2-micron size range, agreeing with commer-
cially published data on such distribution.11
64
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The two participate distributions which were measured also represented
two particle number densities. The water droplet density distribution was
neither stochastic or homogeneous, since the droplets were generated in a
straight stream, and no mixing mechanism was employed to disperse them.
However, the droplet spacing resulted in an effective number density for
a small enough volume, and this could be calculated directly from the aero-
sol generator characteristics. The smoke density, on the other hand, was
measured directly from relative scattered light intensity measurements.
Particle velocity measurements were obtained on these two distribu-
tions. The velocities of the liquid aerosol droplets could be obtained by
measuring the feed pressure applied to the aerosol solution flask, and
using the known flow properties of the orifice as discussed in Section 3.2.
The velocity of the air stream which carried the smoke paniculate was
measured with a hot wire anemometer.
Measurements of light intensity distribution were attempted at various
angles and by various means, both from the holographic images and directly
from the scattering volume. A method was devised by which light intensity
from a small volume of a reconstructed real image of a homogram could be
imaged onto a sensitive detector. This would allow some spatial resolution
of particle size distribution as recorded by the hologram. Figure 3-16
illustrates the optical arrangement schematically. The hologram is assumed
to present an effective aperture of diameter B.
Incident light on the hologram forms a real image of scattered light
from a particulate cloud. A small volume element in this image is located
at aperture 1. The first lens, having focal length y-j, images the first
aperture onto the second aperture, whose purpose it is to shield the detec-
tor lens from seeing stray light from other portions of the scene volume.
The second lens then focuses the light from the test volume onto the
detector.
The first aperture effectively defines the test scene volume, 6Vg
(shown in Section 2.1) and shields the detector field of view from all but
this small volume element. The outlines of the volume element are fuzzy,
and are determined basically by the aperture diameter DI, and the lens
65
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RECONSTRUCTED
REAL
IMAGE
DETECTOR
LENS 2
APERTURE 2,
DIAMETER = D,,
LENS 1
APERTURE 1,
DIAMETER = D
HOLOGRAM.
DIAMETER = B
INCIDENT
RECONSTRUCTION
BEAM
Figure 3-16.
The Optical Arrangement by Which Light Intensity From a
Small Volume Element of the Reconstructed Real Image of
a Hologram is Imaged Onto a Power Sensitive Detector
66
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depth of focus. If the latter is taken as the depth at which point sources
become defocused to the same diameter as the aperture, then the depth of
field can be seen from geometrical considerations in Figure 3-16 to be
21 (DI/B), where Z is the distance from the plane of the hologram to the
plane of the first aperture. We then have the following expression for
the scene volume.
• H Di3
The solid angle intercepted from the scene volume by the first lens may
also be easily computed by integration.
rLl-l//l + (DZ)2) ]
6«= airU-l/v/l + (D^Zr) J (3-5)
This apparatus was set up and tested on a hologram made of a cigarette
smoke cloud (Hologram 13A, Section 3.4). Both apertures were 0.635 mm, and
the objectives lens (lens 1) was a 48-mm-diameter, 57-mm focal length plano-
convex lens. A United Detector Technology power meter was used as a detec-
tor. The sensing element was a silicon pin diode, with a one-square
centimeter area. The detector meter was a digital readout with a maximum
sensitivity of 10~10 watts. The reconstructed scene volume was located in
the first aperture with little difficulty. The process was facilitated by
the presence of a small thread located in the scene volume to provide an
auxiliary intensity reference.
The detector was sensitive enough to read the light transmitted from
the scene volume. However, the problem of optical alignment proved to be
difficult beyond our available resources. No data were obtained by this
method.
The most useful data on light scattering intensity as a function of
angle were determined by visual estimation. These data are discussed in
Section 3.4. Relative intensity estimates were obtained by eye, both from
holographic reconstruction and directly from a real scene. Since the human
67
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perceptive faculty is nonlinear, we made an attempt to calibrate it against
power meter readings of helium-neon laser light incident on ground glass
and transmitted through a 0.635-mm aperture. A series of neutral density
filters was used to reduce the perceived intensity. The results, nonethe-
less, must be regarded as low accuracy numbers, on the order of 30 to 50
percent. Calibration to absolute intensity was made using the power meter.
A series of sixteen holographic recordings were made with the three-'
beam wide angle scattered light apparatus. These holograms were numbered
consecutively. They were all made on standard AGFA8E75 102- by 127-mm (4-
by 5-inch) plates. The first five holograms were single plate holograms of
side scattered light only (6= 90 degrees). Of these, the first four had
just a single reference beam corresponding to light coming from the second
scatterball. During these recordings the scatterballs were in the primary
configuration, shown in Figures 3-5 and 3-6, and were both on the same side
of the plate holder.
Holographic records 6 through 11 were made with three plates each.
The plates were labeled A, B and C corresponding to forward, side, and back
scattered light respectively. The holographic records up through number 8
were all made with a low density of aerosol droplets, so that only two or
three droplets appeared in the scene volume each time. With hologram num-
ber 9 the droplet density was increased, and the smoke generator was added
so that a stream of 50-micron droplets appeared mixed with a cloud of smoke
particles.
Holograms 9 through 11 were made in this fashion, and were the best of
this series of holograms. Hologram number 11 was made with the droplet
generator frequency higher by a factor of three, but all other conditions
the same. Thus, the droplet diameter was 30 microns instead of 50.
For holograms 12 through 16 the scatterballs were relocated near the
alternate configuration, and a small thread was placed in the scene to pro-
vide an auxiliary intensity reference source. These holograms consisted of
three recordings each, of tobacco smoke clouds only. To understand the
reasons behind these changes, we will review the development procedures
for the holocamera.
68
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The first eleven holographic records were made with 12.7-mm stainless
steel spheres for scatterballs. These spheres were placed in the primary
configuration. Several problems became evident as these holograms were
taken. The scatterballs were polished with Wenol jewelers' rouge, but the
surfaces could not be made optically smooth. Tiny nicks and scratches in
the scatterballs affected the quality of the reference beams arriving at
the film plates.
Secondly, the reference light was not distributed uniformly over the
three plates. This made a linear reconstruction impossible to achieve
unless the hologram were put back in position in the holocamera and re-
constructed there. When this was attempted, the reconstructions were
found to be of generally poor quality due to the difficulty of getting
enough reconstruction beam intensity and of masking from stray light.
Thirdly, the holograms were fogging quite badly. This was determined
to be caused by depolarization of the reference beams with respect to
the scene beam and was a characteristic of the geometry. In all cases
the incident scene beam was polarized vertically, or in the plane of the
scattering. The reference beam was depolarized by about 45 degrees upon
reflection from the surface of the scatterball.
Finally, with the scatterballs in their primary location, it was
impossible to use the intensity reference scatterball as a valid calibra-
tion source. The reason for this was the nonuniformity of the reference
light over the plane of the hologram. The furthest scatterball was used
as a reconstruction reference, at an angle of about 25 degrees from the
hologram. The nearer scatterball was tried as an intensity reference.
After the llth holographic record was taken, the holocamera was modi-
fied. The polished stainless steel scatterballs were replaced with two
glass lenses, 10 mm in diameter and 10 mm focal length, and plated first
with silver and then with gold. Both platings proved unable to stand up
under the power density from the ruby laser. When a gold coating was
vacuum-sputtered on to a thickness of 100 angstroms, it was reliable.
69
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The scatterballs were then moved to their new location, near the
alternate configuration but closer to the scattering plane, in order to
minimize depolarization of the reference beams. The 10-rnm radius of cur-
vature was not small enough to spread the reference beams sufficiently to
cover all three film plates at once. A good compromise was achieved by
illuminating the forward 90 degrees with one scatterball and the backward
90 degrees with the other scatterball. This meant that neither scatter-
ball was available as an intensity calibration reference. To provide for
this, a thin fabric thread was stretched through the lower portion of the
scene volume. The scattered light intensity from the thread was measured
with the UDT power meter. It was found to be isotropic.
The last five holographic recordings were made with this modifica-
tions, studying light scattered from cigarette smoke. The holograms were
of generally good quality, and the previously experienced fogging was
absent. The smoke volume could be separately distinguished from the ref-
erence thread. However, reconstruction of the holograms in situ, in the
holocamera, gave rise to the same problems as before. Our resources did
not permit the solution of the problem of obtaining exact reconstructions.
The reconstructions shown in Section 3.4 were made with a Spectra-Physics
124 He-Ne laser with a spatial filter and beam expander. The reconstruc-
tion beam thus obtained is that of a point source at a distance of two or
three times that of the scatterballs from the plate.
70
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3.4 RESULTS
There were three basic phases of this program which deserve to be dis-
cussed in terms of the results they yielded. These include accomplishments
with the Garrett holocamera, the holographic linearity and sensitivity tests,
and the three-beam wide angle scattered light holocamera. We will summarize
and discuss each in turn.
Garrett Holocamera
With the Garrett holocamera, detection of particulate sizes down to 1
micron by forward scattered light was demonstrated. It was visually appar-
ent that some differentiation between particulate size ranges and size dis-
tributions was possible, at least in an unmixed state, by studying varia-
tions in angular scattered light intensity. Although nothing basically new
was learned, the method did demonstrate a consistently higher sensitivity
by virtue of a lower noise-to-signal ratio than has been previously obtained
with similar systems.
The Garrett holocamera may be regarded as an optimum, two-beam scat-
tered light holocamera design for the sensitive forward scattering regime.
The scattering angles which could be visualized were between zero and fif-
teen degrees.
The holocamera was tested by recording holograms of particulate thrust,
blown, or converted into the scene volume (i.e., between the focusing lens
set and the beam stop). Scrutiny of Figure 3-2 shows the nebulizer used to
thrust the larger 40 to 50 microns (in diameter) particles into the scene
volume. It is the plastic bottle just before the model of the portion of
the fan. The nebulizer was a plastic squeeze wash bottle filled with test
powder. A rubber tube was attached to the spout. Blowing into the tube
caused a cloud of particulate to fill the scene volume. The nebulizer was
filled with either phenolic particles or glass micro-balloons. Both samples
consisted of particles primarily in the 30 to 50-micron size range. Photo-
micrographs of these two types of particles are shown in Figures 3-17 and
3-18. The glass micro-balloons appear white like sugar. The phenolic par-
ticles appear brown like freeze-dried coffee.
71
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Figure 3-17.
Photomicrographs of Sample "Micro-Balloons." The
upper picture shows glass particles, which appear
to the eye as white powder. The lower picture
shows phenolic particles, which look brown.
Included in one is a scale, with 100-micron
spacing between major divisions.
72
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Figure 3-18.
High Magnification Photomicrographs of Sample
"Micro-balloons." The upper picture shows glass
particulate. The lower picture shows phenolic
particles. A scale of 10-micron spacing has
been included.
73
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To test the sensitivity of the scheme for particles of even smaller
size, incense was employed as the scattering source.* This material had
been used in earlier tests of scattered light holography conducted at TRW
for EPA.2 This type of incense produces particles in the size range of 1
to 3 microns diameter. The incense burner merely replaced the nebulizer in
the scene volume.
Holograms were made of the three different scattering targets. Expo-
sure was with light from a Kerr cell Q-switched ruby laser. All three size
ranges could be easily recorded, even of the most tenuous clouds. Examples
in terms of photographs of selected reconstructed holograms are shown in
Figures 3-19, 3-20, and 3-21. The first shows examples of the recording of
holograms of incense. The two are pictures of different holograms. The
cloud like character of these particles is clearly evident. Both pictures
suffer from a depth-of-focus problem of the copy camera. Figure 3-20 is a
pair of photos taken from the same hologram of the glass "micro-balloons."
The two pictures differ only by exposure. The picture is clearly more gran-
ular, particles are seen as individual bright points of light. The edge of
the plastic nebulizer is seen in the right-hand picture.
Figure 3-21 is similar except that it is of the phenolic particles,
which are on the whole slightly larger than the glass micro-balloons. These
particles have a tendency to stick together, making large agglomerates sev-
eral hundred microns in diameter. Like the hologram of the glass micro-
balloons, the picture is more granular or less cloud!ike than the incense
smoke which was composed of particles an order of magnitude smaller.
Visual inspection of the holograms showed the expected variation in in-
tensity as a function of scattering angle. This variation and the general
appearance of each type of scattering enable one to recognize one size range
from the other.
In summary, forward scattered light holograms have been recorded or par-
ticles in the size range of 1 to 3 microns. The tests re-established our
ability to holographically record particles of this small size. Comparisons
of these holograms with ones of larger particles (typically, 30 microns)
showed both qualitative and quantitative differences.
*Trappist Incense, produced by Abbey of Our Lady of New Melleray, Dubuque,
Iowa.
74
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en
Figure 3-19.
Photographs of the Reconstruction of Two Different Holograms of Incense
Smoke Recorded in the "Dark Field" Scattered Light Holographic Arrangement
Shown in Figure 3-1. Incense provided a test source of particles of
primarily 1 to 3 micron size.
-------
•-J
cr>
Figure 3-20.
Photographs of the Reconstruction of Same Scattered Light Hologram of
Glass Micro-Balloons of 30-Micron Typical Size. The hologram was
recorded in the holographic apparatus shown in Figure 3-1.
-------
Figure 3-21.
Photographs of the Reconstruction of the Same Hologram of Phenolic
Micro-Balloons Recorded in the Dark Field Scattered Light Holocamera
Shown in Figure 3-1. The micro-balloons were of 30- to 50-micron
size, typically. The lip of the nebulizer is seen in the overexposed
picture.
-------
All the scattered light holograms shown in this report were recorded
with a more conventional Q-switched ruby laser illuminator, namely, a laser
without any coherence-improving elements (such as a chlorophyll dye cell)
within the laser cavity.* As a result, many of the holograms showed the ef-
fects of the limited coherence of the Kerr cell Q-switch ruby oscillator.
For these reasons, analysis was not attempted. Holograms suitable for anal-
ysis should be recorded with a more coherent oscillator.
Holographic Linearity and Sensitivity Tests
The sensitivity of the holographic process was explored directly in
terms of the ratio of scene light intensity to reference light intensity.
This was found to be a significant parameter. A limiting value for this ra-
tion of about 3x10 has been found. Surprisingly, the three-beam config-
uration was not found to contribute significantly to the sensitivity.
During the first set of experiments, the two reference beams were made
to be equal in intensity at the hologram. (See Section 3.2.) The scene
beam was attenuated so as to be 0.3x10" as intense.**
Holograms were recorded on Agfa 8E75 plate; a 1-minute exposure time
developed plates in 2 minutes.
After exposure and development, the dried plate (now a hologram) was
placed back in the three-beam apparatus. The kinematic plate holder reposi-
tioned the plate accurately. The second reference beam was blocked. By
viewing through the plate, the reconstructed image of the scene could be ob-
served. The reconstructed image of the 0.3 x 10 scene point source of
light could be observed with the unaided eye. Unblocking the scene beam
helped to locate the scene beam in space. This experiment verified earlier
tests done in the laboratory on a less sophisticated optical arrangement;
namely, the ability of a hologram with two reference beams to sense a very
weak signal, one of an intensity of 0.3 x 10 of that of the reference
beam.
*
In the AiResearch project, precise timing is a requirement. As a result
the chlorophyll coherence stretcher was removed.
**
The attenuators were lenses from a pair of welding goggles. The transmis-
sion of each was measured at the onset with a silicon photocell and a micro-
voltmeter (Hewlett Packard Model 124).
78
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The question as to the merits of the second reference beam was next
quickly examined. A hologram was recorded with the second reference beam
blocked. That is to say, in this test, the hologram only saw a single ref-
erence beam and the same greatly attenuated scene beam (0.3 x 10"6 as in-
tense as the reference beam). A hologram was exposed. After development,
it was also replaced in the kinematic plate holder and reconstructed. Obser-
vation of the plate with the unaided eye showed the point source reconstruc-
ted! This was actually a surprise and indicates that the merits of a second
reference beam, at least as a means for increasing hologram sensitivity, has
not been established.
A modified set of experiments was then conducted with the apparatus;
namely, a 30-degree angle between the two reference beams, a 45-degree angle
between the axis of the inner reference beam and the axis of the scene beam,
and a 50-degree angle between the plane of the plate and the axis of the
scene beam. The apparatus was improved to the extent that both single and
double reference beam type holograms could be recorded on the same plate.
This minimized the effects of differences in redevelopment. This was achiev-
ed by blocking the upper half of the second reference beam with a strip of
black paper. An attenuator was added to the lower portion of the first ref-
erence beam. The beams were adjusted to make the two reference beams equal.
That is to say, the lower portion of the photographic plate recorded a double
reference beam hologram with reference beams of equal intensity. The upper
portion of the plate recorded a hologram with only a single reference beam.
The upper beam was 1.5 times more intense than either of the lower reference
beams. Intensities of the reference beams, as measured normal to the beam
directions with a silicon photocell, are shown in Table 3-1. Also included
in this table is the measured unattenuated intensity of the scene beam.
Table 3-1. Reference and Scene Beam Intensities in
Terms of Photocell Output
Position
of Plate
Reference Beam
No. 1
Millivolts
Reference Beam
No. 2
Millivolts
Maximum Scene
Beam Intensity,
Millivolts
Single Reference
Portion 0.23 0 0.05
Double Reference
Portion 0.15 0.14 0.05
79
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Adding intensities, one sees initial scene-to-reference beam ratios of
0.22 and 0.17, respectively.
The scene beam intensity was controlled with attenuators placed behind
the 40X microscope objective. Attenuators were either pieces from a welder's
goggle, or Wratten No. 96 (N.D. 1.0) gelatin filters. The attenuation of
these filters as measured independently with a helium-neon laser is presented
in Table 3-2.
As described in the previous report, holograms were recorded with dif-
ferent degrees of attenuation of the scene beam. The beam was attenuated
until it could no longer be seen in the reconstruction with a telescope of
2 centimeters aperture. The results of several experiments are summarized
in Table 3-3. These tests led us to the conclusion that 3.0 x 10" was a
practical lower limit to the scene-reference beam ratio.
After development, the hologram was put back into the apparatus and re-
constructed with the light from the first reference beam. The second ref-
erence beam was blocked. By looking through the developed plate, the loca-
tion of the scene point source was seen through the developed plate. The
scene beam was blocked and the field searched for the reconstruction. Equal-
ly practical was the tilting of the plate and the observation of two point
sources, namely, the original scene through the plate and the reconstruction.
The experiments afforded several interesting side observations. First,
the single beam portion of the hologram reconstructed with more background
noise than the portion of the hologram with the two-reference beams. This
did not, however, limit our ability to recognize the reconstructed point
source. For this reason, the two methods must be judged equal in sensitiv-
ity. The intensity of the reconstructed point in the two-reference beam
portion appeared weaker than in the single-beam portion. Second, reconstruc-
tion of the test holograms with a more intense (80 milliwatt) helium-neon
reconstruction laser did not increase our ability to detect reconstructed
Table 3-2. Transmission of Filters at 0.6328 Micron
Type
Welder's Goggles 1.32xlO~3
Wratten N.D. 1.0 1.03 x 10~]
80
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Table 3-3. Experimental Results
Case Hologram Portion
Initial
Scene-Reference
Ratio
Scene
Attenuation
Net
Scene/Reference
Ratio
Scene
Reconstruction
00
A. Single Reference
Portion of Hologram 0.22
B. Double Reference
Portion 0.17
1.75 x 10"6
(2 welding goggles)
1.75 x 10"6
(2 welding goggles)
3.9 x 10 Visible to naked eye
3.0 x 10 Visible to naked eye
II
A. Single Reference
Portion of Hologram 0.22
B. Double Reference
Portion 0.17
1.8 x 10"7
(2 welding goggles
and Wratten ND 1)
1.8 x 10~7
(2 welding goggles
and Wratten ND 1)
4.0 x 10
-8
3.0 x 10
-8
Visible through
telescope
Invisible through
telescope
-------
points even with lower scene-reference beam ratios (Case II in Table 3-3).
Third, at the level of 3.0 x 10" , location of the reconstructed point source
without prior knowledge of its position was almost impossible. For these
reasons, we now accept 3 x 10 as a practical lower limit to the scene-
reference beam ratio of a two-beam holographic arrangement.
Given 2 or 3 xlO~7 as the minimum scene-to-reference beam intensity re-
quired to reconstruct a hologram of a point source, one can derive an equa-
tion for the amount of laser beam energy needed to record holograms of indi-
vidual small micron-sized particles. For reasons of time and simplicity, we
assume that the particle scatters uniformly. On this basis, the light energy
density or flux scattered by a particle of scattering cross section 2
at a distance r from the hologram, is
Knowing now that the reference beam can be 1/3 x 10" the intensity of the
scene beam, a quantity called K (i.e., K = min scene/reference ratio), the
above equation can be written in terms of minimum reference beam intensity;
T - T
'
where K = 3 xlO" . The reference flux is then equated to the sensitivity of
the plate, a quantity represented by ec (for Agfa 8E75 holographic plate,
2
*s = 10 microjoules/cm ). Sensiometric curves for more popular emulsions
are given in Figure 3-22. Substitution and solving for the laser energy de-
livered over a pulse time T yields
(3-8)
assuming the scattering cross section can be expressed in terms of an effec-
tive scattering diameter d , so that
v - 2. A 2
2sca - 4 ds
82
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-4
o
o
PHOTOCHROMIC GLASS
(BLEACHING)
1
3000
4000
5000' 6000
WAVELENGTH, ANGSTROMS
Figure 3-22. Sensiometric Curves of Emulsions Used in Holography
83
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the above equation yields
I0 - «(^)S" (3-9)
2
Thus, for a 1-micron scattering diameter, «_ 10 microjoules/cm and K =
7
3 x 10" , the flux needed to record a hologram of a single particle a dis-
tance r from the hologram plate is
IT = 4.8 xllO"3 r2 joules/cm2 (3-10)
This equation can be graphed as shown in Figure 3-23.
If light is scattered from an ensemble of particles, the foregoing anal-
ysis should be valid under the condition that there is no multiple scatter-
ing and that the total scattering cross section used corresponds to the sum
of the cross sections of the individual particles. A similar minimum scene-
to-reference ratio (K = 3x10 ) will be required from the ensemble.
Three-Beam Hide Angle Scattered Light Holocamera
The use of a second reference beam in the scattered light holocamera
was found to have merit only inasmuch as it could be used as an intensity
reference. A number of configurational changes were explored in order to
try and use the holocamera to its best advantage in this mode. These were
discussed at some length in Section 3.3.
The main problems in hologram reconstruction and interpretation arose
from the nonuniformity of the reference beams. It may therefore be con-
cluded that the best configuration to facilitate reconstruction and main-
tain linearity, although it was never actually tried during this program,
was one in which the reference beams come from point sources located at
great enough distances from the holographic plate to provide a uniform in-
tensity incident wave front. The point sources could be two spatial filters
with beam expanding optics, such as were used in the three-beam holographic
sensitivity tests discussed in Section 3.2 and illustrated in Figure 3-4.
An alternative' is to expand the beam with a single spatial filter arrange-
ment, and then direct the expanded beam through a beam splitter as illus-
trated in Figure 3-24. This arrangement has also been used successfully in
laboratory experiments.
84
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0.1 1 10 100
DISTANCE OR RANGE OF SCATTERING PARTICLE FROM HOLOGRAM (CM)
Figure 3-23.
Primary Laser Beam Flux to Record Scattered Light
Holograms of Individual Particles on Agfa 8E75 Plate
85
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GLASS WEDGE
BEAM SPLITTER
PHOTODETECTOR TO
MONITOR LASER OUTPUT
RUBY LASER
EXPANDING AND
COLLIMATING
TELESCOPE
13 CM DIA. COLLIMATED
REFERENCE BEAM
GLASS WEDGE
BEAM SPLITTER
CORNER PRISM
FRONT SURFACE MIRROR
SCENE BEAM
SCATTERING CHAMBER
46X46X188 CM
AEROSOL INLET
IN BOTTOM
OF CHAMBER
188 CM
FRONT
SURFACE
MIRROR
FRONT
SURFACE
MIRROR
112 CM
INTENSITY REFERENCE BEAM
HOLOGRAM
Figure 3-24. Schematic Diagram of Scattered Light Three-Beam
Transmission Holocamera Test Setup
86
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It is more difficult to direct two reference beams thus obtained onto
a set of three holographic plates arranged to record light scattered over
a full 180-degree range. However the results of this program also indicate
that no great benefits are derived from doing so. It appears to be much
easier to obtain good information about particulate size distributions from
light scattered through a relatively narrow range of angles, such as forward
scattering, than to attempt to coorelate scattering over the whole range.
(See Section 2.5 for a discussion of the analysis of this problem.)
Usually all the scattering information needed can be recorded on one plate.
Three-beam scattered light holograms were made of 30- and 50-micron
water droplets obtained from the monodisperse droplet generator. Holograms
were also obtained of a sub-micron tobacco smoke, and of mixtures of these
two particulate. The two types of particulate were easily different!able
visually, and apparently also from scattered light angular variation con-
siderations. The incident beam light was polarized in the scattering plane.
Under these conditions, the side scattered light intensity is very low.
The holocamera configuration was not sensitive enough to extract much in-
formation from side scattered light from sub-micron particulate. The for-
ward scattered light, however, was found to be amenable to a size distri-
bution analysis, and was of sufficiently high intensity to seem preferable
for analysis from sensitivity considerations.
Figure 3-25 shows reconstruction photographs of three views of a mix-
ture of tobacco smoke and 50-micron water droplets. They were photographed
from hologram set number 9, the A, B and C holograms corresponding to for-
ward, side and back scattering, respectively. The reconstruction photos
were taken of the real image projected by the hologram. A copy camera with
a 210-mm Schneider Kreuznach lens was used. Figure 3-25a shows the strong
forward scattering at 30 degrees from the droplet stream. The smoke is also
visible behind the droplets. Figures 3-25b and c are both views of hologram
9B, taken at an angle of 90 degrees. In Figure 3-25b, the focal plane is on
the droplets, and the smoke is basely visible behind them. In Figure 3-25c
the camera was focused on the smoke.
These figures are of interest because of the similarity of the size
ranges to a sub-micron industrial fume mixed with wet steam. In a well-
developed fog or vapor the water droplets are in the 10- to 100-micron size
87
-------
(A) VIEW OF HOLOGRAM 9A, SCATTERING ANGLE
30 DEGREES. FOCUS INTERMEDIATE TO DROPLETS
AND SMOKE.
(B) VIEW OF HOLOGRAM 9B, SCATTERING ANGLE OF
90 DEGREES. FOCUS IS ON THE DROPLETS.
(C) VIEW OF HOLOGRAM 9B, SCATTERING ANGLE OF
90 DEGREES. FOCUS IS IN THE SMOKE CLOUD.
Figure 3-25. Reconstruction Photographs of Holograms 9A and 9B, Showing Forward
and Side Scattering. The scene volume contains tobacco smoke, and
50-micron water droplets
-------
range.11 Thus, scattered light techniques should be capable of distinguish-
ing between the fume content and water content of an industrial waste, for
example. This possibility was also analyzed in Section 2.6.
Figure 3-26 shows a reconstruction of a hologram of scattered light
from tobacco smoke, after the configuration of the holocamera was changed.
The hologram number was 12a. Two different scattering angles were viewed,
each corresponding to forward scattering. The first angle was 30 degrees,
normal to the hologram plane. The second angle was about 20 degrees, scat-
tering angle. This image contained a thin thread which was used as a
scattered light intensity reference. In Figure 3-26a, the camera is focused
on a fairly large volume of smoke below and behind the thread. In Figure
3-26b the scattered light is seen to be more intense.
Figure 3-27 shows an unusual effect of secondary light scattered off
the thread being strongly forward scattered by the smoke. This effect was
found in hologram set 16, and was seen in all three views. Figure 3-27a
shows the view at a scattering angle of 30 degrees, and Figure 3-27b shows
the backscattering angle of 150 degrees. In each case, however, the scat-
tered light comes from the thread and the actual scattering angle is about
10 degrees.
Particle Size Distributions
Three separate types of particulates were sized during this.program.
The glass and phenolic micro-balloons used with the Garrett holocamera ex-
periments were described earlier in this section. The size of these was
visually estimated from photomicrographs to be in the 30 to 50 micron range.
The aerosol drop.lets from the monodisperse aerosol generator were 'sized both
by calculations using the generator characteristics, and by direct light in-
terference measurements as described in Section 3.2. Droplets of diameters
50 and 30 microns were formed, and may be estimated to be monodisperse to
within about .10 percent of volume.
The size distribution of the tobacco smoke was also estimated from
scattered light data. These data were obtained by.visual estimation as de-
scribed in Sec'tion 3.3. It is a composite obtained partly by direct visual
observation of the scene volume and partly by inspection of holograms 12,
13 and 14. The curve which was obtained is shown in Figure 3-28, which is
89
-------
(A) FORWARD SCATTERING AT 30 DEGREES
(B) FORWARD SCATTERING AT 20 DEGREES
Figure 3-26.
Reconstruction of Hologram 12A, Showing Forward Scattered
Light From Tobacco Smoke. Two scattering angles are viewed.
The thread was used as a scattered light intensity reference.
-------
(A) HOLOGRAM 16A, SCATTERING ANGLE OF
30 DEGREES
(B) HOLOGRAM 16C,
150 DEGREES.
SCATTERING ANGLE OF
Figure 3-27.
Reconstruction Photos of Hologram 16A at 30 Degrees
Scattering Angle, and Hologram 16C at 150 Degrees
Scattering Angle. The smoke is illuminated by
secondary scattered light from the thread.
91
-------
ro
Z
I
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LU
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z
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_1
Q
LU
16
14
12
10
8
6
4
2
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C
^N
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s
l>
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i
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'ISUALOBSERVATIC
•QRWARD DIFFRACT
CATTERING MODEl
DF FIGURE 2-10
•x.
N,
^X
^x.
IN
/^VKI
— _
20 40 60 80 100 120 140 160 18
SCATTERING ANGLE - DEGREES
Figure 3-28. Observed and Calculated Scattered Light Intensity Distribution
from Tobacco Smoke
-------
a plot of relative scattered light intensity distribution as a function of
scattering angle.
It is worth noting that the shape of this curve shows a strong resem-
blance to the shape of the gain function for totally reflecting particles of
size X - 3. This can be seen from Figure 2-7. A match was sought for the
forward scattered light portion of the distribution by using the Fraunhofer
diffraction scattering model developed in Sections 2.3 and 2.5. A fairly
good fit to the observed forward scattering was obtained from diffraction
scattering from a log-normal distribution having parameters X =1.0 and
"" - 1.7. A value of nQ depends on calibrating the curve to absolute scat-
tered intensity.
The theoretical diffraction scattering for this distribution is also
shown in Figure 3-28. The value X = 1.0 corresponds to a 0.22-micron ge-
ometric mean diameter particulate. The three-sigma distribution limits for
o- 1.7 give a size range from about 0.05 micron to 1.0 micron. This is in
9 in
good agreement with known data on smoke particulate size distributions.
The theoretical points in Figure 3-28 were calculated from the coeffi-
cients of Table 2-2 and. Table 2-4 and have been renormalized on a scale of
15 to agree with the maximum observed scattered light intensity at a scat-
tering angle of 10 degrees. The theoretical points in Figure 3-28 are the
same as were shown in Figure 2-10, where the normalization was to unit num-
ber density, incident beam intensity, and wave number.
Particle Number Density
The three particulate distributions which were measured also represented
three particle number densities. Of these we were able to obtain estimates
of two.
The water droplet density distribution was neither stochastic nor homo-
geneous, since the droplets were generated in a straight stream, and no mix-
ing mechanism was employed to disperse them. However, the droplet spacing
results in an effective number density in a localized volume element, and
this can be calculated directly from the aerosol generator characteristics.
The droplet velocity at a generating frequency of 3 kilocycles and a
volume flow rate of 0.02 cc/sec (as shown in discussion in Section 3.2) can
93
-------
be calculated as 158 cm/sec. The droplet spacing is then equal to the ve-
locity divided by the frequency, and comes out to be 525 microns, or about
10 times the droplet radius. The droplets disperse very little over their
path to the scene volume, as is evident from examination of Figure 3-25. If
we consider each droplet as being contained in a spherical volume element of
diameter equal to the droplet spacing, the resulting number density is of
order 1.3 x 10 particles per cubic centimeter.
The density of the tobacco smoke clouds which were generated can be es-
timated directly from relative scattered light intensity measurements. Using
the Spectra-physics 124 Helium-Neon loser, the beam energy incident on the
scene was measured as
2
I = 28 milliwatts/cm.
o
This measurement was made with the UDT power meter, using a beam diameter
of 0.5 centimeter at the scene volume. With the light scattering thread in
place, the power meter was used to measure an isotropic scattered light dis-
tribution of 10 watts at a distance of 6.4 centimeter from the thread.
With a one-square-centimeter detector area, this gives a scattered light in-
tensity of
Jref 6Vref = 4 x 10"6 watts/sterad
scattered off the whole thread. The thread was approximately 100 microns
in diameter, and the illuminated portion was about one centimeter long.
This gives a reference beam to scene beam intensity of
J * 6V f 2
ref ref _ , ,- ,n-4 cm ,, in
IQ - 1-5 x 10 Hifi-[ (3-11)
for either the He-Ne laser or the pulsed ruby laser. Note the difference
in units of Jref and ID, such that IQ is a power flux as previously defined,
but Jfef has units of watts/cm3-sterad, and 6V ~ is the scattering volume
of the reference thread. The factor 5Vref is of secondary importance since
it cancels out.
94
-------
Now a visual estimate of relative scattered light intensity from the
smoke cloud was obtained from hologram ISA, at a forward scattering angle of
30 degrees. The scattered light intensity per unit area from the smoke, in
o
watts/sterad-cm , was estimated to be about 1 percent of that from the ref-
erence thread. The solid angle subtended was of course the same for both.
The illuminated area of the thread which was visible was about 0.01 square
centimeters, while the smoke cloud presented a viewing area of 2 square
centimeters. Thus the total scattered light from the thread, in watts/
sterad, was about twice the total scattered light from the scene, in watts/
sterad, at 30 degrees scattering angle. This comes from multiplying the ob-
served light intensity in watts/cm^-sterad by the appropriate area. On al-
ternatively, we multiply their ratios. We then have
Jref 6Vref
= 2 (3-12)
where 0 and 6V are the scattered scene light intensity and the scene volume
as previously defined. Multiplying Equation (3-11) by (3-12) we then have
Io - - - -
3
The value of 6V for the smoke-filled scene was about 2 cm , so we have a
o
ratio which can be compared with the first of Equations (2-22).
Here the index j corresponds to the 30-degree scattering angle, and the pro-
duct h.-C. is just the appropriate element of the A matrix which may be found
in Table 2-4 to be equal to 2.686 n . Substituting this in Equation (3-14)
71 1
with k = 4.53 x 10 cm" , and solving for nQ, we find
5 -3
nQ = 4.58 x 10 cm
This is roughly a factor of thirty more than the effective density of the
50-micron water droplets, and leads to an inter-particle spacing of about
100 microns.
95
-------
Particle Velocity
In the Garrett holocamera experiments the phenolic and glass micro-
balloons were thrust into the scene volume with a forced air nebulizer as
discussed previously in this section. The incense smoke was wafted into the
scene volume by convection. In neither case was the velocity measured, but
in either case the velocity was only sever!a feet per second, or 100 cm/sec
or less.
When the monodisperse aerosol generator was used, the velocity of the
stream of water droplets could be readily calculated from the flow charac-
teristics of the orifice. It was found to be about 160 cm/sec at a volume
flow rate of 0.02 cc/sec of alcohol.
The cigarette smoke used to make holographic recordings with the three-
beam wide angle scattered light holocamera was also injected into the scene
volume with forced air. The velocity of this air stream was measured with
a hot wire anemometer, and was found to be about 100 cm/sec.
The objective of these experiments insofar as parti oilate velocity is
concerned was to measure the particle velocity and determine its effects on
the holographic recording process, and on our ability to measure and analyze
the other important particle distribution and light scattering parameters.
In each of the above cases the velocity was low enough and the laser pulse
time fast enough that velocity considerations were not important.
In recording holograms of particles by scattered laser light, one has
to consider the stability of the interference pattern recorded by the photo-
graphic plate. If the interference pattern moves during the exposure time,
then the plate records a smeared or composite interference pattern. The re-
sult is a greatly degraded reconstructed image.
It can be shown from the theory of holography that high quality recon-
structions are realized whenever the optical path does not change more than
one-tenth of the laser's wavelength during the hologram's exposure. At first
glance, this might seem too restricting. The back scatter condition is the
worst case. Here one is limited to low particle velocities, even with short
~ 50 nanosecond duration laser pulses. For example, if a particle is moving
away from the hologram, the path change (A) is twice the product of particle
velocity and laser pulse duration (i.e., A= 2vr). Thus, to keep the
96
-------
interference pattern stationary, the path change must be less than the tenth
wavelength bound. The velocity for back scatter must not exceed
(3-15)
For a conventional Q-switch ruby laser, T ~ 50 nanoseconds and X = 0.6943 .
Thus, vb < 1 meter/second, which is not particularly fast. More recently,
the pulse duration of a ruby laser has been shortened to 2 nanoseconds by
electro-optical chopping techniques. This factor of 25 decrease in pulse
duration means a comparable increase in particle velocity, or a limiting
velocity for the back scatter case of over 25 meters per second. Short
pulses, however, have short coherence lengths which limit the amount of depth
that can be recorded in a scene with a single reference beam. A one nano-
second pulse corresponds to a coherence length of 30 centimeters (1 foot)*
or a scene depth of 15 centimeters (6 inches). This limitation can be over-
come by having a reference beam which is derived from mirrors at increasing
15-centimeter intervals. Such innovations are beyond the intent of the pres-
ent discussion.
Holograms recorded by forward scatter greatly relax the velocity re-
quirements. There are several cases which are best considered separately.
The worst case is where the particle moves parallel to the hologram and view-
ing is at an angle relative to the input beam (the input beam is toward the
viewer). The hologram is parallel to the particle motion. It can be shown
from trigonometric arguments that for this case
A _ X _ /~ -j/-\
vmax < X. sin e 10 T sin e \ - I
(motion) |)
As the viewing angle approaches 0 degrees, the maximum permitted particle
velocity diverges. Table 3-4 compiles some representative values.
If one views in the direction perpendicular to both the particle direc-
tion and the direction of propagation of the laser beam, then it can be
shown that the limiting particle velocity to record a hologram becomes
Vmax0- T ~ T V10
97
-------
Table 3-4. Maximum Velocity for Q-Switch Ruby Laser Forward-
Scattered Hologram With Particle Moving Parallel
to Hologram
Viewing Angle
Relative to Laser Beam
6
(degrees)
1
3
5
10
15
20
vmax. 1 1
(T = 50 nanoseconds)
(meter/sec)
<79.5 meter/sec
< 26.5 meter/sec
<15.9 meter/ sec
<8.0 meter/ sec
<5.3 meter/ sec
<4.1 meter/ sec
where r is the distance of the particle from the hologram. For this case
the velocity is independent of the viewing angle. The direction of propa-
gation of the laser beam is perpendicular to the plane of the holograms.
The viewing is perpendicular to the direction of motion of the particle and
at an angle $ relative to the plane determined by the laser beam and the di-
rection of motion of the particle.
Table 3-5 gives a compilation of the maximum velocities for different
ranges for a 0.6943 n - 50 nanosecond ruby laser pulse. The permitted veloc-
ities are now much high due to the greater insensitivity of this geometry on
particle motion.
Table 3-5. Maximum Velocity for Q-Switched Ruby Laser for Different
Ranges and for Particle Moving Parallel to Hologram and
Viewing Along All Angles Perpendicular to Motion
Range D Maximum Velocity, vmax
(Centimeters) (kilometer/sec) °
1 cm 0.525
10 cm 1.66
100 cm 5.25
1000 cm 16.6
98
-------
An even more insensitive case is where the particle moves either toward
or away from the hologram. It can be shown that for this case
max± ~ T(I . cos e)
(3-18)
where in the above equation is the angle between the direction of viewing
and the direction of propagation of the input laser beam. For this case,
both the direction of viewing and the direction of propagation lie in the
same plane. A compilation of maximum velocities for motions toward and away
from the hologram is given in Table 3-6.
The preceding discussion has shown that velocity restrictions are less
in the forward scattering case than in the back scattering condition. In
addition, more light is scattered in the forward direction, making the re-
cording of the hologram an easier task. Forward scattering holography also
minimizes the coherence requirements on the laser.
Table 3-6. Maximum Velocity for Q-Switched Ruby Laser Forward
Scattered Hologram When Particle Moves Toward or
Away from the Hologram
Viewing Angle
6
(Degrees)
1/2
1
2
3
5
10
15
20
Maximum Velocity
vmaxj.
<35 kilometers /sec
^9 kilometers/sec
<2.3 kilometers/sec
<1.0 kilometers/sec
<360 meters/sec
<91 meters/sec
<41 meters /sec
<20 meters/sec
99
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4. CONCLUSIONS AND RECOMMENDATIONS
4.1 CONCLUSIONS
1) Individual particulates of sizes greater than about 20
microns can be detected, recorded, and reconstructed with
scattered light holography. They may not necessarily be
resolved. It was demonstrated with the three-beam
scattered light holocamera and the monodisperse droplet
generator that there is sufficient angular variation in
the forward scattered light intensity to determine their
sizes by diffraction scattering.
2) Particulates whose diameters are approximately the same
as the wavelength of the scattered light (0.1 to 1.0 micron
for ruby laser light) can be holographically recorded and
reconstructed from any angle to obtain a size distribution.
If there is a holographic intensity reference beam, a
particulate density may also be recovered. Experiments
with both the two-beam and three-beam scattered light
holocameras show that forward scattered light is by far
the easiest to analyze. Besides being more intense and
having more pronounced angular variation, it is independent
of the particulate index of refraction.
3) The use of three holographic beams does not increase the
recording sensitivity. It is necessary, however, if
aggregate densities are to be obtained where no resolution
is possible. This was verified from experiments with the
three-beam scattered light holocamera and with breadboard
holographic sensitivity tests.
4) For particulate larger than the wavelength of the scattered
light, particulate size distribution can be obtained from
forward diffraction scattering which is independent of
particulate optical properties or system resolving power.
5) A limiting value for scene-to-reference beam light intensity
ratio has been established at 3 x 10"7-
4.2 RECOMMENDATIONS
1) The use of a ISO-degree angular range scattered light
holocamera is generally not necessary to obtain adequate data
The preferable method is low angle forward scattering, and
the next preferable is back scattering.
2) A particulate measurement holocamera should include two
reference beams to enable an absolute determination of
scattered light intensity.
3) The two reference beams should both be collimated and of
uniform intensity for best results in reconstruction and
calibration.
100
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REFERENCES
1. Matthews, B.J., and Kemp, R.F., "Development of Laser Instrumentation
for Particle Measurement," TRW Report No. 14103-6003-RO-OO (EPA Con-
tract No. CPA 70-4), June 1971.
2. Matthews, B.J., and Kemp, R.F., "Investigation of Scattered Light
Holography of Aerosols and Data Reduction Techniques," TRW Report
No. 14103-6002-RO-OO (EPA Contract No. CPA 70-4), November 1970.
3. H.C. Van de Hulst, Light Scattering by Small Particles, John Wiley
& Sons, New York, 1957.
4. Milton Kerker, The Scattering of Light and Other Electromagnetic
Radiation, Academic Press, New York, 1969.
5. Kerker, M., Matijevic, E., Espenscheid, W., Farone, W., and Kitani.S.,
J. Colloid Sci. 19, 213, (1964).
6. Wallach, M.L. and Heller, W., J. Phys. Chem. 68, 924, (1964).
7. Chin, J.H., Sliepcevich, C.M., and Tribus, M., J. Phys. Chem. 59,
845 (1955).
8. Shifrin, K.S., and Perelman, A.Y., Tellus ]_8_, 566 (1966).
9. Shifrin, K.S., and Perelman, A.Y., Opt. Spectry. (USSR) (English
Translation) 20, 75, 386 (1966).
10. T.W. Anderson, Introduction of Multivariate Statistical Analysis.
John Wiley & Sons, New York, 1958.
11. Air Pollution Manual: Part II. Control Equipment, American Industrial
Hygiene Association, Detroit, Michigan, 1968.
12. Wuerker, R.F., Heflinger, L.O., and Briones, R.A., "Holographic
Interferometry with Ultraviolet Light," Applied Physics Letters,
12., pp 302-303, May 1968.
13. Wuerker, R.F., Matthews, B.J., and Briones, R.A., "Production Holo-
grams of Reacting Sprays in Liquid Propellant Rocket Engines," Final
Report, JPL Contract #952023, NAS 7-100, TRW Report 68.4712.2-024,
31 July 1968.
14. Wuerker, R.F., "Operation Manual for Transmission Holocamera," Con-
tract F04611-69-C-0015, AFPRL, Edwards, California, February 1970.
15. Wuerker, R.F., "Pulsed Laser Holography," published in E.R. Robertson
and J.M. Harvey, The Engineering Uses of Holography, Cambridge Univer-
sity Press (1970).
101
-------
16. Berglund, R.N., and Liu, B.Y.H., "Generation of Monodisperse Aerosol
Standards," Environmental Science and Technology_7 No. 2, Feb. 1973.
17. Wuerker, R.F., Koboyashi, R.J., Heflinger, L.O., and Ware, T.C.,
"Application of Holography to Flow Visualization Within a Rotating
Compressor Blade Row," Garrett AiResearch Final Report 73-9489,
NASA CR-121264, Sept. 1973.
102
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APPENDIX A
THE IMAGINARY PART OF THE INDEX OF REFRACTION
If the index of refraction has an imaginary part, the propagation of
light is altered. It will be quickly shown that the imaginary part repre
sents an attenuation of a light wave passing through a medium of index n.
In its simplest form the propagation of light may be expressed as:
Wave Ae- (A-l)
where,
AQ is the amplitude of the light wave
e is the base of the natural system of logarithms
j is ,P\
is the angular frequency f of the wave in radians per
unit time (w
t is time
k is the wave number (i.e., k = 2ir/\)
x is distance
The equation represents a wave moving to the right at a constant ve-
locity. This can be seen by setting the argument of the exponent equal to
a constant; namely, u>t-kx = constant. Differentiating x with respect to
t one obtains dx/dt = C. In vacuum, the index of refraction is unity. When
light moves through a media of refractive index not equal to unity, the
wave felocity slows. The index n is related to the velocity v by the fol-
lowing: v = c/n. By substitution, one can write the original equation in
terms of n:
Wave = AQe
(A_2)
103
-------
Now let n = nQ - JA so that the index of refraction contains both a
real (n0) and an imaginary (JA) part. The symbol A represents the numer-
ical value of the imaginary part. Again, by substitution,
Wave = A e Jft'V^0 + J"Ax/c^
A e -(AW/C)X fi j(t-nQx/c)w ^A_3j
Inspection of Equation (A-3) shows that it now contains a term
A0e~(Aw/c)x. This quantity represents an attenuation of the wave ampli-
tude as .the distance x increases. This occurs due to the imaginary part of
the index. The attenuation is multiplied by the function e jlt-nox/c)^
which has already been shown to be the expression for a right traveling
wave [Equation (A-l)]. The wave moves to the right at a velocity
dx/dt = v = c/nQ.
In essence, the real part of the refractive index determines the speed
of light through a given medium while the imaginary part imposes a damping
effect on the light wave resulting in attenuation or absorption of the wave
energy.
104
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APPENDIX B
COMPUTER PROGRAM FOR FORWARD DIFFRACTION SCATTERING
A small, study-type computer program was written in the BASIC language
to compute the elements of the A. matrix for forward diffraction scattering.
The matrix elements are computed using Equation (2-22) with I /4k2 = 1.
The calculation of the H matrix is done as shown in Equations (2-25) and
(2-26), with NQ normalized to one.
The program computes the first five forward diffraction scattering
coefficients, which are the coefficients of x2n, for n = 1 to 5, in the
expression for the scattering gain function as shown in Equations (2-20).
2J, (x sin 8) 2
G
-------
10 PRINT "INPUT THREE ANGLES,DEG."
20 MATINPUT TC3)
30 DIM C<3*5>*DC3)*H<5*3>
40 F0R 1=1 T0 3
50 CCI»1)=1
60 Q=CSINCPI*TCI>/180»t2
65 CCI*2)=-.25*9
70 CCI,3)=C5/192>*CQt2>
73 CCI,4)=-(7/4608>*CQt3>
77 CCI«b)=Cll/184320)*CQf4>
30 NEX'l I
90 PRINT "C2", "04", "C6"»"Gtftl» "CIO"
100 MATPrtINT C
110 PRINT "INPUT 6£3M. MEAN* S.D."
120 INPUT M*S
130 U1=L06CM)
140 U2=L06CS>
150 S=U2t2
160 F'4H 1 = 1 T0 b
170 HCI,1)=EXP(4*CI+1)*S*CU1+(I+1)*S»
180 HCI»2) = 2*(I-H )*HCI» 1)
190 H 1)/(2*U2)
200 NEXT I
205 PRINT "H MA1KIX"
210 HKINT "eAK.'1A">"uBAK"«"i>IG.>'JA"
220 rtATPRINT ri
230 PKItMT "A MA1KIX"
235 MAT AC3*3) =
240 MA'IPRINT A
Figure B-l. A Computer Program in BASIC, to
Calculate the Forward Diffraction
Scattering Distribution
106
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TECHNICAL REPORT DATA
(rlcasc read Instructions on the reverse before completing)
I REPORT NO.
EPA-650/2-74-031-b
3. RECIPIENT'S ACCESSION-NO.
4. TITLE AND SUBTITLE
Application of Holographic Methods to the Measurement
of Flames and Particulate, Volume II
S. REPORT DATE
April 1974
6. PERFORMING ORGANIZATION CODE
11982
7. AUTHOR(S)
B.J. Matthews andC.W. Lear
8. PERFORMING ORGANIZATION REPORT NO.
23523-6001-TU-OO
9. PERFORMING ORGANIZATION NAME ANO ADDRESS
TRW Systems Group
One Space Park
Redondo Beach, CA 90278
10. PROGRAM ELEMENT NO.
1AB014; ROAP 21ADG-51
11. CONTRACT/GRANT NO.
68-02-0603
12, SPONSORING AGENCY NAME ANO ADDRESS
i
EPA, Office of Research and Development
NERC-RTP, Control Systems Laboratory
Research Triangle Park, NC 27711
13. TYPE OF REPORT ANO PERIOD COVERED
Final
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
16. ABSTRACT
The report gives results of an investigation to determine the feasibility
of applying pulsed ruby laser holographic techniques to the measurement of parti-
culate in the 1-micron and sub-micron size range. The investigation included
the design and evaluation of a scattered light holocamera, and evaluation of the
effects of four basic variables on scattered light methods. The variables were:
particle size, angular illumination of the particle (scattering angle), particle
number density, and incident laser beam diameter. The program included an
analysis of the mathematical and physical models from which the transformation
can be made from a scattered light distribution to a particle size distribution.
The experimental portion of the program was conducted to assess the advantages
and limitations of certain promising scattered light holographic methods.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lOENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Group
Air Pollution
Holography
Particle Size
Light Scattering
Air Pollution Control
13B
14B
20N, 20F
l
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