NBSIR 76-1031

Shape Dependence of LightScattering Behavior of Dust

Particles

R. Zerull

Ruhr University

Bochum-Querenburg

West Germany

Translated for: Center for Fire Research

Institute for Applied Technology

National Bureau of Standards

Washington, D. C. 20234

June 1976

Final Report

U S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

NBSIR 76-1031

SHAPE DEPENDENCE OF LIGHTSCATTERING BEHAVIOR OF DUST

PARTICLES

R. Zerull

Ruhr University

Bochum-Querenburg

West Germany

Translated for: Center for Fire Research

Institute for Applied Technology

National Bureau of Standards

Washington, D. C. 20234

June 1976

Final Report

U.S. DEPARTMENT OF COMMERCE, Elliot L Richardson, Secretary

James A. Baker. Ill, Under Secretary

Or. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Acting Director

PREFACE

This report is a translation of paper prepared by Dr. R. Zerull and presented by him at the

Colloquium on Aerosol Measurement Techniques,

March 4, 1975, in Aachen, West Germany. The

Colloquium was presented by the Institute for

Electronics Communication Technology of the

Rheinish-Westfalian Technical College, Aachen,

in conjunction with the Gesamthochschule in Duisburg.

This translation has been prepared to disseminate useful information to interested fire research

personnel on a need-to-know basis and is not an

original work of the Center for Fire Research.

We express our appreciation to the author,

Dr. R. Zerull, for his permission and assistance

in making this information available.

We also express our appreciation to the Joint

Publication Research Service, Arlington, Virginia,

who provided the translation of the original paper.

Richard G. Bright

Program for Fire Detection

and Control Systems

Center for Fire Research
CONTENTS

Page

PREFACE iii

LIST OF FIGURES vi

Abstract 1

1. INTRODUCTION 1

2. COMPUTATIONAL FORMULATION OF A SCATTERING PROCESS . 2

3. DETERMINATION OF SCATTERING FUNCTIONS 3

3.1. Calculation of Scattering Functions 3

3.2. Measurement of Scattering Function 4

3.3. Experimental Setup 5

4. RESULTS OF MEASUREMENT 7

4.1. Isometric Bodies 7

4.1.1. Rough Spheres 7

4.1.2. Cubes 7

4.1.3. Octahedrons 8

4.1.4. Irregular Bodies 8

4.2. Finite Cylinders 9

5. CONCLUSIONS 10

6. REFERENCES 10

v
LIST OF FIGURES

Page

Figure 1. Geometry of a Scattering Process 11

Figure 2. Raleigh Scattering 11

Figure 3. Geometric Optics 12

Figure 4. Microwave Scattering System 12

Figure 5. Principal Circuit Diagram of the Microwave

Scattering Systems 13

Figure 6. Part of the Measured Scattering Bodies . . 15

Figure 7. Scattering Behavior for a Polydisperse

Mixture of Cubes Compared to Spheres ... 15

Figure 8. Scattering Behavior for a Polydisperse

Mixture of "Smaller" Cubes Compared to

Spheres 16

Figure 9. Scattering Behavior for a Polydisperse

Mixture of "Larger" Cubes Compared to

Spheres 16

Figure 10. Scattering Behavior for a Monodisperse

Mixture of Octahedrons, Cubes and Spheres. 17

Figure 11. Scattering Behavior for a Polydisperse

Mixture of Convex and Concave Bodies

Compared to Spheres 17

vi

SHAPE DEPENDENCE OF LIGHT-SCATTERING

BEHAVIOR OF DUST PARTICLES

R. Zerull

Abstract

The most important characteristics which determine the light-scattering behavior of particles is

their size distribution, their concentration, their

shape, and their material composition. This paper

concerns itself with the measurement of the effects

of shape on light-scattering behavior. Only a few

shapes have been appropriately modeled and if the

shape dependence can be determined, the remaining

characteristics pose no special difficulties.

Key words: Aerosols; dusts; light-scattering;

Mie theory; particles; Rayleigh scattering.

1 . INTRODUCTION

Problems connected with light-scattering from dust particles can roughly be divided into two categories. In one case,

the scattering characteristics of a known particle system are

calculated or measured. The second case is the inverse problem; here, conclusions are drawn from measured scattered light

with respect to the composition of the particles producing it.

The most important distinguishing characteristics, on which

the scattering behavior characteristically depends here, are

the material, the form, the size distribution, and the spatial distribution of the particles. To be able to associate

the measured light-scattering characteristics as unambiguously

as possible with a definite particle system, it is therefore

necessary to know as accurately as possible the influences of

the cited distinguishing parameters on the scattering behavior.

Appropriate model calculations have hitherto been possible

only for a few special particle shapes, such as, for example,

spheres, layered spheres, and infinitely- long circular cylinders, whereby variation of the remaining parameters does then

indeed pose no special difficulties. For this reason, measurement of the shape dependence of the scattered radiation

shall occupy the foreground in the present paper.

1
2. COMPUTATIONAL FORMULATION OF A SCATTERING PROCESS

The physical characteristics of the particles are described by the complex index of refraction m = m' - jm" . The

generally customary size parameter a = circumference/wavelength, which is derived from a sphere, is to be used here

to specify the size of a particle.

Figure 1 shows the geometry of a scattering process.

The light source, the scattering body, and the observer who

records the scattered light at a scattering angle 0, span the

so-called scattering plane.

If the scattering process is separately considered for

the two directions of polarization, vertical (Index 1) and

parallel (Index 2) to the scattering plane, the following

relation [1]^ is obtained between the intensities recorded

at the site of the scattering body (Index 0) and the scattering intensity (Index s) , recorded at a distance r from

the scattering body at an angle 9 referred to a fixed plane:

I (6) = — • i (0) • I ( A = Wellenlange)

S ] a 7 ? * O I 4 tt r

^2 < 6)

4 it r

2^ 2 i

2 (e) O 2

In this representation, the scattered radiation is characterized by the scattering functions i and i , which depend on

the characteristics of the scattering body and on the scattering angle 9, but not on the distance of observation r. Their

calculation and measurement will be discussed in the following

sections

.

With this scattering function, the generally customary

degree of linear polarization

P =

- l

1+1 1 2

can be defined. If the incident radiation consists of natural, i.e. unpolarized, light of intensity I the given formalism is exact for spherical particles. For other particles,

''"Numbers in brackets refer to the literature references

listed at the end of this paper.

2
it is often valid to a good approximation if one sets I Io2 = I

Q/2 [2].

All these considerations are first of all valid for an

individual particle in a definite spatial orientation. If

there are several particles, a "resultant scattering function"

is obtained by simple addition of the individual scattering

functions. It is here presupposed, of course, that the particles are sufficiently distant from one another so that the

scattered radiation of neighboring particles is negligible

compared to the intensity of the primary light source; thus

no significant multiple scattering occurs. When several

particles are considered, a distinction is made between monodisperse mixtures (all particles the same size, with statistical orientation) and polydisperse mixtures (particles in a prescribed size distribution and with statistical orientation)

.

If the just-mentioned "resultant scattering function" of

a mixture of particles is divided by the number of particles

the so-called "averaged scattering function" is obtained. It

can be associated with a fictitious particle, which represents the scattering characteristics of a whole mixture. In

the further discussion, the average scattering functions of

monodisperse mixtures will be designated by i, those of polydisperse mixtures by a. The situation becomes somewhat more

complicated when the particles of a mixture occupy such a

large space that different scattering angles are obtained

with respect to the observer and the light source. In this

case, the scattering intensities originating from individual

particles must be added taking into account the different

scattering angles.

3. DETERMINATION OF SCATTERING FUNCTIONS

3.1. Calculation of Scattering Functions

In this section various possibilities are sketched for

computational determination of the scattering functions.

First of all two approximations will be mentioned [1] . Particles whose dimensions are very small compared to the wavelength, behave approximately like electric dipoles. Qualitatively, a scattering diagram thus results as is shown in

figure 2.

The scattering behavior of particles, whose dimensions

are large compared to the wavelength of the incident radiation, can be approximately described by geometric optics.

Here, the scattering diagram is composed of the diffraction

diagram, determined from the Fraunhofer formulas (independent of material) according to the current cross section, and

3
a portion to be calculated from the Fresnel formulas for

reflection and refraction. This becomes clear by following

a ray in figure 3.

The incident ray 1 is partly reflected (2) and partly

refracted. If the refracted ray (3) again strikes the boundary of a body, it is also partially reflected and refracted

(ray 4 and 5) . From the summation of the outward penetrating

rays, there then results the second portion required for composing the scattering diagram. This procedure is indeed quite

perspicuous, but in all quite cumbersome, and furthermore

inaccurate for particle sizes below a = 400. Nevertheless,

all scattering phenomena produced by water droplets (e.g.

increased back scattering, rainbows) can be qualitatively

explained in this fashion. Geometric optics becomes particularly simple when the material of the scattering body is so

strongly absorbing that ray 3 is almost completely attenuated

in its path, and thus only ray 2 needs to be considered.

Since light involves electromagnetic waves, a scattering

process is exactly described by Maxwell's equations. But

solutions for these, until now, exist only for a few cases,

for which the boundary conditions at the boundary surfaces

can be formulated particularly simply. An important special

case is the sphere, for which the solution is known as "Mie

Theory" [1]. This solution makes it possible, with modern

computers, to determine the scattering function of nearly

arbitrarily large spheres, and thus also of mixtures of

spheres. Considering once again all hitherto cited possibilities for calculating scattering functions, the gap is

immediately apparent, which cannot presently be closed with

computationally tolerable effort. These are the scattering

calculations for all non-spherical particles, which are

neither very small nor very large compared to the wavelength.

Although it is not, in principle, impossible to determine the

scattering functions of complicated particles, the problem

can still be, at this time, more easily solved experimentally,

especially when one considers that the scattering behavior of

mixtures of particles with various sizes and different orientations are usually the ones of interest. We thus arrive at

the central theme of this paper, namely, the measurement of

scattering functions.

3.2. Measurement of Scattering Function

The most obvious possibility is to measure the scattering characteristics of particles of interest directly in the

optical domain. The advantage of such measurements lies in

the fact that scattering functions of mixtures can be determined in a short time. But it is here difficult to give the

4
individual particles a definite shape as well as to simulate

prescribed size distributions.

Another possibility for measuring scattering functions

consists in the microwave analog experiment. Here the length

of light waves and the particle size are multiplied by the

same factor (order of magnitude 10 4

) , whereby the microwave

region is attained and the particles take on convenient dimensions. In the microwave range, the same classical electromagnetic laws hold as in the optical range. Of course, for

the microwave experiments, one cannot use the same material

of which the particles consist that are of interest for optical applications, since the index of refraction is often

already strongly frequency-dependent within small intervals.

(This is even more so when the frequency differences amount

to 4 powers of ten.) Accordingly, a material must be selected

for the experiments which has a value in the microwave range

that is of interest for optical problems. An apparatus for

performing microwave analogy experiments is located in the

extraterrestrial physics branch at the Ruhr University

Bochum. Its technical conception will be described in the

following section.

3.3. Experimental Setup

Figure 4 shows a section of the scattering chamber with

the essential parts of the mechanical setup. Antennas are

affixed to the columns. The transmission antenna (right in

the picture) is fixed, while the receiving antenna (left in

the picture) can be moved on a rail about the scattering

body, which can be seen approximately in the middle of the

picture. The scattering body is suspended by four nylon

threads, of which two at a time are tensioned by stepping

motors on the ceiling and on the floor. Various orientations

of the scattering body can thus be set. The threads are so

thin that they are really "invisible" to the microwaves.

The entire scattering chamber and the mechanical setup

are draped with absorbing material to keep reflections at

a low level.

Figure 5 shows the principal circuit diagram for the

transmission-receiving, and data-sensing component. A reflex

klystron serves as transmitter. It operates at a frequency

of 35 GHz (Ka-band) and has a power of 250 mW. The power is

led through a waveguide transmission antenna (a pyramid horn)

.

The intensity scattered by the scattering body at a certain

angle 6 is received by a horn antenna of similar construction,

and is brought to a diode mixing receiver. The intermediate

frequency generated in association with auxiliary oscillator

5
I is 30 MHz. A stabilizing device maintains the transmitter

and the auxiliary oscillator I always at this frequency interval. After selective amplication, the intermediate frequency

signal is transposed into the low frequency range (1 KHz) by

means of an auxiliary oscillator II and a broad band multiplier. Then, it is again amplified selectively and rectified.

If the auxiliary oscillators are correctly adjusted, the signal that is now present is proportional to the received signal

over a power range of more than 4 powers of ten. Various

noise signals are present on the desired scattering signal

of the test body. For one, there are reflections from the

walls and from parts of the setup, which cannot be fully

avoided even with absorbing covers. More critical are signals

which find their way directly from the transmission to the

receiving antenna. Their intensity, especially in the range

of forward scattering, can exceed that of the useful signal

by several orders of magnitude. All these undesired signals

are present even when no scattering body is located in the

field; this offers the possibility of eliminating them by adding a signal of equal amplitude but opposite phase. For this

purpose, part of the transmitted energy is branched-off into

the compensation circuit, where the required signal is adjusted by an attenuator and a phase shifter, and can be superimposed on the received signal by means of a "magic T." After

zero equalization has been achieved, the scattering body is

brought into the field, whose desired scattering signal can

now be recorded without error. Compensation of the noise

level must, of course, be executed anew for each scattering

angle

.

The required measurement time must be kept within economical limits, considering the many necessary individual measurements. For this purpose, the course of measurement has

been substantially automated. Furthermore, the possibility

was provided of obtaining averaged scatter functions by a direct route. As already mentioned, a signal proportional to

the desired scattering signal is available at the rectifier.

The subsequent integrator makes possible direct measurement

of the scattering function, averaged over exactly one rotation of a rapidly-rotating scattering body. Such a measured

value is available in 1-3 seconds, independent of the rotational velocity. Values measured by the digital voltmeter

are stored on paper tape for further processing in the computer. The computer must first convert the recorded scattering signals into associated values of the scattering function.

The required calibration factor results from comparing the

measured scattering diagram with that of a calibration sphere

calculated according to the Mie theory.

6
4 . RESULTS OF MEASUREMENT

4.1. Isometric Bodies

Since only sparse results were available concerning the

scattering behavior of non-spherical shapes particles, it

seemed sensible in the measurements to systematically delimit

it with respect to spheres, by choosing special particle

shapes. Figure 6 shows several of the bodies measured at this

time — first cubes and octahedrons, as regular shapes, then

rough spheres, and finally irregular bodies, which are bounded

by flat or concave surface sections.

Several typical results will be selected in the following

discussion. They will always be juxtaposed on the Mie calculations, whereby equal volumes serve as the basis for comparison. For polydisperse mixtures, a size distribution is

assumed according to the power law

n da ~ a da;

of course, microwave analogy experiments offer precisely the

possibility of also simulating substantially more specialized

distributions [2]. For economic reasons, the steps in body

size had to be chosen relatively coarsely — each individual

scattering body is therefore representative for a relatively

large size interval. To show that no errors arise therefrom,

curves have also been drawn in several of the diagrams, which

result from equally coarse steps in the comparison spheres.

4.1.1. Rough Spheres

The measured spheres had a roughness of about 1/10 wavelengths. The deviation in scattering behavior relative to

smooth spheres was so low, for monodisperse as well as for

polydisperse mixtures, that graphic representation will here

be dispensed with [2]. In particular, the rise in the back

scattering range, typical for mixtures of dielectric spheres,

was fully preserved.

4.1.2. Cubes

Figures 7-9 show the scattering behavior of polydisperse

mixtures of cubes. Figure 7 illustrates the basic differences with respect to spheres: while the diffraction peak is

preserved, essentially isotropic scattering behavior results

for larger scattering angles; the intensity and the mean

angular ranges lie almost one order of magnitude above that

7
of the comparable mixtures of spheres, while the rise in back

scattering, which is typical for the latter, is absent. The

polarization behavior of these cubes is neutral in the middle,

whereas, by contrast, the corresponding mixtures of dielectric

spheres clearly polarize negatively in this size interval.

The mixture of cubes in figure 7 was divided into "smaller"

and "larger" cubes for figures 8 and 9. It thus becomes

clear that the larger cubes are in the first place responsible

for the different course of intensity in figure 7, while small

as well as large cubes contribute to the differences in the

polarization behavior.

4.1.3. Octahedrons

The scattering behavior of octahedrons can be delimited

with respect to spheres in the same manner as that of cubes.

Indeed, the increase in intensity in the medium ranges of

scattering angles turns out to be weaker [2]. This is made

clear in figure 10, where monodisperse mixtures of octahedrons,

cubes, and spheres are compared with one another.

4.1.4. Irregular Bodies

The irregular bodies used for the measurements deviated

from spherical shape in a definite fashion: One series had

10-15 flat surface sections as a boundary ("convex bodies"),

while the examples of the other series, which were always of

equal volume, were bounded by concave spherical or cylindrical surface sections ("concave bodies").

In figure 11, for example, the scattering functions of

polydisperse mixtures of the convex and concave bodies, as

well as of equivalent spheres, are juxtaposed one on another.

The size interval considered is 5.87 <_ a <_ 17.79. It is conspicuous in the diagrams that the diffraction peak, to the

extent that it could be measured, is nearly identical for the

irregular bodies and the mixture of spheres. For larger

scattering angles, by contrast, (6 >_ 20°), the courses of the

curves deviate strongly from one another. The intensity in

the middle range of angles is far higher with the irregular

bodies than with the mixture of spheres (maximally by a factor

of 5) , whereby the scattering intensity of the concave bodies

still lies clearly above that of the convex ones. The

increase in intensity is clearer for a x than for a 2

. Since a mixture of dielectric spheres of the size order

under consideration polarizes predominantly negatively, this

fact indicates a neutral polarization behavior of the irregular bodies. A clear difference in the three courses of

8
curves can furthermore be recognized in the range of back

scattering: in contrast to the strong rise in back scattering,

typical for mixtures of dielectric spheres, the convex bodies

here exhibit only a small rise, while the concave bodies

scatter nearly isotropically in this range.

4.2. Finite Cylinders

The first exact solution of a scattering problem was

found by Rayleigh in 1881 for perpendicular incident radiation

on an infinitely long circular cylinder. The formalism for

this is as follows [3]

si

(e) =

2

it r

\ (8)

'ol

S2 (6) =

2

tt r T 2 (6) "02

are the cylinder scattering functions which are to be

1 1 2 calculated. With the cylindrical scattering problem, the

scattering intensity declines like 1/r. With the transition

to finite cylinders of length 1, the scattering formula cited

in section 2 is again valid, if the observation distance is

sufficiently large (r >> l

2 /\). With the aid of the measurements described below, it is now to be ascertained what connection exists between the cylinder scattering functions

2 T (9) , which are to be calculated, and the scattering

1/2

functions i

i of finite circular cylinders, and to what

extent this 6onnection remains intact with the transition to

non-circular cross sections. Altogether, 27 different cylinders were measured: 3 different cross sections (circular,

hexagonal, square) and in each case 3 different thicknesses

and lengths. The representation of the measured results in

diagram form would exceed the bounds of this paper, so that

here only a capsule-form summary of the results can be given:

The best possible agreement for different cross

sectional shapes results with equal cross sectional

surface.

Agreement with theory is very good for the longest

(£/X = 8) circular cylinders of all thicknesses for

both directions of polarization; maxima and minima

occur at the same scattering angles and have nearly

the same values.

9
° The longest cylinders with non-circular cross

sections still have good agreement, though, of

course, the maxima and minima are less vivid,

through the averaging over various orientations.

Agreement becomes worse with decreasing length,

especially for greater thicknesses. If the bodies

attain isometric dimensions (length = thickness)

,

a resemblance can be recognized only for scattering

angles e < 90°.

5. CONCLUSIONS

Based on measurements performed at this time, the consequence appears that calculations with the Mie theory cannot

be performed carelessly, when the particles in question are

not really spherical. Only small roughnesses in spheres did

not have significant influence on the scattering diagram.

With all other body shapes, aggreement with the Mie theory

could 'be determined only in the range of forward scattering.

The assertions refer in the first place only to nearly

pure dielectric bodies. Investigations concerning the shape

dependence of scattered radiation with strongly absorbing

materials are in preparation. Furthermore, a closer investigation must be made concerning which body shapes still entail

increased back scattering. And finally, another interesting

measurement problem is represented by nonhomogeneous bodies,

for example loose conglomerates of materials.

6. REFERENCES

[1] Kerker, M. , The Scattering of Light and Other Electromagnetic Radiation, Academic Press, New York (1969).

[2] Zerull, R. , Microwave Analogy Experiments for Light

Scattering from Dust Particles, BMFT-FB W73-18 (1973)

.

[3] Hulst, H. C. van de , Light Scattering by Small

Particles, John Wiley, New York (1957).

USCOMM-NBS-DC

10
Geometry of a Scattering Proc

Incident Wave

Direction of Polarization

Scattering Body

Direction of Polarization

Scattered Wave

Observer

ii

0° 90° 180°

Figure 2. Rayleigh Scattering

Figure 1.

1.

2.

3.

4.

5.

6.

11
Figure 3. Geometric Optics

1. RAY 1

Figure 4. Microwave Scattering System

12
1) 5 ) Stabilisier- 18

)

Sender gera t 4f=30Mhz Hi 1 fsoszi 1 lator 1 1 f0

- 35GHz

2)TE

8)

N

EinwegleUung

\

Einwegleitunp

Diodenmi scher I 6)

7)

FREOUENZtlESSUNG Mikro- 10 ) Frequenzmesser Diode 9) amperemeter

22)

Hilfsoszillator II

20)

v

Dampfungsglied

24)

21)Dioden-|| sel .Vorverstarker Mul tipl i zierer 11) LEISTUtiGSf-ESSUNG miscner 11

m W

12)

KOMPENSATIONSLEITUNG 13) 14)

Phasenschieber Dampfungsql led f =0

A

1 5 ) Empfanqshorn

30 MHz X

25) selekt.Verstarker 1 KHz

26) Gleichr ichter

Sendehorn

27)

Schrittmotor- 16 ) mag. T ansteuerung

28)

Zahler integrator 29)

144

Wei lensumpf

/

17)

/

Digital voltmeter 3 0 )

Lochstrei fen stanzer 31 )

L

Streukbrper

Figure 5. Principal Circuit Diagram of the

Microwave Scattering System (See Key on

next page)
KEY (to Figure 5)

11 . ixa.nsiTiiL.Tiei 17 . Termination

Z . i so lator 1 o . Auxiliary Oscillator I

J . Transmission Horn 19 . Isolator

A DCauter C a 4- 4- ^"v~ l <r T~) /--J » r ing DOQy z U . Attenuator

5. Stabilizing Device 21. Diode Mixer II

0 . Diode Mixer I 22 . Auxiliary Oscillator II

-7

8.

Frequency Measurement

Frequency Meter

23

.

Selective Preamplifier

30 MHz

9. Diode 24. Multiplier

10. Mocroampere Meter 25. Selective Amplifier

1 KHz

11. Fower Measurement ZD. Rectifier

.1 z . f"1 C

/-"\rn Ull IJJfc: r*»o n1 1 co ^a

^"LiUIl 1 T*i Jjlllc T l no Z / . Stepping Motor Control

1 J . rfiase ofiiiter T O Z O . Counter

14. Attenuator 29. Integrator

15. Receiving Horn 30. Digital Voltmeter

16. Magic T 31. Paper Tape Punch

14
Figure 6. Part of the Measured Scattering Bodies

Figure 7. Scattering Behavior for a Polydisperse Mixture

of Cubes Compared to Spheres

15
100.

1.91 a oCs 5 87

i

• • • 6 Cubes

Polydisperse Mixture (MIE)

6 Spheres

k <

m« 1.574- 0.006 i

90< e

50

-50

-100.

?<•'.)

180 e 90* 0- 180'

Figure 8. Scattering Behavior for a Polydisperse

Mixture of "Smaller" Cubes Compared to Spheres

o*

too

5 87 sofa 17 79

6 Cubes

Polydisperse MixturiMIE

5^> 6 Spheres

i 90s

-50

-100. 180°

Figure 9. Scattering Behavior for a Polydisperse

Mixture of "Larger" Cubes Compared to Spheres

16
Figure 11. Scattering Behavior for a Polydisperse Mixture

of Convex and Concave Bodies Compared to Spheres

17
l*»A (REV. 7-73)

U .S. DEPT. OF COMM.

did i inr d APHir data

SHEET

1. PUBLICATION OR REPORT NO.

NBSIR 76-1031

[no.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Shape Dependence of Light-Scattering Behavior

of Dust Particles

5. Publication Date June 1976

6. Performing Organization Code

7. AUTHOR(S)

R. Zerull

o. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 4928677

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

same as No. 9

13. Type of Report & Period Covered

Final Report

1 4 • o n s or i ii £ A ^> (.* n c y ( - o d c*

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) .

The most important characteristic which determines the lightscattering behavior of particles is their size distribution,

their concentration, their shape, and their material composition.

This paper concerns itself with the measurement of the effects

of shape on light-scattering behavior. Only a few shapes have

been appropriately modeled and if the shape dependence can be

determined, the remaining characteristics pose no special difficulties .

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons ) ^ -. jj_ i

• i_ j_ . . ,„ • j_t_ Aerosols; dusts; light-scattering; Mie theory;

particles; Rayleigh scattering.

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