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CHEMICAL SYSTEMS LABORATORY CONTRACTOR REPORT

ARCSL-CR-82016

EXTINCTION BY RANDOMLY ORIENTED,AXISYMMETRIC PARTICLES

"by

Ru T. WangDonald W. Schuerman

l June 1982

Space Astronomy LaboratoryUniversity of Florida1810 N. W. 6th Street

Gainesville, Florida 32601

RETURN TOTECHNICAL LIBRARY

CHEMICAL SYSTEMS LABORATORY ueS~~BLDG. E3330 ,

LAberdeen Proving Ground, Maryland 2101,0

~ ~~N . .. .......... . . fo --- p-ublmm m m i c rel ease;ml disti b t o uni mi ted I. I I

DISCLAIMER

The views, opinions, and/or findings contained in this report are those

of the authors and should not be construed as an official Department of the

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SECURITY CLASSIFICATION OF THIS PAGE WhMen Date Entered)__

REPORT DOCUMENTATION PAGE BORED CsORMuTINORs

i. REPORtT NUMBER L2. GOVT ACCESSION NO, ). RECIPIENT'S CATALOG NUMBER

ARCSL-CR-820164. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED

Final, January 28, 1981EXTINCTION BY RANDOMLY ORIENTED, through August 25, 1981

AXISYMMETRIC PARTICLES S. PERFORMING ORG. REPORT NUMBER

7. AUTHOR(q) S. CONTRACT OR GRANT NUMBER('e)

Ru T. Wang DAAK-11-81-M-O010Donald W. Schuerman

S. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASK

Space Astronomy Laboratory AREA A WORK UNIT NUMBERS

University of florida1810 NW 6th Street 1L161102A71A-DGainesville. FL 32601

II. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE

Commander/Director, Chemical Systems Laboratory June 1982Attn: DRDAR-CLJ-R 13. NUMBER Of PAGES

Aberdeen Proving Ground, MD 21010 2114. MONITORING AGENCY NAME & AODRESS(It different from Controlling Office) IS. SECURITY CLASS. (of tile report)

Commander/Director, Chemical Systems Laboratory UNCLASSIFIEDAttn: DRDAR-CLB-PS (Dr. E. Stuebing) 1Sa. DIECLASSIFICATION/DOWNGRADING

Aberdeen Proving Ground, MD 21010 SCHEDULE N/A

IS. DISTRIBUTION STATEMENT (of thli Report)

Approved for public release; distribution unlimited.

17. DISTRIBUTION STATEMENT (of the abtract entered in Block 20, if diflerent from Report)

IS. SUPPLEMENTARY NOTES

This study was sponsored by the Army Smoke Research Program, Chemical SystemsLaboratory, Aberdeen Proving Ground, MD

Contract Project Officer: Dr. E. Stuebing, DRDAR-CLB-PS, (301) 671-3089

19. KEY WORDS (Continue on reverae side It necesarey and Identify by block number)

ExtinctionNonspherical particulates

20. ANSTRACT CmtC an; reverse "%b It necey and ideitify by block nuawber)

The extinction, averaged over random particle orientations, is presented foreach of 49 axisymmetric particles. These 2:1 prolate and oblate spheroids, 4:1cylinders and disks, and 4:1 prolate and oblate spheroids have a variety ofrefractive indexes (m). Most results are from direct microwave analog measure-ments. Some were calculated according to the spheroid theory of Asano andYamamoto (1975). The 49 extinctions are compared with those calculated by Asanand Sato (1980) for spheroids with m = 1.33 and aspect ratios of 2:1, 3:1, and5:1. *Salient features of the composite graph CEXT/G 1s. phase-shift parameter

AM dcr-Lcca whn-.*ere.DOD I Fm 147n EDITION OF 1 NOV 6s IS ODSOLETE

SECUmITY CLAS"IFICATION OF THIS PAGE (Wlhen Data En•{e.ed)

PREFACE

The work performed under Contract No. OAAK-11-81-M-O010 was authorized

under Project No. 1L161102A71A, SA-D, Aerosol Obscuration Science. The work

was performed from January through August 1981.

The use of trade names in this report does not constitute an official

endorsement or approval of the use of such commercial hardware or software.

This report may not be cited for purposes of advertisement.

Reproduction of this document in whole or in part is prohibited except

with permission of the Commander/Director, Chemical Systems Laboratory,

Attn: DRDAR-CLJ-R, Aberdeen Proving Ground, Maryland 21010. However, the

Defense Technical Information Center is authorized to reproduce the document

for United States Government purposes.

ACKNOWLEDGMENTS

This work was funded by the U. S. Army Chemical Systems Laboratory and

the U. S. Army Research Office.

2

TABLE OF CONTENTS

Page

INTRODUCTION 5DEFINITIONS OF EXTINCTION EFFICIENCY 5

TARGET PARAMETERS 6

AVERAGING THE 0=0 SCATTERING QUANTITIES OVER RANDOM PARTICLEORIENTATIONS 10

RESULTS AND DISCUSSION 13

SUMMARY 16REFERENCES 19

LIST OF TABLES

Table #

1 Microwave Target Parameters and Extinction Efficiencies,Averaged Over Random Particle Orientations, for2:1 Spheroids

2 Target Parameters and Extinction Efficiencies, AveragedOver Random Particle Orientations, for AxisymmetricParticles of Aspect Ratio 4:1 9

LIST OF FIGURES

Figure #

1 Target-Orientation Angles (x,i), Scattering Angle (e),and the Geometry of Scattering 11

2A & 2B P,Q Plots of a 4:1 Circular Cylinder (A) and 4:1Circular Disk (B) 12

3 QEXT,V va' pV Plots for 49 Axisymmetric Particles 154A Theoretical Extinction Curves for Randomly Oriented

Oblate Spheroids 17

4B Theoretical Extinction Curves for Randomly OrientedProlate Spheroids 18

3

EXTINCTION BY RANDOMLY ORIENTED, AXISYMMETRIC PARTICLES

INTRODUCTION

The only experimental technique that permits systematic studies of

single-particle extinction is the microwave analog method. The particle

analog, a microwave target, can be arbitrarily oriented with respect to theincident beam so that E;XT, the extinction cross section averaged over a dis-

tribution of particle orientations, can be obtained as the (weighted) arith-

metic mean of CEXT, the orientation dependent, single-particle extinction.

In a previous paper (Wang and Greenberg, 1978), the orientation dependence

of CEXT for 25 spheroids of aspect ratio 2:1 was presented in the form of P,Q

plots (defined in a later section). In this report, the average extinction

efficiency, ýE`XT = C-xET/G (G = an appropriate geometric cross section), for

each spheroid is evaluated for a random distribution of particle orientations.To increase this unique and fundamental data base, 24 similarly averaged

extinction efficiencies recently obtained by Schuerman et aZ. (1981) are

included in the present discussion. The additional results were obtained by

the microwave method and by the spheroid theory of Asano and Yamamoto (1975).They correspond to eight 2:1 spheroids (measured results, two of them also

computed), four 4:1 disks (measured), four 4:1 cylinders (measured) and eight

4:1 spheroids (computed). All particles have axial symmetry, which facili-

tates the evaluation of CEXT. The effects of particle size, and refractive

index on CEXT are best shown by plotting EQxT against the phase-shift parameter

of each particle. These plots are compared to extinction curves from Mie

theory and to recent theoretical results of Asano and Sato (1980).

DEFINITIONS OF EXTINCTION EFFICIENCY

There are a number of ways in which the extinction cross section can be

normalized to define the "extinction efficiency." In most of our former pub-

lications, the circular geometric cross section perpendicular to the rotationaxis of a particle was taken as the normalization area. This simple definition

provides a clear transition to experimental results of cylindrical particles.

As theoretical methods became available for more complex particles and for the

taking of averages over particle orientation, two more size parameters, and

5

hence their normalized cross sections, were introduced (Greenberg et al., 1961;Wang et al., 1977; Wang and Greenberg, 1978; Asano and Sato, 1980). They are

the volume-equivalent size parameter xV = 2vav/x and the surface-area-equivalentsize parameter xS = 2aSs/A. The aV and as are the radii of spheres having re-

spectively the same volume and the same surface area as the nonspherical parti-cle. The random average of the projected area of any convex particle is equalto 1/4 of its total surface area (van de Hulst, 1957), or equivalently, to the

2geometrical cross section Gs(=ras) of the equal-surface-area sphere. Gs isoften used for normalization, and the resulting ýE-XT is denoted by QEXTS Ifinstead, the geometric cross section GV of the equal-volume sphere is used, it

is denoted by QEXT,V" These two extinction efficiencies are obviously related

by:

GSQExT,S = GvQExT,V CEXT. (1)

The often raised question, "what is the most appropriate size parameter to

describe the extinction produced by an arbitrarily oriented, nonspherical par-

ticle?" will remain as the subject of future study. We simply present two ways

(equation 1) of representing the effect of particle size on extinction and pointout that, at least for the size/shape range investigated here, more straightfor-

ward yet interesting extinction pictures are visualized if one chooses GV. This

selection has the further advantage of well describing lossy particles in theRayleigh region where the extinction is primarily proportional to the particle

volume.

TARGET PARAMETERS

Table 1 shows the target parameters as well as the TEXT' for 33 spheroidal

ar.,log particles of aspect ratio 2:1. The first 15 microwave targets describedin that list were molded out of expandable polystyrene. In the next 10, the

polystyrene was mixed with 2.5% carbon dust to introduce absorption. The re-fractive indexes of these 25 particles resemble that of water or dirty ice in

the optical spectrum. P,Q plots which display the subtle orientation dependence

of extinction of these 25 particles were included in a former report (Wang and

Greenberg, 1978) and provided the data base from which the QEXT's were calcu-

lated. The last eight spheroids in table 1 were machined from an acrylic mate-

rial (lucite) and have m = 1.61 - iO.004. They simulate silicate particles in

6

c a

u 0

0r 0. FL C C'J (% 3 CJ (% C4' C4 C'1 C") C4 C4) CV.x (4- .4.)3to 4- Uaa

4)04 00 3% CD C £- I 6 d

it~ U ) S.I

Chru cl. C O c(%c; 4 0 ; % C.;34 ' C4') 40 a

>e~ c 4) SLA CV C 0

0 BUS. a-It CU 0) v'1 -4 L~1C 'Ja-I CDJ InA IC. CV) CV) C") 0% 0% W4

In. aý m wS - qt n (1W c4) 4-) a<4 4e

cC,.S-> I I0L 0.)4 --0 aA

4- v,- x a0N 40uI.1V 4 Ai0 N )CJU)

xu %-, Ol ff.0) C" ýr. 0 .4 aCV) r- L i -W 0 aD CV-) U -) Ln LAI I

4-) S 4-0. a ac0 4-..U r_ 0

O- .. 4 Ia

4-) .Y 00..- r- en- co. I~. LA CO COi 40 0~ qd* 1 00 L A ~ CV') N-x - 4- (n CV) ko 0)W r4% I CJ 4m C '.) m Lo 0 I v' LAto LA U-)

OC% c C 00 C C)I 0'0 0l r-4 -4 In. Iv- m'. to. 00 V 5''C C") CV) I

M -- C" S I- C43 4 4 L 4 C 1

eo IVo -4 0,4C'4- ~ 4 C =>

4-.S AS ý ~ d C) - r4 r - N f mC LAr I'l qw ) IOXCD OU r to) V) co -4, CY J N-) aLA I 0)0r- r I 0) V.A aL 4 N-c LA % I

to Cal ..- CO N-" ffLA£ý:c OLALAI: 40CO AC'0- '-4 .0 C'.' r-'34. V) ~ L CJ CV ' ~ ~

00~ ~ I~-44- ato4-) a- *4-Z l = aI

InD ic ,CV)O(A I Iwaa a- _ 1D0) ON- 0)zr CD t .'0) CV) -)CO* %0CC) N -4 C)

S-% mk CDS 0fLa4 - 0Ln qz o)CVr)N-ý4 lj o0 0) 0 1Lv')i -:9r- 4:C CO ) ) A4 a A O -4 1--L O C 4 N-

dU) rz-)f (A) 0 N-0Q1I" A N- 0 I A L> U to +ar- -;:s

4. X( 0. 4- I4J'S-- 4-'J3 R(U 4- C ' a_ C) m C \ ) 0 o C a 0 - l 4 C

C >3 4) 0 1 ý1 CO 00 ON 0) I k 0 40i 0 ON I LO - CO 14 C'. ) 0 IC. S. , r-24 14'00 ) C C) C CO oi '. 9- LA C V!N C'.9 s-i C'. 40du to ~ 0U cc N- -4 0~ IN- N-l 1~ 0 -4 COO C .' 'l t I

0 >.r- toC.C)4C0I\3 V~~

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Uu =O~ CgOF 0Y V ~ ) CO V) 034 CO CJ Ill ' 0l ) aLC) V)I 0) V) .CV) I4- S tjC) l C CO 00 L I C" C)O C'.' D 0) CDL C)0 CD C)J

tu IfI CV) C) (D a 4IC. V 1J - 4 C.' C.04-J() C)C )C )C I C) CIC )C )C D 0 1 a

0m IW C -aS

r-40 CV) CV) -4 - 1 C J VJ CJIMC) CV) CV)IL LAM A L aA L A L A.04-S- ~00 0 30 00 3 00 0

dU 3 I 0 0 0 0 0 0 0 0 3 0 0 0 O 4-

cm c 4 C 4p V .;C ý C I 6v w; C%1

4) Cl. CY'l w (1%I LO IY- a% OWJ M 0% 1C 00 00 V- D 0 %0 ?ý -4

fl n 0 n rI qr m c rI atI ~ - 4C)r.0

OD to 9 a IJ ~ ý o q l C W I LACD PýC00 to Ln ar10 0 c tC - a 09 1V40 . o O

Iý 64 l - 6 C c i ; V f ;U ; 0 l

Q)

-4% 4 Cr I o ON 0 %to I ONI m %

S0 0

.- C(L AO II LL4C JJ ;'~ 1'~ C0) M~ .J m- ~ '. % 'igV CV) e.J IC~ CJ O C %J 4J~x ) 4 D Ln r I ONO In IC~ c .

090

4-))

0iI0 . 0 A 0- r-) 1o %0 4 Ln LA (%J 10 00 ) -4' %0 10 02 LA gr t

C -0%C o 8 qr n m c)qr 4)ý 0% 0) CIQI m 0CD0-) V) m 6ým m L tI" C - 0 "

4CJ 4-6&- 0~66

S-04 v ~ 0) CD 0 C r-_I C) ON LAc 3 crrýCir CD r6J 0-4 O NCJ0 00 c4

000 C\J4' LA 1%. 11 ICý Cý LA L4 00) me)ýL4A64) r) ~ L> )6

4ý 14 6l I6ý1 1, C; C I 0ý C li I; I

LOL nLOL OL 164C~0 2lCO06CD0 C) CD L C') C' >ý1.. C'. CD 0 ) LA C)m 0 CD CD C)S I % C'J C60 CD C0CDC ) C) 4-

cE _ý 6' c) 1 C- 0!- 60 Cý LAO I O ý LA -40 LA 60 C'J C C; 0

CD CJ CJ C) C) CDb C)- C'. a)I'1 C) ~ -MC M C6 M6V O O M- r4 ýfI - 4 l - 41

0ý Ci "I CaC i C!C ý1 9" c

r-i vLA 6% -L r-4 CO 60 2 r -4 r-4 r-4 -4 r-I CO-I C') r- -4 v-4 ý4 r-

Table 2. Target Parameters and Extinction Efficiencies, AveragedOver Random Particle Orientations, for

Axisymmetric Particles of Aspect Ratio 4:1

a - semi-axis perpendicular *, the axis of rotation; b = semi-axis or ½ lengthalong the rotation axis; - = 2wa/X; X = 3.1835 cm; m =m' - im" = complexrefractive index = 1.61 - iO.004 for all particles; p = 2x(m'-l); QT = extinc-tion efficiency averaged over random orientations - three significant figuresfor experimental values and four for theoretical. Quantities referring to theradius or geometric cross section of equal-az'faae-area and equaZ-voilw spheresare suffitel by S and V. respectively.

Description a(cm) b(cm) xS PS QEXT,S Xv PV QEXT,V

Cylinder 0.785 3.141 3.288 4.011 2.71 2.816 3.436 3.69

Cylinder 0.964 3.856 4.036 4.924 3.09 3.457 4.218 4.21

Cylinder 1.204 4.818 5.043 6.152 3.80 4.320 5.270 5.18

Cylinder 1.457 5.828 6.100 7.442 3.67 5.225 6.374 5.00

Prolate Spheroid 0.928 3.712 3.288 4.011 2.817 2.907 3.546 3.604




Oblate Spheroid 2.213 0.553 3.288 4.011 2.385 2.752 3.357 3.404

Oblate Spheroid 2.717 0.679 4.036 4.924 2.721 3.378 4.121 3.884

Oblate Spheroid 3.394 0.849 5.043 6.152 2.732 4.220 5.148 3.902

Oblate Spheroid 4.106 1.026 6.100 7.442 2.944 5.105 6.228 4.203

Disk 1.924 0.481 3.288 4.011 2.47 2.738 3.340 3.56

Disk 2.361 0.590 4.036 4.924 2.89 3.360 4.099 4.17

Disk 2.950 0.738 5.043 6.152 2.76 4.199 5.123 3.98

Disk 3.569 0.892 6.100 7.442 2.39 5.080 6.198 3.45

9

the optical region. Their extinction efficiencies were recently measured or,

in the two cases denoted by asterisks, computed by Schuerman et at. (1981).The averaged extinction efficiencies for 16 additional axisynmnetric

particles are listed in table 2, together with their target parameters.

These four cylinders, four disks, four prolate spheroids, and four oblate

spheroids have the same aspect ratio (4:1) and the same index of refraction

(1.61 - iO.004). The cylinder and disk data are the microwave results; the

spheroid data are from theoretical computations (Schuerman et al., 1981).

These particles were added to include more elongated/flattened particles, as

well as to increase the range of the phase shift parameter (pv). These 16

particles correspond to the range 3.3 < pV < 6.6 compared to 0.8 < PV < 6.0

for the 2:1 particles. In the latter group, the higher p. values are sparsely

populated.

AVERAGING THE 0=0 SCATTERING QUANTITIESOVER RANDOM PARTICLE ORIENTATIONS

CT is a simple average of orientation-dependent extinctions, but measuring

the single-particle extinction for each member of a large sample of particle

orientations is a time consuming enterprise. For particles with an axis of sym-

metry, an equivalent average can be obtained in a much simplified manner (Wang

and Greenberg, 1978). The symmetry axis needs only be swept through 900 from

the incident f 0 direction in two mutually orthogonal planes, the k-E plane and

and the k-H plane, that contain the tot 0 and the to, ao0vectors of the incident

wave, respectively (see figure 1). At any other arbitrary particle orientation

ix, qo), where x is the tilt angle of the axis from t and * is the azimuth angle

around to, all matrix elements of the e=O complex scattering amplitude (van de

Hulst, 1957) are linear compositions of those obtained in these two orthogonal

planes (Wang, 1968):

S(* = SE(X) COS2* + SH (Xsný+ i [S(X)COS2* + S ( x)sin2j

S2(X,) = S E(x)sin2E + SH(x)Cos2 + i E (x)sin2 + S(x)COS2* , (2)

S3(X,0) = S 4 (Xi,0)= [SH(x)-SE(x)] cosipsinýp + i FSH(x)-SE(x)] cosisiRnj ,

10

where SR(x)and SI(x) are respectively the real and imaginary part of the

complex, e=O scattering amplitude when the symmetry axis is in the k-E plane,

tilted by x from o SH(x) and SH(x) are those in the k-H plane.

X

Target Symmetry

Axis

E-. k

E, / r .

0

zHo

Figure 1. Target-Orientation Angles (x, *), Scattering Angle (8),and the Geometry of Scattering.

The extinction cross section CEXT(X, i) at each orientation follows from

equations (2) and the Optical Theorem:

4• ~ ~ 4•Hx)sin2,CEXT k2 Re {Si(xU)M = SExCOS21 + IRnR

(3)= CExT(X)COS2 + CHxT(x)sin2*,

Here again superscripts E and H denote whether the symmetry axis is in the k-E

or k-H plane. CEXT, the average of CEXT(X,*), is then obtained as

CEXT =iJ Cfd 1 EEXT(X)+CEXT(X)H sinxdx • (4)

11

4:1 CYLINDER , P 4:1 DISC

kk

Jo,

30

E to

-5 -5!

Figures 2A and 2B. P,Q Plots of a 4:1 Circular Cylinder (A)and 4:1 Circular Disk (B).

The two P,Q plots display the target orientation dependence (x, in deg.) of

the complex forward-scattering amplitude S(O) for two axially symmetric par-

ticles. The two curves in each plot are generated by sweeping the particle

axis through 900 from the incident direction t0(x=0 0) toward the to and A 0

directions in two orthogonal planes, the k-E and the k-H plane of the incident

wave, respectively. A vector drawn from the coordinate origin to any point

along the curve gives S(O) at that particle orientation, while the projection

of the same vector onto the calibrated Q-axis yields the extinction efficiency

QEXT,V = CEXT/la . The magnitude of the forward-scattering amplitude, IS(0)I,at any orientation can be determined by comparing the length of its vector to

that Of S(0)H = S(1-'w) whose magnitude is shown in each graph. The target

parameters and the average extinction efficiencies are respectively: (figure

2A) xV = kav = 4.320, m = 1.61-iO.004, QEXT,V = 5.18; (figure 2B) xV = kaV =

4.199, m = 1.61-iO.004, TEXTV = 3.98.

12

Two P,Q plots, obtained by the microwave technique, are shown in figures

2A and 2B. They respectively refer to the third cylinder and the third disk

listed in table 2. Each P,Q plot is a cartesian recording of the complex for-

ward scattering amplitude S(x, *) as a function of particle orientation. The

particle axis is swept from the incident to direction (x=O) to the incident toor Af0 directions (x=-/ 2 ) in the k-E plane (j-=0) and in the k-H plane (*=w/2)

to generate the double curve in each figure. A vector drawn from the coordi-

nate origin to any point on the curves represents S,(x,O or n/2). Its abso-

lute magnitude can be found by comparing the length of this vector with that of

IS(O))H = ISi(j'j)I shown in each figure. The tilt of the S, vector from the

P-axis is the phase-shift *(O) of the e=O scattered wave at this particle ori-

entation, and the projection of this vector onto the Q-axis gives the extinc-

tion efficiency. Both the P and Q axes are calibrated in units of QEXTV for

the particle under investigation. (see also Wang, 1980)

The numerical integration over x for the evaluation of the random average

is accomplished by Simpson's rule with ax = 50 in all experimental cases. The

P,Q plots for cylinders and disks contain curves- rich in loops and cusps, but

it is our experience that 50 increments in x produce errors which are small

compared to other experimental errors. Most of the older spheroid data,

obtained before the target orientation process was automated (Schuerman et aZ.,

1981), were taken with AX = 100 (AX = 300 for very small particles). The larger

increments were mandated by the slower, manual operation of target orientating;

the data had to be obtained before susceptible null-drift (Wang, 1968) occurred.

In such cases, the missing CEXT data points were filled in by a third order

Aitken-Lagrange interpolation technique (Todd, 1967).

RESULTS AND DISCUSSION

It is impossible to combine the three factors of size, shape, and index

of refraction into a single, independent variable that uniquely describes the

full range of resonant extinction phenomena. This impossibility prevails even

when the shape factor is degenerate, as in the case of spheres. Nevertheless,

the use of a single independent variable is a useful, though approximate, method

of describing salient features of the extinction curve. The first to define

such a variable - the phase-shift parameter pV = 2xV(m-1) - was van de Hulst

(1946, 1957) in his anomalous diffraction theory of extinction. The undeviated

but phase-shifted rays passing through the particle form a modified wave-front

13

in the shadow of the particle which interferes with the incident ray to produceresonance phenomena in extinction. The quantity pV is the phase shift suffered

by the diametrically transmitted ray with respect to the unperturbed incident

ray. This approximation theory is known to predict the general futures of

QEXT,V '8. PV curves. The approximation does yield some errors: (a) allspheres possessing the same pV have identical QEXTV' (b) there are no minorripples in the extinction curve, (c) the value of QEXT may have an error of up

to 30% near the resonance peaks, and (d) the shift in peak extinction is under-estimated as the particle absorption increases. While these numerical deficien-

cies can now be easily removed by employing rigorous Mie solutions instead of

the original approximation formula, the essential physics of the extinction phe-nomena is still governed by the single parameter, pV. Its use has been extended

to cases of nonspheres on numerous occasions (Greenberg, 1960, 1968; Greenberg,et aZ., 1961, 1963, 1967, 1971; Wang 1980), and that practice will be continued

here.The dependence of QEXTV on PV for the 49 axisymmetric particles listed in

tables 1 and 2 is plotted in figure 3. Different synmols are used to identify

11 distinct refractive-index and target-shape groups. A nunber of conspicuous

features appear on this plot:

(1) Randomly-oriented, axisymmetric particles do exhibit resonance

extinction with respect to variations in PV, with the largest m = 1.27,2:1 prolate spheroid being the sole exception.

(2) The first major resonance is noticeably broadened. For spheroids,

the greater the aspect ratio, the broader the peak; sufficient data

do not yet exist to test this trend for other shapes.

(3) For the 2:1 spheroids, the magnitude and location of the resonance

are not much different from those predicted by tie theory for spheres

possessing the same refractive index if the minor ripples for the

latter are ignored. The prolate peak is somewhat higher and shifted

toward higher pV"(4) Beyond the first major resonance, all particles obscure the incident

light more efficiently than spheres of the same pV' a feature also

observed for rough particles (Wang, 1980).

(5) Beyond the first major resonance for spheres, the extinction is

strongly dependent on the aspect ratio as well as on shape. Thegreater the aspect ratio, the larger the QEXTV and the larger is

14

A

5 P

4m=I.61-iO.004

3 +

m=1.33-iO.0

•• m=1.33-iO.O

5 6 7 8

Figure 3. QEXT,V ve. p. Plots for 49 Axisymmetric Particles.

2:1 spheroids with low refractive indexes Particles with m = 1.61-iO.004o mi1.11-iO.003 prolate spheroids (silicate like)0 mfl.27-iO.005 prolate spheroids A 4:1 cylinders- mn=1.37-iO.005 prolate spheroids P 4:1 prolate spheroids0 mal.33-iO.05 prolate spheroids + 2:1 prolate spheroids* m=1.33-iO.05 oblate spheroids X 2:1 oblate spheroids

The continuous curves are for spheres. 0 4:1 oblate spheroidsV 4:1 disks

the PV at which the extinction peaks. It is curious that the 4:1

oblate spheroids produce a shoulder in extinction near pV = 4.5

which is absent for the 4:1 disks.

(6) For 4:1 particles, prolates (elongated particles) dim the incident

light more efficiently than oblates (flattened particles) beyond

the resonance in the range 3.5 < PV < 6.3.

(7) From PV = 4 to PV = 0, the difference in extinction due to shape

gradually diminishes and the particle's volume becomes the most

significant factor in extinction.

15

(8) The 2:1 prolate spheroids with m = 1.11 - iO.003 have the smallest

PV for their given sizes. These particles behave like absorbing.spheres with m = 1.33 - iO.05, a phenomenon also observed for rough

particles of similar refractive index (Wang, 1980).

(9) Although some uncertainties in the refractive index (m = 1.33 - iO.05)

of the small-sized 2:1 spheroids can result in errors in their PVscale of up to AV = 0.3, these small, absorbing spheroids seem to

behave also like absorbing spheres of higher Relml and Imrml.

Meanwhile, theoretical results on scattering by randomly oriented

spheroidal particles of various aspect ratios have been published by Asano and

Sato (1980). They plotted QEXT, V vs. xV for water-like spheroids, m = 1.33 -

iO.0, with aspect ratios of 1:1, 2:1, 3:1, and 5:1. Their results for oblate

(figure 4A) and prolate (figure 4B) spheroids were cast in the same format as

our figure 3 by our reading of numerical values from their graphs, converting

their Xv s into Pv'S, and plotting their results on a similar scale. A con-

tinuous curve for a single sphere and a discrete plot for size-dispersed

(Hansen-Travis distribution; see references in Asano and Sato, 1980) spheres

have been added to both figures 4A and 4B. Those spheres have m = 1.33 - iO.O.The overlaying of figure 4A and/or 48 on figure 3 permits a comparison between

the theory and experiment. The above mentioned features (1) through (7) in

figure 3 are also present in figure 4A-4B, notwithstanding the absence of 4:1

spheroids in the latter. The magnitudes and positions of extinction peaksagree in form with those in figure 3 including the shoulder at PV = 4.5 for5:1 oblate spheroids. The numerical differences in magnitude are due to

detailed differences in refractive index, shape, and size. Ripples, a charac-

teristic of spherical particles or smooth particles in fixed orientation, are

not present in these extinction curves even though pronounced ripples may appear

for particles of higher aspect ratios or refractive indexes (Barber et al.,

1982).

SUMMARY

Tentative conclusions derived from this research are:

(1) Extinction by nonspherical particles is best discussed in terms of

their volume-equivalent phase-shift parameters, pV"

(2) Randomly oriented, axisymmetric particles distinctly differ from

spheres in their extinction when pV > 4 (i.e., beyond the first

16

00 ) 0 4.)04- X M 4.) C U C

.0 0 a. 0 0 w 04A 4A L ) r- A4- o 00 w 10 00 A- . 4.) C W U >1

4- -

1/*.0 0 cC/) 4-) 4-) m Li- =C U

-\- F- - ' 4- 0 0_ CA. 4u-0) U) 0.- U)c 04- C 0 0

0 4 .) V e o M 0 O L40 - I SC-~ W C 4-

0) 0

_ _ _ _ _ _ _ U - * t ) _V

C) a m 4- .9- 9-o>_ C; 4- 0>C~0.- 4 CA 'a 4) 00

9 ~ U 10 wCCOP A -C4 %- 4- 4 .En 00 4w 00 4j I

4 0 === COM 4- S- 4-4 W W )

o o 0 C+. 0 0)4

C4-. -0 0

IA~0 U)J> 0. ) . > 1S9- C4-~ .-

4) ~ ~ U 4J 4J M

=U 1- O 00 (UN0 04 0 S.0 S~- M

4. X U.0 W.)000 CL 0 C- 4) (0

40 4) r-) U ) CA

0 U) r_ go 4) ACDV 0 S( c

0 E 1*0- In co .0__ _ __ _ _ __ _ __ _. 0 c0 I1 r- 4 -)

r- U 4JU<- -- 0 4

417W J S

4'

/ 4) CLS- 0

Co 4X)

x_ +

X F4~- 4A410

(D 0-C

CL

K4- to~4

_____ ____4-)'- - C)(0 4-)

4)- 4-3

= CL

4-3 0) 4______) 84.)

oo LL

.r.

LL-

18

resonance) and have higher extinction efficiencies per unit volume

than spheres.

(3) For 3 < PV < 6, elongated particles produce more extinction per unit

volume than do flattened ones if both have the same aspect ratio and

refractive index.

(4) Noticeable differences in extinction exist between equally flattened

disks and oblate spheroids; and, in a less conspicuous way, between

a cylinder and a prolate spheroid of the same elongation.

(5) From P< 4 to PV = 0, the effect of shape gradually diminishes as

the particle volume becomes the dominant factor in extinction.

(6) For P< 1.5, low-absorbing nonspheres behave like spheres with

higher absorption.

Although the nunmer of nonspheres in this report is quite limited, lacking

those particles of very large aspect ratio and unusually high refractive indexes,

their extinction may crudely represent that produced by many naturally occurring

parti cul ates.

REFERENCES

Asano, S. and G. Yamamoto, Appl. Opt. 14. 29, 1975.

Asano, S. and M. Sato, Appl. Opt. 19 962, 1980.

Barber, P. W., J. F. Owen, and R. K . Chang, IEEE Trans. Ant. Prop. AP-3O, 168,

1982.

Greenberg, J. M., J. Appi. Phys. 31 82, 1960.

, in "Nebulae and Interstellar Matter," B. M. Middlehurst, and L. H.

Aller, eds., Univ. of Chicago Press, p. 221, 1968.

Greenberg, J. M., N. E. Pedersen, and J. C. Pedersen, J. Appl. Phys. 32

233, 1961.

Greenberg, J. M., A. C. Lind, R. T. Wang, and L. F. Libelo, in "Electromagnetic

Scattering," M. Kerker, ed., Pergamon, New York, p. 123, 1963.

, in "Electromagnetic Scattering," L. Rowell and R. Stein, eds., Gordon

and Breach, New York, p. 3, 1967.

Greenberg, J. M., R. T. Wang, and L. Bangs, Nature, Phys. Sci. 23, 110, 1971.

Schuerman, D. W., R. T. Wang, B. X. S. Gustafson, and R. W. Schaefer, Appl. Opt.

2 4039, 1981.

19

Todd, J., in "Handbook of Phys.," E. U. Condon and H. Odishaw, eds., McGraw

Hill, New York, p. 1-94, 1967.

van de Hulst, H. C., "Thesis U'.-echt," Recherches, Astron. Obs. d'Utrecht,

11, Part I, 1946.

,_ in "Light Scattering by Small Particles," John Wiley & Sons, New York,

1957.

Wang, R. T., Ph.D. thesis, Rensselaer Polytechnic Institute, Troy, New York,

1968.

, in "Light Scattering by Irregularly Shaped Particles," D. W. Schuerman,

ed., Plenum Press, New York, p. 255, 1980.Wang, R. T. and J. M. Greenberg, Final Report, NASA NSG 7353, August 1978.

Want, R. T., R. W. Detenbeck, F. Giovane and J. M. Greenberg, Final Report,

NSF ATM75-15663, June 1977.

20

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