aberd-etc f/g 20/6 extinction measurements-etcfu… · 1l162662a554, smokelobscurant technology....

36
AO-A099 494 ARMY ARMAMENT RESEARCH AND DEVELOPMENT COMMAND ABERD-ETC F/G 20/6 DETERMINATION OF OPTICAL CONSTANTS FROM EXTINCTION MEASUREMENTS-ETCfU) APR 81 M E MILHAM. R H FRICKEL, J F EMRY UNCLASSIFIED ARCSL-TR-81031 SBIE-AD-E41O 396 NL E'WEEEEEE*EE~lll *lflflfllmlllll

Upload: ngongoc

Post on 07-Sep-2018

213 views

Category:

Documents


0 download

TRANSCRIPT

AO-A099 494 ARMY ARMAMENT RESEARCH AND DEVELOPMENT COMMAND ABERD-ETC F/G 20/6DETERMINATION OF OPTICAL CONSTANTS FROM EXTINCTION MEASUREMENTS-ETCfU)APR 81 M E MILHAM. R H FRICKEL, J F EMRY

UNCLASSIFIED ARCSL-TR-81031 SBIE-AD-E41O 396 NLE'WEEEEEE*EE~lll*lflflfllmlllll

11111_L-

MICROCOPY Rl',OLU~ION 111,1 OiAIA

MMIL-

M

-T-7

.1

~ ~

UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE (Ih..n dds BRI-.4_________________

REPORT DOCMENTATION PAGE BEFOR COMPLECTINORM1. REPORT NUmUeR =2 OVT ACCESSION NO: 3. RECIPIENT CATALOG NUNDER

ARCSL-TR-8 1031 'm -74. TITLE (aid Subtfie)&WSTYEORPRTAEIDCVRD

DETERMINATION OF OPTICAL CONSTANTS FROM Technical ReportEXTINCTION MEASUREMENTS April-September 1980

6PERFORMING ORG. REPORT NUMBER

7. AUTHOR(. CONTRACT OR GRANT NUMUER1(s)

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT, TASK

Commander/Director, Chemical Systems Laboratory AREA A WORK UNIT NUMBERS

ATTN: DRDAR-CLB-PS Project IL I62662A554Aberdeen Proving Ground, Maryland 2 10 10

11. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE

Commander/Director, Chemical Systems Laboratory April 1981ATTN: DRDAR-CLJ-R -13. NUMBER OF PACES

Aberdeen Proving Ground, Maryland 21010 3314. MONITORING AGENCY NAME G AOORESS(if diferent haom Contulling Office) IS. SECURITY CL.ASS. (of this report)

UNCLASSIFIED

A~ a, DECLASSIFICATION"OWNGRADING

ISSCH4EDULE NAIS. DISTRIBUTION STATEMENT (at this Report)

Approved for public release; distribution unlimited.

I7. DISTRIBUTION STATEMENT (of A.e abstract nered i block 20, it different Arom Report)

* III. SUPPLEMENTARY NOTES

IS. KEY WORDS (Continue, an rover** side i necessary and lImifify by block number)

Optical constants o-Phosphoric acidParticulate materials Kramers-Kronig analysisAerosols Lorenz-Mie calculationsExtinction data

11L ABSTRACT (amfiou on roer oft nowessa sd Ddmaa by block mbst.)Traditional methods of determining the optical constants of particulate materials by means oftransmission, absorption, and reflectance measurements are known to be inherently inaccurate. Theuse of the Lorenz-Mie formalism to derive the optical constants from extinction data overcomes theproblems associated with the traditional methods; but, as currently practiced, this method hassevere limitations. In this paper, we report an entirely new approach to determining the optical

(Continued on reverse side)

PD I~ 143 (9110 OFI NO 655 OmETEUNCLASSIFIED

SECURITY CLASSIFICATIONI OP THIS PAGE (0bon Date Entered)

NEED

UNCLASSIFIEDMTUEyV LM PIAT1 or TM PAOU(1tm Dae De

20. ABSTRACT (Contd)

constants of aerosols from extinction data. This is an iterative method which uses the Lorenz-Mieformalism in conjunction with the Kramers-Kronig dispersion relations in order to derive theoptical constants of the aerosol material. The theory of the method is developed in detail and isapplied successfully to find the optical constants of an o-phosphoric acid aerosol in the 7- to14-pm infrared. The numerical procedure is shown to introduce an error of less than I percent inthe determination of the o-phosphoric acid optical constants. Limits on n,k and the particle sizedistribution for which the method is valid are indicated.

2 UNCLASSIFIEDSuCURIY CLASSIFICATION Of THIS PAOsIEvh. Data Eaoeed)

- -. ---- ---- - -

PREFACE

The work described in this report was authorized under Project1L162662A554, SmokelObscurant Technology. This work was started In April 1980 andcompleted in September 1980.

The use of trade names in this report does not constitute an officialendorsement 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 exceptwith permission of the Commander/Director, Chemical System Laboratory, ATTN:DRDAR-CLJ-R, Aberdeen Proving Ground, Maryland 21010. However, the Defense

Technical Information Center and the National Technical Information Service areauthorized to reproduce the document for United States Government purposes.

Acknowledgments

The authors express their appreciation to Professor Marvin Querry of theUniversity of Missouri-Kansas City for a critical reading of the manuscript.

Accessicn For

NTIS C- 1&I

DTTC T' +'-,u r'..' r , .•lJrflt i.' LI- :t u

DTICS ELEECTE D.i t r .t..o.JN1 19811 A vail!t.iiity Codes

Av : ! I z:id/orDist :Special

B A

3

CONTENTS

Page

1 INTRODUCTION ............... 7

2 THEORY .............. #.......................o............................ 9

2.1 Computation of n(A 0).... ......... ....... ....................... 92.2 Calculation of k(X) ............................. .................. 02.3 Algorithm for Computing Optical Constants .......................... 12

3 EXPERIMENTAL PROCEDURE AND RESULTS ..................................... 12

4 OPTICAL CONSTANT RESULTS ............................................... 13

5 CONCLUSION ............................................................. 14

LITERATURE CITED............ ....................... 15

APPENDIX, Figures ....... ............................................. 17

DISTRIBUTION LIST. ...... . 0. ................ ........................ 31

a..

DETERMINATION OF OPTICAL CONSTANTS FROM EXTINCTION MEASUREMENTS

1 • INTRODUCTION

The interaction of electrovwgnetic radiation with spherical particles is

described by the well-known Lorenz-Miw formalism.1 3 The optical properties of the

particulate material enter into this formalism by way of the optical constants (n,

k) which are, respectively, the real and imaginary components of the spectral

complex refractive index.

N(X) - n(X) - ik(X) (1)

where X denotes the wavelength. With the advent of modern high-speed computers and

the development of reliable Mie scattering codes,4-6 it has become a commonplace

numerical procedure to predict the extinction produced by an ensemble of sphericalaerosol particles 7-1 1 once the optical constants (n,k) and the particle size

distribution are known. The inverse problem of determining the optical constants

from the Lorenz-Mie formalism when measured values of the spectral extinction and

the particle size distribution are known has proved to be quite intractable; this is

the problem which this paper addresses.

12-14

As noted by several workers, the experimental difficultiesassociated with determining the optical constants by transmission, absorption, and

reflectance measurements performed on small samples of the aerosol material lead tohighly questionable results. A few techniques which avoid these difficulties by

using the Lorenz-Mie equations to invert measurements of particulate optical15 adPuhnproperties to find the optical constants have been reported. Wyatt and Pluchinoet al. 16 have measured the angularly dependent intensity of laser light scattered

from single particles which were suspended in a Millikan oil drop apparatus; the

Lorenz-Mie equations were then used to fit the angular scattering data by

curve-fitting techniques in which (n,k) appear as parameters.

Another approach is to use extinction measurements which areexperimentally simpler than angular scattering measurements, but they have the

disadvantage that the Lorenz-Mie inversions are not unique with respect to (n,k) as

they are with the angular scattering measurements. Janzen 14 has described a

technique for determining the optical constants of a carbon black-water colloid by

using the Mie equations to obtain a least squares fit to measured extinction

spectra. Janzen's technique overcomes many of the difficulties of the traditional

methods, but there are three limitations to his approach: (1) the polydispersity of

the particulate material is not accounted for, (2) the optical dispersion of the

material is not taken into account, and (3) the optical constants which are found by

this technique satisfy the Mie equations, but they are not necessarily the unique(n,k) pair which characterizes the optical behavior of the material. In this paper,

we will describe a method of deriving the optical constants of an aerosolized

material from extinction measurements; this method overcomes the limitations cited

above.

7 HarGUCDM FAG UKAWIW niU=L II,,II 1* tL a k

The extinction coefficient (m2/g) of an aerosol at wavelength, X, isdefined as

ZeC M __ (2)

where

st - optical cross section of the ith particle (m2)

mt - the mass of the ith particle (gm)

and the sum extends over the ensemble of particles contained in the optical path.For a continuous distribution of particles, the expression for the extinctioncoefficient becomes

a = f (z)dH (3)

where

a(z) - extinction coefficient for a particle of size zdM - the mass distribution function of the particles

In order to apply the Lorenz-Mie formalism, each aerosol particle will be consideredto be spherical with an extinction coefficient which is given by

3Q[i(X) ,x]a 0

,24)o 2pD

where

Qe = the efficiency factor for extinctionX =-wD/X, the size parameter

p - the particle density (gm/cms)D - the particle diameter (um)

It is also convenient to define the dimensionless extinction coefficient

a2 - a e P (5)

Dd

The difficulties of using extinction measurements to determine the

optical constants are illustrated in figure A-I.* For a given wavelength, a valueof s may correspond to any (n,k) pair lying on the pertinent aD isopleth;

similarly, for a given particle size distribution, the (n,k) pair corresponding to aparticular value of aD is not unique. However, over a wavelength spectrum, the

values of [n(X), k(X)] are subect to the constraint imposed by the Kramers-Kronig

((K) dispersion relation. In the development which follows, an iterativeprocedure will be described which, after an initial estimate of n(A) over the

wavelength spectrum, employs a simple numerical algorithm to fit the k(X) spectrumto the measured extinction spectrum and the KK dispersion to establish a newestimate of the n(X) spectrum. It will be shown that this procedure will correctlydetermine the optical constants of the airborne material.

2. THEORY

2.1 Computation of n(X0 ).

The Kramers-Kronig relationship between n( o) and the k(A) spectrum isgiven by:

2X2

n( - i +~ . k(X)dXn 0o) +

2 (6)

where P indicates that the Cauchy principal value is to be taken. The integral inequation 6 is to be evaluated over the entire electromagnetic spectrum; and, sincek() is known only over a finite region (Xmin 4 X 4 Xmax) of the spectrum, it is

necessary to extend the k-spectrum beyond the wavelength region where data are knownexperimentally.

The inaccuracies introduced by extending the k-spectrum can be reduced torelative insignificance by employing a subtractive Kramers-Kronig analysis (SKK).Assume that the real part of the refractive index, n(A1), is known at somewavelength, X , and subtract the KK expression for n(X1) from the KK expression for

n(Xo ) in order to obtain the subtractive Kramers-Kronig relationship:19- l

2 ( X2 X2 ) k X d 7

n(X (X) + P f )k(dX (7)0 1 0 (X2 _ X 2) (X2 _ X 2)

The integral is now evaluated by letting k(X) - k(X min) for 0 < X min and k(X)

k(Xinx) for X 4 X • -. In general, these are not good physical approximations

* All figures are in the appendix.

9

for k(.) in the spectral regions where kW.) has not been measured; but, as mentionedpreviously, this approximation vill have an insignificant effect on the resultproduced by the SIR algorithm.

2.2 Calculation of kWX).

In the previous section, it was shown that SKK analysis can be used tocalculate n( 0) once n. 1 ) and k(X) are known. A method of obtaining k(X) from

measurements of the extinction spectrum, a(X), and the particle size distributionwill now be developed. For a continuous distribution of spherical particles, theexpression for the extinction coefficient of a single spherical particle with

diameter, D, (equation 4) may be integrated to find an expression for the extinction

coefficient of the particle enseuble at wavelength X:

a(n,k) - f ao(n,k,D) dM (8)

For this study the mass size distribution was described by the log-normaldistribution function

M e -1I2[1n(DfDm)/Xng 2 dinD (9)g

where

Du M mass median diameter (MMD)a - geometric standard deviationg

It will now be assumed that an estimate of n(X) w no is available from the SKKanalysis; and, therefore, the extinction coefficient depends on k only

a(k) - a(n ,k) (10)

The isopleths of aD, shown in figure A-i, depict the behavior of the integralkernel, a , in the expression for a(n,k) as the size parameter varies. Many of theinteresting features of these isopleths are due to optical resonance phenomena. 10

The resonance due to the first surface polariton mode for X + 0 is located at thepoint C. M (0, v-) and moves according to the equation

22

k- + ( 1 + 6/5 x2)1/2 (11)

to larger values of k as the size parameter increases. Also, the resonances due to

the bulk polariton modes can be seen to move along the n axis toward the k axis asthe size parameter increases (figure A-1, E to I).

10

Let us now divide the n,k plane by a horizontal line through the locusand acc et values of k which lie in the lover half of the divided n,k plane; i.e., 0f k T. In this region, the extinction coefficient is a single-valued function inthe vicinity of the first surface polariton resonance and no significant loss ofgenerality is incurred by imposing this condition since most condensed matter has kvalues which lie in this region. If n(X) is now considered to be fixed at somevalue no , it can be seen in figure A-1 that, in general, the dimensionlessextinction coefficient increases monotonically with respect to k; this fact formsthe basis of the procedure for computing k(X). Since the isopleths of aD representthe integral kernel of equation 10, a(k) itself is expected to be monotonic withrespect to k over a wider range of n than is indicated in figure A-1. This has beenpreviously demonstrated in work by Jennings et al. 1 1 who computed isopleths in n,kspace of the extinction coefficient at 10.6 urm for log-normally distributed aerosolswhich had number median diameters, Dn, of 2.0 and 20.0 vtm and a 1.5. For these

cases, a(k) is shown to be monotonic for 10- 3 4 k e /2, when 0.1N n 4 8 for Dn2.0 Pm and when 0.1 4 n 4 4 for Dn = 20.0 Pm.

The effects on the monotonicity of the extinction coefficient whichresult from changing the particle size distribution and the real part of the complexrefractive index are shown in the curves of figure A-2. In these curves, thedimensionless extinction coefficient, integrated over the indicated log-normal sizedistribution functions, is plotted with n fixed as a function of the mass mediansize parameter

X D ArDf/ (12)

m m

for values of k between 0 and V-. The range in Xm over which ao remains monotonicis determined by the interaction between the resonances due to the bulk polaritonsand the tendency of the polydispersity to smooth out such resonance effects. Also,

since a nonzero imaginary part of the refractive index acts to damp out theresonances, the extinction curves for 0(0) display the most abundant resonantstructure. For small values of X, a D(k) increases monotonically with respect to k;this monotonic behavior of a (k- continues as X increases until the a (0) curve

D m Dcrosses the nearest neighboring cLD(k) curve. The value of Xm at this crossing pointdefines an upper limit, Xi, below which QD(k) is monotonically increasing withrespect to k. The value of X , depends both on the polydispersity of the aerosoland on the value of the real part of the complex refractive index. The table showsthe approximate values of X,, for the curves of figure A-2. Once X becomes largerthan XmI, the behavior of D(k) is not generally predictable since it depends inlarge measure on the resonant structure of the a D(0) curve. For X larger than X,m ntit does not appear possible to determine k uniquely from extinction data. FigureA-3 shows explicitly the variation of the dimensionless extinction coefficient withk as X increases for the case in which n - 2 and a - 1.4. The curves for X1.38 and X - 1.44 bracket X for this case (see the lable).

ItI

Table. Approximate Values of the Upper Monotonicity Limitfor the Mass Median Size Parameter

a .1.33 2.0 3.0

1.1 3.55 1.35 0.89

1.4 3.55 1.41 0.81

2.0 4.68 1.78 0.89

3.0 9.77 3.39 1.23

From the discussion above, it may be concluded that the extinctioncoefficient will be monotonic with respect to k for the range of optical constantsand particle sizes likely to be encountered in many practical problem in aerosolphysics. As shown in figure A-4, it now becomes, in principle, a simple r::- todetermine k numerically. a is the extinction coefficient computed from eqkation 10c

using the current estimate for k and the experimentally determincd sizedistribution; a is the measured value of the extinction coefficient. Successive

estimates of k are made until Jac - a e 1 6, where 6 is determined by the precisionto which the extinction coefficient can be measured.

2.3 Algorithm for computing optical constants.

The procedures developed above may be combined into an algorithm forcomputing the optical constants as shown in the flow chart of figure A-5. Thecomputation is started by taking n(X) equal to a constant which we usually choose tobe 1.3. Successive calculations of k(X) and n(A) are then made until convergence isobtained. The algorithm was implemented by means of a FORTRAN program written foruse on a Univac 1108 computer. All Mie calculations were carried out by means of a

modified version of Dave's DBMIE subroutine, 4 and the original version of the SKKroutine used in this study was developed by Querry.*

3. EXPERIMENTAL PROCEDURE AND RESULTS

An extinction spectrum and particle size distribution for o-phosphoricacid were measured in order to confirm the theory developed in section 2. FigureA-6 shows a diagram of the experimental arrangement employed for thesemeasurements. The o-phosphoric acid was disseminated in a 22-m 3 test chamber byspraying the acid solution through a pneumatic nozzle; the acid aerosol was stirredcontinuously throughout the experiment in order to maintain a uniform aerosolconcentration. An Exotech model 10-24 radiometer with a circular variable filtermonochrometer was used to scan the 7- to 14-um infrared region at a rate of 15 scansper minute; the path length through the aerosol was 3.05 m. The radiometer datawere recorded on analog tape with a Hewlett-Packard model 3960 recorder. Particle

* Querry, M. R. Private communication. 1967.

12

.,

size samples were taken vith an Andersen model 2000 cascade impactor, and theaerosol mass concentration was determined from samples taken on glass fiber filters.

A Quad Systems model 721 digitizer was used to convert the analogradiometer data to digital form, and the digitized data were written on a magnetic

tape for use in subsequent computer processing. The extinction spectrum was

determined from the digitized data by Beer's law

-1a - Ln T (13)e CL

where

C = aerosol mass concentration (gm/m )

L - optical path length (m)T = transmittance

The measured acid concentration of the aerosol droplets was approximately 65% byweipt and the log-normal particle size distribution as estimated from the cascadeimpatLor results had the parameters D - 3.3 um and a = 2.0. Figure A-7 comparesthe experimentally determined extinction spectrum with a spectrum computed using theoptical constant data 2 3 for 65% by weight of o-phosphoric acid. The experimentalspectrum was produced by averaging 45 radiometer scans; and figure A-8 shows a plotof the percent difference between the computed and experimental spectra as a

function of wavelength.

4. OPTICAL CONSTANT RESULTS

The experimental data for o-phosphoric acid were analyzed according tothe procedure described in figure A-5; the known value of n(X) was taken to be 1.604at 10.0 um. 23 After four iterations, the calculations converged to produce thesolution shown in figure A-9 for n(X) and in figure A-10 for k(X). For purposes ofcomparison, n(X) and k(X) for 65% o-phosphoric acid are also plotted in figures A-9and A-10; figures A-11 and A-12 are plots of the percent difference between thecomputed values of the optical constants and the measured values for 65% o-phosphoric acid. Notice that the spectral structure of the percent difference for

a(X) (figure A-8) is very similar to the spectral structure of the percent

difference for k(X) (figure A-12). This suggests that differences between thecomputed and measured values of the optical constants are due to experimental error

In measuring the extinction spectrum and particle size distribution. In order to

determine the amount of error introduced by the computational procedure, thecomputed spectrum from figure A-7 was used as the input extinction spectrum fromwhich the optical constants were to be computed. The computation converged afterfive iterations, and the results for the optical constants are compared with the

measured 65% o-phosphoric acid data in figures A-13 and A-14. The average percentdifference between the computed and the measured results for (n,k) was less than 1percent over the 7- to 14-pm spectral region. Therefore, it was concluded that thedominant contribution to the difference between the optical constants computed from

13

- - . . - 9.-.- .*Y - 'AM . . .

the o-phosphoric acid extinction data and the measured values was due to error in

measuring the extinction spectrum and the particle size distribution of the aerosol.

5. CONCLUSION

We have described an entirely new approach to the determination of theoptical constants of particulate materials. This new method avoids the experimentaldifficulties and errors associated with the traditional methods of finding theoptical constants of aerosol materials. It is an iterative procedure which, afteran initial estimate of n(X) over the wavelength spectrum, employs a simple numericalalgorithm to fit the k(X) spectrum to a measured extinction spectrum and the KKdispersion to establish a new estimate of the n(X) spectrum. The values of k(X) arerestricted to the range 0 to /r, and the numerical algorithm for finding k(X) isvalid for a wide range of n(X) and particle size distributions as shown in thetable. The value of n(A) must be known for one wavelength in the spectral regionbeing investigated.

The theory of the method was developed in detail and was successfullyapplied to the determination of the optical constants of an o-phosphoric acidaerosol in the 7- to 14-m infrared. The numerical procedure was shown to introducean error of less than I percent in the determination of the o-phosphoric acidoptical constants.

14

LITERATURE CITED

1. Van da Hulot, H. C. Light Scattering by Small Particles. Wiley, New

York, New York. 1957.

2. Deirinndjian, D. Electromagnetic Scattering on Spherical Polydisper-

sions. Elsevier, Now York, New York. 1969.

3. Kerker, M. The Scattering of Light and Other Electromagnetic Radiation.Academic Press, Now York, Nev York. 1969.

4. Dave, J. V. Report No. 320-3237. IBM Scientific Center, Palo Alto,California. 1968.

5. Grehan, G., and Gouesbet, G. Appl. Opt. 18, 3489 (1979).

6. Wiscombe, W. J. Ibid. 19 1505 (1980).

7. Wells, W. C., Gal, G., and Munn, M. W. Ibid. 16, 654 (1977).

8. Patterson, E. M. Ibid. _16. 2414 (1977).

9. Jennings, S. G., Pinnick, R. G., and Auvermann, H. J. Ibid. 17, 3922

(1978).

10. Roessler, D. M., and Faxvog, F. R. Ibid. 18, 1399 (1979).

11. Jennings, S. G., Pinnick, R. G., and Gillespie, J. B. Ibid. _18 1368

(1979).

12. Bergstrom, R. W. Beitr. Phys. Atmos. 46, 198 (1973).

13. Toon, 0. B., Pollack, J. B., and Khare, B. N. J. Geophys. Res. 81, 5733(1.976).

14. Janzen, J. J. Colloid Interface Sc. 69, 436 (1979).

15. Wyatt, P. J. Appl. Opt. 19, 975 (1980).

16. Pluchino, A. B., Goldberg, S. S., Dowling, J. M., and Randall, C. M.

Ibid. 19. 3370 (1980).

17. Cardona, M. Optical Properties of Solids. S. Nudelman and S. S. Mitra,

editors. Plenum Press, Hew York, New York. 1969.

18. Landau, L. D., and Lifshitz, E. H. Electrodynamics of Continuous

Media. Pergamon Press, Oxford, England. 1960.

19. Bachrach, R. Z., and Brown, P. C. Phys. Rev. B1, 818 (1970).

.15

20. Ahrankiel, R. K. J. Opt. Soc. An. 61, 1651 (1971).

21. Hale, G. M., and Querry, H. R. Appl. Opt. 12, 555 (1973).

22. Gilra, D. P. Collective Excitations in Small Solid Particles andAstronomical Applications. Ph.D. Thesis. 1972.

23. Quarry, M. R. Molecular and Crystalline Electromagnetic Properties ofSelected Condensed Materials in the Infrared. Final Report. DAAG-29-76-GS-085.US Army Research Office, Research Triangle Park, North Carolina 27709. 1979.

16

APPENDIX

FIGURES

SPHERE X - 0.01 SPHERE X - 0.1 SPHERE X u 0.2

.7 . . 22070 /2 70 0

I -

2.0 2.10 210

0020

.30 30 3

.30 .3 1.90 Z10 2.70 30 Wo Io 210 2o70 io i0 1 210 27O

N4 N N

A B C

SPHERE X - 0.5 SPHERE X = 0.75 SPHERE X = 0.85

270- 270- 270-

210. 210. 2 10-

150 100 1 00

P. e

I,0 00/

Is* 90. 90- "

30.0 30 )ft ........ 30

30 00 10 210 270 1 90 1S0 2 10 270 30 150 2 10 2 70

N NN

DE F

i0SP H E R E X IM 1 .0 2 n S P H E R E X h1.5 i1no lS P H E R E X

2 ld210 210.

150

00 700

31 4- 00

30010

30 90 ISO 2 10 270 90 0 1 O0\\0 2'7

N NN

0 H

Figure A-1. Isopletha in n,k Space of the Dimensionless ExtinctionCoefficient for Spheres vith the Indicated Size Parameters

17

'0-1 to, I to1;101 0

.0.3 .. 0 t! ,0

2 .2

tot. '0 12

Figure A-2. Dimensionless Extinction Coefficient, aD. for Log-normallyDistributed Spheres as a Function of Mass Median Size Parameter, X

Individual curves are for k - 0, 0.2, 0.4, 0.6, 0.8, 1.0, 2 and areeasily identified, since a.0 is monotonically increasing with respect to k at the

left-hand side of the plots.

Appendix 18

0 C4

4CC

0

00

o 0

~ ON L~ , NIf 4-4 i i I BB I

0rEScE SEExx x

Xj-

>)G

Lq C! Lq q i q IN In C14

JLN331:14303NOLLNLLX SS3NOIS3W -.

Appendix 1

a~c 0,0l

( '

C 0

0---k- 1.0 \2

Figure A-4. Illustration of the Numerical Procedure for Calculating k

a is the measured extinction coefficient and a is the computede cextinction coefficient.

Appendix 20

START

COMPUTE

COPUTE

O(?IWFROMSKK

nod., ko,) NOSTATIONARY?

YES

STOP

Figure A-5. Flowchart of the Algorithm for Determining theOptical Constants n,k from Extinction Measurements

index. no is an initial, assumed value of the real part of the refractiveinde. nis typically taken to be 1.3.

Appendix 21

4,

EXOTECHRADIOMETER

L ~ L INFRAREDL SOURCE

WR - Radiometer Window - Polyethylene

W- Source Window - Polyethylene

L - Path Length, 3.05 m

V - Chamber Volume, 22 m

Figure A-6. Experimental Arrangement Used for o-PhosphoricAcid Aerosol Measurement

Appendix 22

@1

VL

044

E

I-J

-4

ad

@0

* 0

r% CR Lq l (i N1 q V0 0 0 0 0 0 0 04

(WO/FLw) IN31314dI3O NOI.L3NI1X30

I.c

Appendix 23

0

LUJu00

4)0

V4 a)

700%

Appendix 24

- ,-

Oin

.44

'.4

9- 4j

I* 40

j 464

64 0'44

I-,

I ,..zocm 44

uC

4.c

Apeni 25

o

4>

* w2

* N

-4.

0

En

4)0

.44C)

co- w

LU 0~

0

coi

00

Appendix 26

-C.

44

V4

1.4

0

4..

I0

'I

0

jI-

f 44

co 0)

- 630

I--

d 2CD-

2

, , ,. , wu euoo ! %.J

63

63

__ - .. .6:3 ...

C 044

0

0

0

"o

zU

H0

N0

41~

wu.I..-

F40

%2

Appendix 2

X.

0sl

EE

_jd

IIn

W. 4.

Appendix 2

m0I

@3

LU'

0 tz

o

4j4L>$A

'-

I0I- w..I

9.- w

o. .

oi

!~I

DISTRIBUTION LIST 5

Names Copies Names Copies

CHEMCAL YSTMS LBORAORYDeputy Chief of Staff for Research,ATTN: DRDAR-CLF I Development & AcquisitionATTN: DRDAR-CLJ-R 3 ATTN: DAMA-CSS-CATTN: DRDAR-CLJ-L 3 ATTN: DAMA-ARZ-DATTN: DRDAR-CLJ-M 1 Washington, DC 20310ATTN: DRDAR-CLJ-P 1ATTN: DRDAR-CLT-E I US Army Research and StandardizationATTN: DRDAR-CLN 2 Group (Europe)ATTN: DRDAR-CLW-C 1 ATTN: DRXSN-E-SCATTN: DRDAR-CLB-C I Box 65, FPO New York 09510ATTN; DRDAR-CLB-P 1ATTN: DRDAR-CLB-PA 1 HQDA (DAMI-FIT)ATTN: DRDAR-CLB-R I WASH, DC 20310ATTN: DRDAR-CLB-T IATTN: DRDAR-CLB-TE 1 CommanderATTN: DRDAR-CLY-A 1 DARCOM, STITEURATTN: DRDAR-CLY-R 1 ATTN: DRXST-STIATTN: DRDAR-CLR-I I Box 48, APO New York 09710

COPIES FOR AUTHOR(S): CommanderResearch Division 4 US Army Science & Technology Center-

Far East OfficeDEPARTMENT OF DEFENSE ATTN: MAJ BorgesI

APO San Francisco 96328Defense Technical Information CenterATTN: DTIC-DDA-2 12 CommanderCameron Station, Building 5 2d Infantry DivisionAlexandria, VA 22314 ATTH: EAIDCOM

APO San Francisco 96224i L Director

Defense Intelligence Agency CommanderATTN4: DB-4Gi 1 5th Infantry Division (Mach)Washington, DC 20301 ATTN: Division Chemical OfficerI

Fort Polk, LA 71459Special Agent In ChargeAROO 902d Military Intelligence GP OFFICE OF THE SURGEON GENERALATTN: IAGPA-A-ANAberdeen Proving Ground, MD 21005 Commander

US Army Medical Bloengineering ResearchCommander and Development LaboratorySED, HQ, INSCOM ATTN: SGRD-UBD-ALIATTN: IRFM-SED (Mr. Joubert) 1 Fort Detrick, Bldg 568Fort Meade, NO 20755 Frederick, MD 21701

DEPARTMENT OF THE ARMY HeadquartersUS Army Medical Research and

HQDA (DAMO-NCC) I Development CommandWASH DC 20310 ATTN: SGRD-PLI

Fort Detrick, MD 21701

31

Commander Commander

USA Biomedical Laboratory US Army Natick Research and

ATTN: SGRD-UV-L I Development Command

Aberdeen Proving Ground, MD 21010 ATTN: DRDNA-VR 1

ATTN: DRDNA-VT 1US ARMY HEALTH SERVICE COMMAND Natick, MA 01760

Superintendent US ARMY ARMAMENT RESEARCH AND

Academy of Health Sciences DEVELOPMENT COMMAND

US Army

ATTJN: HSA-CDH I CommanderATTN: HSA-IPM I US Army Armament Research and

Fort Sam Houston, TX 78234 Development CommandATTN: DRDAR-LCA-L I

US ARMY MATERIEL DEVELOPMENT AND ATTN: DRDAR-LCE IREADINESS COMMAND ATTN: DRDAR-LCE-C

ATTN: DRDAR-LCU 1Commander ATTN: DRDAR-LCU-CE 1US Army Materiel Development and ATTN: DRDAR-PMA (G.R. Sacco)

Readiness Command ATTN: DRDAR-SCA-W

ATTN: DRCLDC I ATTN: DRDAR-TSS 2ATTN: DRCSF-P I ATTN: DRCPM-CAWS-AM 1

5001 Eisenhower Ave ATTN: DRCPM-CAWS-SI IAlexandria, VA 22333 Dover, NJ 07801

Project Manager Smoke/Obscurants Director

ATTN: DRCPM-SMK Ballistic Research Laboratory

Aberdeen Proving Ground, MD 21005 ARRADCOM

ATTN: DRDAR-TSB-S 1Commander Aberdeen Proving Ground, MD 21005

US Army Foreign Science & Technology CenterATTN: DRXST-MT3 I US ARMY ARMAMENT MATERIEL READINESS

220 Seventh St., NE COMMAND

Charlottesville, VA 22901

Commander

Director US Army Armament Materiel

US Army Materiel Systems Analysis Activity Readiness Command

ATTN: DRXSY-MP 1 ATTN: DRSAR-ASN 1

ATTN: DRXSY-T (Mr. Metz) 2 ATTN: DRSAR-PDM 1Aberdeen Proving Ground, MD 21005 ATTN: DRSAR-SF I

Rock Island, IL 61299CommanderUS Army Missile Command Commander

Redstone Scientific Information Center US Army Dugway Proving Ground

ATTN: DRSMI-RPR (Documents) 1 ATTN: Technical Library Docu Sect 1

Redstone Arsenal, AL 35809 Dugway, UT 84022

Director US ARMY TRAINING & DOCTRINE COMMANDDARCOM Field Safety Activity

ATTN: DRXOS-C 1 Commandant

Charlestown, IN 47111 US Army Infantry School

ATTN: NBC Division 1

Fort Banning, GA 31905

32

Comasndar

Commandant Navel Weapons CenterUSAMP&CS/TC&FM ATTN: Technical Library (Code 343)

ATTN: ATZN-CM-CDM 1 China Lake, CA 93555

Fort McClellan, AL 36205

Commander Officer

Commander Naval Weapons Support Center

US Army Infantry Center ATTN: Code 5042 (Dr. B.E. Douda)ATTN: ATSH-CD-MS-C I Crane, IN 47522

Fort Banning, GA 31905

US MARINE CORPS

Commander

US Army Infantry Center Director, Development Center

Directorate of Plans & Training Marine Corps Development and

ATTN: ATZB-DPT-PO-NBC Education Command

Fort Banning, GA 31905 ATTN: Fire Power Division

Quantico, VA 22134

Commander

USA Training and Doctrine Command DEPARTMENT OF THE AIR FORCE

ATTN: ATCD-Z

Fort Monroe, VA 23651 HQ Foreign Technology Division (AFSC)

ATTN: TQTR

Commander Wright-Patterson AFB, OH 45433

USA Combined Arms Center and

Fort Leavenworth HQ AFLC/LOWMM

ATTN: ATZL-CA-COG I Wright-Patterson AFB, OH 45433ATTN: ATZL-CAM-IM 1

Fort Leavenworth, KS 66027 OUTSIDE AGENCIES

Commander Battelle, Columbus Laboratories

US Army TRADOC System ATTN: TACTEC

Analysis Activity 505 King Avenue

ATTN: ATAA-SL 1 Columbus, OH 43201

White Sands Missile Range, NM 88002Toxicology Information Center,

US ARMY TEST & EVALUATION COMMAND WG 1008National Research Council

Commander 2101 Constitution Ave., NW

US Army Test & Evaluation Command Washington, DC 20418

ATTN: DRSTE-CM-F 1ATTN: DRSTE-CT-T I ADDITIONAL ADDRESSEE

Aberdeen Proving Ground, MD 21005

CommanderDEPARTMENT OF THE NAVY US Army Environmental Hygiene Agency

ATTN: Librarian, Bldg 2100

Commander Aberdeen Proving Ground, MD 21010

Naval Explosive OrdnanceDisposal Facility Stimson Library (Documents)

ATTN: Army Chemical Officer Academy of Health Sciences

Code AC-3 1 Bldg. 2840Indian Head, MD 20640 Fort Sam Houston, TX 78234

33

.. , - d ... lF , ._ .-

Figure A-4. illustration or rne numericai rrucouuc

exQncio e ji the measured extinction coefficient and a

rary (Code 343) 155

rt Center

r. S.E. Douda)I

nt Centeropment andind

)Iv I a on

kiR FORCE

gy Division (AFSC)

B8, OH 45433

-B, OH 45433

Laborator ies

lion Center,

CouncilAve., NW418

EE

tal Hygiene Agency

Bldg 2100round, MD 21010

ocuegents)Sc iences

TX 76234