AD A O 7 RM R A E T RSEARCH AND D EV EL/OPMNT CO9RANO A SRD- TC F/Sl 20/B

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UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE ("oen Dete Entered)

READ INSTRUCTIONSREPORT DOCUMENTATION PAGE BEFORE COMPLETING FORM. REPORT NUMBER Z 'OVT ACCESSION NO . 3REC4 ENT'S CATALOG %UMBER

ARCSL-TR-81088 1W __

4. TITLE (awd Subtitle) S TYPE OF REPORT & PERIOD COVERED

Technical Report */- fAN ASCII FORTRAN SUBROUTINE FOR COMPUTING THE May 1980ELECTROMAGNETIC RADIATION SCATTERED BY A SPHERE 6 PERFORMINGORG REPORTNUMBER

7. AUTHOR(&) 8 CONTRACT OR GRANT NUMBER(@)

/ Merrill E. Milham

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 IL162662A554Aberdeen Proving Ground, MD 21010

11. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE

Commander/Director, Chemical Systems Laboratory November 1981ATTN: DRDAR-CLJ-R 13. NUMBER OFP AGES

Aberdeen Proving Ground, MD 21010 4614. MONITORING AGENCY NAME & ADDRESS(If dlfferent from Controlling Office) IS. SECURITY CLASS. (of this report)

UNCLASSIFIED

IS&, DECLASSIFICATION/DOWNGRADINGSCHEDULE NA

16. DISTRIBUTION STATEMENT (of this Report)

Approved for public release; distribution unlimited.

17. DISTRIBUTION STATEMENT (of the abstract entered In Block 20, It dilferent from Report)

IS. SUPPLEMENTARY NOTES

Smoke/Obscurant Technology

19. KEY WORDS (Continue an reree* ride If neceew , and Identify by block number)

ASCII FORTRAN compiler Lorenz-Mie calculationASCMIE subroutine Memory allocation processorDBMIE code Mie scattering calculationsElectromagnetic radiation Refractive index

, Homogeneous spherical particle Smoke-aerosol research

20. fISTRACT (Centinue on revre.taide If noceseey ind Identify by block number)

This report describes the ASCMIE subroutine for performing Mie scatteringcalculations by means of the downward recursion algorithm developed byJ. V. Dave. ASCMIE is written in UNIVAC 1100 series ASCII FORTRANlanguage. The ASCII FORTRAN compiler is a modern, state-of-the-art compiler

which implements the ANSI FORTRAN 77 standard; this compiler is intended asa future replacement for the UNIVAC 1100 series FORTRAN V compiler. Ratherthan carry out a straightforward conversion of the FORTRAN V Mie scattering

D I M 1473 EDITION Of I NOV S5lI OBSOLETE UNCLASS IF I ED

v SECURITY CLASSIFICATION Of THIS PAGE (Uh ..i ote Entered)

SECuMITY CLASIFICATION Of THIS PA4I (When Data Enlted)

routine to ASCII FORTRAN, the code was completely rewritten In order toincorporate new ASCII FORTRAN language elements. The result Is a morestructured, modular, Mie scattering code which executes faster than theFORTRAN V code.\

2 UNCLASSIFIEDSECURITY CLASSIFICATION OF-THIS PA83IEe Dae EwIIe'*'')

PREFACE

The work described in this report was authorized under Project1L162662A554, Smoke/Obscurant Technology. This work was started andcompleted in May 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 Systems Laboratory,ATTN: DRDAR-CLJ-R, Aberdeen Proving Ground, Maryland 21010. However, theDefense Technical Information Center and the National Technical InformationService are authorized to reproduce the document for United StatesGovernment purposes.

tA

I

CONTENTS

Page

I INTRODUCTION ................ ........................ 7

2 SOFTWARE DESIGN AND CODING CONVENTIONS ....... ............... 7

3 RESULTS ............... ............................. 9

3.1 Sample Problem ............ ....................... 93.2 Timing Study .......... ......................... ... 10

4 CONCLUSIONS ............ ............................ . 11

LITERATURE CITED ........... .......................... ... 13

APPENDIXES

A. FTN Compilation Listing of Subroutine ASCMIE ......... ... 15

B. FTN Compilation Listing of Main Program MIECHK ........ .31

C. MAP Listing of Absolute Element ASCMIE ... .......... . 37

D. Sample Output from Execution of AbsoluteElement ASCMIE .......... .................... 39

DISTRIBUTION LIST .......... ......................... ... 43

t l

AN ASCII FORTRAN SUBROUTINE FOR COMPUTING THE ELECTROMAGNETIC RADIATION

SCATTERED BY A SPHERE

1 INTRODUCTION

The Lorenz-Mie formalism1' 2 3 is the analytical solution for the farfield radiation which results when plane electromagnetic waves are scatteredby a homogeneous spherical particle. With the advent of modern high speedcomputers programmed to provide numerical results, the Lorenz-Mie formalismmay be regarded as an idealized experimental tool which is capable ofpredicting with certainty the scattering produced by spherical

particulates.3

The development and use of computer codes to perform Lorenz-Miecalculations are of prime importance for smoke/aerosol research. Forexample, the excellent and widely used FORTRAN subroutine DBMIE, 4 whichwas developed by J. V. Dave,5 has been the mainstay for performing suchcalculations at Chemical Systems Laboratory (CSL). The DBMIE code wasmodified for use on the ARRADCOM UNIVAC 1108 computer as a FORTRAN Vsubroutine.6 The FORTRAN V compiler will be replaced in the near futureby the UNIVAC 1100 series ASCII FORTRAN compiler. 7 The ASCII compiler isa modern, state-of-the-art compiler which implements the ANSI FORTRAN 77standard.8 Rather than carry out a straightforward conversion of theFORTRAN V Mie scattering subroutine, the code was completely rewritten toincorporate new ASCII FORTRAN language elements. The result was the ASCMIEsubroutine which is a more structured, modular, Mie scattering code whichexecutes faster than the FORTRAN V code.

2 SOFTWARE DESIGN AND CODING CONVENTIONS

A compilation listing of the ASCMIE subroutine is given in appendix A;the reader should become familiar with this listing before proceeding. Thissubroutine is an implementation of the downward recursion algorithm ofDave.5 A call to subroutine ASCMIE requires the specification of the

following input arguments:

X = D/A, the size parameter for a sphere of diameter Dilluminated by electromagnetic radiation of wavelength X.An error condition is generated and the execution of ASCMIEis halted if X < 0. X is a double precision variable.

N = the real part of the complex refractive index, m. Aprinted warning is generated if N : 1 because thealgorithm has been thoroughly tested for N > 1 only. N isa double precision variable.

K = imaginary part of the complex refractive index, m. An

error condition is generated and the execution of ASCMIE ishalted if K < 0. K is a double precision variable.

{ 7

THETAD a a double precision array containing the scattering anglesIn degrees. The maximum number of scattering angles Is setby the PARAMETER variable MXTHET at 100 angles. An errorcondition is generated and the execution of ASCMIE ishalted If any value of the scattering angle exceeds 90degrees.

NTHETA - the number of scattering angles at which the Lorenz-Miesolutions are sought. NTHETA should not exceed 100 unlessASCMIE Is recompiled with MXTHET set larger. An errorcondition Is generated and the execution of ASCMIE ishalted If NTHETA > MXTHET. NTHETA Is an Integer variable.

All the input arguments specified above are checked for error and warningconditions before a decision is made to proceed or halt execution. Eacherror or warning is described by a printed message. Also, a check is madeto determine if sufficient array storage is available to perform thecalculations before the program is allowed to proceed.

The subroutine returns the following outputs:

QEXT - efficiency factor for total extinction. QEXT is a double

precision variable.

QSCAT - efficiency factor for scattering. QSCAT is a doubleprecision variable.

CTBRQS = product of the asymmetry factor and QSCAT. CTBRQS is adouble precision variable.

FMX = elements of the transformation matrix. FMX (4,MXTHET,2) isa double precision array.

Definitions of the efficiency factors, asymmetry factor, and thetransformation matrix can be found in any of several excellent treatises onthe Lorenz-Mie Theroy.1, 2 ,3

An attempt was made to make the ASCMIE code as structured as possible.The beginning of this program module is indicated by the SUBROUTINEstatement and the program module ends with the END statement. All of theFORTRAN code which implements the algorithm between the SUBROUTINE and ENDstatements was divided into blocks according to the following scheme:

(a) BLOCK 0 contains all specifications statements.(b) BLOCKS 100 to 600 are blocks of FORTRAN code which implement

algorithmic tasks.

(c) Each BLOCK is divided into as many SUBBLOCKS as necessary forclarity and convenience.

48

Each BLOCK of the code was constructed according to the following stylerules:

(a) Each BLOCK starts with a statement labelled:

0, 100, 200, . ., 600

(b) Each SUBBLOCK starts with a statement labelled:

0, 10, 20, • ., 90100,110,120, .,190200,210,220, . .,290

600,610,620, .. ,69o

The smallest available label is used.

(c) 9000 series labels are FORMAT statements. Each digit following the9 serves to identify the BLOCK and SUBBLOCK in which the FORMATstatement occurs.

Using the conventions described above, the ASCMIE code is represented bythe following skeleton:

START OF MODULE: SUBROUTINE ASCMIE (X, N, K,THETAD, NTHETA, QEXT, QSCAT, CTBRQS, FMX)

BLOCK 0: SPECIFICATIONSBLOCK 100: CHECK FOR INVALID OR

OUT-OF-RANGE ARGUMENTSBLOCK 200: INITIALIZING CALCULATIONSBLOCK 300: SERIES SUMMATIONSBLOCK 400: CALCULATE FINAL RESULTSBLOCK 500: RETURNBLOCK 600: ERROR SECTION

END OF MODULE: END

3 RESULTS

3.1 Sample Problem. A FORTRAN main program, MIECHK, was written to call theASCMIE subroutine and produce numeric results for sample problems. MIECHKis essentially the same program as that used previously by Dave 5 for thesame purpose; a compilation listing of program MIECHK is given in appendixB. A MAP (Memory Allocation Processor) listing of the absolute elementASCMIE, which was produced by including MECHK and ASCMIE, is given inappendix C. This absolute element was executed for Dave's sample problemm = 1.342 - 0.1i, X = 1571.0.5 The results produced by ASCMIE are givenin appendix D and are in agreement with previous results. 5

9

3.2 Timing Study. An important consideration in choosing a Mie scatteringcode is the computer time required to produce numeric results. The timerequired to execute ASCMIE for the sample problem described above (section3.1) was compared as the size parameter was varied from 0.1 to 1571 withsimilar results for two FORTRAN V versions of the Dave subroutine - MEMIE*and MIE2.** The results of the timing study are presented in table 1, wherethe times shown are the central processing unit times as listed by theUNIVAC 1108 accounting algorithm.

Table 1. Comparison of Execution Times for Three Mie Scattering Subroutines

Time

ASCMIE MEMIE MIE2

sec sec sec

0.1 .947 .979 .995

1.0 1.018 1.049 1.051

10.0 1.427 1.490 1.592

100.0 4.021 4.068 5.004

1000.0 27.758 28.952 34.671

1571.0 41.166 42.137 51.637

In every case ASCMIE took less time to compute the same results than the

MEMIE and MIE2 subroutines. Independent of the value of X, we find that

TA < TM1 < TM2 (1)

where

TA = time required when using the ASCMIE subroutine

TM1 = time required when using the MEMIE subroutine

TM2 = time required when using the MIE2 subroutine

Because of the uncertainties inherent in computer timing operations andthe cursory nature of this timing study, these results should be regarded assuggestive but not definitive.

*Unpublished data by M. E. Milham.

**Unpublish d data by . H. Frickel. I10

II I-M

4. CONCLUSIONS

The ASCMIE subroutine:

(a) Is based on the downward recursion scheme of Dave.

(b) Uses many of the FORTRAN 77 features available in the UNIVAC 1100series ASCII FORTRAN language.

(c) Is more modular and structured than the original Dave code.

(d) Executes faster than FORTRAN V versions of the Dave code (MEMIE,MIE2).

I-!1

ti

LITERATURE CITED

1. Van de Hulst, H. C. Light Scattering by Small Particles. JohnWiley and Sons, Inc., New York, New York. 1957.

2. Kerker, M. The Scattering of Light and Other ElectromagneticRadiation. Academic Press, New York, New York. 1969.

3. Deirmendjian, D. Electromagnetic Scattering on SphericalPolydispersions. Elsevier Publishing Company, New York, New York. 1969.

4. Plass, G. N. Comment on: The Effects of Particle Size on ContrastImprovement by Polarization Discrimination for Underwater Targets. Appl.Opt. 9, 1932 (1970).

5. Dave, J. V. Report No. 320-3237. Subroutines for Computing theParameters of the Electromagnetic Radiation Scattered by A Sphere. IBMScientific Center, Palo Alto, California. May 1968.

6. FORTRAN V Programmer Reference. UP-4060. Sperry Univac Corp.1976.

7. FORTRAN (ASCII) Programmer Reference. UP-8244. Sperry UnivacCorp. 1976.

8. American National Standard Programming Language FORTRAN. ANSIX3.9-1978. American National Standards Institute. New York, New York.1978.

13

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APPENDIX A

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Appendix D 4

DISTRIBUTION LIST 5

Names Copies Names Copies

CHEMICAL SYSTEMS LABORATORY

CommanderATTN: DRDAR-CLB-C I SED, HQ, INSCOMATTN: DRDAR-CLB-P 1 ATTN: IRFM-SED (Mr. Joubert)ATTN: DRDAR-CLB-PA I Fort Meade, MD 20755ATTN: DRDAR-CLB-R I

ATTN: DRDAR-CLB-T 1 DEPAR'MENT OF THE ARMYATTN: DRDAR-CLB-TE I

ATTN: DRDAR-CLC I HQDA (DAMO-NCC)ATTN: DRDAR-CLF 1 WASH DC 20310ATTN: DRDAR-CLJ-R 2ATTN: DRDAR-CLJ-L 3 Deputy Chief of Staff for Research,ATTN: DRDAR-CLJ-M 1 Development & AcquisitionATTN: DRDAR-CLJ-P 1 ATTN: DAMA-CSS-C

ATTN: DRDAR-CLT-E 1 ATTN: DAMA-ARZ-DATTN: DRDAR-CLN 1 Washington, DC 20310

ATTN: DRDAR-CLN-D IATTN: DRDAR-CLN-S 3 US Army Research and Standardization

ATTN: DRDAR-CLN-ST 2 Group (Europe)ATTN: DRDAR-CLR-I I ATTN: DRXSN-E-SC

ATTN: DRDAR-CLW-C I Box 65, FPO New York 09510ATTN: DRDAR-CLW-P 1

ATTN: DRDAR-CLY-A I HQDA (DAMI-FIT)ATTN: DRDAR-CLY-R I WASH, DC 20310

COPIES FOR AUTHOR(S): CommanderResearch Division 1 DARCOM, STITEUR

RECORD SET: ATTN: DRDAR-CLB-A I ATTN: DRXST-STI

Box 48, APO New York 09710DEPARTMENT OF DEFENSE

CommanderDefense Technical Information Center US Army Science & Technology Center-ATTN: DTIC-DDA-2 12 Far East OfficeCameron Station, Building 5 ATTN: MAJ BorgesAlexandria, VA 22314 APO San Francisco 96328

Director CommanderDefense Intelligence Agency 2d Infantry Division

ATTN: DB-4G1 ATTN: EAIC.OMWashington, DC 20301 APO San Francisco 96224

Special Agent In Charge CommanderARO, 902d Military Intelligence GP 5th Infantry Division (Mech)ATTN: IAGPA-A-AN ATTN: Division Chemical OfficerAberdeen Proving Ground, MD 21005 Fort Polk, LA 71459

43

i . J

Commander Project Manager Smoke/ObscurantsUS Army Nuclear & Chemical Agency ATTN: DRCPM-SMK 3ATTN: MONA-WE (LTC Pelletler) I Aberdeen Proving Ground, MD 210057500 Backl ick Rd, Bldg 2073Springfield, VA 22150 Commander

US Army Foreign Science & Technology CenterArmy Research Office ATTN: DRXST-MT3 IATTNt DRXRO-CB 1 220 Seventh St., NEATTN: DRXRO-MA I Charlottesville, VA 22901P.O. Box 12211

Research Triangle Park, NC 27709 Director

US Army Materiel Systems Analysis ActivityOFPICE OF THE SURGEON GENERAL ATTN: DRXSY-FJ (SAWG) I

ATTN: DRXSY-MP ICommander ATTN: DRXSY-CA (Mr. Metz) 2,S Army Medical Bloengineering Research Aberdeen Proving Ground, MD 21005

and Development LaboratoryATTN: SGRD-UBD-AL CommanderFort Detrick, Bldg 568 US Army Missile CommandFrederick, MD 21701 Redstone Scientific Information Center

ATTN: DRSMI-ROC (B. Fowler) IHeadquarters ATTN: DRSMI-RPR (Documents) 1US Army Medical Research and Redstone Arsenal, AL 35809

Development CommandATTN: SGRD-PL DirectorFort Detrick, MD 21701 DARCOM Field Safety Activity

ATTN: DRXOS-C ICommander Charlestown, IN 47111USA Medical Research Institute of

Chemical Defense CommanderATTN: SGRD-UV-L US Army Natick Research andAberdeen Proving Ground, MD 21010 Development Command

ATTN: DRDNA-VR 1US ARMY HEALTH SERVICE COMMAND ATTN: DRDNA-VT 1

Natick, MA 01760SuperintendentAcademy of Health Sciences US ARMY ARMAMENT RESEARCH AND

US Army DEVELOPMENT COMMANDATTN: HSA-CDH 1ATTN; HSA-IPM 1 CommanderFort Sam Houston, TX 78234 US Army Armament Research and

Development Command.b ARMY MATERIEL DEVELOPMENT AND ATTN: DRDAR-LCA-L I

READINESS COMMAND ATTN: DRDAR-LCE 1ATTN: DRDAR-LCE-C 1

Commander ATTN: DRDAR-LCU 1US Army Materiel Development and ATTN: DRDAR-LCU-CE I

Readiness Command ATTN: DRDAR-PMA (G.R. Sacco) IATTN: DRCLDC1 ATTN: DRDAR-SCA-W 1ATTN: DRCSF-P 1 ATTN: DRDAR-TSS 5

5001 Eisenhower Ave ATTN: DRCPM-CAWS-AM IAlexandria, VA 22333 ATTN: DRCPM-CAWS-SI I

Dover, NJ 07801

44

Commander Commander

USA ARRADCOM USA Training and Doctrine Command

ATTN: DRDAR-QAC-D 5 ATTN: ATCD-Z

Abordeem Proving Ground, MD 21010 Fort Monroe, VA 23651

Director CommanderBallistic Research Laboratory USA Combined Arms Center and

ARRADCOM Fort LeavenworthATTN: DRDAR-TSB-S ATTN: ATZL-CA-COG

Aberdeen Proving Ground, MD 21005 ATTN: ATZL-CAM-IMFort Leavenworth, KS 66027

US ARMY ARMAMENT MATERIEL READINESSCOMMAND Commander

US Army TRADOC System Analysis Activity

Commander ATTN: ATAA-SL

US Army Armament Materiel White Sands Missile Range, NM 88002

Readiness Command

ATTN: DRSAR-ASN 1 Commander/Director

ATTN: DRSAR-PDM 1 Atmospheric Sciences Laboratory

ATTN: DRSAR-SF I ATTN: DELAS-EO (Dr. Niles) 5

Rock Island, IL 61299 ATTN: DELAS-EO-MO I

White Sands Missile Range, NM 88002Commander

US Army Dugway Proving Ground US ARMY TEST & EVALUATION COMMANDATTN: Technical Library Docu Sect 1

Dugway, UT 84022 Commander

US Army Test & Evaluation CommandUS ARMY TRAINING & DOCTRINE COMMAND ATTN: DRSTE-CM-F 1

ATTN: DRSTE-CT-T I

Commandant Aberdeen Proving Ground, MD 21005US Army Infantry School

ATTN: NBC Division 1 DEPARTMENT OF THE NAVYFort Benning, GA 31905

CommanderCommandant Naval Air System Command

USAMP&CS/TC&FM AIR-310C (H. Rosenwasser)

ATTN: ATZN-CM-CDM 1 Washington, DC 20361

Fort McClellan, AL 36205Commander

US Army Chemical School Naval Explosive Ordnance

ATTN: ATZN-CM-AL 1 Disposal Facility

Fort McClellan, AL 36205 ATTN: Army Chemical Officer (Code AC-3)

Indian Head, MD 20640CommanderUS Army Infantry Center Commander

ATTN: ATSH-CD-MS-C 1 Naval Weapons Center

Fort Benning, GA 31905 ATTN: Technical Library (Code 343)

China Lake, CA 93555

CommanderUS Army Infantry Center Commanding OfficerDirectorate of Plans & Training Naval Weapons Support Center

ATTN: ATZB-DPT-PO-NBC 1 ATTN: Code 5042 (Dr. B.E. Douda)

Fort Benning, GA 31905 Crane, IN 47522

45

1. ......... .

_ '~I....

US MARINE CORPS ADDITIONAL ADDRESSEE

Uirector, Development Center Commander

Marine Corps Development and US Army Environmental Hygiene Agency

Education Command ATTN: Librarian, Bldg 2100ATTN: Fire Power Division I Aberdeen Proving Ground, MD 21010

Quantlico, VA 22134

Stimson Library (Documents)DEPARTMENT OF THE AIR FCRCE Academy of Health Sciences

Bldg. 2840HQ Foreign Technology Division (AFSC) Fort Sam Houston, TX 78234ATTN: TQTR

Wright-Patterson AFB, OH 45433

HQ AFLC/LOWMM

Wright-Patterson AFB, OH 45433

OUTSIDE AGENCIES

Battelle, Columbus Laboratories

ATTN: TACTEC

505 King Avenue

Columbus, OH 43201

Toxicology Information Center, WG 1008

National Research Council2101 Constitution Ave., NW

Washington, OC 20418

46

ii'I.