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.... .. .... ~ TR-01 16 Reports Control Symbol OSD-1366 A GENERAL ALGORITIH FOR THE CALCULATION 'a' OF LASER BEAN SPREADING AUGUST 1982 BY N. B. Richardson Approved for public release; distribution unlimited. US Army Electronics Research and Deveopment Command LAJ Atmospheric Sciences Laboratory * White Sands Missile Range, NM 88002 LA- ~ * *C~ . - .t. . .- -.- - - - - - - - - - - - - -- . -CY

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~ TR-01 16 Reports Control SymbolOSD-1366

A GENERAL ALGORITIH FOR THE CALCULATION'a' OF LASER BEAN SPREADING

AUGUST 1982

BY

N. B. Richardson

Approved for public release; distribution unlimited.

US Army Electronics Research and Deveopment Command

LAJ Atmospheric Sciences Laboratory* White Sands Missile Range, NM 88002

LA- ~

* *C~ . - .t. . .- -.- - - - - - - - - - - - - -- . -CY

NOTICE$

Disclaimers

The findings in this report awe not to he construed as asoffical Department of the Amy position, unless so desig-nated by other authorized documents.

The citation of trade names a&d names of manufacturer@ inthis report is not to be construed an official Gayffamentindorsmest or approval of comtmercial products or servicesrae eced hereis.

Disposition

Detro this report when it is so longer needed. Do aotMumor it to the originator#

IV

ERRATA

ASL-TR-0116

A GENERAL ALGORITHM FOR THE CALCULATION OF LASER BEAM SPREADING

Please change subject document as follows.

Page 10 Second line from top of page, change "... [(equations

(1) and (2a)]" to ". . . [equations (1) and (2a)]"

Page 10 Third line from top of page, change "... equations

(3), (4), (5), and (6" to " . . [equations (3), (4),

(5), and (6)]"

Page 11 First line on page, change " . . [(equations (2a) and (2b)]"

to " [equations (2a) and (2b)]"

Page 14 Last line in figure 3 caption, change " . = to 20" to

-Sm" . . = 2.0".

0 , 1

?i ' .

SECURITY CLASSIFICATION OF THIS PAGE (Wh,. Date, EB,.t- READ INSTRUCTIONSREPORT DOCUMENTATION PAGE BEFORE COMPLETING FORM

-.,. REPORT NUMBER 2. GOVT ACCESSION NO4 3. RECIPIENT'S CATALOG NUMBER

:':i ASL-TR-0 116

4. TITLE (Mmd Subetlie) S. TYPE OF REPORT & PERIOD COVERED]

A GENERAL ALGORITHM FOR THE CALCULATION OF LASER Final ReportBEAN SPREADING S. PERFORMING ORG. REPORT NUuER

7. AUTHOR(,) S. CONTRACT OR GRANT NUMNERCC)

N. B. Richardson

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASKAREA& jPX f T_

US Army Atmospheric Sciences Laboratory I L ' -1O ll -

White Sands Missile Ranges NNO 88002 DA Task X4 I M -

I1. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE

US Amy Electronics Research and August 1982Development Command IS. 1UMBER O PAGES

Adelphti NO 20783 2814. MONITORING AGENCY NAMER ADDRESS(I dlUeeant km Canblohfn Ofic) IS. SECURITY CLASS. (.1 this u,;f-

UNCLASSIFIED

IS.. DEI SIICATION/OOWNGRAOINGSCHEUL

t. OISISTwUTION STATEMENT (of We Relewt)

Approved for public release distribution unlimited,

17. DISTRIBUTION STATIEMINT (.f5 6e64&A Ied i*d In B006 0, If aliffemt ko wReet)

IS. SUPPLENMENTARY NOTES

Is. KEY WORDS (Continu man rewreo aide It nec.emv &W Identiy by block numbor)

TurbulenceScintillationResolution

8&- ASNACT (CiNiS M 8in N n0****aeM' a s Iy by blokm)

This paper compares two different bean spreading formalisms in the limits ofnear- and far-field, short exposure and long exposure. A description is givenof an interpolation algorithm bridging the limits, giving entirely reasonableresults in the intermediate regimes while having the proper limiting values.

O 143 EWnOW Of I NOV 6s 1s OBSOLETE

SECURITY CLASSIFICATION OF THIS PAGE (WIM Dato EfaetdO)

SECURITY CLASUSFCAION OF THIS PAGStMhin DsM MWW@*

SECURITY CLASSIFICATION OF THIS PAGEr~hon Data Bnteptd)

CON4TENTS

LIST OF FIGURES. . .. ... . . . . . . ... .. . ... ............. *** *** *** *** 4

LIST OF TABLES ............ .... *.** ...... ... .. . ........... .. . 4

Short and Long, Exposure LimitExpressons.. ............. o......... 6

Short Exposure Comparison: Near-Field, Far-Field and Inter-mediate cases. .. . ... .. . .. . . ..... o .... *o .. . .. . _.o .. .. * ***** ***** 10

Long Exposure Compari sons. ... . .. .. o . . .. ... .. ... . .. .. . ... .. . .. ... . ... ... 12

Short, Long, and Intermediate Exposure Comparison...... .... ........ 12

SLNMARY OF BEAM4 SPREADING RESULTS. . .. . .. ... .. .. .. . .. o .. .. .. .. . ... ..... o 16

77..

,.. ,:!./ : -/ ._,- ,, / -- - - ," -'.. .L :- -I: : - -. --- _ :, .- --- ; - i- .' - i .-. , '- , .. - .- .°- - -

LIST OF FIGURES

1. Normalized resolution R as a function of strength of turbulence

D i. in the near-field, short exposure limit; far-field, short0exposure limit; and long exposure limit .............. 8

2. Normalized resolution R as a function of strength of turbulence

Di n the short exposure limit; long exposure limit; and inter-r

0pol ated case............................... .......... 14

3. Beam spread (in meters) as a function of strength of turbulenceD n the short exposure, long exposure and interpolated cases.... 14

0

LIST CF TABLES

1. COMPARISON OF BREAUX'S ANALYTICAL EXPRESSION (6) WITHFRIED'S INTEGRAL EXPRESSION (2a) IN THE NEAR-FIELD,:.:SHORT TERM LIMIT ...................... .... ....................... 10

2. BEAN SPREAD IN SHORT EXPOSURE LIMIT ............................... 11

3. COMPARISON OF BREAUX'S ANALYTICAL EXPRESSION (5) WITHFRIED'S INTEGRAL EXPRESSION (2c) IN THE LONG EXPOSURELIMIT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 13

4. BEAM SPREAD IN THE SHORT EXPOSURE, LONG EXPOSURE, AND INTER-SEDIATE CASE ...................................................... 15

INTROOUCTION

Laser beam spreading is an unavoidable consequence of finite aperture size(resulting in diffraction) and atmospheric turbulence (resulting in temporalvariations in the index of refraction, which in turn induces bean spread).Although the quantification of beam spreading is important in the design andsubsequent performance of electro-optical systems, (e.g., laser designatorsand homing seekers), previous calculations of turbulence effects have been

Stlimited to the cases of very short exposure in the near-field and far-fieldand to the case of very long exposure.1

* The difficulty in quantifyingturbulence effects is in the accurate representation of the stochastic natureof turbulence.

In the near-field limit, the beam profile maintains its initial shape. As thebeam propagates, however, in the absence of turbulence the beam profile

radually changes to a diffraction-induced profile in the far-field limit(e.g., an "Airy pattern" for a uniform circular beam). An indication ofwhether we are in the near-field or far-field limit is determined by the value

of the Fresnel number a =-k-.The variables are the wavenumber k = 2 =

wavelength, D = aperture diameter, and L = path length. When o >> 1, we arein the near-field limit; when n << 1, we are in the far-field limit.

It is readily apparent that for typical laser designator parameters (e.g., x =10.6om, D = 0.1 m, and L = 3 km), n = 2; thus, neither the near-field or far-field limit is applicable. The condition of short or long exposure isdetermined by a comparison of the pulse duration time t with the time tc It

takes a turbulent eddy whose size is on the order of the beam size to crossthe beam. An indication of whether we are in the short or long exposure limit

tcis given by the parameter = -, where I * 1 in the short exposure

limit and t * 0 in the long exposure limit. For an eddy o 0.1 m and an eddy

velocity -P 10 m/s, t c 1 10 ms. Since pulse duration times range from

nanoseconds (T - 1) to seconds (T s 0), neither the short nor long exposure

limits are, in general, applicable.

'Fried, D. L., "Optical Resolution Through a Randomly Inhomogeneous Medium forVery Long and Very Short Exposures," J Opt Soc Am, 56:1372, 1976.

"Breaux, Harold J., "Correlation of Extended Huygens-Fresnel TurbulenceCalculations for a General Class of Tilt Corrected and Uncorrected LaserApertures," BRL IMR 600, Ballistic Research Laboratory, Aberdeen Proving

Ground, RD, 1978.

US

Since, as shown above, the limiting cases do not apply to typical scenarios, ageneral expression for beam spreading, valid for arbitrary values of a and t,is needed. Using an interpolation scheme, this paper describes an algorithmthat bridges the near- and far-field, short exposure and long exposurelimits. Also, comparisons are made of laser beam spreading due to turbulenceas calculated by Fried' in the near-field, short exposure and long exposurelimits, with that calculated by Breaux.2

Short and Long, Exposure Limit Expressions

Fried' derived expressions for the average resolution of very long and veryshort exposure images in terms of the modulation transfer function (MTF). Inthe short exposure case, the image sharpness and the MTF are insensitive tothe tilt of the wavefront. In the long exposure case, the random variationsin the tilt substantially add to the image spreading and, therefore, result inpoorer resolution.

Beam spreading, using Fried's' resolution expressions, is calculated from thefollowing equation.

rT Dr. ) R (1)r0 l

where rT = turbulence- and diffraction-induced beam spread,

rD = diffraction-induced beam spread,

= strength of turbulence,i~i ro

0 = aperture diameter,• L z

r = coherence length = 1.67 f Cn (z) W(z)dz}-3/50

C = refractive index structure constant,

W = geometry-dependent weighting function, and

L = total propagation distance.

The function R, using the notation of Fried,' is given by

'Fried, D. L., "Optical Resolution Through a Randomly Inhomogeneous Medium forVery Long and Very Short Exposures," J Opt Soc Am, 56:1372, 1976.

*'Breaux, Harold J., "Correlation of Extended Huygens-Fresnel TurbulenceCalculations for a General Class of Tilt Corrected and Uncorrected LaserApertures," BRL IMR 600, Ballistic Research Laboratory, Aberdeen ProvingGround, MD, 1978.

6

p-o

)i': 0 fRo 1-1/2OR 0 near-field, short exposure limit (o >>1, -0),

,.: R i 0 -/

Ru a far-field, short exposure limit (a <<1, r .0),

maxj:" R, ]-1/2

R."M 1/2 long exposure limit (r - 1),

max

where the expressions for the resolution, normalized by the limitingresolution Rmax, are given by

,fR 0(16 DL 2 1 rd o-1 1 ul /2 x 2a

5/3 S/3/31/3

= x exp 70J)" (2c)

,. The quantity in braces corresponds to the optical-system MiT and the~exponential factor corresponds to the abmospheric MTF.

' In figure 1 the normalized resolutions given in equations (2a), (2b), and (2c1i~i-are plotted as a function of strength of turbul ence. Note that in the limits

of very strong (0> 1)n ey ek( < 1) turbulence, the results

0 0

- approach a single curve. In the limit of strong turbulence, the exponentialfactors in (2a), (2b), and (2c) go zero. In this case all the resolutions

approach the value of the lroting resolution in the long exposure limit,Rmx; thus, the normalized resolutions all approach unity. In the limit of

weak turbulence, the exponential factors go to unity. In this case, all the

7o h v f h l t u i

Rmx; thus, the normalize~~~~~~dreouin alaprahnty Inheimtf

normalized resolutions are proportional to the factor (D-) 2 which shows up as

the linear section of the curve seen in figure 1. However, in the

intermediate regime (9- 3), all three expressions differ by as much as ar:.. r

0factor of 5. Because turbulence is often encountered in this intermediateregime,' the need exists for an expression for beam spreading that givesvalues intermediate to the extremes.

Breaux'st approach to the calculation of beam spreading was to develop beam*.i. spreading algorithms in terms of a scaling variable in the near-field limit.

The scaling variable chosen was the strength of turbulence - for various0

beam shapes, where D is the effective aperture diameter and ro is the

coherence length.

o / Nt

I'::I - // - u ,,:,,., .. ,t-

-LEING-EXPOSIRFE LIMIT--- II. FllI.lI). S II(RT-XI' .IM IT

\EAII-IIEII. SIIORT-tEXP LIMITI, " I 1 IlldI I t ll I I I ll I IJ1 7 Ill",lIW filI fl

III-' 1W' Ill) IlI' lip

STRENGT11 OF TURlLtENCE (D/Rk))

*. Figure 1. Normalized resolution R as a function of strength of turbulence L0

* in the near-field, short exposure limit; far-field, short exposure

limit; and long exposure limit.

.. 'Walters, D. L., and K. E. Kunkel, "Atmospheric Modulation Transfer Function

Vr for Desert and Mountain Locations: The Atmospheric Effects on ro," J pt SocAu, 71:397, 1981.

* .'Breaux, Harold J., "Correlation of Extended Huygens-Fresnel Turbulere

Calculations for a General Class of Tilt Corrected and Uncorrected LaserApertures," BRL IMR 600, Ballistic R, search Laboratory, Aberdeen Proving

U' Ground, MD, 1978.F 8

• • ....

Breaux's2 expression for beam spreading,

rT - sR-/ (3)

is calculated as a function of the Strehl ratio,

SI T

SR Tr (4)

where IT = on-axis irradiance with turbulence and diffraction and

ID = on-axis irradiance with only diffraction. The quantities rT and rD

have the same meanings as in equation (1).

For a uniform beam, the long-term Strehl ratio is

SRLT =[1 + (D)2 -

For a uniform beam, the near-field, short exposure Strehl ratio is

[1 + 0.182(1)2 -1 < 3ror o ( 6a)

SRST=

1 + 2 1.18 )5/3 1 D > 3

1+- • (6b)r o oo

2Breaux, Harold J., "Correlation of Extended Huygens-Fresnel TurbulenceCalculations for a General Class of Tilt Corrected and Uncorrected LaserApertures," BRL IMR 600, Ballistic Research Laboratory, Aberdeen ProvirgGround, MD, 1978.

9

Short Exposure Comparison: Near-Field, Far-Field and Intermediate Cases

Fried's' integral expression [(equations (1) and (2a)] are compared withBreaux's" analytical expression equations (3), (4). (5), and (6) in the near-field, short exposure limit in table 1. EqLation (2a) was evaluatednumerically using a 1/2 Simpson rule integration. The agreement between the

two sets of results is excellent. For 2, the results are within 1

percent of each other; for - . 4, the results are within 6 percent of eachother. 0

TABLE 1. COMPARISON OF BREAUX'S ANALYTICAL EXPRESSION (6) WITHFRIED'S INTEGRAL EXPRESSION (2a) IN THE NEAR-FIELD, SHORTTERM LIMIT.

(path length = 2 km, wavelength = 10.6pm)

2 -2/3 Beam Spread rT (m)D) 2 (m-2/3) ro(m) D Fried(2a) Breaux(6a,b)Dnm) Cn 0

0.1 1 x 10-1 0.2363 0.4233 2.964 0.2441 0.2430

0.1 5 x 10- 0.0900 1.112 2.964 0.2646 0.2647

0.1 1 x 10-1 0.0593 1.685 2.964 0.2921 0.2945

0.4 1 x 10-1 0.2363 1.693 47.42 0.0731 0.0737

0.4 5 x 10- 0.0900 4.447 47.42 0.1445 0.1534

0.4 1 x 10-12 0.0593 6.740 47.42 0.2505 0.2540

For the far-field, short exposure limit, a similar comparison cannot be made

owing to the lack of an analytical expression analogous to (6) in the far-

field limit. However, for values of - unity, the near-field and far-field,

short exposure values can differ by more than 50 percent. In order to bridgethe near-field and far-field limits, the short exposure limit resolutions

'Fried, D. L., "Optical Resolution Through a Randomly Inhomogeneous Medium for

* -Very Long and Very Short Exposures," J Opt Soc Am, 56:1372, 1976.

'Breaux, Harold J., "Correlation of Extended Huygens-Fresnel Turbulence

Calculations for a General Class of Tilt Corrected and Uncorrected LaserApertures," BRL IMR 600, Ballistic Research Laboratory, Aberdeen ProvingGround, MD, 1978.

10

[(equations (2a) and (2b)] were combined in the following interpolationexpression:

inR~ 0 x exp -3.44(k-) 5"3u5/3(1~ 1/3

m1ax0 1-F u ) (7)

where is the MTF of the optical system listed in (2a), the near-

field/far-f leld interpolation factor F - +2 and a is the Fresnel number.

The interpolated, normalized resolution given in equation (7) was used inconjunction with equation (1) to get the beam spread.

In table 2 we compare Fried' near-field and far-field, short exposureresults for beam spreading with the interpolation expression. Consistent withthe resolutions shown in figure 1, the beam spread values approach one another

for L= 0.4233, diverging forL 1. The interpolation formula in the

present study correctly goes to the proper limits in the near-field (a >> 1)cases. For intermediate cases (a -~ 1), the results fall between the near- andfar-field limits.

TABLE 2. BEAM SPREAD IN SHORT EXPOSURE LIMIT.*

(path length - 2 kin, wavelength - 10.6ma)

Beam Spread rT (

near-field far-field in t

2 ft

D(m) C2 ro(m) L a (2a) tb) (7)n r

0.1 1 x 10-1 0.2363 0.4233 2.964 0.2441 0.2565 0.2491

0.1 5 x 101 0.0900 1.112 2.964 0.2646 0.3266 0.29060.1 1 x 10-11 0.0593 1.685 2.964 0.2921 0.4128 0.3457

0.4 1 x 101 0.2363 1.693 47.42 0.0731 0.1035 0.07460.4 5 x 10-11 0.0900 4.447 47.42 0.1445 0.2386 0.15390.4 1 x 10-12 0.0593 6.740 47.42 0.2505 0.3604 0.2651

wincludes diffraction and turwuencet in = interpolation

'Fried, D. L., "Optical Resolution Through a Randomly Inhomogeneous uediu forVery Long and Very Short Exposures," J Opt Soc Am, 71:397, 1981.

reut o em pedn th h n1 pltinepeso.1ossetwt

Though the interpolation scheme is ad hoc, the results are reasonable sinceone expects a smooth, continuous shift from the near-field to far-fieldresults, as a function of decreasing Fresnel number.

Long Exposure Comparison

In the limit of long exposures, the random tilt variations are responsible formost of the distortion and beam spread. Thus, no distinction between near-field and far-field is necessary.

Fried's' integral expression is compared with Breaux's' analytical expressionin the long exposure limit in table 3. A reasonably good agreement existsbetween the two sets of calculations, always within at least 7 percent of eachother. The results, using Breaux's formalism, yield slightly smaller valuesfor the beam spread; the differences are not considered significant.

Beam spread in the long exposure limit has larger values compared with beamspread for the same parameters in the short exposure limit (compare tables 3and 2). This diffeiance occurs because the long exposure beam spread consistsof random tilt variations along with the short exposure beam spreading;therefore, beam spread in the long exposure limit will always be larger thanin the short exposure limit.

Short, Long, and Intermediate Exposure Comparison

Analogous to the interpolation scheme used to bridge the near-field/far-fieldresults, an interpolation factor for short and long exposures was incorporatedinto an expression for the normalized resolution. The normalized resolutionnow becomes:

___RsLE x exp -3.44(--) 5 /3u5 / 3 * (1 -r F u1/ 3 ) (8)

where i is the short exposure/long exposure interpolation factor.

'Fried, D. L., "Optical Resolution Through A Randomly Inhomogeneous Medium forVery Long and Very Short Exposures," J Opt Soc Am, 56:1372, 1976.

"Breaux, Harold J., "Correlation of Extended Huygens-Fresnel TurbulenceCalculations for a General Class of Tilt Corrected and Uncorrected LaserApertures," BRL IMR 600, Ballistic Research Laboratory, Aberdeen ProvincGround, MD, 1978.

12

TABLE 3. COMPARISON OF BREAUX'S ANALYTICAL EXPRESSION (5) WITHFRIED'S INTEGRAL EXPRESSION (2c IN THE LONG EXPOSURELIMIT.

(path length = 2 km, wavelength l0.6mm)

Dm) 2Beam Spread rT (m)Dim) m~n 3 rto(m) L a Fried(Zc) Breaux(5)

n r 0

0.1 1 x 10" 1 0.2363 0.4233 2.964 0.2685 0.2597

0.1 5 x 10- 13 0.0900 1.112 2.964 0.3802 0.3576

0.1 1 x 10"112 0.0593 1.685 2.964 0.5013 0.4686

0.4 1 x 10- 0.2363 1.693 47.42 0.1258 0.1176

0.4 5 x 10-' 0.0900 4.447 47.42 0.2864 0.2725

0.4 1 x 10" 0.0593 6.740 47.42 0.4232 0.4074

In figure 2 the normalized resolutions given in the short exposure limit usingthe near-field/far-field interpolated resolution given in equation (7), thelong exposure limit using equation (2c), and and the interpolated case usingthe short exposure/long exposure resolution given in equation (8) arepresented as a function of strength of turbulence. For the interpolatedresolution, the Fresnel number a was set to 2 and the pulse time over eddycrosstime t/tc was set to 0.11. Note that the interpolated results always lie

between the two limiting results and that, as in figure 1, the results go tothe same values in the limit of weak or strong turbulence.

Beam spreading, using the normalized resolutions plotted in figure 2, istabulated in table 4 for a pathlength of 2 kin, wavelength of 10.60n, and ashort/long exposure interpolation factor r of 0.5. Note that the longexposure beam spread is always larger than the short exposure value--as itshould be. The interediate cases all fall between the long and short

exposure values. For small values of - (e.g., the first entry in table

4, -L= 0.4233), the differences between the three formulations are small.

For values of L > 1, the differences become appreciable. For the 0.4 mr0- aperture diameter, F- 4.447 entry, the long exposure value is 86 percent

greater than the short exposure value. The intermediate value is 56 percentlarger than the short exposure value and 19 percent smaller than the longexposure value.

Beam spread in the short, long, and intermediate exposure cases is plotted asa function of strength of turbulence in figure 3. In calculating the valuesfor the intermediate cases, a was set to 2 and t/tc 0.11 (equivalent to r =

* 13

- - - " -' - - -- - . - - -. . - 2, . . -lip,. .

- N-FEV. SE-I.C l\TKI. %TIN1-- u'M.-IcArOSi REi I.IIMIT

\ AR N 1 FillI ~ll.ll.~h)EN'LIMITI"'. III i ild .1111

311VENIWTI OF T1RIW1ANT VE1/R)

Figure 2. Normalized resolution Rt as a function of strength of turbulencer0

in the short exposure limit (using the niear-field/far-fieldinterpolated resolution given by equation (7)); long exposurelimi t, and interpolated case (using the short exposure/longexposure resolution given by equation (8)). For the interpolatedcase, a - 2.0 and t/tc 30.11.

lollI I i ll~ 1 - 1 1 'It

U.NAR-FIEIAh. SlRT-EXI'o1StkI LIMIT

- AIN;-EU'OslIII: IMIT I

- N-FF. SE.I.I INTERPOI.ATIN

STREN;TI OF TIRB1I.ENV (D/R41

* Figure 3. Beam spread (in meters) as a function of strength of turbulence D-

in the short exposure, long exposure and interpolated cases. Forthe interpolated case, a =to 2 0 and t/tc 0.11.

14

0.9). Again note the convergence to the same beam spread value for

weak (<< 1) and strong (DL >> 1) turbulence. The intermediate exposurer r0

curve 0 falls between the two extremes with the differences largest

around 1.

TABLE 4. BEAM SPREAD IN THE SHORT EXPOSURE, LONG EXPOSURE, ANDINTERMEDIATE CASE.

(path length = 2 km, wavelength = lO.6um and r = 0.5)

Beam Spread rT (m)2. 2/3,D

D(m) Cn(m 2" ro(m) Do 5EI)w LE(ZC)t 1N5(Hn 0

0.1 1 x 10-1' 0.2363 0.4233 2.964 0.2491 0.2685 0.2589

0.1 5 x 10"" 0.0900 1.112 2.964 0.2906 0.3802 0.3380

0.1 1 x 1012 0.0593 1.685 2.964 0.3457 0.5013 0.4326

0.4 1 x 10"" 0.2363 1.693 47.42 0.0746 0.1258 0.1040

0.4 5 x 10-1' 0.0900 4.447 47.42 0.1539 0.2864 0.2397

0.4 1 x 10"" 0.0593 6.740 47.42 0.2651 0.4232 0.3619

*SE short exposuretLE a Long exposurewIN a Intermediate

I..:K 151l ... _

SU14MARY OF BEAM SPREADING RESULTS

Comparison of Fried's' near-field, short exposure expressions and Ion- exposure expressions with those of Breaux* showed excellent overal?

agreement. The interpolation expression of the present study shows the properK limiting results in the near- and far-field, short exposure cases and in thelong exposure case. It also gives entirely reasonable results in theintermediate cases. It would be preferable--for ease of computation--to havean analytical interpolation expression similar to the limiting expressionsdeveloped by Breaux. The lack of an analytical, far-field, short exposureexpression, however, prevents formulating such an expression.

The complete beam spreading expression is given by

r r .16 D 2 cos-1 - 2 1/2T DUro 0"

x exp[-3.44(-) 5/3u5/3 (1--rF.u1/3 )] -1/2

(9)

= tC 2 0+1where r t-+ -c and F * , and

where interpolates between the short and long exposure limits and Finterpolates between the near- and far-field limits.

0

'Fried, D. L., "Optical Resolution Through a Randomly Inhomogeneous Medim forVery Long and Very Short Exposures," J Ot Soc A, 56:1372, 1976.

Breaux, Harold J., wCorrelation of Extended Huygens-Fresnel TurbulenceCalculations for a General Class of Tilt Corrected and Uncorrected LaserApertures," BRL IMR 600, Ballistic Research Laboratory, Aberdeen ProvingGround, MD, 1978.

16

REFEREN4CES

1. Fried, D. L., "Optical Resolution Through a Randomly Inhomogeneous Mediumfor Very Long and Very Short Exposures," J Opt Soc Am, 56:1372, 1976.

L.2. Breaux, Harold J., "Correlation of Extended Buygens-Fresnel TurbulenceCalculations for a General Class of Tilt Corrected and Uncorrected LaserApertures," BRL IMR 600, Ballistic Research Laboratory, Aberdeen ProvingGround, I'D, 1978.

3. Walters, D. L., and K. E. Kunkel, *Atmospheric Modulation Transfer* Function for Desert and Mountain Locations: The Atmospheric Effects on ro,"

Opt Soc Am, 71:397, 1981.

. . .. ... . . °.. . -. *• o- .- .. • ,

_W

ELECTRO-OPTICS DISTRIBUTION LIST

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Redstone Arsenal, AL 35809NASA/Marshall Space Flight CenterATTN: ES-83 (Otha H. '!aughan, Jr.) CommanderHuntsville, AL 35812 US Army Missile Command

ATTN: DRSMI-REO (Mr. Gene Widenhofer)NASA/Marshall Space Fligh t Center Redstone Arsenal, AL 35809Atmospheric Sciences DivisionATTN: Code ES-81 (Dr. William W. Vaughan) CommanderHuntsville, AL 35812 US Army Missile Command

ATTN: DRSMI-RHC (Dr. Julius Q. Lilly)Nichols Research Corporation Redstone Arsenal, AL 35809ATTN: Dr. Lary W. Pinkley4040 South Memorial Parkway CommanderHuntsville, AL 35802 US Army Missile Command

Redstone Scientific Information Center

John M. Hobbie ATTN: DRSMI-RPRD (Documents Section)c/o Kentron International' Redstone Arsenal, AL 358092003 Byrd Spring RoadHuntsville, AL 35802 Commander

US Army Missile CommandMr. Ray Baker ATTN: DRSMI-RRA (Dr. Oskar Essenwanger)Lockheed-Missile & Space Company Redstone Arsenal, AL 358094800 Bradford BlvdHuntsville, AL 35807 Commander

US Army Missile CommandCommander ATTN: ORSMI-RRO (Mr. Charles Christensen)US Army Missile Command Redstone Arsenal, AL 358ATTN: DRSMI-OG (Mr. Donald R. Peterson)Redstone Arsenal, AL 35809 Commander

US Arw Missile CommandCommander ATTN: ORSNI-RRO (Dr. George A. Tanton)US Army Missile Command Redstone Arsenal, AL 35ATTN: ORSHI-OGA (Dr. Bruce W. Fowler)Redstone Arsenal, AL 35809

Is

Coinnder SRI InternationalommUS Arm Comnicatons Command ATTN: Mr. J. E. Van der LeanATTm: Cc-oS-mm 333 Ravenswood AvenueFort Iuachuca, AZ 85613 Menlo Park, CA 94025

Commander Joane MayUS Army Intelligence Center A School Naval Environmental PredictionATTN: ATSI-CD-CS (Mr. Richard G. Cundy) Research Facility (NEPRF)Fort Huachuca, AZ 85613 ATTN: Library

Monterey, CA 93940CommanderUS Army Intelligence Center A School Sylvania Systems Group,ATTN: ATSI-CD-MD (Mr. Harry Wilder) Western DivisionFort Huachuca, AZ 85613 GTE Products Corporation

ATTN: Technical Reports LibraryCommander P.O. Box 205US Army Intelligence Center & School Mountain View, CA 94042ATTN: ATSI-CS-C (2LT Coffman)Fort Huachuca, hZ 85613 Sylvania Systems Group

Western DivisionCommander GTE Products CorporationUS Army Yuma Proving Ground ATTN: Mr. Lee W. CarrierATTN: STEYP-MSA-TL P.O. Box 188Bldg 2105 Mountain View, CA 94042Yuma, AZ 85364

Pacific Missile Test CenterNorthrop Corporation Geophysics DivisionElectro-Mechanical Division ATTN: Code 3250-3 (R. de Violini)ATTN: Dr. Richard D. Tooley Point Mugu, CA 93042500 East Orangethorpe AvenueAnaheim, CA 92801 Pacific Missile Test Center

Geophysics DivisionCommander ATTN: Code 3253 (Terry E. Battalino)Naval Weapons Center Point Mugu, CA 93042ATTN: Code 3918 (Dr. Alexis Shlanta)China Lake, CA 93555 Effects Technology Inc.

ATTN: Mr. John 0. CarlyleHughes Helicopters 5383 Hollister Avenue

* Army Advanced Attack Helicopter Weapons Santa Barbara, CA 93111ATTN: Mr. Charles R. HillCentinela and Teale Streets CommnderBldg 305, MS T-73A Naval Ocean Systems CenterCulter City, CA 90230 ATTN: Code 532 (Dr. Juergen Richter)

San Diego, CA 92152

* CommanderUS Army Combat Developments Commander

Experimentation Command Naval Ocean Systems CenterATTN: ATEC-PL-M (Mr. Gary G. Love) ATTN: Code 5322 (Mr. Herbert G. Hughes)Fort Ord, CA 93941 San Diego, CA 92152

* SRI International CommanderATTN: K2060/Or. Edward E. Uthe Naval Ocean Systems Center333 Ravenswood Avenue ATTN: Code 4473 (Tech Library)Menlo Park, CA 94025 San Diego, CA 92152

* 19

The RAND Corporation CommanderATTN: Ralph Huschke US Army Signal Center A Fort Gordon1700 Main Street ATTN: ATZHCD-CSSanta Monica, CA 90406 Fort Gordon, GA 30905

Particle Measuring Systems, Inc. CommanderATTN: Dr. Robert G. Knollenberg US Army Signal Center A Fort Gordon1855 South 57th Court ATTN: ATZHCD-OBoulder, CO 80301 Fort Gordon, GA 30905

US Department of Commerce USAFETAC/DNENational Oceanic and Atmospheric Admin ATTN: M-. Charles GlauberEnvironmental Research Laboratories Scott AFB, IL 62225ATTN: Library, R-51, Technical Reports325 Broadway Commander

* Boulder, CO 80303 Air Weather ServiceATTN: AWS/DNDP (LTC Kit G. Cottrell)

US Department of Commerce Scott AFB, IL 62225National Oceanic and Atmospheric AdminEnvironmental Research Laboratories CommanderATTN: R45X3 (Dr. Vernon E. Derr) Air Weather ServiceBoulder, CO 80303 ATTN: AWS/DOOF (MAJ Robert Wright)

Scott AFB, IL 62225" US Department of Commerce

National Telecommunications and CommanderInformation Administration US Army Combined Arms Center

Institute for Telecommunication Sciences & Ft. LeavenworthATTN: Code 1-3426 (Dr. Hans J. Liebe) ATTN: ATZLCA-CAA-Q (Mr. H. Kent Pickett)Boulder, CO 80303 Fort Leavenworth, KS 66027

* AFATL/DLODL CommanderTechnical Library US Army Combined Arms CenterEglin AFB, FL 32542 & Ft. Leavenworth

ATTN: ATZLCA-SAN (Robert DeKinder, Jr.)Commanding Officer Fort Leavenworth, KS 66027Naval Training Equipment CenterATTN: Technical Information Center Commander

* Orlando, FL 32813 US Army Combined Arms Center& Ft. Leavenworth

Georgia Institute of Technology ATTN: ATZLCA-SAN (Mr. Kent 1. Johnson)Engineering Experiment Station Fort Leavenworth, KS 66027ATTN: Dr. Robert W. McMillan

* Atlanta, GA 30332 CommanderUS Army C-ibined Arms Center

Georgia Institute of Technology A Ft. LeavenworthEngineering Experiment Station ATTN: ATZLCA-WE (LTC Darrell Holland)ATTN: Dr. James C. Wiltse Fort Leavenworth, KS 66027Atlanta, GA 30332

PresidentCommandant USAARENBDUS Army Infantry Center ATTN: ATZK-AE-TA (Dr. Charles R. Leake)ATTN: ATSH-CD-MS-E (Mr. Robert McKenna) Fort Knox, KY 40121Fort Benning, GA 31805

20

Commander Conmander/DirectorUS Army Armor Center and Fort Knox Chemical System Laboratory

I ATTN: ATZK-CD-MS US Amy Armament ResearchFort Knox, KY 40121 & Development Command

.. ATTN: DRDAR-CLB-PS (Dr. Edward Stuebing)

Conmander Aberdeen Proving Ground, MD 21010US Army Armor Center and Fort KnoxATTN: ATZK-CD-SD Com nder/DirectorFort Knox, KY 40121 Chemical System Laboratory

US Army Armament Research

Aerodyne Research Inc. A Development CommandATTN: Dr. John F. Ebersole ATTN: DRDAR-CLB-PS (Mr. Joseph Vervier)Crosby Drive Aberdeen Proving Ground, MD 21010Bedford, MA 01730

Commander/Di rectorCommander Chemical Systems LaboratoryAir Force Geophysics Laboratory US Army Armament ResearchATTN: OPA (Dr. Robert W. Fenn) & Development CommandHanscom AFB, MA 31731 ATTN: DRDAR-CLY-A (Mr. Ronnald Pennsyle)

Aberdeen Proving Ground, 14D 21010CommanderAir Force Geophysics Laboratory CommanderATTN: OPI (Dr. Robert A. McClatchey) US Army Ballistic Research Laboratory/

ATTN: ORDAR-TSB-S (STINFO)Massachusetts institute of Technology Aberdeen Proving Ground, MD 21005Lincoln LaboratoryATTN: Dr. T. J. Goblick, B-370 CommanderP.O. Box 73 US Army Electronics ResearchLexington, MA 02173 & Development Command

ATTN: DRDEL-CCM (W. H. Pepper)

Massachusetts Institute of Technology Adelphi, 1ID 20783Lincoln LaboratoryATTN: Dr. Michael Gruber CommanderP.O. Box 73 US Army Electronics ResearchLexington, MA 02173 & Development Command

ATTN: DRDEL-CG/DRDEL-DC/DRDEL-CSRaytheon Company 2800 Powder Mill RoadEquipment Division Adelphi, 143 20783ATTN: Dr. Charles M. Sonnenschein430 Boston Post Road CommanderWayland, MA 01778 US Arwy Electronics Research

& Development CommandCommander ATTN: DRDEL-CTUS Army Ballistic Research Laboratory/ 2800 Powder Mill Road

ARRADCOM Adelphi, 14 20783* ATTN: DRDAR-BLB (Mr. Richard McGee)

Aberdeen Proving Ground, 14) 21005 CommanderUS Army Electronics Research& Development Command

ATTM: DRDEL-PAO (M. Singleton)2800 Powder Mill RoadAdelphi, 143 20783

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11"1

Project Manager DirectorSmoke/Obscurants US Army Materiel Systems Analysis ActivityATTN: DRDPM-SMK ATTN: DRXSY-J (Mr James F. O'Bryon)

(Dr. Anthony Van de Wal, Jr.) Aberdeen Proving Ground, MD 21005Aberdeen Proving Ground, MD 21005

Director; Project Manager US Army Materiel Systems Analysis Activity- Smoke/Obscurants ATTN: DRXSY-LM (Mr. Robert M. Marchetti)

ATTN: DRDPM-S14K-T (Mr. Sidney Gerard) Aberdeen Proving Ground, MD 21005Aberdeen Proving Ground, MO 21005

CommanderF Comander Harry Diamond LaboratoriesUS Army Test & Evaluation Command ATTN: Dr. William W. CarterATTN: DRSTE-AD-M (Mr. Warren M. Baity) 2800 Powder Mill RoadAberdeen Proving Ground, MD 21005 Adelphi, V. 20783

Commander CommanderUS Army Test & Evaluation Command Harry Diamond LaboratoriesATTN: DRSTE-AD-M (Dr. Normnan E. Pentz) ATTN: DELHD-R-CM (Mr. Robert McCoskey)Aberdeen Proving Ground, MD 21005 2800 Powder Mill RoadDirco Adelphi, MD 20783

.- Di rector

US Army Materiel Systems Analysis Activity CommanderATTN: DRXSY-AAM (Mr. William Smith) Harry Diamond LaboratoriesAberdeen Proving Ground, MD 21005 ATTN: DELHD-R-CM-NM (Dr. Robert Humphrey)

2800 Powder Mill RoadDirector Adelpht, MD 20783US Army Materiel Systems Analysis ActivityATTN: DRXSY-CS (Mr. Philip H. Beavers) CommanderAberdeen Proving Ground, MD 21005 Harry Diamond Laboratories

ATTN: DELHD-R-CM-NM (Dr. Z. G. Sztankay)Director 2800 Powder Mill Road

W US Army Materiel Systems Analysis Activity Adelphi, MD 20783ATTN: DRXSY-GB (Wilbur L. Warfield)

* Aberdeen Proving Ground, MD 21005 CommanderHarry Diamond Laboratories

Director ATTN: DELHD-R-CMNI (Dr. Joseph Nemarich)US Army Materiel Systems Analysis Activity 2800 Powder Mill RoadATTN: DRXSY-GP (Mr. Fred Campbell) Adelphl, MD 20783Aberdeen Proving Ground, MD 21005

CommanderDirector Air Force Systems CommandUS Army Material Systems Analysis Activity ATTN: WER (Mr. Richard F. Picanso)ATTN: DRXSY-GP (H. Stamper) Andrews AFB, MD 20334Aberdeen Proving Grounds, MD 21005

Martin Marietta LaboratoriesDirector ATTN: Jar Mo Chen

US Army Materiel Systems Analysis Activity 1450 South Rolling RoadATTN: DRXSY-GS Baltimore, MD 21227

* (Mr. Michael Starks/Mr. Julian Chernick)Aberdeen Proving Ground, MD 21005

l -_22

Commander Dr. A. D. BelmontUS Army Concepts Analysis Agency Research DivisionATTN: CSCA-SMC (Mr. Hal E. Hock) Control Data Corporation8120 Woodmont Avenue P.O. Box 1249Bethesda, MD 20014 Minneapolis, MN 55440

Director DirectorNational Security Agency US Army Engr Waterways Experiment StationATTN: R52/Dr. Douglas Woods ATTN: WESEN (Mr. James Mason)Fort George G. Meade, MD 20755 P.O. Box 631

Vicksburg, MS 39180ChiefIntelligence Materiel Development Dr. Jerry Davis& Support Office Department of Marine, Earth

US Army Electronic Warfare Laboratory and Atmospheric SciencesATTN: DELEW-I (LTC Kenneth E. Thomas) North Carolina State UniversityFort George G. Meade, MD 20755 Raleigh, NC 27650

The Johns Hopkins University CommanderApplied Physics Laboratory US Army Research OfficeATTN: Dr. Michael J. Lun ATTN: DRXRO-GS (Dr. Leo Alpert)John Hopkins Road P.O. Box 12211Laurell, MD 20810 Research Triangle Park, NC 27709

Dr. Stephen T. Hanley Commander1720 Rhodesia Avenue US Army Research OfficeOxon Hill, MD 20022 ATTN: DRXRO-PP (Brenda Mann)

P.O. Box 12211

Science Applications Inc. Research Triangle Park, NC 27709ATTN: Mr. G. D. Currie15 Research Drive CommanderAnn Arbor, MI 48103 US Army Cold Regions Research

& Engineering LaboratoryScience Applications Inc. ATTN: CRREL-RD (Dr. K. F. Sterrett)ATTN: Dr. Robert E. Turner Hanover, NH 0375515 Research DriveAnn Arbor, MI 48103 Commander/Director

US Army Cold Regions Research

Commander & Engineering LaboratoryUS Army Tank-Automotive Research ATTN: CRREL-RG (Mr. George Aitken)& Development Command Hanover, NH 03755

ATTN: DRDTA-ZSC (Mr. Harry Young)Warren, MI 48090 Commander

US Army Cold Regions Research

Commander & Engineering LaboratoryUS Army Tank Automotive Research ATTN: CRREL-RG (Mr. Roger H. Berger)& Development Command Hanover, NH 03755

ATTN: DRDTA-ZSC (Mr. Wallace Mick, Jr.)Warren, MI 48090 Commander

US Army Armament Research& Development Command

ATTN: DRDAR-AC (Mr. James Greenfield)Dover, NJ 07801

23

Commander CommanderUS Army Armament Research US Army Electronics Research

& Development Command & Development CommandATTN: DRDAR-TSS (Bldg #591 ATTN: DDEL-SA (Mr. Walter S. McAfee)Dover, NJ 07801 Fort Monmouth, NJ 07703

Coumander OLA, 2WS (MAC)US Army Armament Research Holloman AF, Nm 88330

& Development Command CommanderATTN: DRCPM-CAWS-EI (Mr. Peteris Jansons) Air Force Weapons LaboratoryDover, NJ 07801 ATTN: AFWL/WE (MAJ John R. Elrick)

Kirtland, AFB, NM 87117CommanderUS Army Armament Research Director& Development Command USA TRADOC Systems Analysis Activity

ATTN: DRCPM-CAWS-EI (Mr. G. H. Waldron) ATTN: ATAA-SL" Dover, NJ 07801 White Sands Missile Range, NM 88002

* Deputy Joint Project Mai.ager Directorfor Navy/USMC SAL GP USA TRADOC Systems Analysis Activity

ATTN: DRCPM-CAWS-NV (CPT Joseph Miceli) ATTN: ATAA-SL (Dolores Angulano)Dover, NJ 07801 White Sands Missile Range, NM 88002

* Commander/Director DirectorUS Army Combat Surveillance & Target USA TRADOC Systems Analysis Activity

Acquisition Laboratory ATTN: ATAA-TDB (Mr. Louie Dominguez)ATTN: DELCS-I (Mr. David Longinotti) White Sands Missile Range, NM 88002Fort Monmouth, NJ 07703

DirectorCommander/Director USA TRADOC Systems Analysis ActivityUS Army Combat Surveillance & Target ATTN: ATAA-TDB (Mr. William J. Leach)

Acquisition Laboratory White Sands Missile Range, NM 88002ATTN: DELCS-PE (Mr. Ben A. Di Campli)Fort Monmouth, NJ 07703 Director

USA TRADOC Systems Analysis ActivityCommander/Director ATTN: ATAA-TGP (Mr. Roger F. Willis)US Army Combat Surveillance & Target White Sands Missile Range, NM 88002

Acquisition LaboratoryATTN: DELCS-R-S (Mr. Donald L. Folani) DirectorFort Monmouth, NJ 07703 Office of Missile Electronic Warfare

ATTN: DELEW-M-STO (Dr. Steven Kovel)Director White Sands Missile Range, NM 88002US Army Electronics Technology &

Devices Laboratory Office of the Test DirectorATTN: DELET-DD (S. Danko) Joint Services EO GW CM Test ProgramFort Monmouth, NJ 07703 ATTN: DRXDE-TD (Mr. Weldon Findley)

White Sands Missile Range, NM 88002Project ManagerFIREFINDER/REMBASS CommanderATTN: DRCPM-FFR-TM (Mr. John M. Bial'o) US Army White Sands Missile RangeFort Monmouth, NJ 07703 ATTN: STEWS-PT-AL (L3urel B. Saunders)

White Sands Missile Range, NM 88002

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Commander CommandantUS Army R&D Coordinator US Army Field Artillery SchoolUS Embassy - Bonn Morris Swett LibraryBox 165 ATTN: Reference LibrarianAPO New York 09080 Fort Sill, OK 73503

Grumman Aerospace Corporation CommanderResearch Department - MS A08-35 Naval Air Development CenterATTN: John E. A. Selby ATTN: Code 301 (Mr. George F. Eck)Bethpage, NY 11714 Warminster, PA 18974

Rome Air Development Center The University of Texas at El PasoATTN: Documents Library Electrical Engineering Department

TSLD (Bette Smith) ATTN: Dr. Joseph H. PierluissiGriffiss AFB, NY 13441 El Paso, TX 79968

Dr. Roberto Yaglio-Laurin CommandantFaculty of Arts and Science US Army Air Defense SchoolDept. of Applied Sc.ence ATTN: ATSA-CO-SC-A (CPT Charles T. Thorn)26-36 Stuyvesant Street Fort Bliss, TX 79916

U New York, NY 10003Commander

Air Force Wright Aeronautical Laboratories/ HQ, TRADOC Combined Arms Test ActivityAvionics Laboratory ATTN: ATCAT-OP-Q (CPT Henry C. Cobb, Jr.)

ATTN: AFWAL/AARI-3 (Mr. Harold Geltmacher) Fort Hood, TX 76544Wright-Patterson AFB, OH 45433

CommanderAir Force Wright Aeronautical Laboratories/ HQ, TRADOC Combined Arms Test Activity

Avionics Laboratory ATTN: ATCAT-SCI (Dr. Darrell W. Collier)ATTN: AFWAL/AARI-3 (CPT William C. Smith) Fort Hood, TX 76544Wright-Patterson AFB, OH 45433

CommanderCommandant US Army Dugway Proving GroundUS Army Field Artillery School ATTN: STEDP-MT-DA-LATTN: ATSF-CF-R (CPT James M. Watson) Dugway, UT 84022Fort Sill, OK 73503

CommanderCommandant US Army Dugway Proving Ground

V US Army Field Artillery School ATTN: SrEDP-MT-DA-M (Mr. Paul E. Carlson)ATTN: ATSF-CD-MS Dugway, UT 84022Fort Sill, OK 73503

CommanderCommandant US Army Dugway Provin, GroundUS Army Field Artillery School ATTN: STEDP-MT-DA-T (Mr. John Trethewey)ATTN: ATSF-CF-R Dugway, UT 84022Fort Sill, OK 73503

CommanderCommandant US Army Dugway Proving GroundUS Army Field Artillery School ATTN: STEDP-MT-DA-T (Mr. William Peterson)ATTN: NOAA Liaison Officer Dugway, UT 84022

(CDR Jeffrey G. Carlen)Fort Sill, OK 73503

25

'U

Defense Documentation CenterATTN: DDC-TCA System Planning Corporation

K Cameron Station Bldg 5 ATTN: Mr. Daniel criedmanAlexandria, VA 22314 1500 Wilson Boulevard12 Arlington, VA 22209

Ballistic Missile Defense Program Office System Planning CorporationATTN: DACS-BMT (Colonel Harry F. Ennis) ATTN: COL Hank Shelton5001 Eisenhower Avenue 1500 Wilson BoulevardAlexandria, VA 22333 Arlington, VA 22209

Defense Technical Information Center US Army Intelligence & Security ConmandATTN: DDA-2 (Mr. James E. Shafer) ATTN: Edwin Speakmdn, Scientific AdvisorCameron Station, Bldg 5 Arlington Hall StationAlexandria, VA 22314 Arlington, VA 22212

Commander CommanderUS Army Materiel Development US Army Operational Test

& Readiness Command & Evaluation AgencyATTN: DRCBSI-EE (Mr. Albert Giambalvo) ATTN: CSTE-ED (Mr. Floyd I. Hill)5001 Eisenhower Avenue 5600 Columbia PikeAlexandria, VA 22333 Falls Church, VA 22041

Commander Commander and DirectorUS Army Materiel Development US Army Engineer Topographic Laboratories& Readiness Command ATTN: ETL-GS-A (Mr. Thomas Neidringhaus)

ATTN: DRCLDC (Mr. James Bender) Fort Belvoir, VA 220605001 Eisenhower AvenueAlexandria, VA 22333 Director

US Army Night Vision &Defense Advanced Rsch Projects Agency Electro-Optics LaboratoryATTN: Steve Zakanyez ATTN: DELNV-L (Dr. Rudolf G. Buser)1400 Wilson Blvd Fort Belvoir, VA 22060Arlington, VA 22209

DirectorDefense Advanced Rsch Projects Agency US Army Night Vision &ATTN: Dr. James Tegnelia Electro-Optics Laboratory

* 1400 Wilson Blvd ATTN: DELNV-L (Dr. Robert S. Rodhe)Arlington, VA 22209 Fort Belvoir, VA 22060

" Institute for Defense Analyses DirectorATTN: Mr. Luclen M. Biberman US Army Night Vision &400 Army-Navy Drive Electro-Optics Laboratory

* Arlington, VA 22202 ATTN: DELNV-VI (Mr. Joseph R. Moulton)Fort Belvoir, VA 22060

" Institute for Defense AnalysesATTN: Dr. Ernest Bauer Director400 Army-Navy Drive US Army Night Vision &Arlington, VA 22202 Electro-Optics Laboratory

ATTN: DELNV-VI (Luanne P. Obert)Institute for Defense Analyses Fort Belvoir, VA 22060ATTN: Dr. Hans G. Wolfhard

* 400 Army-Navy DriveArlington, VA 22202

26

L

Director Department of the Air ForceUS Army Night Vision HQS 5 Weather Wing (MAC)& Electro-Optics Laboratory ATTN: 5 WW/DN

- ATTN: DELNV-VI (Mr. Thomas W. Cassidy) Langley Air Force Base, VA 23655Fort Belvoir, VA 22060

CommanderDirector US Army INSCOM/Quest Research CorporationUS Army Night Vision & ATTN: Mr. Donald WilmotElectro-Optics Laboratory 6845 Elm Street, Suite 407

ATTN: DELNV-VI (Mr. Richard J. Bergemann) McLean, VA 22101Fort Belvoir, VA 22060

General Research CorporationDirector ATTN: Dr. Ralph ZirkindUS Army Night Vision & 7655 Old Springhouse RoadElectro-Optics Laboratory McLean, VA 22102

ATTN: DELNV-VI (Dr. James A. Ratches)Fort Belvoir, VA 22060 Science Applications, Inc.

8400 Westpark DriveCommander ATTN: Dr. John E. CockayneUS Army Training & Doctrine Command McLean, VA 22102ATTN: ATCD-ANFort Monroe, VA 23651 US Army Nuclear & Chemical Agency

ATTN: MONA-WE (Dr. John A. Berberet)Commander 7500 Backlick Road, Bldg 2073JS Army Training & Doctrine Command Springfield, VA 22150ATTN: ATCD-AN-MFort Monroe, VA 23651 Director

-. US Army Signals Warfare LaboratoryCommander ATTN: DELSW-EA (Mr. Douglas Harkleroad)US Army Training & Doctrine Command Vint Hill Farms StationATTN: ATCD-F-A (Mr. Chris O'Connor, Jr.) Warrenton, VA 22186Fort Monroe, VA 23651

Di rectorCommander US Army Signals Warfare LaboratoryUS Army Training & Doctrine Command ATTN: DELSW-OS (Dr. Royal H. Burkhardt)ATTN: ATCD-IE-R (Mr. David M. Ingram) Vint Hill Farms StationFort Monroe, VA 23651 Warrenton, VA 22186

- Commander CommanderUS Army Training & Doctrine Command US Army Cold Regions Test CenterATTN: ATCD-M-I/ATCD-M-A ATTN: STECR-TD (Mr. Jerold Barger)Fort Monroe, VA 23651 APO Seattle, WA 98733

. Commander HQDA (SAUS-OR/Hunter M. Woodall, Jr./U IS Army Training & Doctrine Command Dr. Herbert K. Fallin)ATTN: ATDOC-TA (Dr. Marvin P. Pastel) Rm 2E 614, PentagonFort Monroe, VA 23651 Washington, DC 20301

Department of the Air Force COL Elbert W. Friday, Jr.OL-I, AWS OUSDREFort Monroe, VA 23651 Rm 3D 129, Pentagon

Washington, DC 20301

27

KI i ." -: , .-..-., .:, .: , .' ....- " :• • ; . .

Defense Communications Agency National Science FoundationTechnical Library Center Division of Atmospheric SciencesCode 222 ATTN: Dr. Eugene W. BierlyWashington, DC 20305 1800 G. Street, N.W.

Washington, DC 20550DirectorDefense Nuclear Agency DirectorATTN: Technical Library (Mrs. Betty Fox) Naval Research LaboratoryWashington, DC 20305 ATTN: Code 4320 (Dr. Lothar H. Ruhnke)

Washington, DC 20375Di rectorDefense Nuclear Agency Commanding OfficerATTN: RAAE (Dr. Carl Fitz) Naval Research LaboratoryWashington, DC 20305 ATTN: Code 6009 (Dr. John MacCallum, Jr.)Director AencyWashington, OC 20375

* Defense Nuclear Agency Commanding OfficerATTN: SPAS (Mr. Donald J. Kohler) Naval Research LaboratoryWashington, DC 20305 ATTN: Code 6530 (Mr. Raymond A. Patten)

Washington, DC 20375

U eFense Intelligence Agency

ATTN: DT/AC (LTC Robert Poplawski) Commanding Officer* Washington, DC 20301 Naval Research Laboratory

ATTN: Code 6533 (Dr. James A. Dowling)HQDA (DAMA-ARZ-D/Dr. Verderame) Washington, DC 20375Washington, DC 20310

HODA (DAMI-ISP/Mr. Beck)

Washington, DC 20310

Department of the ArmyDeputy Chief of Staff forOperations and Plans

ATTN: DAMO-RQWashington, DC 20310

Department of the ArmyDirector of Telecommunications and

Command and ControlATTN: DAMO-TCZWashington, DC 20310

Department of the ArmyAssistant Chief of Staff for IntelligenceATTN: DAMI-TSWashington, DC 20310

HQDA (DAEN-RDM/Dr. de Percin)Casimir Pulaski Building20 Massachusetts AvenueRoom 6203Washington, DC 20314

28