Model of the rotational Raman gain coefficients forN2 in the atmosphere

G. C. Herring and William K. Bischel

A model for stimulated Raman scattering in the atmosphere is described for the pure rotational transitions inN2. This model accounts for the wavelength dependence of the N2 polarizability anisotropy, altitude andseasonal temperature variations in the atmosphere, and the 02 foreign-gas density broadening. Thisinformation is used to calculate the steady-state plane-wave Raman gain profile over the lower 100 km of theatmosphere. Over altitudes of 0-40 km, temperature variations produce 30% changes in the gain coefficientsof 1 km-' cm2 MW-' for the strongest lines at Stokes wavelengths of 350 nm.

1. Introduction

Several nonlinear effects, summarized by Zuev,l arepossible when a high intensity laser beam propagatesthrough the atmosphere. Recent work2A has focusedon the possibility that stimulated rotational Ramanscattering in N2 may have the lowest threshold intensi-ty. Stimulated Raman scattering then limits the max-imum laser intensity that can be transmitted throughthe atmosphere if the divergence of the beam is re-quired to remain unchanged. To establish this maxi-mum intensity, it is necessary to obtain an accuratedescription of the steady-state Raman gain coefficientin the atmosphere.

This paper describes a model of the Raman gaincoefficient for the N2 S-branch rotational transitionsin the atmosphere. This model is based on our recentstudy3 of the temperature dependence of the rotation-al Raman gain. In the present atmospheric work, weuse the same temperature dependence as described inRef. 3, although we also include the effect of foreign-gas (02) broadening on the N2 Raman lines. Thistemperature-dependent Raman gain coefficient isused with a published atmospheric model5 to calculatethe atmospheric N2 Raman gain coefficient. The im-portant new contribution of this paper is a tempera-ture-dependent description of the rotational N2 Ra-

The authors are with SRI International, Chemical Physics Lab-oratory, Menlo Park, California 94025.

Received 2 February 1987.0003-6935/87/152988-07$02.00/0.© 1987 Optical Society of America.

man gain coefficient as a function of altitude (0-100km) in the atmosphere.

The modeling of the propagation of a high intensitylaser pulse through a Raman medium, such as theatmosphere, requires a propagation code that includestransient effects, off-axis propagation for the generat-ed beams, the inclusion of all possible Stokes and anti-Stokes orders that can be generated, and the provisionfor a variable pump laser bandwidth. Codes includingsome of these effects are currently being developed inseveral laboratories including our own.6 The model ofthe steady-state gain coefficient presented here is animportant input to these codes.

II. Model Description

A. Atmospheric Model

In our atmospheric gain model, the Raman gaincalculation uses the altitude-dependent temperature,N2 density, and 02 density as input data. We havetaken these data from actual atmospheric measure-ments at Wallops Island, VA (380N), as published byBanks and Kockarts.5 Slightly different results areexpected if the standard atmospheric model7 is used.Temperatures and densities for N2 and 02 were takenfrom Table 3.1 of Ref. 5. Densities were extrapolatedfor the first 15 km (omitted from Table 3.1 of Ref. 5) byassuming an exponential decay with increasing alti-tude, an e-1 altitude of 8 km, and relative densities of78 and 21% for N2 and 02, respectively. The averageatmospheric temperature profiles for this model areshown in Fig. 1. Maximum variations are indicated byhorizontal bars for summer and by shading for winter.Temperatures for the first 15 km (also omitted fromTable 3.1 of Ref. 5) were determined from the averageof the summer and winter values in Fig. .

2988 APPLIED OPTICS I Vol. 26, No. 15 / 1 August 1987

90

80

70

60

wE

I"I-.!-a

50

40

30

20

160 200 250 280

TEMPERATURE {K)

Fig. 1. Temperature profiles used in the Raman gain calculations.Maximum variations are indicated by horizontal bars for summer

and by shading for winter (from Ref. 5).

B. Raman Gain Model

The temperature dependence of the rotational Ra-man gain is described in Ref. 3 and summarized below.The steady-state plane-wave Raman gain coefficient isgiven by2

XAN a, / p), (1)hvs oSQ

where f(bv) is the area-normalized Raman line shapeand 6v = P- S - VR, where vp,s are the pump/Stokeslaser frequencies, VR is the Raman transition frequen-cy, and Xs is the Stokes wavelength in the gain medium.

The spontaneous scattering cross section per molecule,auaia, is temperature independent, whereas the popu-lation difference AN and the line shape f(lv) are thetemperature-dependent factors. At the peak (v = 0)of a Lorentzian-shaped transition, Eq. (1) reduces toEq. (1) of Ref. 3. Table I briefly summarizes theparameters used in the present Raman gain calcula-tion.

The cross section is9o 2 2 7rvs 4 (J+ 1) J+ 2) 2

iQ 15 c / (2J+1) (2J+ 3) (2)

for pump and Stokes polarizations that are linear andparallel, which is the only geometry considered in thiswork. The polarizabilty anisotropy y is wavelength-dependent, and the details for determining the wave-length dependence are given in Ref. 3. All the resultspresented in this study are for a Stokes wavelength Xsof 350 nm and a polarizability anisotropy of 7.39 X10-25 cm 3 . We neglect the rotational quantum num-ber J dependence of y, an excellent approximation forN2 , as discussed in Ref. 3.

The population density difference is given by

AN = N(J) - /2J+ I N(J) (3)

N(J) is the number density of molecules with rotation-al quantum number J, where primed and unprimed Jdenote the upper and lower state, respectively. Thepopulation difference AN was calculated from a Boltz-man distribution using the N2 rotational constants inRef. 8.

Only the high density limit was considered for thegain calculations of Ref. 3, and thus Lorentzian func-tions were used for f(6P). For the present atmosphericmodel, we use a more general Voigt function for f(6v).In the most general case, the Galatry (or other relatedline shapes9) line shape is a more accurate line profilefor transitions that have line shapes with significantcontributions from collisional narrowing. However,our use of Voigt line shapes is a good approximation forrotational N2 lines in the atmosphere for two reasons.First, at low altitudes (<20 km), pressure broadeningdominates over Doppler broadening (5 MHz), and thuscollisional narrowing is negligible. Second, at higheraltitudes where Doppler broadening is appreciable, the

Table I. Parameters Used In the S(8) Gain Calculation for Xs = 350 nm

Altitude Temperature AN Voigt AVFWHM Gain coefficient(km) (K) N (MHz) f(bv = 0) (cm2 km-' MW-)

0 285 0.0349 2960 0.000215 0.6810 225 0.0441 784 0.000813 0.9220 219 0.0451 180 0.00354 0.9530 235 0.0424 39.8 0.0164 0.8740 268 0.0373 10.5 0.0595 0.6450 274 0.0365 5.7 0.121 0.3660 253 0.0396 4.9 0.166 0.1770 211 0.0464 4.5 0.209 0.06780 197 0.0489 4.3 0.216 0.01690 197 0.0489 4.3 0.218 0.0029

100 209 0.0468 4.4 0.212 0.00049

1 August 1987 / Vol. 26, No. 15 / APPLIED OPTICS 2989

density is too small for significant collisional narrow-ing. Thus pure Voigt line shapes were used for all ourresults.

The width of the Lorentzian contribution to theVoigt was obtained by adding the linewidths due toself-broadening and to 02 foreign-gas broadening.The linewidth measurements used here are summa-rized in Ref. 10. Self-broadening coefficients not giv-en in Table I of Ref. 10 were determined by assuming alinear J dependence. Foreign-gas broadening coeffi-cients for temperatures and J terms not given in TableV of Ref. 10 were determined by assuming that theforeign-gas values are 85% of the corresponding self-broadening values in Table I of Ref. 10. Finally, allbroadening coefficients were assumed to have the lin-ear temperature dependence described in Ref. 10.These three assumptions are based on the trendsshown by the data of Ref. 10.

Our calculations assume that the laser linewidth ismuch smaller than the Raman linewidth. These cal-culations will also be valid if the laser linewidth islarger than the Raman linewidth, provided that theStokes field is phase locked to the pump laser field.11 -14

Ill. Results

A. Altitude Dependence

Figure 2(a) shows the peak (5v = 0) Raman gain coeffi-cient of S(8) as a function of altitude for the tempera-ture profile described in Sec. II.A. The two quantitiesAN and APT that combine to produce this altitudeprofile are also shown in Figs. 2(b) and (c) for the sametemperature profile (APT is the FWHM Ramanlinewidth.) The Raman gain is about constant below40 km and drops to zero above 40 km. This occursbecause the peak Raman gain depends on the ratioAN/IAPT. Below 40 km, Figs. 2(b) and (c) show thatAN and APT decrease with altitude at about the samerate, yielding an -approximate constant value of gain.Above 40 km, Fig. 2(b) shows that AN continues todecrease, whereas Fig. 2(c) shows that APT becomesconstant with altitude; thus the Raman gain also de-creases with altitude. The Raman linewidth is con-stant at high altitudes because the collisional broaden-ing becomes negligible compared with theapproximate constant Doppler broadening.

Because the Raman line shape is predominantlycollisionally broadened over the 0-40-km region, apure Lorentzian line shape should be a good approxi-mation in the atmospheric gain calculation. For com-parison, the dashed line in Fig. 2(a) shows the gain ifthe line shape function f(Av) in Eq. (1) is calculatedfrom a Lorentzian profile with a FWHM linewidthgiven by

APT = (AvP + AV) 22. (4)

The quantities AVG and AVL are the Doppler and colli-sional FWHM linewidths, respectively. The approxi-mation is in good agreement with the full Voigt calcu-lation except for a 20% discrepancy in the 50-70-kmregion. This small difference is important for the gain

hi 0.8

CN 0.6E

z 0.4

0 0.2

lo-110-2

io 1 -3

,- 10-4Ez 10 5

q 10-6

1o-7

10-8

_; 104

I

0I 102zE 100

I

0 20 40 60 80 100ALTITUDE (km)

Fig. 2. Raman gain vs altitude. The solid curves show (a) the peak,steady-state plane-wave Raman gain coefficient; (b) the populationdifference AN, and (c) the Raman linewidth (Voigt FWHM) as afunction of altitude for S(8) in N2. The dashed curve in (a) showsthe gain if the approximation, APT = Av2 + AV2, is used in place ofthe Voigt calculation of (c). APT, AVG, and AVL are the total, Gauss-

ian, and Lorentzian linewidths, respectively.

calculation of the S(0) through S(4) transitions. Thecomparison of Fig. 2(a) shows that a simple approxi-mation of the N2 line shape is sufficient to predictaccurately the atmospheric Raman gain for the mostimportant transitions. However, we note that the restof the results presented here were obtained with com-plete Voigt calculations.

The peak Raman gain coefficients for the strongestStokes transitions are summarized as a function ofaltitude in Fig. 3. The difference between Figs. 3(a)and (b) is that the vertical scale of Fig. 3(b) is magni-fied by a factor of 3 to better illustrate the small gaincoefficients of S(0) through S(4). The number indi-cated next to each curve is the lower rotational quan-tum number J for that particular transition. Peaksand valleys that occur at an altitude of 15 km are due tothe temperature minimum (200 K) that exists at thisaltitude. Decreasing temperatures tend to transfermolecules from the higher rotational levels to lowerlevels; thus AN for S(14) and S(16) is decreasing whileAN for S(6) and S(8) is increasing at the temperatureminimum. In Fig. 3, S(8) and S(10) have the largestgains at sea level, in agreement with the observation of

2990 APPLIED OPTICS I Vol. 26, No. 15 / 1 August 1987

-1-----------1-------------1 �I I - I I_,__ -1 , , r I ,I

. . . . . I . I I

1.0

0.8

0.6

0.4

EE

zC

0.2

0

0.3

0.2

0.1

00 20 40 60 80 100

ALTITUDE (km)

Fig. 3. Peak Raman gain coefficients for (a) the strongest transitions and (b) some of the weaker transitions as a function of altitude.

Henesian et al.2 and our previous calculations.3 The

results of integrating the gain coefficients over thedepth of the atmosphere (from sea level to 100 km) aretabulated in Table II, where we see that S(6), S(8), andS(10) dominate the Stokes conversion process in theatmosphere. The odd-numbered J transitions areonly half as strong as their adjacent even-numberedneighbors and are omitted from this investigation.

Raman gain coefficients for frequencies other thanthose at the peak [by = 0 in Eq. (1)] of the Ramantransitions were also calculated. Figure 4(a) showsthe S(8) gain coefficient as a function of altitude fordetuning values of 0, 10, 100, and 800 MHz. Theintegrated (from 0 to 100 km in altitude) gain coeffi-

Table I. Peak Raman Gain Coefficients (Integrated from Sea Level to100 km) for Stokes Rotational Transitions of N2

Gain coefficientTransition S(J) (cm2 MW-1)

0 2.162 13.84 29.16 39.38 43.4

10 39.812 32.614 22.616 15.2

1 August 1987 / Vol. 26, No. 15 / APPLIED OPTICS 2991

I I I I \ I I I I I

S(2) \S(4)_ " (b)

SO "\ S/ ' \".N

11

S(O)

I I I I I I -

R 1.0

I 0.8E

g 0.6U

z 0.4

{D 0.2au,

I'

102

E 101z< 1000

10-1ccUJ

L- 10-2Z 1

0 20 40 60 80 10ALTITUDE (km)

10 11

0

)l 102 103

DETUNING (MHz)

Fig. 4. S(8) Raman gain coefficient (a) as a function of altitude fordetunings of 0, 10, 100, and 800 MHz from the line center and (b)integrated (from 0 to 100 km in altitude) gain coefficient as a func-

tion of detuning.

cient for S(8) is plotted vs detuning in Fig. 4(b). Theinformation illustrated in Fig. 4 is useful for determin-ing the effective bandwidth that experiences substan-tial gain over the entire lower 100 km of the atmo-sphere. This bandwidth is needed to calculate thepump laser intensity required to reach threshold.2'4We estimate this effective bandwidth from the detun-ing value, where the generated Stokes intensity is

E3C..

E

z

__e

oo

Cn

1.0

0.8

0.6

0.4

0.2

00

down by a factor of 2. From Fig. 4(b), this bandwidthis 2 MHz and is to be compared to the value of -3 MHzthat we estimate from Eq. (16) of Ref. 4.

B. Temperature Variations

All the results of Figs. 2-4 were obtained for thespecific temperature profile of Table 3.1 of Ref. 5.The effect of atmospheric temperature fluctuations issummarized in the four curves of Fig. 5. The change inRaman gain of S(8), due to seasonal variations of tem-perature, is illustrated with four different gain profiles.The four temperature profiles used in the calculationsof Fig. 5 were determined from Fig. 1. The curveslabeled maximum are the gains for the highest tem-peratures shown for that season, whereas those labeledminimum are the gains for the lowest temperaturesshown for that season. Figure 5 shows that maximumvariations in the Raman gain due to temperaturechanges in the atmosphere are -10% at all altitudes.

IV. Discussion

This is the first study to consider the effect of tem-perature variations on the Raman gain, and thus it isuseful to compare the present work with a previousatmospheric gain calculation that neglects the tem-perature effects.4 These two models are compared inFig. 6, where the S(8) gain coefficient is plotted vsaltitude for each model. Table III lists the most im-portant parameters associated wtih the gain coeffi-cient for both models. The two largest differences inthese two models are the temperature distribution ofthe atmosphere and the density broadening coeffi-cients that were used. Both the density broadeningcoefficients and the population difference change by20-25% for S(8) when the temperature changes from

20 40 60 80 100

ALTITUDE (km)Fig. 5. S(8) peak Raman gain variations for typical variations in atmospheric temperatures.

2992 APPLIED OPTICS / Vol. 26, No. 15 / 1 August 1987

I I I I I I I I I

(a)

-\00 100 10 \ MHz

_ \ \ \~~~~"

I I I . , I

(b)

I , , , j I

I

I

I

104

27

E

(9

e )

1.2

1.0

0.8

0.6

0.4

0.2

0.00 20 40 60 80 100

ALTITUDE (km)

Fig. 6. Comparison of the temperature-independent model of Ref.4 and the present temperature-dependent model of the atmospheric

Raman gain coefficient for S(8).

Table lit. Atmospheric Rotational Raman Gain Coefficient and Associated Parameters for the S(8) Line In N2 at Xs = 350 nm

Room temperatureself-broadening Polarizability Sea level Sea level Sea level Threshold

coefficient anisotropy temperature AN gain coefficient intensity(MHz/amagat) (10-25 cm- 3) (K) N (Cm2 km-' MW-1) (MW/cm 2 )

This work 3280 7.39 285 0.0349 0.68 0.85Ref. 2 0.85aRef. 4 2600 7.47 300 0.035 0.83a 0.86

a Gain coefficients were scaled to 350 nm using a 1/As dependence.

300 to 200 K. The combined effect of the atmospherictemperature variation on Raman gain coefficient isillustrated by the difference between the solid anddashed curves of Fig. 6. The broadening coefficientsused in the present work10 are'-20% larger than those15

used in Ref. 4, and this difference is the major contrib-utor to the 15% difference in the two sea-level (or roomtemperature) gain coefficients of Fig. 6. To bettervisualize the effects on the gain due only to temperturevariations, this 15% sea-level difference should be ig-nored. Thus the maximum difference between thetemperature dependent gain and the temperature-in-dependent gain occurs at 15 km, where the tempera-ture-dependent model would give a gain coefficient30% larger than the temperature-independent model.

Once the altitude dependence of the gain coeffi-cients is known, the integrated gain can be computedand used to estimate the threshold intensity for appre-ciable Raman conversion. We calculate the thresholdintensity with the expression

I = IN exp(-IfSg(z)dz), (5)

where z is the atmospheric altitude, g(z) is the Ramangain coefficient, Ip is the pump intensity, Is is thegenerated Stokes intensity, and IN is the spontaneousnoise intensity from the first gain length. To com-pare with Ref. 4, we consider an atmospheric pathperpendicular to the ground and define threshold to beIs/Ip = 0.01. The threshold intensities for the two gainprofiles shown in Fig. 6 are listed in the last column ofTable III. The agreement between these two numbersillustrates the accuracy of the temperature-indepen-dent model when averaging over the entire depth of theatmosphere.

Other smaller differences between our work and thatof Ref. 4 include the wavelength dependence of thepolarizability anisotropy and the 02 foreign broaden-ing. We have used the wavelength dependence of therotational transitions,3 and the results of Ref. 4 arebased on the wavelength dependence of the vibrationaltransitions.16 Another small difference is that we haveaccounted for the foreign-gas broadening contributiondue to 02. Each of these effects alters the gain coeffi-cient by a few percent.

The uncertainties in the Raman gain coefficientsreported for this study depend on how well the tem-perature of the gain medium is known. If the tem-perature is accurately known (e.g., laboratory condi-tions), the uncertainties in the gain coefficients arelimited by the uncertainties in the linewidths and thepolarizability anisotropy. Both of these uncertaintiesare -1-2%; thus the gain coefficient uncertainties are-5%. In the atmosphere, where the temperature isnot well known, the uncertainties in the gain coeffi-cients are dominated by temperature uncertainties.Therefore, gain coefficient uncertainties are -10%, asillustrated in Fig. 5.

V. Summary

The Raman gain of the Stokes rotational lines in N2has been modeled as a function of altitude for the lower100 km of the atmosphere. Calculations were com-pleted for the even J transitions, S(0) through S(16).The strongest lines, S(6) through S(10), have maxi-mum gain coefficients of 1 cm2 MW-1 km-' at analtitude of 15-20 km and smoothly decrease to zeroover the 20-80-km region. Effects on the Raman gainare described for altitude and seasonal temperature

1 August 1987 Vol. 26, No. 15 / APPLIED OPTICS 2993

I I I l I I I I

Temperaturee pendent

C TemperatureIi Independent

l , , , |I , ,

fluctuations in the atmosphere and detuning from theline center of the Raman transition. The results ofthis work provide useful input for simulation codesthat model the stimulated Raman process in the atmo-sphere.

We thank David L. Huestis for stimulating conver-sion during this study. This work was supported bythe Office of Naval Research under contract N00014-84-C-0256.

References1. V. E. Zuev, Laser Beams in the Atmosphere (Consultants Bu-

reau, New York, 1982).2. M. A. Henesian, C. D. Swift, and J. R. Murray, "Stimulated

Rotational Raman Scattering in Long Air Paths," Opt. Lett. 10,565 (1985).

3. G. C. Herring, M. J. Dyer, and W. K. Bischel, "Temperature andWavelength Dependence of the Rotational Raman Gain Coeffi-cient in N2 ," Opt. Lett. 11, 348 (1986).

4. M. Rokni and A. Flusberg, "Stimulated Rotational Raman Scat-tering in the Atmosphere," IEEE. J. Quantum Electron. QE-22,3671 (1986); see correction to be published in IEEE J. QuantumElectron. QE-23, 000 (July 1987).

5. P. M. Banks and G. Kockarts, Aeronomy (Academic, New York,1973), Chap. 3.

6. A. P. Hickman, J. A. Paisner, and W. K. Bischel, "Theory ofMultiwave Propagaton and Frequency Conversion in a RamanMedium," Phys. Rev. A 33, 1788 (1986).

7. U.S. Standard Atmosphere, 1976, NOAA-S/T 76 1562 (Nation-al Oceanic and Atmospheric Administration, Washington DC,1976).

8. K. P. Huber and G. Herzberg, Molecular Spectra and MolecularStructure IV. Constants of Diatomic Molecules (Van Nos-trand Reinhold, New York, 1979), p. 420.

9. P. L. Varghese and R. K. Hanson, "Collisional Narrowing Ef-fects on Spectral Line Shapes Measured at High Resolution,"Appl. Opt. 23, 2376 (1984).

10. G. C. Herring, M. J. Dyer, and W. K. Bischel, "Temperature andDensity Dependence of the Linewidths and Lineshifts of theRotational Raman Lines in N 2 and H2," Phys. Rev. A 34, 1944(1986).

11. A. Flusberg, "Stimulated Raman Scattering in the Presence ofStrong Dispersion," Opt. Commun. 38,427 (1981).

12. E. A. Stappaerts, W. H. Long, Jr., and H. Komine, "Gain En-hancement in Raman Amplifiers with Broadband Pumping,"Opt. Lett. 5, 4 (1980).

13. W. R. Trutna, Jr., Y. K. Park, and R. L. Byer, "The Dependenceof Raman Gain on Pump Laser Bandwidth," IEEE J. QuantumElectron. QE-15, 648 (1979).

14. A. Flusberg, D. Kroff, and C. Duzy, 'The Effect of Weak Disper-sion on Stimulated Raman Scattering," IEEE J. Quantum Elec-tron. QE-21, 232 (1985).

15. K. Jammu, G. St. John, and H. Welsh, "Pressure Broadening ofthe Rotational Raman Lines of Some Simple Gases," Can. J.Phys. 44, 797 (1966).

16. W. K. Bischel and G. Black, "Wavelength Dependence of Ra-man Scattering Cross Sections from 200-600 NM," in AIP Con-ference Proceedings, No. 100, Subseries on Optical Science andEngineering, No. 3, Excimer Lasers-1983, C. K. Rhodes, H.Esser, and H. Pummer, Eds. (AIP, New York, 1983).

APTs continued from page 2965While a handful of telescopes have been automated

for research purposes in the past, all required a certainamount of human supervision or assistance. The APTsnot only operate unsupervised night after night, but auto-matically make the initial data reductions for the astrono-mers by providing the data in a ready-to-be-analyzedform. The astronomer typically receives the data on afloppy disk by mail.

Vanderbilt University astronomer Douglas Hall, amember of the APT Service science advisory panel, wasthe first professional astronomer to use data from an APT.When the first Fairborn system began operation in Phoe-nix in late 1983, Hall used a 10-inch telescope to studyvariable stars with surfaces dappled by spots. These starsrequire nearly nightly monitoring if the changing and ap-parently cyclic nature of these active regions is to be un-derstood.

In the first year, the APT not only made long-termobservations to refine measurements of known variables,but discovered several new ones. "APTs are particularlygood at detecting variables whose properties, such as along period, make it likely they would be missed by theshort observing runs prevailing at most observatories,"Hall says. Hall also appreciates the efficiency of the APTs."The telescope doesn't get tired-and it doesn't have totake a break for dinner," he says.

The early success of the APT led to a search for abetter site, away from city lights and pollution. The Whip-

ple Observatory offered just such conditions, and in Sep-tember 1985, at the invitation of the Smithsonian Astro-physical Observatory, the Fairborn Observatory beganprovisional operation of one telescope installed in an oldsatellite-tracking building at the 7,600-foot level of MountHopkins. A formal agreement between the Smithsonianand Fairborn observatories was signed early this year, andsince March, three APTs, including a 16-inch Vanderbilttelescope, have been on line.

"For a number of years, professional astronomersdabbled in automatic telescopes for ground-based obser-vatories," says David Latham, associatedirector for opticaland infrared astronomy at the Harvard-Smithsonian Cen-ter for Astrophysics in Cambridge, Mass. "But it took acouple of dedicated amateurs to make the concept into aworking and productive reality. "We at the Smithsonianare pleased to share our fine site with the Fairborn Obser-vatory and are proud that their innovations are payingoff," Latham says.

For example, Smithsonian astronomer Sallie Baliunasused data supplied by an APT Service 10-inch-diametertelescope for studies of more than 60 different giant vari-able stars (see Research Reports, No. 48, Spring 1986).Many of these stars pulsate, ejecting enormous amounts ofmatter-some as much as one-millionth of the sun's massannually.

The time scales of this mass loss, however, canchange by a factor of two in several days. Accuratelymeasuring these variations requires sustained observing.

continued on page 3060

2994 APPLIED OPTICS Vol. 26, No. 15 / 1 August 1987