Bistatic imaging lidar technique forupper atmospheric studies

Byron M. Welsh and Chester S. Gardner

The bistatic imaging lidar technique is fundamentally different from traditional monostatic lidar techniques.The vertical density of an atmospheric layer, such as the mesospheric sodium layer, is measured by imaging anilluminated spot within the layer. The spot is illuminated with a laser and imaged with a telescope in abistatic configuration. Profiles through the image contain information about the vertical structure of thelayer as well as the laser beam cross section. These profiles can be interpreted as the output of a linear filterhaving the density profile of the layer as input and an impulse response which is related to the laser beam crosssection and imaging geometry. The theoretical vertical resolution can be quantified in terms of laserbeamwidth and separation distance between the laser and telescope. Theoretical analysis of the techniqueand experimental data verifying the feasibility and basic performance of the technique are presented.

I. Introduction

The stuctural characteristics of the mesopheric sodi-um (Na) layer have received considerable attention inrecent years. The impetus for much of the current Nalayer measurements is the study of the mesopausedynamics. Knowledge of the Na layer dynamics hasproved particularly useful for studying the influence ofgravity waves and tides on the structure of the meso-sphere. Much of the past and current experimentalresearch on the mesospheric Na layer has been con-ducted using monostatic lidar systems.lA4 Bistatic li-dar techniques have also been proposed for upper at-mospheric studies.5 These lidar systems measure thevertical structure of the layer by transmitting a shortlaser pulse and recording the return flux as a functionof time. These profiles are calibrated and scaled toprovide measurements of the Na layer density as afunction of altitude. The vertical resolution of amonostatic system is proportional to cAt/2, where At isthe pulse length and c is the speed of light. An alter-nate approach is to use bistatic lidar configurationconsisting of a long pulse or cw laser and an imagingsystem. The laser illuminates the Na layer while theimaging system records the spot created by the reso-nant Na scattering. In contrast to the time domain

The authors are with University of Illinois, Department of Electri-cal Engineering, Champaign-Urbana, Illinois 61801.

Received 19 July 1988.0003-6935/89/010082-07$02.00/0.( 1989 Optical Society of America.

approach this approach measures the denstiy charac-teristics of the layer by a direct spatial measurement.One advantage of this approach is the use of relativelysimple transmitting and receiving equipment. Thelaser transmitter can be a cw or long pulse laser, andthe receiver can be a simple narrowband telescope witha 1-D detector array. In contrast, the time domainapproach requires a short pulse laser and a wide band-width time gated receiver. Another advantage of theimaging technique is the possibility of improved spa-tial resolution. In the following sections we demon-strate that vertical resolution of the order of 10 m isfeasible.

In Sec. I we discuss the configuration of the bistaticimaging lidar and derive the fundamental equationsdescribing the image data as a function of layer densityprofile and laser beam cross section. These results arediscussed in Sec. II in terms of familiar linear systemsconcepts. The limits imposed on the system resolu-tion by atmospheric turbulence and shot noise are alsodiscussed in Sec. II. Finally, in Sec. III experimentaldata are presented.

11. Analysis

Figure 1 illustrates the configuration of the bistaticimaging lidar. The telecsope and laser are separatedby a distance d. The laser is pointed in the vertical zdirection, and the telescope is pointed at the center ofthe spot created by the resonant scattering. The im-aged laser spot will be elliptical in shape due to separa-tion between the telescope and laser. A zenith angle Xprofile through the recorded image contains informa-tion about the sodium layer's vertical structure, whilean azimuth angle a profile contains information about

82 APPLIED OPTICS / Vol. 28, No. 1 / 1 January 1989

the laser beam cross section. From the geometry illus-trated in Fig. 1 we see intuitively how vertical resolu-tion Ar is affected by laser beamwidth and separationdistance d. The resolution can be improved by de-creasing the laser beamwidth or increasing the separa-tion d. Exactly how much the resolution is improvedbe these two actions is quantified in the followinganalysis.

The theoretical system performance is found bystarting with an expression describing the measuredimage data as a function of the layer density profileand laser beam cross section. This expression is de-rived by applying the lidar equation3 to the geometryillustrated in Fig. 1. To facilitate the analysis, we firstassume that the angular extent of the laser spot is verysmall. For the nominal altitude of the Na layer (90km) and a reasonable beam divergence this assump-tion is justified.

Applying the lidar equation to the geometry illus-trated in Fig. 1, we can write the photon flux distribu-tion y at the telescope detector as a function of obser-vation angles q5 and a as

,y(ia) =lArTiTXPreff47rhc

pX I(r sino cosa - d,r sino sina)ns(r cosk)r2 sini Y

Xo dr + b'

(1)

where¢ = zenith angle,a = azimuth angle,r = radial distance from the imaging system in the

observation direction (m),ns(z) = sodium density as a function of altitude

z(m- 3 ),I(x,y) = laser beam cross section at the nominal

sodium layer height (m-2),, = overall imaging system efficiency,

Ti = atmospheric transmittance for the imagingsystem,

T1 = atmospheric transmittance for the laser,X = optical wavelength (m),P = laser power (W),

Ar = telescope aperture (M2 ),o-eff = effective backscatter cross section (m 2 ),

h = Planck's constant (6.63 X 10-34 J s),c = velocity of light (3.0 X 108 m/s),

Yb = flux due to background and detector darkcounts (s-1).

Also note that the laser beam cross section I(x,y)satisfies the following relationship:

E. J I(x,y)dxdy = 1. (2)

Equation (1) describes the total flux intensity for aparticular observation direction (,a). In deriving Eq.(1) we have assumed that the altitude dependent ab-sorption losses within the Na layer are negligible. Atthis point we can estimate the constant noise term fYb

and subtract it from the total flux giving the signal flux

n,(z) Sodiumi Density

Profile

tion

z = NominalLayerHeight

Fig. 1. Imaging lidar configuration.

VS. Yb can be estimated by measuring the flux levelswhen the laser is turned off. For the remainder of thissection we base our analysis on this signal flux ys Ifthe layer density does not change for small variationsin azimuth a, the only information contained in theazimuthal data is the shape of the laser beam crosssection. Since we are primarily interested in the verti-cal structure of the layer Eq. (1) can be simplified byintegrating over a. Assuming that the laser beamcross section I(x,y) is separable and using the smallangle approximations for cosa and sina, the integra-tion over a gives

YS() = '1?ArTiTlXPaeff Ad I(r sin - d)ns(r cosk) dr,

47rhc Jo r(3)

where I(x) describes the laser beam cross section in onedimension. The integration along the observationpath r can be converted to an integration along thevertical path z' by making the change of variables; z' =r coso. Carrying out this change of variables we obtain

llArTiTIXPaeff J: I(z' tant - d)ns(z')dz',SM ~f= 4rhc -,rh cz (4)

The flux distribution zys can be written as a corre-sponding distribution in altitude by relating the obser-vation angle 0 to the altitude z by the geometric rela-tionship tans = d/z (see Fig. 1). We transform theflux distribution ys(0) to the flux distribution (s(z)using

do _ (sin) 2 _ ddz d d2 +z 2 (5)

and the constraint 0s(z)dz = -ys(o)do. This transfor-mation yields

(6)=S 4flril2 +f /) zt ns(z')dz'z)=4-e-hc(d' + Z2) f o

Equation (6) is approximated by replacing the factor1z' in the integrand with z. This is a reasonableapproximation if the width of the kernel I(z'd/z) is

1 January 1989 / Vol. 28, No. 1/ APPLIED OPTICS 83

small compared with the magnitude of z. The rmswidth of I(z'd/z) is equal ajz/d, where al is the rmswidth of the laser beam cross section. This rms widthis small compared with z when o-I/d << 1. We furthersimplify Eq. (6) by replacing the quotient d/z in theargument of the kernel I(z'd/z) with the constant d/zs,where z is the nominal centroid height of the layer.This approximation is reasonable, since the width ofI(z'd/z) will only vary by -10% for the typical altituderange of interest (z = 80-100 km). Making the de-scribed replacements results in the following convolu-tional form:

t (z) flArTiTXP( effd -_I(Z'- ns(z')dz'. (7)W -47rhc(d2+

2)ZS Jo \ s/d

111. Discussion

The convolution in (7) can be interpreted using fa-miliar concepts of linear system theory. {S(z) may beregarded as the output of a linear filter with input ns(z)and impulse response I(zd/zs). To obtain the mostaccurate representation of ns(z) from (s(z) the spatialbandwidth of I(zd/zs) should be at least as large as thespatial bandwith of ns(z). In other words, the width ofI(zd/zs) must be small compared with the smalleststructure in ns(z). If this condition is satisfied, theestimate of the density profile ns(z) is given byK~s(z),where K is simply a normalizing constant,

Since the width of I(zd/zs) determines the verticalresolution of the imaging lidar we would like to equatesome measure of this width to the system resolutionAr. In many cases I(x) will be well approximated by aGauusian beam cross section. The Gaussian beamcross section is completely described by its rms width,and we use this width as a measure of system resolutionAr. We can easily show that the rms width of I(zd/zs)is

500

E

0

"I

101

100

0 20 40 60 80 100

BEAM DIVERGENCE (prad)

Fig. 2. Vertical resolution of the imaging lidar vs laser beam diver-gence for several values of the separation distance d.

500

io2

2

0

0I

10I

100

10-1

0 2 3

SEPARATION DISTANCE d (kn)

Fig. 3. Vertical resoluton of the imaging lidar vs separation dis-tance d for several values of the laser beam divergence.

ii ( d + c

Ar = -,

d (8)

where rl is the rms width of the laser beam crosssection. Two approaches to improve resolution areevident from Eq. (8). The first is simply decreasingwidth of the laser beam. The second is increasing theseparation d between the laser and telescope. Figures2 and 3 show how the resolution given in Eq. (8) varieswith separation distance d and rms beamwidth al (orequivalently beam divergence). For example, toachieve a resolution of the order of 100 m with d = 1000m and z = 90 km, we must have a rms beamwidth of1.11 m, which corresponds to a FWHM beam diver-gence of -50 ,rad.

In addition to the detailed structure of the layer, thegross characteristics of the layer, such as centroidheight and rms width, are also of interest. Using thealtitude profile (s(z) in Eq. (7) we compute the profi-le's centroid height and rms width. This computationreveals that the centroid height of the image profile(S(z) is equal to the centroid height of density profilens(z). In a similar manner, computing the rms widthai of the image profile s(z) we find

= lAr2 + o, (9)

where s is the true rms width of the Na layer. If Ar <<as the measured rms width cr will closely approximatethe true rms width, o-s.

For cases in which the vertical resolution Ar is largerthan the smallest spatial structure of ns(z), a simplescaling of the image data will not give an accuraterepresentation of ns(z). To obtain a more accuraterepresentation we could mathematically invert Eq. (7)by performing a deconvolution. This approach is lessdesirable because of the inherenet problems encoun-tered when attempting to recover high frequency in-formation from shot noise contaminated data. Shotnoise effects arise because of the random nature ofphoton arrival times at the telecope receiver. In prac-tice the telescope receiver cannot determine the in-stantaneous flux (s(z) given in Eq. (7). Instead thereceiver counts photons over an integration time r andestimates s(z) . The deconvolution process is verysensitive to the shot noise inherent in this estimationprocess.6 As a result, small perturbations in the esti-mated values (s(z) due to shot noise cause large pertur-bations in the deconvolution result.

84 APPLIED OPTICS / Vol. 28, No. 1 / 1 January 1989

IV. Factors Affecting Resolution

For a given separation d, Eq. (8) implies that verticalresolution is only limited by the size of the laser spot.If the optics of the laser system are large enough,atmospheric turbulence will ultimately limit the mini-mum spot size. Once this minimum size is reached,resolution can only be improved by increasing d. At-mospheric turbulence limits the minimum spot size toa full width angular diameter 2.44X/ro, where r is theatmospheric seeing cell diameter. The seeing cell di-ameter r was first introduced by Fried,7 and it repre-sents the diameter of the largest aperure achievingdiffraction-limited performance in the presence of at-mospheric turbulence. Also note that ro is wavelengthdependent varying as 6/5. Calculating the smallestpossible rms beamwidth in the presence of atmospher-ic turbulence we obtain

(2.44X (10)

Substituting Eq. (10) into Eq. (8) gives the followinglower bound on Ar:

0.43XzsAr > * (11)

rod

The right-hand side of the inequality (11) is plotted vsr0 in Fig. 4 for a range of separation distances d. In thisplot we have assumed zs = 90 km and X = 589 nm.Consider, for example, a desired resolution of 100 m.For an offset distance of 1000 in, the seeing cell diame-ter ro must be >2 cm (poor seeing conditions). On theother hand, for a resolution of 10 m, the seeing celldiameter r must be >20 cm (excellent seeing condi-tions). Values of ro > 20-30 cm can only be achieved atthe best observatory sites.

Up to this point resolution has been discussed interms of the smallest vertical cell size the system is ableto resolve. We can also speak of resolution in terms ofthe system's ability to observe the vertical structure ofmesospheric gravity waves. If the imaging system hasan adequate vertical resolution in the sense discussedabove (i.e., Ar < 100 m), the system's ability to measureshort-wavelength gravity waves is ultimately limitedby shot noise. Gardner and Voelz4 found that to de-tect vertical wavelengths as short as 1 km, the shotnoise levels in the power spectrum of a typical imageprofile (s(z) must be of the order of -50 dB, or equiva-lently the number of signal counts/profile must be ofthe order of 105. The total expected signal count perprofile is obtained by integrating Eq. (7) over z giving

Ns =nTjTjXP-.ffCsT (12)4irhc(d2 + s

where Xr is the exposure time and Cs is the sodium layercolumn abundance. Consider, for example, the nomi-nal atmospheric and lidar system parameter valueslisted in Table I. The listed atmospheric parametervalues are typical of those expected for a low altitudesite like Urbana, IL.4 The receiver efficiency 1 isrepresentative of that possible with available telescopeand detector equipment.

500

-s

0

02 101

1 0° 0 I I I0 5 10 15 20 25 30

SEEING CELL DIATER ro (cm)

Fig. 4. Minimum vertical resolution vs the atmospheric cell size rofor several values of the separation distance d.

Substituting these nominal values into Eq. (12) andimposing a maximum shot noise level of -50 dB (i.e.,N > 105) give

PArT > 10. (13)

If, for example, the product PAr is 0.1 W M 2 (i.e., a 1-mdiam receiving aperture and a 130-mW laser) the inte-gration time r must be >100 s. A system with thesecharacteristics will be able to observe gravity waveshaving wavelengths as short as 1 km.

V. Experimental Data

Initial tests of the imaging lidar were conducted inJan. 1987 at the University of Hawaii's Mauna KeaObservatory. The laser spots were generated by theUniversity of Illinois monostatic lidar system and im-aged by the University of Hawaii 2.2-m telescopeThe horizontal separation between the laser and tele-scope was 117 m. Figures 5 and 6 illustrate contourplots of two imaged laser spots. The images in Figs. 5and 6 were taken on 20 and 21 Jan., respectively. Thespot dimensions were -0.87 X 1.4-mrad FW at e 2 .The thin horizontal contours in the images were causedby stars drifting through the telescope FOV during the8-min exposures. Consider integrated photocountprofiles of the imaged spot. These integrated profilesare obtained by first summing the data over the axisperpendicular to the profile axis and then plotting theresulting 1-D data. A profile through the narrow axisof the spot corresponds to the azimuth ax direction andis a measure of the laser beam cross section. A profilethrough the broad axis of the spot corresponds to the

Table 1. Atmospheric and Imaging System Parameters

Atmospheric parameters T - Ti = 0.3Cs = 5 X 1013 m- 2

zs = 90 kmUeff = 9 X 10-16 m2

(FWHM laser linewidth < 0.5 pm)

Imaging system parameters X = 589 nmt = 0.075d = 1000 m

1 January 1989 / VoI. 28, No. 1/ APPLIED OPTICS 85

I I I I I I I I I

0~

i I I _Or * ~~~~

9'

I I_

50 100 150 200 250PIXELS

300 350 400 450 Fig. 7. Integrated azimuth

240

210

M0

0

0

0.

180

150

120

PIXELS

a angle profileFig. 5.

through the image in

Fig. 5. Photocount contour plot of the laser spot image taken 20Jan. The contours are 350, 400, 500, 600, 700, 800, 900, 1000, 1100,

1200, and 1400 counts/pixel. The pixel size is 3.4,urad.

180

150 F-

_j 250

0- 200

00 250 300 350 400 450PIXELS

Fig. 6. Photocount contour plot of the laser spot image taken 21Jan. The contours are 150, 200, 300, 400, 500, 600, 800, and 900

counts/pixel. The pixel size is 3.4 grad.

zenith direction and is a measure of the Na densityprofile. Figures 7 and 8 illustrate these narrow andbroad axis profiles for the image shown in Fig. 5. Theprofile in Fig. 7 is equivalent to integrating Eq. (1) over0 and plotting vs a. The profile in Fig. 8 is equivalentto integrating Eq. (1) over a and plotting vs 0. Com-puting the rms beamwidth from the narrow axis profilegives al = 20.5 m. Substituting ae, d = 117 m, and z =95 km into Eq. (8) gives a rms vertical resolution of 16.6km for the imaging lidar. Figures 9 and 10 illustrateNa density profiles obtained by performing a simplescaling of the image profiles. Also shown are Na densi-ty profiles derived from simultaneous monostatic lidardata. In contrast to the relatively poor resolution ofthe image data, the monostatic lidar data had a verticalresolution of 150 m. Comparing the image data to themonostatic data reveals the large amount of smearingand loss of spatial detail resulting from the poor resolu-

120 F-0

C)

90 1

600 50 100 150 200 250 300 350 400

PIXELS

Fig. 8. Integrated zenith 0 angle profile through the image in Fig. 5.

tion of the experimental configuration. The poor res-olution was caused primarily by the small separation(117 m) between the laser and telescope.

The centroid height and rms width of the Na densityprofiles were also computed and compared. The cen-troid heights computed from the image profiles were105 and 100 km on the 20th and 21st, respectively.The centroid heights computed from the monostaticlidar data were 94.8 and 93.8 km. The difference inthese results is due partly to the uncertainty in thepointing angle of the telescope and partly to the vary-ing width of the kernel I(z'D/z) in Eq. (6). The widthof the kernel increases with increasing altitude z.Normally this effect would be negligible for high reso-lution systems (r << as), but in this case the resolutionis comparable to the total width of the layer. Since thewidth of the kernel is so large, the small percentageincreases in the width with increasing altitude have theeffect of shifting the observed centroid higher in alti-tude. A similar effect was noted for the rms widthcalculations. The rms widths ai of the image profileswere 18.1 and 18.5 km on the 20th and 21st, respective-ly. Substituting these values into Eq. (9) and solvingfor the rms width of the layer as resulted in values of7.21 and 8.17 km. In contrast, the rms widths ascomputed from the monostatic lidar data were 5.35and 5.28 km.

86 APPLIED OPTICS / Vol. 28, No. 1 / 1 January 1989

450

400

350

300 _UI, 250

CL 200 k

150 _

100 _

50

00

90

600 50 100 150 200 250 300 350 400

I

I I

I I

110 (16. 6 km resolution)

105

100

! 95

4J, 90

M~onostatic Lidar Data85 - (150 m resolution)

80

75 / . .0 2000 4000 6000 8000 10000 12000 14000

Ha Density (cm 3 )

Fig. 9. Na density profiles computed from the azimuthally inte-grated data shown in Fig. 5 and from simultaneous monostatic lidardata. The imaging lidar had a vertical resolution of 16.6 km, while

the monostatic lidar had a resolution of 150 In.

115

110

105

a 100

03 95ai

4J 90

85

80

750 1000 2000 3000 4000 5000 6000 7000

Na Density (cm 3)

Fig. 10. Na density profiles computed from the azimuthally inte-grated data shown in Fig. 6 and from simultaneous monostatic lidardata. The imaging lidar had a vertical resolution of 16.6 km, while

the monostatic lidar had a resolution of 150 m.

The scaled photocount profiles gave a very poorestimate of ns(z) for our particular configuation of theimaging lidar. This conclusion is immediately obviousfrom Figs. 9 and 10. We alternately considered invert-ing Eg. (7) by performing a deconvolution. Since thesolution obtained by a deconvolution is very sensitiveto shot noise, we first quantified the shot noise levelover the spatial frequency range of interest. Figures11 and 12 illustrate comparisons of the power spectraof the imaging and monostatic lidar data. The imagedata were obviously shot noise limited for spatial fre-quencies >0.1 km-1 (i.e., for spatial structure havingcharacteristic dimensions of <10 km). The imagedata shot noise level was approximately -65 dB. Thislevel matched the expected shot noise level computedfrom the total signal photocount Ns. Ns was equal to5.01 X 106 and 3.06 X 106 on the 20th and 21st, respec-tively. Comparing the spectra of the image data to themonostatic data reveals that the frequency compo-nents >0.1 km-1 were suppressed by at least 30 dB.This high frequency suppression was a result of the

aW:

oW

-10

-20

-30

-40

-50

-60

-70100

SPATIAL FREQUENCY (km1)

Fig. 11. Power spectra of the Na density profiles in Fig. 9.

0

-10

-20

-30

-40

-50

-60

-70 10 -2 100

SPATIAL FREQUENCY (km_)

Fig. 12. Power spectra of the Na density profiles in Fig. 10.

narrow frequency response of the kernel I(zd/zs).The theoretical frequency response of I(zd/zs) is alsoillustrated in Figs. 11 and 12. This response was de-rived assuming a Gaussian laser beam cross sectionwith a rms width of al = 20.5 m. From these results weconcluded that a deconvolution would be infeasible.

Before concluding this section, we comment brieflyon the calibration procedure employed for our experi-ments. In this type of measurement the measuredflux levels must be calibrated to determine the abso-lute magnitude of the density profiles. The imagingsystem was partially calibrated by measuring the fluxlevels from a natural star. This calibration procedureeliminated the unknowns associated with the telescopeand atmospheric transmission but did not eliminatethe unknowns in the laser. The laser characteristicsmust be known precisely for complete calibration ofthe flux levels. For our particular configuration thelaser power was not known precisely, thus preventingan absolute calibration of the measured density pro-files. As a result, the density profiles computed fromthe image data were normalized to the column abun-dance computed from the monostatic data.

VI. Conclusions

We have shown theoretically that the bistatic imag-ing lidar can achieve or exceed the vertical resolution

1 January 1989 / Vol. 28, No. 1/ APPLIED OPTICS 87

115 0

of pulsed monostatic lidar systems without the use ofwideband pulsed laser and time gated receivers. Thesimplicity of the imaging lidar's transmitting and re-ceiving equipment, in contrast to the more complextransmitting and receiving equipment of pulsed lidarsystems, is the main advantage of the bistatic imagingtechnique. In terms of analysis, the operation of theimaging lidar is easily expressed in terms of linearsystems. The image profiles can be interpreted as theoutput of a filter having the Na density as the inputand an impulse response which is related to the laserbeam cross section and imaging geometry. From thislinear systems interpretation we found that verticalresolution was proportional to the laser beamwidthand inversely proportional to the separation betweenthe laser and telescope.

The vertical resolution of the imaging lidar is ulti-mately limited by atmospheric turbulence effects. At-mospheric turbulence limits how small we can focusthe laser spot in the Na layer. Once this limit isreached resolution can only be improved by increasingthe laser and telescope separation. For a site withpoor seeing conditions (ro 2 cm) and laser-telescopeseparation of 1000 m, the best possible resolution is-100 m. If this same site has excellent seeing condi-tions (ro 20 cm), 10-m resolution is possible.

Resolution can also be thought of in terms of thesmallest observable vertical wavelength of mesospher-ic gravity waves. Shot noise effects ultimately limitedthe systems ability to detect short-wavelength waves.To detect wavelengths as short as 1 km the shot noiselevel must be down by at least 50 dB (i.e., Ns > 105).The laser power, receiver aperture, and integrationtime are the main system parameters we can choose toset the shot noise level. For typical atmospheric con-ditions (see Table I) and PAI = 0.1 W M2 , integrationtimes of >100 s are required to observe vertical wave-lengths as short as 1 km.

The experiments described in Sec. IV were conduct-ed primarily to test the feasibility of creating laser

guide stars for adaptive imaging in astronomy.8 Theimaging lidar concept was developed after these ex-periments. Unfortunately, the experimental configu-ration resulted in such a poor resolution (Ar = 16.6 km)that the measured data failed to demonstrate the im-aging lidar's full capability. The experimental datadid show, however, the feasibility of creating and imag-ing a laser spot on the mesopheric sodium layer for usein the bistatic imaging technique.

This work has been supported in part under NASAcontract NSF ATM 88-11771.

References1. G. Megie, F. Bos, J. E. Blamont, and M. L. Chanin, "Simulta-

neous Nighttime Lidar Measurements of Atmospheric Sodiumand Potassium," Planet. Space Sci. 26, 27 (1977).

2. K. H. Fricke and U. von Zahn, "Mesopause Temperature Derivedfrom Probing the Hyperfine Structure of the D2 Resonance Lineof Sodium by Lidar," J. Atmos. Terr. Phys. 47, 499 (1985).

3. C. S. Gardner, D. G. Voelz, C. F. Sechrist, Jr., and A. C. Segal,"Lidar Studies of the Nighttime Sodium Layer over Urbana,Illinois 1. Seasonal and Nocturnal Variations," J. Geophys. Res.91, 13659 (1986).

4. C. S. Gardner and D. G. Voelz, "Lidar Studies of the NighttimeSodium Layer over Urbana, Illinois 2. Gravity Wave Measure-ments," J. Geophys. Res. 92, 4673 (1987).

5. J. A. Reagan, D. M. Byrne, and B. M. Herman, "Bistatic Lidar: ATool for Characterizing Atmospheric Particulates: Part 1-TheRemote Sensing Problem," IEEE Trans. Geosci. Remote SensingGE-20, 000 No. 3 (July 1982).

6. J. R. Rowlett and C. S. Gardner, "Signal Processing of SodiumLidar Photocount Data," RRL Publication 504, Radio ResearchLaboratory, Department of Electrical Engineering, U. Illinois(Sept. 1979).

7. D. L. Fried, "Optical Resolution Through a Randomly Inhomo-geneous Medium for Very Long and Very Short Exposures," J.Opt. Soc. Am. 56, 1372 (1966).

8. L. A. Thompson and C. S. Gardner, "Experiments on Laser GuideStars at Mauna Kea Observatory for Adaptive Imaging in Astron-omy," Nature London 328, 229 (1987).

L. D. Hutchinson of Raychem, photographed by W. J. Tomlinson ofBellcore during OFC '88 in New Orleans.

88 APPLIED OPTICS / Vol. 28, No. 1 / 1 January 1989