double-ended lidar technique for aerosol studies

Double-ended lidar technique for aerosol studies

Herbert G. Hughes and Merle R. Paulson

The technique of inverting a single-ended lidar return to obtain range-dependent atmospheric extinctioncoefficients requires an assumption concerning the relationship between the volumetric backscatter andextinction coefficients. By comparing the powers returned from a volume common to each of two lidarslocated at opposite ends of a propagation path the need for this relationship can be eliminated, and theextinction coefficient is determined as a function of position between the two lidars. If the lidars arecalibrated, the backscatter coefficients and their relationship to extinction can then be determined as afunction of position. We present measurements obtained with two lidars which were operated reciprocallyover a slant path of -1 km during reduced visibility conditions. The measured extinction and backscattercoefficients determined by this method provide the boundary value inputs to both the forward and reverseintegration algorithms for inverting the single-ended lidar returns. The accuracies by which both single-ended integration schemes can reproduce the double-ended measurements are examined by allowing the ratioof backscatter to extinction coefficients to be either constant or varying with position between the two lidarsas measured.

1. Background

The solutions to the single-ended lidar equation forthe case where the ratio of backscatter to extinctioncoefficients is assumed to be invariant with range, i.e.,3/r = const., are well known. ' 2 For the case where the

integration is performed in the forward direction froma range r, where the transmitted beam and receiverfield of view overlap, to a final range rf is given by

= ) exp[S(r)] (1)exp[S(ro)] 2J ex[~'Id

r(ro

where o-(ro) is the unknown contribution to extinctionout to the overlap range. S(r) is defined as ln[P(r)r2 ],where P(r) is the power returned from the scatteringvolume at range r. Klett2 discussed the instabilitiesinherent in Eq. (1) due to the negative sign in thedenominator and the uncertainties in the boundaryvalue u(ro). Kunz3 proposed that, for situations wherethe lower levels of the atmosphere are horizontallyhomogeneous, c(ro) could be determined from the re-turn of a horizontal lidar shot by means of the slopemethod and then used as the boundary value in Eq. (1)for calculating the extinction in the vertical direction.

The authors are with U.S. Naval Ocean Systems Center, Ocean &Atmospheric Sciences Division, San Diego, California 92152-5000.

Received 30 October 1987.

This approach necessarily assumes that the ratio O/rremains constant with altitude.

The instabilities in Eq. (1) can be overcome by per-forming the integration in the reverse direction fromthe final range r in toward the transmitter. In thiscase the extinction coefficient is given by2

(r) = exS exp[S(r)]Iexp[S(rf)] + 2 r exp[S(r')]dr'

(2)

where o-(rf) is the unknown value of extinction at thefinal range. While Eq. (2) is stable, it is difficult to usein a practical sense unless the lidar measurement isprivileged to another independent determination ofa(rf). For fog conditions the first term in the denomi-nator of Eq. (2) becomes negligible, but in these situa-tions the single-scatter lidar equation may not be ap-plicable depending on the receiver's field of view.Carnuth and Reiter4 used a novel approach to invertlidar returns beneath stratocumulus clouds by assum-ing a(rf) to be equal to accepted values of a cloud baseextinction coefficient [10 km-' a(rf) < 30 Km-'].This approach is still left with the assumption that f/ris invariant with altitude. Lindberg et al.

5 have alsopresented measurements beneath stratus clouds inEurope. Extinction coefficients determined by thereverse integration technique agreed well with thosecalculated from balloonborne particle measurements.The method by which o-(rf) was chosen is not clear,since the authors only stated that an iteration proce-dure was used. Ferguson and Stephens6 also used aniterative scheme in an attempt to select the value of

1 June 1988 / Vol. 27, No. 11 / APPLIED OPTICS 2273

r(rf). The value of ac(rf) at a close-in range (where thereturned signal is well above the system noise) wasvaried until the cr(r) determined from Eq. (2) allowedcalculated and measured values of S(r) to agree. Thechosen value of ac(rf) was then used as vi(ro) in Eq. (1) tointegrate out from the transmitter. This procedurerequires the system to be calibrated accurately and thevalue of 1/a to be specified and invariant with range.Hughes et al.

7 showed the extinction coefficients cal-culated with this algorithm were not unique and wereextremely sensitive to the chosen value of 1/cr. Bisson-nette8 pointed out that unless the system calibrationsand /a are accurately known, this algorithm is nomore stable than the forward integration solution.

Solutions to the single-scatter lidar equation havebeen presented for the reverse9 and forward8 integra-tion cases where the relationship between the back-scatter and extinction coefficients is assumed to varywith range according to

(r) = C(r)a(r)k,

where k is a constant. For the forward integration c,the extinction coefficient as a function of range is giNby

a(r) =

1 COr exp[S(r)]

exp[S(ro)] - r 1C(r0)(r) jr C(r') exp[S(r')]dr'

and for reverse integration by

a(r) =C(r) exp[S(r)J

exp[S(rf)] 2r 1

C(rf)a(rf) + C(') exp[(r')]dr'

(3)

ise,en

We examine the effects of spatial inhomogeneitieson the single-ended lidar inversion algorithms using adouble-ended lidar technique, which has recently beendeveloped independently by two researchers.1314 Inthis technique, the assumption concerning the rela-tionship between the backscatter and extinction coef-ficients is eliminated by comparing the powers re-turned from a volume common to each of the two lidarslocated at opposite ends of the propagation path.However, the receiver gain of both lidars must be accu-rately known.

11. Mathematical Formulation

Consider two lidars separated by a distance d. If weassign the origin of the propagation path to be locatedat lidar 1, the range compensated power S(r) receivedby lidar 1 from a volume at range r is determined by thesingle-scatter lidar equation to be

S(r) = nK, + ln[3(r)] - 2 J (r')dr',

and that received by lidar 2 isd

S(r)2 = nK2 + ln[,f3(r)l - 2 (r')dr',

(6)

(7)

where K, and K2 are the instrumentation constants foreach of the lidars, and a(r) and :(r) are the volumetric

(4) extinction and backscatter coefficients, respectively.If the scattering particles are assumed to be spherical,the backscatter coefficients are eliminated by sub-tracting Eq. (7) from Eq. (6), and we are left with

S(r) - S(r)2 = ln(KI/K2) - 2 (r')dr'r

-, (5)

where the constant k has been chosen to be unity.While these solutions allow for variable backscatterand extinction coefficients, their usefulness requires apriori knowledge of the ratio C(r) as a function ofrange. Salemink et al.10 determined values of and1from horizontal lidar shots using the slope methodwhen the atmosphere appeared to be horizontally ho-mogeneous. They then presented a parametrizationbetween values of 1/ and relative humidity (33% <RH < 87%). When the parametrization was used toinvert visible wavelength lidar returns in the verticaldirection, the derived extinction coefficient profiles(using radiosonde measurements of relative humidity)sometimes agreed reasonably well with those mea-sured by aircraft mounted extinction meters. In con-trast, de Leeuw et al.11 using similar types of lidarmeasurement did not observe a distinct statistical rela-tionship between backscatter and extinction ratiosand relative humidity. Fitzgerald12 pointed out thatother factors such as the aerosol properties can strong-ly affect the relationship between P/ and relativehumidity and that the power law relationship of Eq. (3)is not necessarily valid for relative humidities of lessthan -80%. A unique relationship between C(r) andrelative humidity, which is dependent on the air masscharacteristics, is yet to be developed.

+ 2 J a(r')dr'.

Sinced I r

J a(r')dr = J| a(r')dr' -fJ a(r')dr'.

Equation (8) becomes

rr8(r) 1 - 8(r) 2 = ln(K/K 2 ) -4 J 0(r')dr'

d+ 2 o Y(r')dr'.

(8)

(9)

(10)

Taking the derivative of Eq. (10) with respect to rangewe obtain

a(r) = - d [S(r), - S(r)2].4 dr

(11)

The determined values of (r) can then be used withthe system constants in either Eq. (6) or (7) to deter-mine the associated backscatter coefficients.

Ill. System Description and Calibration Procedure

The lidar systems employed in this study were theAN/GVS-5 rangefinder-based Visioceilometers whichwere developed by the U.S. Army Atmospheric Sci-ences Laboratory and have been described elsewhereby Lindberg et al.

5 Basically, each system is a hand-held Nd:YAG laser which nominally emits a 10-mJ 6-

2274 APPLIED OPTICS / Vol. 27, No. 11 / 1 June 1988

ns pulse at a wavelength of 1.06 Aim. The receivertelescope has an aperture of 5.1 cm with a 3-mrad fieldof view. The range at which the receiver field of viewand the transmitter beam overlap is 112.5 m. A signalprocessing unit clocks the output of a silicon photoava-lanche detector at a 20-MHz rate giving a 7.5-m sam-pling interval. The digitized results are transferred toa microprocessor and then to a Memodyne cassettetape recorder for off-line processing. Because of ex-traneous data processing routines built into the sys-tems, the lidars can only be fired once or twice perminute.

Lidar 2 was calibrated15 with the assistance of per-sonnel from The Physics and Electronics LaboratoryTNO, The Hague, The Netherlands. Basically, thelaser transmitter was used to trigger a light-emittingdiode (LED) at 1.06 Am, which was directed toward thereceiver aperture. Calibrated neutral density filterswere then inserted between the LED and aperture toattenuate the diode power. The digitized output volt-age of the microprocessor was then plotted vs the loga-rithm of the incident power. Linear regression analy-sis of this plot then provided the slope and interceptconstants of the calibration curve, which, with thesystem constants (laser energy and geometrical fac-tors), allows the values of S(r) to be calculated.

Following the calibration of lidar 1 in the Nether-lands, both lidars were compared by firing them sideby side over the ocean from a shore station located onthe Point Loma Peninsula near San Diego, CA. Forthese comparisons, twenty-five simultaneous lidar re-turns were chosen when the atmosphere appeared tobe reasonably horizontally homogeneous, i.e., whenthe plot of S(r) vs range decreased linearly with range.For lidar 2, the slope and intercept constants for eachof the twenty-five lidar returns were determined bylinear regression analyses, and the average values weredetermined. The receiver gain constants of lidar 1were then adjusted so that its averaged slope and inter-cept values agreed with those of lidar 2. Subsequentto the dual-lidar measurements reported here, theTNO method of calibration was repeated several timeswith each lidar, and we have found that the originalcalibrations could be repeated within 5%.

IV. Measurements and Analyses

Measurements were made using the two lidars over a0.9825-km slant path near the ocean on the PointLoma Peninsula. Lidars 1 and 2 were located -38 mand 135 above mean sea level, respectively. Each lidarwas pointed -3 or 4 m away from the other's receiver,and the firings were offset in time by -1 s to avoidamplifier saturations and signal contaminations. Thedata presented here are samples of two returns takenon 27 Oct. 1986 and separated by -3 min during aperiod of reduced visibility and when conditions alongthe path were observed to be varying both spatiallyand with time.

In Figs. 1(a) and 2(a), the S(r) values calculated fromthe individual lidar returns are shown for data sets 1and 2, respectively. In each case the ranges are refer-

U)

-0.1 0 0.1 0.3 0.5 0.7RANGE FROM LIDAR 1, km

0.1 0.3 0.5RANGE FROM LIDAR 1, km

0.9 1.1

0.7 0.9

Fig. 1. (a) Measured values for data set 1 of the range compensatedpower return S(r) for lidars 1 and 2 vs the range from lidar 1. (b)Differences in the S(r) values for lidars 1 and 2 vs the range from

lidar 1.

-2

-3

-4

-5

U)-6

-7

-8

-0.1 0 0.1 0.3 0.5 0.7 0.9RANGE FROM LIDAR 1, km

a)

U7U)

1.1

0.1 0.3 0.5 0.7 0.9RANGE FROM LIDAR 1, km

Fig. 2. (a) Measured values for data set 2 of the range compensatedpower return S(r) for idars 1 and 2 vs the range from lidar 1. (b)Differences in the S(r) values for lidars 1 and 2 vs the range from

lidar 1.

enced to the location of lidar 1. Similarities in thelarger atmospheric irregularities are evident in eachdata set. However, there are differences in the finestructure of the individual S(r) curves, which may be


(a) DATA SET 1-3

LIDAR 2-4

-5

-64-7-

-8

-9 l l l l l l l l l l l l

-

related to the slightly offset sampling volumes andfiring times of the two lidars, as well as the differentbackground scenes viewed by each lidar. However,the background only adds a constant value to the ob-served backscatter signals. This contribution wasfound to be small in all cases, since the SNR for bothlidars exceeded 10 dB at a range of 800 m. In anyevent, data smoothing was necessary, and an eleven-point (82.5-m) running averages of each S(r) curve wasdetermined before taking the differences. The differ-ences in the smoothed S(r) curves for each data set arethen shown in Figs. 1(b) and 2(b). The derivatives ofthe S(r) difference curves were calculated with a run-ning range interval of fifteen points (112.5 in), and thevalues of (r) for each case, calculated from Eq. (11),are shown in Figs. 3(a) and 4(a). These curves ofextinction demonstrate the time-varying inhomogen-eous conditions over the propagation path.

The corresponding backscatter coefficients 13(r)were then determined, using the calculated values ofa(r) with the appropriate S(r) values and system con-stants in either Eq. (6) or (7), and are shown in Figs.3(b) and 4(b). The backscatter coefficients deter-mined for lidars 1 and 2 are in good agreement in bothcases. The slight differences occurring within a rangeof 450 m may reflect the precision by which both sys-tems could be calibrated. It is interesting to note thatthe backscatter coefficients for data set 1 [Fig. 3(a)] donot show the striking fluctuations of the extinctioncoefficients [Fig. 3(a)]. The dissimilarities are not asevident for data set 2 (except for ranges greater than-500 m) but indicate that the ratios of backscatter andextinction coefficients were not constant with range.Using the calculated extinction coefficient profiles andthe backscatter coefficient profiles for lidar 2, theirratios C(r) were determined [assuming the value of k inEq. (3) to be unity] and are presented in Figs. 3(c) and4(c). The values of C(r) between 0.6 and 0.7 km in Fig.3(c) and near 0.7 km in Fig. 4(c) (where the extinctioncoefficients are a minimum) are near factors of 2 great-er than those determined from polar nephelometermeasurements' 6 over a wide range of visibilities andthose calculated from size distribution measurementsin maritime stratus.' 7 Whether drizzle or mist oc-curred over this portion of the path during the mea-surements, which might explain the large values ofC(r), cannot be determined. The effects of multiplescattering on the measured backscatter signals canalso be discounted. The optical depths calculatedfrom the vr(r) curves are 0.76 and 1.06 for cases 1 and 2,respectively. Based on Monte Carlo simulations oflidar returns from turbid atmospheres, Kunkel andWeinmanl8 showed, that for a receiver field of view of 5mrad (compared with 3 mrad for our systems) and for awavelength of 0.7,4m, the mean extinction coefficientcorrection factor due to multiple scattering effects infog to be <10% for optical depths near 1.0. Klett 2 alsoconcluded from references cited in his paper that it wasunlikely that multiple scattered radiation could makea crucial difference in 'the applicability of the single-scatter lidar equation even for a dense fog.

7E i

0.06(b)

70.04 ~ .LDR

0.02 A" _ ,

0.2


Fig. 3. (a) Extinction coefficient (r), (b) backscatter coefficient(r), and (c) backscatter/extinction ratio C(r) vs the range from lidar

1 for data set 1.

3

E

. OX

E 0 .

Ah O-(

0

(a) DATA SET 2.0

.0

.0 -

0.1 0.3 0.5 0.7 0.9RAIJGE FROM LIDAR 1, km

Fig. 4. (a) Extinction coefficient a(r), (b) backscatter coefficientAl(r), and (c) backscatter/extinction ratio C(r) vs the range from lidar

1 for data set 2.

V. Test of Single-Ended Lidar Inversion Algorithms

The procedure here is to calculate the extinctioncoefficients as a function of range for the forward andreverse integration cases using the individual lidarreturns and compare them with those determined bythe double-ended technique when C(r) is assumed tobe either a constant or allowed to vary with range'according to Figs. 3(c) and 4(c). The results of the


. ~ (a) ~ DATA SET 11

(b)6 LIDAR 1 %

.4 -< u

02 - - . LDAR 2

O 1 l 1 l l l

(C)

01 S

0

1

11.u

E

4

3

E2

0

7

b


Fig. 5. Comparison of extinction coefficients (r) vs range fromlidar 1 calculated from lidar 1 and 2 individual returns using forwardintegration and those measured using the double-ended techniquefor (a) data set 1 and (b) data set 1 and when C(r) is assumed to be

constant.

double-ended lidar technique provide the close-in orfaraway boundary values for each lidar.

Figures 5(a) and (b) show the comparisons for theforward integration case determined using Eq. (1)when C(r) is assumed to be constant over the propaga-tion path. For data set 1, there is little or no agree-ment between the extinctions determined by eitherlidar and those of the double-ended measurementseven though the boundary values were specified.Near a range of 600 m, where the values of C(r) increase[Fig. 3(c)], the extinctions by lidar 1 exhibit the well-known instabilities in that they tend to increase with-out bound. For data set 2, there is fair agreementbetween the extinctions by lidar 1 and the double-ended measurements out to -400 m and beyond 600 m.The disagreement between these ranges does not ap-pear to be associated with changes in C(r) as in data set1. The extinctions by lidar 2 in this data set alsoexhibit the instabilities by tending to zero at the fur-ther ranges. These data demonstrate the sensitivityof the instabilities to the magnitude of the boundaryvalues.

Figures 6(a) and (b) show the comparisons for thereverse integration case determined using Eq. (2) whenC(r) is assumed to be constant. Although the solu-tions are stable, there is little agreement between thedouble-ended measurements and the extinctions de-termined by either lidar for data set 1. Good agree-ment is seen in data set 2 for lidar 2 out to -500 m,where the values of C(r) begin to increase [Fig. 4(c)].While the extinction profiles of lidars 1 and 2 aresimilar, their magnitude differences are determinedmainly by the differing boundary values.

(a) DATA SET 1

REVERSE INTEGRATION [C(r) = CONST]3

LIDAR 2

2 ~ j --.-.; DOUBLE-ENDED

- ---'. ~ ~ ~ ~~. .. ... .......

_LIDARl 1

0

(b) DATA SET2

3-LIDAR 2 DOUBLE-ENDED

2 _.....

1 /0 _ I I I I


Fig. 6. Comparison of extinction coefficients o(r) vs range fromlidar 1 calculated from lidar 1 and 2 individual returns using reverseintegration and those measured using the double-ended techniquefor (a) data set 1 and (b) data set 2 and when C(r) is assumed to be

constant.

E

E


Fig. 7. Comparison of extinction coefficients u(r) calculated fromlidar 1 and 2 individual returns using forward integration vs rangefrom lidar 1 for (a) data set 1 and (b) data set 2 and when C(r) is

allowed to vary as measured.

If the values of C(r) are allowed to vary with range asshown in Figs. 3(c) and 4(c), excellent agreements areobtained between lidars 1 and 2 extinctions calculatedusing Eqs. (4) and (5) for both data sets. The extinc-tion coefficient profiles for both the forward [Figs. 7(a)and (b)] and reverse [Figs. 8(a) and (b)] integrationsare nearly identical with the corresponding double-ended measurements shown in Figs. 3(a) and 4(a).


(a) DATA SET 1

FORWARD INTEGRATION [C(r) = CONST)3

LIDAR 22 .. .... .... D LEENDED2 _ / ,,. , ,, ,,w,,' LIDAR2|

"I

(b) DATA SET 2

I 1 at tz ~DOUBLE-ENDED

>~~~~~~~~~~~~~~L DA X

)IA --2-t

(a) DATA SET 1

FORWARD INTEGRATION [MEASURED C(r)]

-. . LI DAR 2

LIDARi

(b) DATA SET 23-

3 H e ,, ~~~~~LIDAR 2

1 L DAR 1 \ . ;-:

\

.1

2

l

7

E7

3(a) DATA SET 1

REVERSE INTEGRATION [MEASURED C(r)2 - LIDAR 1

1

0

(b) DATA SET 2

3

10vX, LIDARI.s-.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

RANGE FROM LIDAR 1, km

Fig. 8. Comparison of extinction coefficients a(r) calculated fromlidar 1 and 2 individual returns using reverse integration vs rangefrom lidar 1 for (a) data set 1 and (b) data set 2 and when C(r) is

allowed to vary as measured.

VI. Discussion

This study has demonstrated that if the value of C(r)varies with range, but is assumed to be a constant,neither the single-ended forward nor reverse integra-tion algorithms will allow range-dependent extinctioncoefficients to be determined with any assured degreeof accuracy even if the initial boundary values arespecified. If, however, the manner in which C(r) var-ies is specified, both the forward and reverse single-ended inversions for this data set reproduce the dou-ble-ended measurements remarkably well. Whetherthe same is true for other situations needs to be deter-mined.

If the conditions in which the forward inversionalgorithm is stable can be established, a single-endedlidar inversion technique would be possible when aug-mented with a close-in measurement of extinction andmeasurements to relate C(r) to air mass characteristicsand relative humidity.

While the works of Mulders1 9 and de Leeuw et al.11have concluded that no relationship exists betweenC(r) and relative humidity, their measurements didnot account for changes in the air mass characteristics.Whether such a relationship can ever be identified in apractical sense is yet to be determined. For thosetypes of study, however, the double-ended lidar tech-nique would be a valuable tool in determining extinc-tion and backscatter coefficients.

The authors are indebted to Juergen H. Richter whoinitiated the lidar research effort at the Naval OceanSystems Center and for many helpful discussions. Wealso wish to thank Gerardus J. Kunz of the Physics andElectronics Laboratory TNO, The Hague, The Neth-erlands, for his assistance in calibration of one of thelidars. This work was supported by The Office of

Naval Technology under Program Element 624359N,Project RM35G80, and Task N02C/02.

References1. R. H. Kohl, "Discussion of the Interpretation Problem Encoun-

tered in Single-Wavelength Lidar Transmissometers," J. Appl.Meteorol. 17, 1034 (1978).

2. J. D. Klett, "Stable Analytical Inversion Solution for ProcessingLidar Returns," Appl. Opt. 20, 211 (1981).

3. G. J. Kunz, "Vertical Atmospheric Profiles Measured with Li-dar," Appl. Opt. 22, 1955 (1983).

4. W. Carnuth and R. Reiter, "Cloud Extinction Profile Measure-ments by Lidar Using Klett's Inversion Method," Appl. Opt. 25,2899 (1986).

5. J. D. Lindberg, W. J. Lentz, E. M. Measure, and R. Rubio, "LidarDeterminations of Extinction in Stratus Clouds," Appl. Opt. 23,2172 (1984).

6. J. A. Ferguson and D. H. Stephens, "Algorithm for InvertingLidar Returns," Appl. Opt. 22, 3673 (1983).

7. H. G. Hughes, J. A. Ferguson, and D. H. Stephens, "Sensitivityof a Lidar Inversion Algorithm to Parameters Relating Atmo-spheric Backscatter and Extinction," Appl. Opt. 24,1609 (1985).

8. L. R. Bissonnette, "Sensitivity Analysis of Lidar Inversion Al-gorithms," Appl. Opt. 25, 2122 (1986).

9. J. D. Klett, "Lidar Inversion with Variable Backscatter/Extinc-tion Ratios," Appl. Opt. 11, 1638 (1985).

10. H. W. M. Salemink, P. Schotanus, and J. B. Bergwerff, "Quanti-tative Lidar at 532 nm for Vertical Extinction Profiles and theEffect of Relative Humidity," Appl. Phys. B 34, 187 (1984).

11. G. de Leeuw, G. J. Kunz, and C. W. Lamberts, "HumidityEffects on the Backscatter/Extinction Ratio," Appl. Opt. 25,3971 (1986).

12. J. W. Fitzgerald, "Effect of Relative Humidity on the AerosolBackscattering Coefficient at 0.694- and 10.6-,gm Wavelengths,"Appl. Opt. 23, 411 (1984).

13. M. R. Paulson, "Evaluation of a Dual-Lidar Method for Measur-ing Aerosol Extinction," Naval Ocean Systems Center TechnicalDocument 1075 (Apr. 1987).

14. G. J. Kunz, "Bipath Method as a Way to Measure the SpatialBackscatter and Extinction Coefficients with Lidar," Appl. Opt.26, 794 (1987).

15. J. A. Ferguson and M. R. Paulson, "Calibration of the Hand-Held Lidars Used by the Naval Ocean Systems Center," NavalOcean Systems Center Technical Document 996 (Dec. 1986).

16. 0. D. Barteneva, "Scattering Functions of Light in the Atmo-spheric Boundary Layer," Bull. Acad. Sci. USSR Geophys. Ser.12, 32 (1960).

17. H. G. Hughes and B. L. Thompson, "Estimates of Optical PulseBroadening in Maritime Stratus Clouds," Opt. Eng. 23, 38(1984).

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double-ended lidar technique for aerosol studies

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