atmospheric correlation-time measurements and effects on coherent doppler lidar

Vol. 4, No. 2/February 1987/J. Opt. Soc. Am. A 367

Atmospheric correlation-time measurements and effects oncoherent Doppler lidar

Gerard M. Ancellet and Robert T. Menzies

Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California 91109

Received March 3, 1986; accepted September 3, 1986

The time for which the backscatter from an ensemble of atmospheric aerosol particles remains coherent was studied

by using a pulsed TEA CO2 lidar with coherent detection. Experimental results are compared with predictions by

using model pulse shapes appropriate for TEA CO2 laser transmitters. The correlation time of the backscatter

return signal is important in studies of atmospheric turbulence and its effects on optical propagation and backscat-

ter. Techniques for its measurement are discussed and evaluated.

1. INTRODUCTION

In this paper we consider the combined effects of atmo-spheric turbulence and transmitted-pulse characteristics onthe temporal coherence of a signal that arises from the back-

scatter of a distant volume element containing aerosol parti-cles that are moving with mean velocity equal to the bulk

wind velocity. The theoretical formulation of the spatio-temporal correlation function for the return-signal field of apulsed lidar, recently developed by Churnside and Yuraland Yura and Churnside, 2 is used to provide correlation-time estimates that are compared with experimental results.(This formalism applies to turbulence scale sizes larger than

the inner limit of the inertial subrange.) In this study wehave incorporated a laser pulse shape that is a better approx-imation of a TEA CO2 laser pulse than the Gaussian pulseshape used as an example by Yura and Churnside. 2 Theanalytical results obtained are used to gain a better under-standing of experimentally observed return signals using aninjection-controlled TEA CO2 coherent lidar system de-scribed in an earlier publication. 3 The experimental obser-vations of correlation time are deduced from the statisticaldistribution properties of the return-signal intensity fromshot to shot. Another way to estimate the correlation time isto compute the width of the backscatter-signal power spec-trum by using discrete spectral processing or discrete auto-covariance processing. However, this requires a deconvolu-tion of the atmospheric spectral-broadening effect and thosebroadening effects arising from the power-spectrum compu-tation itself. These affect the spectral width, sometimes in away that is difficult to determine with high degree of preci-sion, as will be shown in more detail in Section 3. The

limitations of the mean and variance estimations of thepower spectrum obtained from a discrete Fourier transform(DFT) of the return signal are also discussed, as they pertain

to the calculation of the Doppler shift of the lidar returnsignal.

The measurement of atmospheric wind velocities using a

pulsed range-gated Doppler lidar4'5 is a technique that hasseveral exciting applications in meterology, including its use

to generate global wind-field measurements that can be usedto improve numerical weather prediction.6 The assessmentof this technique's sensitivity and accuracy depends on the

0740-3232/87/020367-07$02.00

knowledge of all the sources of broadening of the return-signal spectrum. The pulsed CO2 lidar with coherent detec-tion has been the preferred technology for use in this con-text, and emphasis has been placed on development of sin-

gle-frequency TEA CO2 laser transmitters that haverelatively long pulses (i.e., several microseconds) with low-frequency chirp. 7' 8 Once the chirp has been reduced to 500

kHz or lower, other sources of spectral broadening of thereturn signal may become relatively important, and studiesof the correlation time of the Doppler-shifted return signalthat is provided by aerosol backscatter are necessary in or-der to assess the value of any further improvements in laser-transmitter pulse stability.

Experimental investigations of the temporal dependenceof the autocovariance function calculated from aerosol re-turns have been conducted by Hardesty et al.,9 using a cw

CO2 laser focused at ranges of 30, 100, and 500 m. A value of2 ,4sec was deduced for the correlation time. Returns from apulsed lidar as used in this study might exhibit significantdifferences from those of a focused cw system because of themuch larger illuminated volume. In addition, the pulsedlidar allows one to study the atmospheric turbulence at vari-ous ranges, or altitudes, in a relatively short time span.Hardesty' 0 recently reported observing typical velocitystandard deviations of 2 msec- 1 , based on pulsed CO2 Dopp-ler-lidar spectral widths, corresponding to a correlation timeof 0.7 lisec. Such a short correlation time, if representativeof typical atmospheric conditions, places a significant limi-tation on the temporal coherence of a monochromatic laserpulse that is backscattered from a distant volume and wouldhave major implications on the performance characteristicsof coherent Doppler lidars in the visible and infrared wave-lengths. Further studies of this sort are important in assess-ing the effects of the atmosphere in various shear and stabil-ity regimes on the correlation time of aerosol backscatter.

Menyuk and Killinger1 l also studied atmospheric effectson temporal decorrelation of lidar signals by using a dual-pulsed CO2 lidar system and stationary targets. These re-sults applied to the effects of refractive-index eddies onpropagation (e.g., beam wandering and defocusing and, inthe case of heterodyne detection, the movement of thespeckle pattern produced by the scattering of the laser pulsefrom the rough hard target) and did not include the decorre-

© 1987 Optical Society of America

G. M. Ancellet and R. T. Menzies

368 J. Opt. Soc. Am. A/Vol. 4, No. 2/February 1987 G. M. Ancellet and R. T. Menzies

lation effects produced by random motions of aerosol parti-cles in an atmospheric backscattering volume element.

2. THEORY

A. Temporal Autocovariance FunctionThe temporal autocovariance function of the pulsed lidarreturn-signal amplitude U(t) is defined as (U(t)U(t + r))and can be written as in.Ref. 1:

r(T) = J dvJ d2 vTJ dzd 2pU(t)U(t + r)p(vZ)p(vT)/V.f0 X v

(1)

V is the aerosol volume that produces the return signal, theprobability-density function (PDF) of position is assumed tobe given by'

p(p, z) = 1/V (p, Z)EV

= 0 otherwise,

and v, and VT are the wind components of the aerosol particlealong and perpendicular to the transmit/receive axis, respec-tively. Although turbulence is not a Gaussian process,small-scale velocity turbulence can be considered as isotro-pic and Gaussian.12 Large-scale turbulence (>100 m) tendsto be anisotropic and non-Gaussian and is therefore moredifficult to model. Consequently, although this assumptiondoes not strictly apply to the large-scale turbulence, we as-sume that the aerosol velocity distributions p(vz), P(vT) areassumed to be Gaussian within the volume of interest (100-500 m):

p(v2 ) = exp[-(v - v) 2/2 aj, (2)

P(VT) = 1 2exp[-(VT - VT) /2 aT], (3)

where vZ, VT and rZ2, aT 2 are the means and variances of thecorresponding wind components. These two conditions andthe expression for Eq. (1) are valid only within the inertialsubrange, considering that the outer scale of turbulence isapproximately equal to the distance to the ground or thenearest stable layer. Using Eqs. (1)-(3) and the expressioncommonly used for the return-signal amplitude, we maywrite'

J' t - + ) P(t + T 2z)]1/2 #(z) T 2(Z)

X exp[-2k2 CZ2 T2 - (-2 + k a 2 T2]

X exp[-2ikvZr]dz,(4)

where P(t) is the transmitted power at time t, a is the trans-mitted beam radius, /(z) is the aerosol backscatter coeffi-cient at range z, T(z) is the atmospheric transmission atrange z, and k = 27r/X. Our use of Eq. (4) assumes that thebackscatter occurs over a volume located at a distant rangenear z = zo, where zo = ct/2 and t >> T. This equationincludes only the effect of the turbulent eddies of the orderof the beam diameter and smaller, which are the main

sources of motions of the aerosol particles relative to oneanother. We assume that the laser pulse duration t, issufficiently small that 3(z)/z, T(z), oz, VT, and v, are nearlyconstant over the distance AR = ctp/2. (For the laser trans-mitter usually considered in the wind-measurement feasibil-ity, the pulse duration may be as short as 100 nsec and maylast as long as 10 ,sec.) The phase term in Eq. (4) representsthe Doppler shift and can be discarded in the followingdiscussion. The second term in the exponential argumentcan also be neglected because of the transmitted-beam radi-us, typically a = 7.5 cm much larger than vTT if T < 100 Msecand much smaller than 4zX/7rvTT if T < 100 ,usec, for a 1-kmrange z. From this, the expression for r(r) reduces to

r(T) = f(z! T2(z)exp(-2k2 2C2 2)

2z2

X J dt'[P(t - t')P(t + T - t']/2 .

When /(z) varies significantly over the range gate, the inte-gral in Eq. (5) will become the autocorrelation of the product[,B(z)P(t)] 1/2. Then the results obtained by using Eq. (5) canbe extended to the case in which /3(z) is no longer constant,by transferring the /(z) variation to an equivalent laser pulseenvelope variation.

Using Eq. (5), we can calculate the temporal autocovar-iance function of the return-signal field for modeled laserpulse shapes. A good approximation to the TEA CO2 laserpulse is a two-step function. For the laser used in this study,the first step, amplitude y = 1, duration T1 = 200 nsecrepresents the narrow-gain-switched spike; and the secondone, amplitude y < 1, duration r2 = xr, represents the tail.Three different laser pulse shapes were considered, togetherwith aerosol velocity fluctuation levels of o- = 0 and o-z = 1msec-1 . The relationship between a, and E, the viscousdissipation rate of turbulence, is obtained by assuming theKolmogorov spectrum, where the spectral density of theaverage kinetic energy of the turbulence is S(k)dk = AE2/3k- 5

/3 dk,13 where A 0.5 for longitudinal velocity fluctua-

tions.14 By integrating the spectral density over the inertialsubrange and assuming an outer scale length Lo = 100 m(kmin = 27r/Lo), the value for E that is determined for r- = 1msec-1 is e = 1.7 X 10-2 m2 sec- 3. This corresponds to"light-to-moderate turbulence,"'15"6 and, following the anal-ysis of Tatarski,1 3 the equivalent value for Cn2 is 2 X 10-16m2/ 3 in a convective mixing region 100 m above the surface(or another boundary where there is considerable shear). Astudy'7 of turbulence over land resulted in the conclusionthat the dependence of C,2 on height, h(m), above the sur-face obeys the relation

Cn2(h) = C"2(h = 1 m)h- 4 /3

during sunny daytime conditions within the convective mix-ing region. Thus the above value for CQ2 at h = 100 m wouldcorrespond to C,2 - 10-13 m-2 3 at h = 1 m above the surface,which is typical for moderate daytime turbulence. Har-desty' 0 reported observing typical velocity standard devi-ations of nearly 2 msec- 1, based on CO2 Doppler-lidar signalspectral widths, with even larger widths being observed inregions of large shear. These values were obtained by de-convolving the signal spectrum and the transmitted-pulse

(5)

(6)


1

k O.

00 1 2

T(ysec)3 4

Fig. 1. Temporal autocovariance function versus time for three laser pulse shapes, a, b, and c. The ratios of the tail amplitude to the gain-switch-spike maximum amplitude are 7, 5, and 6 for a, b, and c, respectively. a, is the longitudinal velocity fluctuation amplitude.

spectrum, but there may have been residual contributions tothe spectral width due to the processing itself that weredifficult to remove. (Effects of the DFT process itself oncomputed spectral width are briefly discussed in Subsection3.B.)

The results of the temporal autocovariance calculationsshown in Fig. 1 indicate that the correlation time -r [r(Tr) =1ie)] is almost independent of the velocity fluctuations forthe shortest pulse considered and that the correlation timevaries between 0.8 and 1.8 ,sec for the 3-Atsec-long pulse andbetween 0.9 and 3 pAsec for the 5-,4sec pulse, which indicatesthat the correlation times shown in cases b and c of Fig. 1 areclearly governed by the atmospheric fluctuations for a tur-bulent atmosphere. This point is even clearer in the case ofa long rectangular pulse of 5-Asec duration, as is shown inFig. 2.

B. Statistical Distribution of Return-Signal IntensityThe statistics of monochromatic, fully developed specklepatterns correspond to those of Rayleigh phasors with aRayleigh-distributed amplitude and a uniformly distributed

0.5 -5

0~~~~~~~~~~~

0 1 2 3 4r(Asec)

Fig. 2. Temporal autocovariance function versus time for a longrectangular laser pulse for various a, (longitudinal velocity fluctua-tion amplitude).

phase, and the PDF's of the intensity obey an exponentialdistribution.'8 This is applicable to atmospheric aerosolbackscatter signals detected when a coherent receiver isused. The PDF of the atmospheric return intensity changesfrom an exponential distribution-to a gamma distribution asthe turbulence level increases and as a temporal averaging ofthe signal is performed (long laser pulse or low-pass filteringat the output of the receiver).'9' 20 The first and the secondmoments of the statistical distribution of the received powerPr, (Pr), and var(Pr) are from their ratio (Pr)/[var(Pr)]"/2 ameasure of the relative amplitude accuracy. This ratio isreferred as the inverse relative root variance (IRRV) and isrelated to the carrier-to-noise ratio (CNR) and to the IRRVoof the atmospheric signal21' 22:

IRRV =[ CNR/2R 2 1/2 (7)

In the limit of large signal (CNR > 5), the IRRV is reduced toIRRVo. When this is the case and when the received signalis subsequently smoothed by an RC filter, the IRRV is givenas2 3

IRRV = (1 + 47rT/Tr) 2 , (8)

where T is the RC and Tc is the correlation time of theatmospheric backscatter signal. Consequently, a measureof IRRV leads to a measure of the correlation time.

3. EXPERIMENTAL RESULTS

A. Correlation TimeThe correlation time of the atmospheric backscatter signalwas first measured by using the above-described techniqueof calculating IRRV of the received power under large-CNRconditions. Our coherent lidar receiver has the capability torecord the heterodyne signal either at a 30-MHz intermedi-ate frequency, which is determined by the frequency offsetbetween the transmitter and the local oscillator, or after


370 J. Opt. Soc. Am. A/Vol. 4, No. 2/February 1987 G. M. Ancellet and R. T. Menzies

Fig. 3.line.

I I I I I I

0.0Oscilloscope trace of a TEA

5.0 gseclaser output tuned to the 9R24

Table 1. Experimental Results of the CorrelationTime Using Various Receiver Bandwidths

Integration CorrelationTime (Asec) IRRV Time (usec)

RC-filter 0.35 1.79-1.92 1.7-2.1integration 0.77 2.32 2.3

1.65 2.78-2.94 2.7-2.9Numerical 0.48a 2.08 1.8

integration 0.9 5b 2.63 2.0

a r = 1.2 psec.b T' = 2.4 Asec.

smoothing by a 10-MHz-bandwidth linear video detectorand amplifier. The IRRV was measured from a set ofsuccessive aerosol return signals at a range of 1.3 km along anearly horizontal path. A relatively small number of shotswere used (100-200 shots, 15-30 min); however, as pointedout by Flamant et al.,24 the statistical results should besignificant with such a number of shots. The atmospherewas quite stable, and the mean wind velocity was low. Thegas mixing of the TEA laser was adjusted to obtain a 3-,aseclong pulse, as is shown in Fig. 3. In the first mode of opera-tion, the video signal was recorded and displayed on a 1-MHz, 12-bit transient recorder and averager, the input mod-ule of which contained a selectable RC filter. The ampli-tude was read in one channel and squared on each shot, andthe PDF's were estimated by a nearest-neighbor densityfunction.24 Different integration times were used and thenormalized standard deviation calculated in each case. In asecond mode of operation, the video signal and the laserpulse energy were recorded, respectively, on a 100-MHz, 8-bit and a 32-MHz, 8-bit analog-to-digital (A/D) CAMACmodule, both being interfaced with a LECROY 3500 data-acquisition computer. In that case, for each shot, the ampli-tude was squared, divided by the laser pulse energy, andintegrated over a selectable number of channels. (The sam-ple frequency was 25 MHz.) Following the same procedureas in the first mode of operation, the normalized standarddeviation was calculated for two values of the integrationtime T'. (The transfer function of this filtering process is a

sinc function in the frequency space; so, to apply the RC-filter formula of IRRVO, this integration time T' has to bereduced by a factor of 2.4 in order to be consistent with theintegration time appropriate for a Lorentz function, which isthe transfer function for the RC filter.) The normalizedstandard deviation of the laser pulse energy was also mea-sured and found to be smaller than 5%; thus the results of thefirst mode of operation are still significant even if no normal-ization of the return signal to the laser pulse energy wasmade. Results of calculation of normalized standard devi-ations and correlation time are reported in Table 1 for bothmodes of operation. Despite the range of the results forlarge integration time, a value of 2-2.5 Isec can be deducedfor the correlation time.

Another way to estimate the correlation time is to pick upthe intermediate-frequency (IF) signal before the video de-tector and to record it. In order not to use the A/D CAMACmodule LECROY TR8818 at a speed higher than 50 MHz,where the A/D conversion is not accurate enough for ourpurpose, the 30-MHz IF signal was converted to 10 MHzthrough a rf mixer followed by a 20-MHz filter. This IF isstill large enough to measure radial wind speeds of up to 50mnsec1 . A typical 10-MHz IF lidar return is displayed in

Fig. 4. The envelope exhibits a 2 -Asec modulation, andphase shifts also seem to occur at a 2-,usec recurrence time.This visual estimate is consistent with the previously ob-tained value of the correlation time, using the IRRV con-cept.

The experimental results indicated a value of 2-2.5 Itsecfor the correlation time and are consistent with the theoreti-cal formulation of the temporal correlation function in thecase of low-velocity fluctuations. However, it is likely thatthe correlation time would be smaller for high wind condi-tions and shorter laser pulses, as predicted by the theoreticalmodel. For instance, an experimental value of the IRRV (=2.6) was deduced by Fukuda et al.

2 2 for atmospheric back-scatter signals, using their coherent CO2lidar, for an integra-tion time T = 0.35,4sec and a laser pulse similar to case a ofFig. 1. This corresponds, in that case, to a value of 0.76 Isecfor the correlation time of the return signal, which is consis-tent with our model prediction.

Using the IRRV technique and the first mode of opera-tion, we conducted several additional correlation-time mea-surements under various atmospheric conditions. In orderto reduce the spectral broadening induced by the pulselength, the TEA laser was operated at subatmospheric pres-

-J0:A:

9.0 14.12TIME (Asec)

19.24

Fig. 4. A/D module output of the IF signal arising from aerosolbackscatter.

) L 1 L_ -l 11 1 1 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _


.- I0Ln 0

0

WC-

0

Lii

C-,Cf

C-,

I6

5

4

3

2

1

n1 2 3 4 km

ALTITUDE ABOVE THE LI DAR

Fig. 5. Logarithm of (range-corrected) aerosol backscatter-signalpower versus altitude, i.e., ln[PrR2 /O(R)], where Pr is the return-signal power from range R and O(R) is the telescope overlap at rangeR. Short-dashed line, the slope or extinction coefficient within themixing layer, where the aerosol backscatter is considered to behomogeneous.

sure (400 Torr), and a pulse length of 5 psec was obtainedwith a reduction of the transmitted energy by a factor of 2.On a cool and cloudy day characterized by low surface heat-ing and an unusually low wind regime, we recorded along ahorizontal path IRRV values close to 1, which indicates apulse-limited correlation time and no atmospheric decorre-lation effect. On a sunny and slightly hazy day with a lowwind regime, correlation times of 2 gsec were recorded,which indicates, according to our model, moderate velocityfluctuations (0.5 msec'). Measurements along a slant pathwere also conducted to investigate the top of the boundarylayer. The upper limit of the boundary layer is frequentlyassociated with a large reduction in the aerosol content. 2 5

In Fig. 5, aerosol backscatter data are displayed versusrange, and the arrow indicates a discontinuity in the slope ofthe profile and, consequently, the altitude of the interfacebetween the boundary layer and the free troposphere. (Theincreased slope above the discontinuity indicates a decreas-ing aerosol backscatter with increasing altitude.) Correla-tion times as low as 220 nsec were measured at this particularrange, a result similar in that case to the large velocity stan-dard deviations reported by Hardesty.10 This behaviormight be due to small-scale turbulent eddies, to wind shearfrequently seen at the interface with the free troposphere,2 6

or more likely to a combination of both.

B. Discrete Spectral ProcessingThe influence of the correlation time derived from this ex-perimental study on the spectral broadening of the lidarDoppler signal was also assessed. Two mean-frequency es-timators can be used to process the lidar (radar) Dopplersignal. They are based either on the discrete autocovar-iance or on the DFT of the signal. The second has beenrecognized as more accurate for large (>1/2ir) normalized

standard deviation of the power spectrum. 2 7 However, alimitation of both the autocovariance and the DFT processesrelates to the window effect arising from the limited numberof points in the calculation, since the size of the time windowTo can be no longer than the correlation time -r, of the returnsignal. 2 8

In order to calculate the window effect on the bias of themean frequency and on the frequency standard deviation,


these two parameters were studied in the case of the DFToperating on a pure sinusoid of frequency f,. Two differentapproaches to the problem were a numerical calculation ofthe mean frequency f and standard deviation U using a sincfunction:

f {E kP(k)1 k=O

f =To N12 , E P(k)

kayO _

11/2

1U= To

(9)

r..JM

CfI~

0.2

0

-0.3

0.2

c

Cf I0

To 1.28 gsec

6.0 7.0FREQUENCY (MHz)

To= 2.56 Msec3 ; | I -0. 3

FREQUENCY (MHz).

Fig. 6. Bias of the DFT estimator in the case of a pure sinusoid f,.The dots represent the results when a frequency generator is used.

o 20

LU ~2 =I,

C1cc;f

v)

2

C: I-.M =

V-U,

2.5

0

7.5

0

- To = 1.28 gsec

I f f ~ ~~I I

6.0 7.0FREQUENCY (MHz)

9.5 10.5

FREQUENCY (MHz)

Fig. 7. Standard deviation of the DFT estimator in the case of apure sinusoid f,. The dots represent the results when a frequencygenerator is used.

9.5 10.5

I - I I I

SLANT ANGLE = 650LIDAR ALTITUDE = 400 m

TOP OFBOUNDARYLAYER

I I IX

I I I 2 1 l L I ITo = 2.56 Asec

Ir I

l

I

372 J. Opt. Soc. Am. A/Vol. 4, No. 2/February 1987

I:

U 1. 28TIME (,usec)

Fig. 8. A/D module output of the IF signal arising fromtarget return.

where

a solid-

[sin(k - TJf)7r sin(k + TJof 12P(k) = [sin(k - Tof.9) r (k + TJo)zr (10)

and an experimental study using a frequency generator con-nected to a frequency counter to provide the sinusoid and afast-Fourier-transform (FFT) algorithm to compute thepower spectrum. For a 20-nsec spacing between the data inthe time series, the calculations were performed for To = 1.28gsec (N = 64) and To = 2.56 tsec (N = 128). The bias andthe standard deviation are displayed versus the frequency ofthe sinusoid in Figs. 6 and 7. The maximum value of thebias is 0.1 MHz for 128 points and does not exceed 0.3 MHzfor 64 points.

The short-term pulse-to-pulse frequency stability and thesingle-shot frequency standard deviation were also mea-sured for a series of successive aerosol return signals, such asthat shown in Fig. 4, and for another series of solid-target(located 2 km away from the lidar) return signals, such asthat shown in Fig. 8. The FFT calculation was performedon each return with 64 points for the solid-target return andwith 128 points for the aerosol return, with the time spacingbetween the digitized data points being 20 nsec. In the caseof series of solid-target returns, since the aerosol velocityfluctuations have no effect, these are characteristic of theinstrumental spectral-broadening effects, such as the pulse-to-pulse fluctuations of the frequency offset between theTEA laser and the local-oscillator and intrapulse fluctua-tions of the TEA laser frequency (e.g., chirp). The maxi-mum observed single-shot standard deviation value (1.5MHz) in that case does not exceed the maximum valueobtained with a pure sinusoid, and this indicates a smallchirp. The short-term pulse-to-pulse fluctuations of themean frequency have been observed to be as large as 0.9MHz, and this indicates that the shot-to-shot stability of theelectronic feedback loops employed by us for laser frequencystabilization and injection-locking control is not much bet-ter than 1 MHz. In the case of the series of atmospheric

-aerosol return signals, results are characteristic of both in-strumental and atmospheric influences on spectral broaden-ing of the signal. The observed maximum single-shot stan-dard deviation was measured to be 1.2 MHz larger than themaximum value obtained with a pure sinusoid, and thisindicates that atmospheric decorrelation due to relative mo-tion of groups of aerosol particles is occurring in the return-signal zone where the FFT calculation is performed. How-

ever, even with this spectral broadening of the signal, theshort-term stability of the mean frequency (0.9 MHz) re-mains as good as the stability measured with a solid-targetreturn.

4. CONCLUDING REMARKS

Temporal autocovariance function calculations have beenpresented, using modeled pulse shapes, that will give thosewho use coherent lidar systems, in particular, a better under-standing of the relative contributions of atmospheric turbu-lence and of laser pulse shape on the correlation time of thereturn signals for a variety of atmospheric situations.

The use of the IRRV concept, as described in this paper, todeduce values for the atmospheric coherence time shows lesssusceptibility to error than a determination based on thewidth of a discrete autocovariance or a DFT. Our experi-mental studies of temporal correlation of the aerosol back-scatter signal with a 10-Am-wavelength lidar result in arange between 2 and 2.5,asec for the coherence time underatmospheric conditions for which the turbulence-inducedaerosol-particle dephasing was considered to be small tomoderate, and much lower values were found for higherturbulence as encountered at the interface between theboundary layer and the free troposphere. Characterizationof clear-air turbulence appears to be possible when theIRRV concept is used; however, further developments of thisstudy require, for the purpose of comparison, supportinginformation about the atmospheric turbulence based onstandard meteorological data.

These results imply that, for CO2 Doppler-lidar measure-ments of wind velocities, the time window of the returnsignal, from which the power spectrum is calculated, be nolonger than 2.5,4sec in order to avoid spectral broadening ofthe signal and consequent reduction of frequency measure-ment accuracy. The use of longer coherent integrationtimes in feasibility studies of Doppler-lidar performancemay lead to overly optimistic conclusions. (This also im-plies that the typical correlation time of atmospheric aerosolbackscatter signals using X = 1.06-,4m coherent lidar29 will bearound 250 nsec or lower, owing to the more rapid dephasingof the multiple-particle scattering for a given velocity vari-ance in an illuminated volume.) The theoretical error of themean-frequency estimator, using an FFT algorithm, arisesfrom the time-window effect when the CNR is higher than 10dB and is as small as 0.1 MHz for a 2.5-,4sec window. Ourmean-frequency estimate for a series of successive atmo-spheric return signals was degraded because of the fluctuat-ing offset (0.9 MHz) between the TEA laser transmitter andthe local oscillator from shot to shot. This problem may bealleviated by recording this offset frequency for each shot inorder to define a zero for the Doppler-shift spectrum of thereturn signal.

ACKNOWLEDGMENTS

The authors are grateful to M. J. Kavaya and 0. Lindquistfor their various contributions to the data processing. G.Ancellet is a National Aeronautics and Space Administra-tion-National Research Council resident research associateand is grateful to the NRC for his financial support.

. - Ih � � I 1 1 I , . I

IMI M1 I -h- - , .' ' � �1 �1 � d 11 �� i 6 � A A .U -1 I/ V \Z ";; II II I 1. I �1 1� U V V -�



The research described in this paper was carried out bythe Jet Propulsion Laboratory, California Institute of Tech-nology, under contract with NASA.

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atmospheric correlation-time measurements and effects on coherent doppler lidar

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