Pd

b

Spectral diversity technique for heterodyne Doppler lidarthat uses hard target returns

Philippe Drobinski, Pierre H. Flamant, and Philippe Salamitou

A two-mode CO2 laser is used as transmitter in a 10-mm heterodyne Doppler lidar ~HDL! to takeadvantage of a spectral diversity technique, i.e., independent realizations obtained with different spectralcomponents. The objective is to improve the properties ~i.e., less variance! of power returns from a hardtarget. The statistical properties are presented first for a broad-spectrum laser transmitter and then fora two-mode laser transmitter. The experimental results for a cooperative diffuse hard target show thatthe return signals for a frequency separation Df 5 15 MHz can be decorrelated, depending on the angleof incidence and the target roughness. The experimental results show that the spectral diversitytechnique improves the performance of the HDL. © 2000 Optical Society of America

OCIS codes: 010.3640, 030.6140, 040.2840, 280.1910, 290.5880.

mi

1. Introduction

Environmental monitoring studies call for the mea-surement of atmospheric parameters such as humid-ity, trace-gas species density, and optical propertiesof airborne particles and of atmospheric primaryvariables, i.e., temperature, wind velocity, and tur-bulence. These parameters need to be recorded in ashort period of time, if not simultaneously, to accountfor atmospheric dynamics or photochemical pro-cesses. Given species densities, the wind plays a keyrole in both transport and dispersion of atmosphericpollutants.

Differential absorption lidar ~DIAL! and Dopplerlidar techniques are effective tools for making remotemeasurements at long range. However, in practicea lidar instrument is dedicated to one application, i.e.,Doppler1–8 or DIAL,9–15 and to one species only. Soat least two lidars ~or more, depending on the numberof atmospheric parameters to be measured!, would benecessary for simultaneous measurement of morethan one atmospheric property ~e.g., densities of par-ticles and wind velocity!. It is highly desirable tocombine the DIAL and Doppler lidar capabilities in a

The authors are with the Laboratoire de Meteorologie Dy-namique du Centre National de la Recherche Scientifique, Ecole

olytechnique, Palaiseau 91128 Cedex, France. The e-mail ad-ress for P. Drobinski is philippe.drobinski@lmd.polytechnique.fr.Received 14 May 1999; revised manuscript received 28 Septem-

er 1999.0003-6935y00y030376-10$15.00y0© 2000 Optical Society of America

376 APPLIED OPTICS y Vol. 39, No. 3 y 20 January 2000

single, multifunctional instrument for these applica-tions.

It is possible to use a heterodyne Doppler lidar~HDL! for simultaneous range-resolved measure-

ents of atmospheric constituents and wind velocityn the boundary layer. The use of 10-mm HDL16,17

was investigated recently. Those studies showedthat the accuracy requirements for power estimates~DIAL application! and velocity estimates ~Dopplerapplication! conflicted with those for pulse durationand shot accumulation.18 At high carrier-to-noiseratios, accurate power estimates require a large num-ber of independent realizations or a short signal cor-relation time that depends on the duration of thetransmitter pulse, the intrapulse frequency chirp,and the atmospheric decorrelation effect. Accuratevelocity estimates, however, require a long correla-tion time. An average of several independent real-izations would improve accuracy.18,19

Independent realizations can be obtained on asingle-shot basis with a multiarray receiver in a10-mm HDL, as was shown by Favreau et al.20 Inthe same study, the advantage of a coherent summa-tion was compared with the improvement that re-sults from an incoherent summation ~oraccumulation! as they affect accuracy of power andradial velocity measurements.

We use a different method in this study and con-sider the spectral diversity technique, using a multi-mode laser transmitter to obtain independentrealizations. We use a two-mode CO2 laser in a10-mm HDL. The return signals come from a coop-erative diffuse target deployed at a remote distance.

*

d

as

The benefit of such a technique is that it increases thenumber of uncorrelated samples to increase the re-turn heterodyne power statistics as well as the num-ber of HDL signals that can be accumulated ~forimprovement in the accuracy and reliability of thevelocity estimate!. The spectral diversity techniquehas proved to be useful for Doppler radars, but notmuch information on that technique has appeared inthe literature.21 A drawback when one is operatingon two or more modes as opposed to using a single-mode transmitter with the same total energy perpulse is that the carrier-to-noise ratio must be di-vided by the number of modes in each mode. Inpractice, a compromise has to be made, but this pointis beyond the scope of this study. In Section 2 wedeal with theoretical considerations of HDL signalsand their statistical properties. In Section 3 weelaborate on the statistical properties of a GaussianHDL model22 to derive the relevant analytical equa-tions for comparison with experimental results. InSection 4 we present the experimental setup. Thefindings are presented in Section 5.

2. Theoretical Background

A. Heterodyne Doppler Lidar

The electromagnetic ~EM! field backscattered off atarget captured by the HDL receiver is a summationover the waves scattered by every elementary area ofthe target. These elementary areas are consideredindependent scatterers. Within the framework ofthe paraxial approximation for laser beam propaga-tion and in the backpropagated local oscillator~BPLO! formalism,23,24 the complex HDL signal S~k,t! in the photomixer plane is ~see Appendix A fordefinitions of the notation!

S~k, t! 5 2 (i

aiUT~ri, k, t!UBPLO*~ri!, (1)

where ri 5 xi 1 ziez and xi 5 xiex 1 yiey ~bold-faceletters represent vectors! and * is the complex conju-gate. UT is the transmitted EM field. ai are ran-dom Gaussian variables that are due to the randomphase of the elementary scatterers such as ^aiai9& 5dii9. UBPLO is the BPLO field such that UBPLO*~ri! 5

G~ri, h!ULO*~h, 0!dh, where G is the unitary Greenpropagator for the atmosphere, h is the spatial coor-

inate in the receiver plane, and ULO is the local-oscillator ~LO! EM field.

Let us now consider the case of a wave reflected bydiffuse hard target. The rough surface is de-

cribed by a height function hi 5 h~ri! that representsthe departure of the surface from its mean position.The incident plane wave arrives at an angle b to thenormal ~see Fig. 1!. Height function hi is assumed tobe a stationary random process. The relation be-tween the height function and the complex EM fieldin the target plane is complex if it is developed withrigor. Here we adopt a simple relation proposed byGoodman25 that is often used and is reasonably ac-

curate if the surface slopes are small. Under theseconditions, Eq. ~1! can be rewritten as

S~k, t! 5 2 (i

aiUI~ri, k, t!exp@ jk~1

1 cos b!hi#UBPLO*~ri!, (2)

where UI is the complex field that is incident upon thesurface.

The intensity onto the photomixer is a function ofthe complex heterodyne signal S~k, t!:

I~k! 51T * T~t!S~k, t!S*~k, t!dt, (3)

T~t! is the processing gate such that T 5 * T~t!dt,where T is the pulse duration, and the quantity k isthe transmitted wave number, k 5 2pyl, where l isthe wavelength. The ensemble-averaged signal in-tensity is then

^I~k!& 5 4 (i(

i9UBPLO~ri!UBPLO*~ri9!

1T * T~t!

3 ^aiai9*UI~ri, k, t!UI*~ri9, k, t!&dt. (4)

Assuming a full decorrelation among the variousscatterers, i.e., aiai9* 5 0 when i Þ i9, results in

^I~k!& 5 4 (i

uUBPLO~ri!u21T * T~t!^uai u2uUI~ri, k, t!u2&dt.

(5)

The target reflectivity is assumed to be constant in arestricted spectral domain, r 5 r~ri, k! 5 uaiu

2, i.e., itdoes not depend on the viewing angle and the trans-mitted wavelengths, so the signal intensity is

^I~k!& 5 4r (i

PLO~ri!PI~ri, k!, (6)

Fig. 1. Rough surface and the height function.

20 January 2000 y Vol. 39, No. 3 y APPLIED OPTICS 377

it

WsMt

pH

3

where PLO~ri! and PI~ri, k! are the BPLO and thencident average powers falling onto an elementaryarget area, respectively.

B. Statistical Properties of Heterodyne Doppler LidarSignals Scattered from Hard Targets

1. General CaseThe statistical properties, e.g., the probability-density function ~PDF! p of HDL return signals ~orbackscattered intensity I! from a hard target, aredictated by the number of independent samples in theprocessing gate or the so-called number of specklecells M ~Refs. 25 and 26!:

p~I! 5MM

^I&M

IM21

G~M!expS2M

I^I&D (7)

hen the processing gate is equal to a single signalample, the normalized variance is equal to unity,

5 1, and the PDF is a negative exponential func-ion.

The number of speckle cells is an experimentalarameter ~equal to the normalized variance of theDL signals! such that

M 5 ^I&2ysI2. (8)

In the general case for a spectrum made from manyspectral components, Eq. ~8! can be rewritten as

M 5

K* I~k!dkL2

** ^I~k!I~k9!&dkdk9 2 ** ^I~k!&^I~k9!&dkdk9

5

K* I~k!dkL2

** ^I~k!&^I~k9!&um~k, k9!u2dkdk9

5

F* ^I~k!&dkG2

** ^I~k!&^I~k9!&um~k, k9!u2dkdk9

, (9)

where m~k, k9! is the mutual correlation function ofS~k, t! and S~k9, t! such that

um~k, k9!u2 5^I~k!I~k9!&

^I~k!&^I~k9!&2 1. (10)

We define a coherence spectral width, using the mu-tual correlation function, as follows25:

sc 5c

2p *2`

`

um~Dk!u2dDk, (11)

78 APPLIED OPTICS y Vol. 39, No. 3 y 20 January 2000

where c is the speed of light.

2. Two-Mode Laser Transmitter HeterodyneDoppler LidarWe consider a two-mode laser transmitter ~wave-lengths, l1 and l2!, and we denote the two returnsignals I1 5 I~k1! and I2 5 I~k2!. The normalizedvariance of the total intensity ~I1 1 I2! ~i.e., the in-verse of the number of speckle cells M! is

1M

5sI11I2

2

^I1 1 I2&2

5~^I1

2& 1 ^I22& 2 ^I1&

2 2 ^I2&2! 1 2~^I1 I2& 2 ^I1&^I2&!

^I1 1 I2&2

5^I1&

2yM1 1 ^I2&2yM2 1 2^I1&^I2&um~k1, k2!u2

^I1 1 I2&2 , (12)

where M1 and M2 are the number of speckle cells thatcorrespond to k1 and k2, respectively. The cross-correlation term ^I1I2&–^I1&^I2& makes the normalizedvariance smaller when the two modes are decorre-lated. This is the effect that we can manipulate toimprove the signal statistics ~i.e., to lower the nor-malized variance!. The first part of the cross-correlation term is

^I1 I2& 51

T2 * T2~t!^S~k1, t!S*~k1, t!S~k2, t!S*~k2, t!&dt

51

T2 * T2~t!@^S~k1, t!S*~k1, t!&^S~k2, t!S*~k2, t!&

1 ^S~k1, t!S*~k2, t!&^S~k2, t!S*~k1, t!&#dt

5 ^I1&^I2& 11

T2 * T2~t!u^S~k1, t!!S*~k2, t!!&2dt.(13)

^I1&^I2&um~k1,k2!u2

In Eq. ~13! it is assumed that S~k1, t! and S~k2, t! forma Gaussian process.25 When the cross-correlationterm um~k1, k2!u2 5 0, the normalized variance is equalto 0.5 ~i.e., M 5 2!, provided that the transmittedenergies in the two modes are equal. M 5 2 meansthat the speckle patterns of the two modes are inde-pendent. When the two modes are correlated, i.e.,when their frequency separation is less than the cor-relation width defined by Eq. ~11!, the normalizedvariance is equal to unity, i.e., M 5 1. This meansthat the two modes behave as if there were only onemode, so the speckle pattern does not change withfrequency. When the transmitted energies in thetwo modes are not equal, the normalized varianceranges from 0.5 to 1 ~i.e., M ranges from 2 to 1!.

srlbfu

BDT

t

w

T

t

3. Gaussian Model Approximation for HeterodyneDoppler Lidar

In this section our aim is to derive an analyticalequation within the framework of the Gaussian ap-proximation proposed by Frehlich and Kavaya.22

A. Scattered Gaussian Spectrum

An analytical equation for M can be derived in thecontext of a scattered Gaussian spectrum:

^I~k!& } expS2k2

2W2D , (14)

where W is the e21y2 line width. Then

M 52pW

** expS2k2 1 k92

2W2 Dum~k, k9!u2dkdk9

. (15)

Now, with K 5 ~k 1 k9!y2 and Dk 5 k 2 k9, andassuming that m depends only on Dk,

M 52ÎpW

* expF2~Dk!2

4W2 Gum~Dk!u2dDk

. (16)

Equation ~16! is similar to Parry’s27 Eq. ~3.50! andhows the effect of the HDL spectral width, as aesult of chirped transmitter emission or wind turbu-ence, on the number of speckle cells. In Section 5elow we further address the link between the HDLrequency chirp and the number of speckle cells forse in interpreting the experimental results.

. Two-Mode Laser Transmitter Heterodyneoppler Lidarhe quantity um~k1, k2!u2 in Eq. ~13! is the key to

finding the correlation among various spectral sam-ples. It applies to the two-mode laser transmitterconsidered in the present study. We use various ap-proximations and assumptions to arrive at practicalanalytical equations. In the approach of Frehlichand Kavaya the transfer functions are Gaussian forthe transmitter and the receiver. The additional as-sumption and approximations are ~1! a paraxial ap-proximation for the beam propagation transmitted tothe target and for the scattered power backpropa-gated to the receiver ~i.e., the target is at a remotedistance such that the variations in range for thewhole illuminated area on the target are negligible!,~2! that the hard target reflectivity is the same at thewo transmitted frequencies, and ~3! that the varia-

tions in solid angle sustained by the illuminated tar-get area at the receiver plane are negligible.

We consider Gaussian beams for both the trans-

mitter and the BPLO, so the laser wave fields for thetransmitter and the BPLO are given by28,29

UI~ri, k, t! 5PI~k!1y2Îcos b

Îp sI

expS2xi

2 1 yi2 cos2 b

2sI2 D

3 expF2jkxi

2 1 yi2 cos2 b

2R~zi!G

3 exp~22jkzi cos b!, (17)

UBPLO~ri, k, t! 5PLO

1y2Îcos b

Îp sLO

expS2xi

2 1 yi2 cos2 b

2sLO2 D

3 expF2jkxi

2 1 yi2 cos2 b

2R~zi!G

3 exp~22jkzi cos b!, (18)

here R~zi! is the radius of curvature and sLO and sIare the e21y2 amplitude radii of the BPLO and theincident EM fields, respectively. Assuming that thetarget is at a remote distance from the HDL waistand that the HDL beam divergence is small, R~zi! isapproximately equal to the distance between theHDL and the hard target. Equations ~17! and ~18!lead to the following expressions for PI~ri, k! andPLO~ri, k!:

PI~ri, k! 5PI~k!cos b

psI2 expS2

xi2

sI2DexpS2

yi2 cos2 b

sI2 D ,

(19)

PLO~ri! 5PLO cos b

psLO2 expS2

xi2

sLO2DexpS2

yi2 cos2 b

sLO2 D .

(20)

he resultant signal intensity @see Eq. ~6!# is

^I~k!& 54r cos bPLOPI~k!

p~sLO2 1 sI

2!. (21)

The normalized variance of the intensity, i.e., theinverse of the number of speckle cells, is

1M

5

PI2~k1!yM1 1 PI

2~k2!yM2 1 2PI~k1!PI~k2!um~k1, k2!u2

@PI~k1! 1 PI~k2!#2 .

(22)

According to Eqs. ~17! and ~18! and assuming that thearget is made from independent scattering areas, we

20 January 2000 y Vol. 39, No. 3 y APPLIED OPTICS 379

w

o

sc

e

w

n1fl

3

can write the normalized cross-correlation functionum~k1, k2!u2 as

um~k1, k2!u2 5 HU4rPLOPI cos2 b

p2sLO2sI

2 (i

expS2xi

2

sE2D

3 expS2yi

2 cos2 b

sE2 DKexpF2jDk

xi2

2R~zi!G

3 expF2jDkyi

2 cos2 b

2R~zi!G

3 exp~22jDkzi cos b!exp@2jDkhi~1

1 cos b!#LU2JY16r2 cos2 bPLO2PI~k1!PI~k2!

p2~sLO2 1 sI

2!2 ,

(23)

here 1ysE2 5 1ysLO

2 1 1ysI2, Dk 5 k1 2 k2, and

PI 5 @PI~k1!PI~k2!#1y2. The individual ranges zi foran elementary scattering area of index i are functionsf ~1! the angle incidence of on the target, b ~2! target

roughness hi, and ~3! the transverse coordinate onthe target, xi. Assuming that R~zi! ' R,

R < ~zi 1 hi!cos b 1 xi sin b, (24)

o the terms in the sum in the numerator of Eq. ~23!an be written as

xp~22jDkR! (i

exp~2Kxi2!exp~2jDkxi sin b!Ç

term I

3 (i

exp~2Kyi2 cos2 b!exp~2jDkyi sin b!

term II

3 ^exp@2jDkhi~1 1 3 cos b!#&Ç

term III, (25)

ith K 5 1ysE2 1 jDky~2R!. Terms I and II are

Fourier transforms, and term III is equal toexp@2Dk2sh

2~1 1 3 cos b!2y2#, where sh2 is the vari-

ance of hi and hi is a random Gaussian process.Equation ~23! can then be rewritten as

um~k1, k2!u2 5

1sE

4

S 1sE

4 1Dk2

4R2D expF22Dk2~1ysE

2!sin2 b

1ysE4 1 Dk2y4R2G

3 expF22Dk2~1ysE

2!tan2 b

1ysE4 1 Dk2y4R2G

3 exp@2Dk2sh2~1 1 3 cos b!2#. (26)

Within the framework of the Gaussian model and theparaxial approximation, the normalized variance,i.e., M21, can be expressed as a function of M1 andM2, the number of speckle cells for the two modes

80 APPLIED OPTICS y Vol. 39, No. 3 y 20 January 2000

taken separately, and as a function of the transmitterparameters and target parameters:

1M

5 HPI2~k1!yMI 1 PI

2~k2!yM2

1 2PI2 1ysE

4

~1ysE4 1 Dk2y4R2!

3 expF22Dk2~1ysE

2!sin2 b

1ysE4 1 Dk2y4R2G

3 expF22Dk2~1ysE

2!tan2 b

1ysE4 1 Dk2y4R2G

3 exp@2Dk2sh2~1 1 3 cos b!2#JY

@PI~k1! 1 PI~k2!#2 . (27)

C. Numerical Applications

The numerical applications are made for the actualparameters of the Laboratoire de Meteorologie Dy-namique’s 10-mm HDL with a two-mode transmitterCO2 laser ~sLO 5 1.7 m and sT 5 0.6 m at targetrange; the divergence is 1.5 mrad!. The roughnessparameter is sh 5 10 mm for a flame-sprayed alumi-

um target, and the actual range to the target is R 5.8 km. Figure 2 displays m~Dk! as a function of therequency separation ~Df 5 f1 2 f2! between the twoaser modes ~of frequencies f1 and f2! for angles of

incidence b 5 30°, 45°, 60°. When b 5 0°, m~Dk! ' 1over the frequency range Df 5 0–300 MHz. Thenumerical application shows that b is more effectivethan surface roughness and mode separation Df for adecorrelation of the two modes. A simple physicalexplanation can be given easily, as follows: A mod-erate incident angle results in a large difference inoptical path length for a wide beam in the targetplane ~even at short range!, much larger than ly4.That results in an effective decorrelation among thespectral components of the scattered signal. How-

Fig. 2. Normalized mutual correlation function, calculated fromEq. ~26!, versus frequency for three values of incident angle b.sT 5 0.6 m, sLO 5 1.7 m, sh 5 10 mm, R 5 1.8 km ~see Table 1!.

c

s

i

vmbtdgrtrld

m

Aoi

Table 1. Parameters of the Two-mode 10-mm HDL Operated by the

R

D

E

L

T

ever, when b 5 0°, an effective spectral decorrelationould be observed for Df 5 10–20 GHz only, which is

much larger than the mode separation that is achiev-able for a practical CO2 laser resonator ~1 GHz for0.15-m resonator length!. Coherence spectral width

c is 106, 146, 91, and 57 for values of 0, 30, 45, and60 MHz, respectively, with sI 5 0.6 m ~the divergences 1.5 mrad, sLO 5 1.7m, sh 5 10 mm, and R 5 1.8 km

~see Table 1!.Figure 3 displays m~Dk! as a function of Df for three

alues of the transmitter divergence: 1, 1.5, and 2.0rad. The angle of incidence on the target is set at5 45°. The figure shows the divergence of the

ransmitted beam as it affects the frequency sampleecorrelation: The larger the divergence, the stron-er the decorrelation effect. For the same physicaleason as given above ~difference in path length!, theransmitter divergence has an effect on spectral deco-relation for a wide beam in the target plane and aong range to the target. In fact, the effect scales asivergence times R ~sLO, sI, and so sE scale as diver-

gence times R!. Coherence spectral widths sc are132, 91, and 70 MHz for values of the transmitterlaser divergence of 1, 1.5, and 2, respectively, for b 545°, sLO 5 1.7 m, sh 5 10 mm, and R 5 1.8 km ~seeTable 1!. The coherence spectral width decreases by

Laboratoire de Meteorologie Dynamique

Transmitter, pulsed TE-CO2 laser ~SAT!Operating line, wavelength 10P20, 10.6 mmEnergy per pulse 50 mJPulse repetition rate 1 HzMode and beam characteristics Two modes or single mode,

Gaussian shape in farfield

Intrapulse chirp 10 MHzPulse duration 3 msDivergence 1.5 mrad

eceiver, off-axis Cassegrain telescope ~Stigma Optics!Primary diameter 17 cmMagnification 73

etector, Single mercury cadmium telluride ~SATySAGEM!Size 300 mm 3 300 mm squaredc Quantum yield 0.71Sensitivity ~D*! 3.7 3 1010 cm Hz1y2 W21

Bandwidth 300 MHzOperating temperature 77 K ~8-h Dewar, liquid

nitrogen!

lectronic chainAmplifier 64 dBFilter bandpass, center frequency 612.5 MHz, 30 MHzTransient digitizer ~Tektronics! 100-MHz sampling fre-

quency, 8 bits

ocal oscillator, cw CO2 laser ~SAGEM!Operating line, wavelength 10P20, 10.6 mmOutput power ~stability! 2 W ~1%yday!Mode and beam characteristics Single mode, TEM00

Frequency stability Better than 0.1 MHz dur-ing 1 ms

Divergence 4.6 mrad

approximately a factor of 2 when the divergence ofthe transmitted beam is increased by a factor of 2.For both sLO and sT as functions of range and trans-mitter divergence, the mode correlation @expressed by

~Dk! and sc# decreases when these two parametersincrease.

The number of speckle cells ~or the inverse normal-ized variance of the signal! increases when the spec-tral width of the transmitted beam increases. Thetheoretical numbers of speckle cells M, computedfrom Eqs. ~16! and ~26!, are 1, 1.01, 1.02, and 1.06,respectively, for values of linewidths cy2p of 1, 3, 5,and 10 MHz. A variation of 6% is reported for laserlinewidths up to 10 MHz.

4. Experimental Setup

A schematic of the 10-mm HDL operated by the Labo-ratoire de Meteorologie Dynamique is shown in Fig.4, and the lidar parameters are listed in Table 1.The HDL is set in a monostatic configuration thatincludes an off-axis beam expander ~73 magnifica-tion!, a Brewster plate, and a quarter-wave plate toseparate the transmitted beam from the backscat-tered signal before detection. The heterodyne re-ceiver is made from a single-element mercurycadmium telluride photomixer and a CO2-laser LO.The frequency offset between the transmitter laserand the LO is set at 30 MHz. The 10-mm HDL isinstalled in a laboratory on the second floor of a build-ing at the Ecole Polytechnique. A scanning mirror~not shown in Fig. 4! enables the experimenters to firethe HDL at remote targets to an accuracy of 620 cm.

n aluminum flame-sprayed hard target is deployedn the building roof at R 5 1.8 km. The angle ofncidence on the target is b ' 45°.

The CO2 laser transmitter operates first in singlemode. Single-mode emission results from a shortcavity length ~;50 cm! and an unstable resonatorconfiguration. Figure 5 shows the return signalfrom the hard target for single-mode emission. Fig-ure 5~a! displays the pulse shape, Fig. 5~b! the corre-

Fig. 3. Normalized mutual correlation function, calculated fromEq. ~26!, versus frequency for three values of the transmitter laserdivergence. b 5 45°, sLO 5 1.7 m, sh 5 10 mm, R 5 1.8 km ~see

able 1!.

20 January 2000 y Vol. 39, No. 3 y APPLIED OPTICS 381

M

tcSdagm

stmst

T

3

sponding signal backscattered from the diffuse hardtarget, Fig. 5~c! the transmitted pulse spectrum, andFig. 5~d! the return signal spectrum. A significantfrequency chirp occurs during the pulse emission,which generates lobes at the bottom of the main spec-tral peak @Fig. 5~c!#. In Fig. 5~b!, the signal at arange of ,1 km is optical interference. The electricsignals are filtered by two passband filters ~band-width, 25 MHz! centered at 30 MHz. Note that thereturn spectrum does not look exactly like the trans-mitted spectrum. A comparison of Figs. 5~c! and5~d! shows a slight difference in the bottom of thespectrum, i.e., both sides are truncated and show adiscernible frequency decorrelation within 5 MHzthat corresponds to the broad-spectrum case de-scribed in Section 3.

For the purpose of this study we purposely detune

Fig. 4. Instrumental setup: MCT, mercury cadmium telluride,M’s, mirrors; BS, beam splitter; L, lens.

Fig. 5. ~a! Pulse shape, ~b! signal backscattered from the harddiffuse target, ~c! pulse spectrum, ~d! backscattered signal spec-trum.

82 APPLIED OPTICS y Vol. 39, No. 3 y 20 January 2000

the resonator cavity to force the CO2 laser to operatein two transverse modes ~with frequencies f1 and f2!.Figure 6 is a histogram of the frequency separationbetween the two modes Df 5 f1 2 f2 for 280 consec-utive laser shots. The mean frequency separation isDf ' 15 MHz. The return signals from the hardtarget are filtered in the rf domain by use of a low-pass filter to separate the two lines and then a sharp-edged sixth-order-Butterworth filter ~bandwidth, 14

Hz! centered about the line center of modes f1 andf2.

5. Results

During the course of the experiment it has been ourintention to compare the PDF’s of the return signalsfrom a hard target for both single-mode and two-mode laser transmitter emissions.

For one signal sample, as expected with a hardtarget, the successive return signals are decorrelatedas a result of target vibration and velocity turbulence.As expected, the PDF for single-mode laser emissionfollows an exponential distribution, and the numberof speckle cells ~i.e., the inverse normalized variance!is M 5 1.1 @calculated from Eq. ~8!#. A value slightlyabove unity ~by 10%! may be expected for a broadransmitted spectrum associated with a frequencyhirp, as displayed in Fig. 5. We showed above inubsection 3.C that a frequency chirp results in aecorrelation among the frequency samples and thatfrequency chirp of ;10 MHz leads to M 5 1.06, in

ood agreement with our experimental measure-ents.Figure 7 displays the transmitted and scattered

pectra from the hard target for a two-mode laserransmitter emission. Figure 7~a! shows the trans-itted spectrum and Fig. 7~b! the scattered two-mode

pectrum; Figs. 7~c! and 7~d! display separately thewo spectral components about f1 and f2, respectively,

after digital filtering. As shown in Fig. 5, the returnspectrum does not resemble the transmitted spec-trum because of spectral decorrelation as described inSection 3 ~broad spectrum and two spectral modes!.

he two PDF’s for each mode analyzed separately

Fig. 6. Histogram of the frequency beating ~Df 5 f2 2 f1! betweenthe first ~ f1! and the second ~ f2! modes.

ossc

bgiFmpndmtt

ndpnnbs

t

s

after low-pass filtering are displayed in Fig. 8. ThePDF’s for f1 and f2 have close to an exponential dis-tribution with M 5 1.1 @calculated from Eq. ~8!#.25

The same PDF is observed for single-mode laseremission.

Figure 9 shows the PDF for the total return signal~ f1 1 f2!. The PDF follows a gamma function withM 5 1.45, which we calculated from Eq. ~8!, whereasthe theoretical maximum number of speckle cells isM 5 2 ~see Section 3! when the transmitted energiesin the two modes are equal. The PDF for M 5 2 isshown for comparison. As we discussed above Fig. 7shows that M , 2. To compare with theory, werecorded the transmitted energy in the two modes.We used the same procedure as for the return signals;i.e., we calculated the ratio of the relative energies inthe two spectra after low-pass filtering at the rf level.The experimental values of PI~k1!yPI~k2! ' 0.7 lead toa maximum theoretical value of M ' 1.9, assumingno correlation. Now, in view of the incidence upon

Fig. 7. ~a! multimode pulse spectrum, ~b! corresponding backscat-tered signal spectrum, ~c! f1 mode signal spectrum, ~d! f2 modeignal spectrum.

Fig. 8. PDF’s for the filtered backscattered signal in the case of amultimode pulse signal: ~a! f1 mode ~M 5 1.1!, ~b! f2 mode ~M 51.1!. The number of speckle cells was calculated from Eq. ~8! andwas used to compute the theoretical PDF’s @see Eq. ~7!#, plotted asthe solid curves.

the hard target between b ' 40° and b 5 50°, thenormalized mutual correlation function is m~Dk! '0.9 and m~Dk! ' 0.7, respectively, which in turn cor-responds to M ' 1.1–1.32. For a 10% increasewing to a frequency chirp ~as observed for bothingle-mode laser emission and two-mode laser emis-ion analyzed separately!, M ' 1.2–1.42, which islose to the experimental value ~M 5 1.45! for both

experimental errors and approximations used to de-rive the analytical equations.

6. Conclusion

A summation or accumulation of several independentrealizations is needed to improve the performance ofHDL with respect to reducing the variance in thereturn signal power for DIAL application. The re-duction can be achieved in any of several ways: ~1!y successive lidar shots, but at the expense of inte-ration time, ~2! by simultaneous independent real-zations with a multiarray receiver, as discussed byavreau et al.,17,20 ~3! by spectral diversity with aultimode laser transmitter as presented in this pa-

er, or ~4! by any combination of these three tech-iques. Here we have addressed the spectraliversity technique that uses a two-mode laser trans-itter in a 10-mm HDL. For the sake of simplicity,

he field tests were conducted with a remote hardarget.

The experimental results show that the return sig-als for a frequency separation of Df 5 15 MHz areecorrelated, depending on the incidence angle of therobing beam on the hard target and on target rough-ess. They show that the spectral diversity tech-ique is effective in improving the HDL performancey decreasing the normalized variance of the returnignals.We stress the simplicity of the spectral diversity

echnique for improving scattered power statistics.

Fig. 9. PDF’s for the backscattered signal in the case of a multi-mode pulse signal ~M 5 1.45!. The number of speckle cells wascalculated from Eq. ~8! and was used to compute the theoreticalPDF @see Eq. ~7!#, plotted as a solid curve. Thick dashed curve,the theoretical PDF computed with the theoretical maximum num-ber of speckle cells in the case of a two-mode laser transmitter.M 5 1 is plotted for comparison.

20 January 2000 y Vol. 39, No. 3 y APPLIED OPTICS 383

ssrt

r

3

As a matter of fact, it can accommodate multimodeemission with power fluctuation within the modesand pulse-to-pulse frequency fluctuation with respectto the LO frequency. These two attributes are theresult of the transmitter laser resonator design. Ithas been shown that the shot-to-shot frequency fluc-tuation may be less than 5 MHz for a CO2 TE laser.30

As a consequence, this technique can also be appliedto velocity measurement and velocity turbulence byuse of each mode after digital filtering for accumula-tion and for frequency estimation ~the mode separa-tion must be large enough, i.e., 20 MHz or more!.

The main problem remains improvement of thepatial beam quality to achieve good heterodyne andystem efficiencies, which will be addressed in futureesearch as well as in studies of aerosol distributedargets.

Appendix A. Notation Used

ai Random Gaussian variables,c speed of light,

f, f1, f2 frequencies,G unitary Green propagator for the atmo-

sphere,hi target roughness,

I, I1, I2 backscattered intensities,i, i9 index,

j complex number j 5 =21,k, k9, k1, k2 wave numbers,M, M1, M2 number of speckle cells,

PLO transmitted LO power,PI incident average power on the hard tar-

get,p PDF,R distance from the HDL to the hard dif-

fuse target,i, xi, xi, yi, zi, h space coordinates,

T processing gate,t time coordinate,

UBPLO BPLO EM field,UI Laser EM field incident upon the hard

target,ULO LO EM field,

UT transmitted laser EM field,W e21y2 linewidth of the spectrum,b angle of incidence,

l, l1, l2 laser wavelengths,m mutual correlation function,r target reflectivity,

sc coherence spectral width,sh standard deviation of hi,

sLO e21y2 amplitude LO radius,sI e21y2 amplitude incident laser beam

radius.

This research was conducted at the Laboratoire deMeteorologie Dynamique, Ecole Polytechnique. Theauthors thank Claude Loth, Alain Dabas, and XavierFavreau for fruitful discussions. They thank Ber-nard Romand for technical support. The researchwas supported by the Centre National d’Etudes Spa-

84 APPLIED OPTICS y Vol. 39, No. 3 y 20 January 2000

tiales. The target was calibrated at the Jet Propul-sion Laboratory, California Institute of Technology~courtesy of R. T. Menzies and D. Haner!.

References1. M. J. Post and W. D. Neff, “Doppler lidar measurements of

winds in a narrow mountain valley,” Bull. Am. Meteorol. Soc.67, 274–281 ~1986!.

2. P. J. Neiman, R. M. Hardesty, M. A. Shapiro, and R. E. Cupp,“Doppler lidar observations of a downslope windstorm,” Mon.Weather Rev. 116, 2265–2275 ~1988!.

3. W. L. Eberhard, R. E. Cupp, and K. R. Healy, “Doppler lidarmeasurement of profiles of turbulence and momentum flux,” J.Atmos. Oceanic Technol. 6, 809–819 ~1989!.

4. R. M. Banta, L. D. Olivier, and D. H. Levinson, “Evolution ofthe Monterey Bay sea-breeze layer as observed by pulsedDoppler lidar,” J. Atmos. Sci. 50, 3959–3982 ~1993!.

5. R. M. Banta, L. D. Olivier, W. D. Neff, D. H. Levinson, and D.Ruffieux, “Influence of canyon-induced flows on flow and dis-persion over adjacent plains,” Theor. Appl. Climatol. 52, 27–42~1995!.

6. R. M. Banta, L. D. Olivier, P. H. Gudiksen, and R. Lange,“Implications of small-scale flow features to modeling disper-sion over complex terrain,” J. Appl. Meteorol. 35, 330–342~1996!.

7. R. M. Banta, P. B. Shepson, J. W. Bottenheim, K. G. Anlauf,H. A. Wiebe, A. Gallant, T. Biesenthal, L. D. Olivier, C. J. Zhu,I. G. McKendry, and D. G. Steyn, “Nocturnal cleansing flows ina tributary valley,” Atmos. Environ. 31, 2147–2162 ~1997!.

8. P. Drobinski, R. A. Brown, P. H. Flamant, and J. Pelon, “Ev-idence of organized large eddies by ground-based Doppler li-dar, sonic anemometer and sodar,” Boundary-Layer Meteorol.88, 343–361 ~1998!.

9. G. Megie and R. T. Menzies, “Complementarity of UV and IRdifferential absorption lidar for global measurements of atmo-spheric species,” Appl. Opt. 19, 1173–1183 ~1980!.

10. K. Asai and T. Igarashi, “Interference from differential reflec-tance of moist topographic targets in CO2 DIAL ozone mea-surement,” Appl. Opt. 23, 735–739 ~1984!.

11. E. E Uthe, “Airborne CO2 DIAL measurements of atmospherictracer gas concentration distributions,” Appl. Opt. 25, 2492–2498 ~1986!.

12. A. Papayannis, G. Ancellet, J. Pelon, and G. Megie, “Multi-wavelength lidar for ozone measurement in the troposphereand the lower stratosphere,” Appl. Opt. 29, 467–476 ~1990!.

13. D. Bruneau, H. Cazeneuve, C. Loth, and J. Pelon, “Double-pulse dual-wavelength alexandrite laser for atmospheric wa-ter vapor measurement,” Appl. Opt. 30, 3930–3937 ~1991!.

14. G. Ehret, C. Kiemle, W. Renger, and G. Simmet, “Airborneremote sensing of tropospheric water vapor using a near in-frared DIAL system,” Appl. Opt. 32, 4534–4551 ~1993!.

15. C. B. Carlisle, J. E. van der Laan, L. W. Carr, P. Adam, andJ. P. Chiaroni, “CO2 laser-based differential absorption systemfor range-resolved and long-range detection of chemical vaporplumes,” Appl. Opt. 34, 6187–6199 ~1995!.

16. W. A. Brewer, V. Wulfmeyer, R. M. Hardesty, and B. J. Rye,“Combined wind and water-vapor measurements using theNOAA mini-MOPA Doppler lidar,” in Proceedings of the Nine-teenth International Laser Radar Conference ~National Aero-nautics and Space Administration, Washington, D.C., 1998!,pp. 565–568.

17. X. Favreau, A. M. Dabas, P. Delville, P. Salamitou, J. Pelon,and P. H. Flamant, “Simultaneous range resolved measure-ments of atmospheric constuents and wind velocity by CO2

coherent lidar,” in Advances in Atmospheric Remote Sensingwith Lidar, A. Ansmann, R. Neuber, P. Rairoux, and U.

Wandinger, eds. ~Springer-Verlag, Berlin, 1996!, pp. 467–

2

time domain for heterodyne coherent laser radar,” Appl. Opt.

470.

18. B. J. Rye and R. M. Hardesty, “Discrete spectral peak estima-tion in incoherent backscatter heterodyne lidar. I. Spectralaccumulation and the Cramer–Rao bound,” IEEE Trans.Geosci. Remote Sens. 31, 16–27 ~1993!.

19. A. M. Dabas, P. Drobinski, and P. H. Flamant, “Chirp-inducedbias in velocity measurements by a coherent Doppler CO2

lidar,” J. Atmos. Oceanic Technol. 15, 407–415 ~1998!.0. X. Favreau, A. Delaval, P. Delville, C. Loth, and P. H. Flamant,

“Use of a detector array in the LMD CO2 coherent laser radar,”in Proceedings of the Ninth Conference on Coherent Laser Ra-dar ~Swedish Defense Research Establishment, Linkoping,Sweden, 1997!, pp. 152–155.

21. R. J. Doviak and D. S. Zrnic, Doppler Radar and WeatherObservations ~Academic, San Diego, Calif., 1984!, p. 143.

22. R. G. Frehlich and M. J. Kavaya, “Coherent laser radar per-formance for general atmospheric refractive turbulence,” Appl.Opt. 30, 5325–5352 ~1991!.

23. B. J. Rye, “Primary aberration contribution to incoherentbackscatter heterodyne lidar returns,” Appl. Opt. 21, 839–844~1982!.

24. P. Salamitou, A. Dabas, and P. H. Flamant, “Simulation in the

34, 499–505 ~1995!.25. J. W. Goodman, “Statistical properties of laser speckle pat-

terns” in Laser Speckle and Related Phenomena, J. C. Dainty,ed. ~Springer-Verlag, Berlin, 1984!, pp. 20–53.

26. J. H. Churnside and H. T. Yura, “Speckle statistics of atmo-spherically backscattered laser light,” Appl. Opt. 22, 2559–2565 ~1983!.

27. G. Parry, “Speckle patterns in partially coherent light,” inLaser Speckle and Related Phenomena, J. C. Dainty, ed.~Springer-Verlag, Berlin, 1984!, pp. 77–121.

28. A. E. Siegman, Lasers ~University Science, Mill Valley, Calif.,1986!, pp. 626–697.

29. I. P. Christov, “Generation and propagation of ultrashort puls-es,” in Progress in Optics, E. Wolf, ed. ~North-Holland, Am-sterdam, 1991!, Vol. 29, pp. 201–291.

30. P. Delville, C. Loth, P. H. Flamant, D. Bruneau, T. Le Floch,and J. C. Farcy, “A new TE-CO2 laser for coherent lidar andwind applications,” in Coherent Laser Radar: Technologyand Applications, Vol. 19 of 1995 OSA Technical Digest Series~Optical Society of America, Washington, D.C., 1995!, pp. 297–300.

20 January 2000 y Vol. 39, No. 3 y APPLIED OPTICS 385