Four-Element Receiver for Pulsed 10-μm Heterodyne Doppler Lidar

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<ul><li><p>ls</p><p>t, A</p><p>er hapowanceummplituosed.Theon oracy</p><p>40, 0</p><p>ments of ~i! density of gaseous species and opticalproperties of airborne particles and ~ii! atmosphericvariables such as wind velocity and turbulent param-eters. All these parameters need to be recordedwarrl</p><p>mThus it is highly desirable to combine the capabilitiesof DIAL and Doppler lidar in a multifunctional in-strument.</p><p>One can use the heterodyne Doppler lidar ~HDL!</p><p>pithin a short period of time, if not simultaneously, toccount for atmospheric motion and photochemicaleactions. In this respect, the wind field plays a keyole in transport and dispersion of atmospheric pol-utants.</p><p>Differential absorption lidar ~DIAL! and Dopplerlidar techniques are effective tools for atmosphericmonitoring at ranges of several to tens of kilometers.Most of the time, a lidar instrument is dedicated to aspecific application, e.g., DIAL or Doppler. So itwould be necessary to use two lidars or more, depend-ing on the number of atmospheric variables to be</p><p>technique for simultaneous range-resolved measure-ments of molecular density and wind velocity in theboundary layer. The technique has been investi-gated for a 10-mm HDL.1 The required accuraciesfor both backscattered power and wind velocity leadto contradictory requirements for signal correlationtime. At a high carrier-to-noise ratio2 ~CNR!, uncer-tainty in the collected power backscattered off aerosoltargets is driven by the speckle effect. It depends onthe signal correlation time, which in turn depends onthe duration of the transmitted pulse, the intrapulsefrequency chirp, and the effects of decorrelation thatare due to wind turbulence, wind shear, andrefractive-index turbulence. An average of indepen-dent samples improves the accuracy of the powerestimates. The speckle effect is also detrimental tovelocity estimates, even at high CNR; thus it is nec-essary to accumulate independent samples.3</p><p>One objective of the present study is to obtain sev-eral independent samples for every HDL single shotto improve performance when the time for measure-ment is limited. We use a four-element photomixerreceiver in a pulsed 10-mm HDL to conduct simulta-neous measurements of backscattered power andwind velocity on distributed aerosol targets. The</p><p>X. Favreau, A. Delaval, P. H. Flamant ~flamant@lmd.olytechnique.fr!, and P. Delville are with the Laboratoire de Me-</p><p>teorologie Dynamique du Centre National de la RechercheScientifique, Ecole Polytechnique, Palaiseau Cedex F-91128,France. X. Favreau is also affiliated with the Centre dEtudes duBouchet, Vert le Petit F-91710, France. A. Dabas is with Meteo-France, Centre National de la Recherche Meteorologique, ToulouseF-31000, France.</p><p>Received 17 May 1999; revised manuscript received 28 January2000.</p><p>0003-6935y00y152441-08$15.00y0 2000 Optical Society of America</p><p>20 May 2000 y Vol. 39, No. 15 y APPLIED OPTICS 2441Four-element receiver for puDoppler lidar</p><p>Xavier Favreau, Arnaud Delaval, Pierre H. Flaman</p><p>A four-element photomixer receiva reduction of the variance of thekm. An improvement in performsingle shot are combined. Two scoherent summation of signal amnique for the four signals is propself-consistent packets ~SCPs!.tained with a coherent summatiimprovement, and velocity accuSociety of America</p><p>OCIS codes: 280.3640, 040.28</p><p>1. Introduction</p><p>Environmental monitoring studies call for measure-ed 10-mm heterodyne</p><p>lain Dabas, and Patricia Delville</p><p>s been tested in a 10-mm heterodyne Doppler lidar. It addresseser scattered off distributed aerosols targets at ranges as long as 8</p><p>is expected when the four independent signals recorded on everyation techniques of the four signals have been implemented: a</p><p>de and an incoherent summation of intensities. A phasing tech-It is based on a more suitable correlation time with discernible</p><p>SCP technique has been successfully tested, and the results ob-f the four signals, i.e., variance reduction, carrier-to-noise ratioimprovement, are in agreement with theory. 2000 Optical</p><p>30.6140, 030.1670.</p><p>measured, to fulfill measurement objectives ~e.g.,easurement of molecular densities and wind speed!.</p></li><li><p>four-element receiver provides four samples for everysingle shot. We implement a coherent summation of</p><p>pmdasitrnontdtfapFtsicpnesf</p><p>atnocm~ppcserrpnrpmut</p><p>K</p><p>cllofiaa</p><p>vst2prFd</p><p>2the four signals ~summation of amplitudes afterhase adjustment of the four signals! to improve theean CNR and to decrease both the normalized stan-</p><p>ard deviation in backscatter power and the fluctu-tions in wind-velocity estimates. The decrease inignal variance is expected to be maximum for fourndependent samples. We address this point in Sec-ion 2, with consideration of the use of a four-elementeceiver in a HDL and a coherent summation tech-ique. In Section 3 we describe the 10-mm HDLperated by the Laboratoire de Meteorologie Dy-amique. In Section 4 we elaborate on the charac-eristics of simultaneous radio-frequency ~rf ! signalselivered by a four-element-receiver HDL. In Sec-ion 5 we present a new technique for phasing theour rf signals. The findings of a field experimentre presented in Section 6. The multifunctional ca-ability of a four-element receiver is addressed.irst, a comparison of coherent summation ~summa-</p><p>ion of amplitudes after phase adjustment of the fourignals! and incoherent summation ~summation ofntensities! of the four rf signals is presented. Theomparison addresses an improvement in signalower statistics ~gain in CNR and decrease in theormalized standard deviation of backscattered pow-r!. Then a comparison is made between coherentummation and accumulation of the four rf signalsor wind-velocity estimates.</p><p>2. Theory</p><p>The coherent summation of rf signals has beenstudied by Fink and Vodopia,4 who showed that themean CNR ~5S# yN# !, where S# and N# are the signal</p><p>nd the noise mean powers, respectively, is a per-inent parameter for optimal summation of rf sig-als. Shot-noise-limited detection by the local-scillator power was assumed. Subsequently, twooherent summation methods for radiomobile com-unication,5 referred to as a maximal ratio receiver</p><p>MRR!, in which the rf signals are amplified pro-ortionally to their instantaneous CNR beforehasing and summation, and the equal-gain re-eiver ~EGR!, in which the signals are phased beforeummation, were studied. Recently the two coher-nt summation techniques were compared theo-etically.6 It was shown that the maximal ratioeceiver technique results in 20% ~or 0.8-dB! im-rovement in CNR and 3% improvement of theormalized standard deviation for a four-elementeceiver. Because this modest improvement inerformance was obtained at the expense of muchore complexity in signal processing, we decided tose the EGR technique in the research reported inhis paper.</p><p>3. Experimental Setup</p><p>The EGR technique for coherent summation wastested on a four-element receiver implemented in apulsed 10-mm HDL.7 Figure 1 is a schematic of the10-mm HDL setup for atmospheric measurements.</p><p>442 APPLIED OPTICS y Vol. 39, No. 15 y 20 May 2000The main components are a TEA CO2 laser operatingat 10.6 mm,8 a 17-cm-diameter off-axis telescope, afour-element HgCdTe ~MCT! photomixer cooled at 77</p><p>, and a cw CO2 laser used as a local oscillator forheterodyne detection. The frequency shift betweenthe TEA laser and the local oscillator is set at 30 MHz~in the rf domain!. A ZnSe beam splitter is set at theBrewster angle, and a quarter-wave plate separatesthe transmitted laser beam ~linearly polarized! fromthe radiation backscattered off aerosol targets. Theparameters of the 10-mm HDL operated by the Labo-ratoire de Meteorologie Dynamique are summarizedin Table 1. A close view of the four-element photo-mixer is presented in Fig. 2. A circular piece of MCTmaterial ~500-mm diameter! is divided by isolatingstripes ~25-mm width! into four sensing areas. Theharacteristics of the four individual detectors areisted in Table 2. The four MCT detectors are fol-owed by four identical rf electronic chains composedf a low-noise 64 dB rf amplifier, a 25-MHz bandpasslter centered at 30 MHz, and a 250 MHzy8 bitsnalog-to-digital converter. The digital rf signalsre stored in a computer.Figure 3 displays four simultaneous rf signals pro-</p><p>ided by the four-element photomixer for a singlehot. The four signals display a high CNR from dis-ributed aerosol targets at ranges between 1.8 and.4 km. The 10-mm HDL looks horizontally into thelanetary boundary layer. The measurements wereecorded at 2:30 pm under clear-sky conditions on 21ebruary 1997. The four rf signals display a well-eveloped speckle effect.9 In the present study we</p><p>performed coherent summations on digital rf signals,</p><p>Fig. 1. Schematic of the 10-mm HDL operated by the Laboratoirede Meteorologie Dynamique: Ms, mirror; BS, beam splitter; L,lens.</p></li><li><p>tsgcbotcrmo</p><p>clsa</p><p>r</p><p>cct</p><p>Table 1. Parameters of the 10-mm HDL Operated by the Laboratoire de Meteorologie Dynamiquea</p><p>Subsystem Parameter Value</p><p>~walsen ratarac</p><p>rpuenc</p><p>eter</p><p>eld!pera</p><p>s ~cetizer~wa</p><p>aracbilityusing the EGR technique. The phase-adjustmenttechnique is described in Section 5 below.</p><p>4. Multielement Receiver</p><p>The efficiency of coherent summation depends on ~i!he presence of uncorrelated rf signals with identicaltatistical distributions and ~ii! the use of an equal-ain receiver. In practice, requirement ~ii! is met byareful design of the four-element receiver ~i.e., withalanced detectors and electronics chains!. Carefulptical alignment of the 10-mm HDL is also impor-ant ~the backscattered power is imaged onto the cir-ular four-element MCT photomixer!. In practice,equirement ~i! is key for improvement of the perfor-ance and needs to be addressed in the design phase</p><p>f a multielement receiver.Assuming no optical or electronic leakage ~i.e.,</p><p>ross talk! among the four MCT elements, uncorre-ated rf signals are expected to occur because severalpeckle cells ~set by the transverse correlation length!re observed. In a previous study,10 2.6 speckle cells</p><p>are predicted for a monostatic diffraction-limitedHDL, even in the absence of refractive-index turbu-</p><p>Fig. 2. Geometry of the four-element photomixer. A circularpiece of MCT material ~500-mm diameter! is divided by isolatingstripes ~25 mm! into photosensitive areas.</p><p>Transmitter: pulsed TEA CO2 laser ~SAGEM! Operating lineEnergy per puPulse repetitioMode ~beam chIntrapulse chiInterpulse freqPulse duration</p><p>Receiver: off-axis Cassegrain telescope ~SigmaOptics!</p><p>Primary diamMagnification</p><p>Detector: four-element MCT ~SATySAGEM! Overall sizedc quantum yiSensitivity ~D*Operating tem</p><p>Electronic chain AmplifierFilter bandpasTransient digi</p><p>Local oscillator: cw CO2 laser ~SAGEM! Operating linePowerMode ~beam chFrequency sta</p><p>aSee also Fig. 1.lence ~Cn2 5 0!. In addition, the number of speckle</p><p>cells increases with increasing Cn2 values.</p><p>The cross-correlation coefficient between twopoints on the HDL telescope primary mirror11 is C~d!5 exp$22 @~dyD!2 1 ~dyr0!</p><p>5y3#%, where d is the sepa-ation between the two points considered, D is the</p><p>primary mirrors diameter, and r0 is the atmospherictransverse correlation length. We set C~d! 5 0.1 asan upper limit for uncorrelated signals. In the pres-ence of turbulence, the transverse correlation lengthr0 is ~1.09k</p><p>2RCn2!23y5, where R is the range, k 5</p><p>2pyl, l is the wavelength, and Cn2 is the refractive-</p><p>index structure constant. For Cn2 5 10213 m22y3</p><p>and R 5 2 km, we found that r0 5 4.6 cm and d 5 4.8m. For Cn</p><p>2 5 10213 m22y3 and R 5 10 km, r0 5 2.6m and d 5 2.8 cm. These numerical examples showhat, when Cn</p><p>2 $ 10213 m22y3, the distances betweenthe receivers @d~1, 2! 5 6.20 cm and d~1, 3! 5 8.75 cm#are greater than the distances that meet the criteriagiven above for decorrelation. A decorrelationamong the various elements is illustrated by the rf</p><p>velength! 10P20 ~10.6 mm!250 mJ</p><p>e 4 Hzteristics! Single mode ~Gaussian shape in the far field!</p><p>&gt;1.2 MHzy jitter &gt;1.0 MHz</p><p>&gt;2.5 ms17 cm73Circular, 500 mm-diameter&gt;0.65&gt;8 3 1010 cm Hz1y2 W21</p><p>ture 77 K ~8-h-Dewar, liquid nitrogen!64 dB</p><p>nter frequency! 25 MHz ~30 MHz!~Tektronics! 250 MHz-sampling frequency, 8 bits</p><p>velength! 10P20 ~10.6 mm!1 W</p><p>teristics! Single mode ~TEM00!Better than 0.20 MHzyms</p><p>Table 2. Characteristics of the Four Individual HgCdTe Detectors ThatMake Up the Four-Element Receivera</p><p>Characteristic</p><p>Detector Number</p><p>1 2 3 4</p><p>Quantum yield ~unit! 0.66 0.67 0.62 0.66Detectivity D* ~cm</p><p>Hz1y2 W21 3 106!8.3 8.5 7.7 8.6</p><p>Inverse resistance ~kV! 31.9 39.6 34.5 41.7Series resistance ~V! 9 12 10 10</p><p>aSee also Fig. 2. The quantum yield is measured for no local-oscillator power. The inverse resistance is given for 110-mVinverse polarization. The series resistance is indicated for nolocal-oscillator power on the detectors.</p><p>20 May 2000 y Vol. 39, No. 15 y APPLIED OPTICS 2443</p></li><li><p>eo0caccra</p><p>a</p><p>rs2</p><p>es5w</p><p>2signals displayed in Fig. 3. It can be seen that thepeaks and fading segments of the four rf signals areuncorrelated. The correlation coefficient betweenany two signals ~si and sj! is Cij 5 ~sisj!y=si2sj2 . Thexperimental values for moderate Cn</p><p>2 conditions inthe planetary boundary layer are listed in Table 3.The correlation coefficient is an average of ten suc-cessive signal samples, at a point that is equivalent to0.040 ms or a spatial resolution of 6 m, and 200 shotsr a time resolution of 50 s. A processing window of.04 ms is long enough for accurate detection ~thearrier frequency is 30 MHz! and short enough not toverage over the speckle effect. The 12 correlationoefficients are all smaller than 0.10, matching theriteria used for uncorrelated rf signals. These cor-elation coefficients account for a possible leakagemong the four MCT detectors.These results were confirmed with the inverse rel-</p><p>tive root variance ~IRRV! technique12 on return sig-nals from a hard target located 1.65 km away. The10-mm HDL was operated in direct detection.13 Theesults show that M 5 34 for each of the four rfignals ~we derived the statistical properties by using00 shots!.</p><p>Fig. 3. Simultaneous rf signals delivered by a four-element re-ceiver from 1.8 to 2.4 km. The HDL schematic is displayed in Fig.1; the HDL parameters are listed in Table 1.</p><p>Table 3. Correlation Coefficients between Two Simultaneous rf Signals~si, sj! Delivered by the Four-Element Photomixer</p><p>a</p><p>DetectorNumber</p><p>Detector Number</p><p>1 2 3 4</p><p>1 20.067 20.046 20.0422 20.067 0.094 0.0433 20.046 0.094 0.0714 0.042 0.042 0.071 </p><p>aSee Fig. 2. The rf signals are averaged on 10 signal samples~equivalent to a 6-m spatial resolution! and 200 shots ~50 s!.</p><p>444 APPLIED OPTICS y Vol. 39, No. 15 y 20 May 20005. Self-Consistent Packets Technique</p><p>Coherent summations were performed with the EGRtechnique at the digital level after phase adjustmentof the four simultaneous rf signals. The phasingoperations were conducted during a time periodshorter than the signal correlation time ~tc!.14 Apractical value of tc can be derived from experimentalconsiderations. We considered two approaches:the IRRV technique12 ~tc! and the self-consistentpackets ~SCPs! technique ~^t&amp;!.</p><p>The IRRV technique addresses a statistically rele-vant parameter...</p></li></ul>