Effectiveness of simultaneous independent realizationsat low carrier-to-noise ratio to improve heterodyneDoppler lidar performance. II. Experimental results

Gaspard Guerit, Philippe Drobinski, Beatrice Augere, and Pierre H. Flamant

A 1.55-�m continuous-wave heterodyne Doppler lidar �HDL� with three receiver–detector units is usedto validate experimentally the findings presented in the Guerit et al. companion paper �Appl. Opt. 41,2232 �2002�� on the effectiveness of independent realizations to improve HDL performance �velocity orpower estimates or both� at a low carrier-to-noise ratio �CNR�. In fact, noise has a detrimental effect onthe accumulation techniques, so in the Guerit et al. companion paper, the chances of getting “heavy”speckles in HDL signals from many receiver–detector units on a single- or several-shot basis areinvestigated theoretically and numerically with the Zrnic HDL model. The experimental results enableus to conclude there is a very good agreement �better than 95%� between the performance computed fromactual HDL data and from the theoretical predictions. © 2002 Optical Society of America

OCIS codes: 010.3640, 040.2840, 030.1640, 040.3780.

1. Introduction

In the Guerit et al. companion paper,1 effectiveness ofsimultaneous independent realizations to improvepower and velocity estimates by an accumulationtechnique �incoherent2 or coherent3� has been consid-ered at low to high wideband carrier-to-noise ratios�CNRs� �i.e., the ratio of signal energy to backgroundnoise power�. Our aim is to produce the best possi-ble estimate of the presence of the atmospheric echoin the heterodyne Doppler lidar �HDL� signal �to im-prove velocity estimates, for instance� as a function ofthe HDL parameters �e.g., CNR, HDL signal spectralwidth, and length of the processing range gate� andthe number of independent realizations. Guerit etal.1 investigated theoretically and numerically �usingthe Zrnic HDL model4� the chances of getting “heavy”speckles in HDL signals from many receiver–detector units on a single- or several-shot basis. The

G. Guerit, P. Drobinski �philippe.drobinski@aero.jussieu.fr�, andP. H. Flamant are with the Laboratoire de Meteorologie Dy-namique, Ecole Polytechnique, Palaiseau, France. G. Guerit isalso with, as is B. Augere, the Office National d’Etude et RechercheAeronautique, Palaiseau, France. P. Drobinski is also with theService d’Aeronomie, Universite Pierre et Marie Curie, Paris,France.

Received 25 February 2002; revised manuscript received 24 July2002.

0003-6935�02�367510-06$15.00�0© 2002 Optical Society of America

7510 APPLIED OPTICS � Vol. 41, No. 36 � 20 December 2002

theory considers good and bad HDL signals selectedby use of the quality-control procedure developed byRye and Hardesty5: They proposed to use a statis-tical variable, the log likelihood difference �LLD�,which can be computed for every single HDL mea-surement. When the LLD is less than a giventhreshold value, the data are discarded.

In this concise study we intend to validate experi-mentally the main results presented in Guerit et al.1Here we use a 1.55-�m continuous-wave �cw� multi-receiver HDL. The HDL concept is based on a singletelescope with three fiber collimators acting as inde-pendent receivers. The experimental results arediscussed in relation to those of Frehlich et al.6 witha 2-�m pulsed HDL. They operated their 2-�mpulsed HDL at a low CNR and used an incoherentaccumulation technique of consecutive signals to im-prove HDL performance.

Section 2 presents the methodology, and Section 3presents the experimental results and a comparisonwith theoretical and numerical predictions. Theperformance obtained when simultaneous HDL sig-nals are used is given as a function of the parameterssuggested by Frehlich and Yadlowsky7, � � NwsTs,and the effective photocount for one HDL shot andone receiver � � N CNR. N is the number ofsamples in the processing range gate, and ws is thebackscattered signal spectral width. Section 4 con-cludes the article and suggests future prospects.

2. Methodology

The methodology applied to actual HDL signals inSection 3 consists of �i� detecting the good HDL sig-nals, �ii� estimating the probability of detecting si-multaneous good HDL signals, and �iii� comparingthe estimated probabilities to the theoretical predic-tion discussed in Guerit et al.1

To discriminate between good and bad HDL sig-nals, we use Rye and Hardesty’s procedure5; Rye andHardesty5 treated the problem of detecting an atmo-spheric echo within the signal delivered by a HDL.Their detection procedure was based on the compu-tation of an indicator that normally takes valuesabove a given threshold when an atmospheric echo isactually present in the signal and correctly detectedand values below the threshold otherwise. Theyconsidered the best possible indicator, that is, thelogarithm of the likelihood ratio or LLD, i.e., the log-arithm of the ratio of the probabilities of observingthe analyzed signal conditioned to the presence orabsence of a relevant atmospheric echo:

ln��x, �N, �s�� � n �i�1

N xi

�N� n �

i�1

N xi

�� fi�

� n �i�1

N

ln��� fi�

�N� , (1)

where x is the vector formed with the N signal spec-tral components xi, n is the number of accumulatedsignals, �N is the constant noise level, �s� fi� is theexpected value for the power-density function of theatmospheric echo at frequency fi, and �� fi� � �N �s� fi�. The false-alarm probability PFA is the prob-ability that a HDL signal produces a LLD greaterthan a threshold value Tth when the atmosphericecho might be, but in fact is not, present. The false-alarm probability PFA is calculated from the proba-bility density function of LLD values obtained fromnoise-only data samples. In the following, we usePFA � 1% to set Tth, like in Guerit et al.1

By use of this detection procedure, the probabilityX of obtaining a good HDL signal from a detectedsignal can be estimated. In the same way, the prob-abilities Xr

q, Xr�q of detecting q and at least q simul-

taneous good HDL signals �r � q� are computed andcompared with the theoretical probabilities given by1

Xrq �

r!q!�r � q�!

Xq�1 � X�r�q �binomial law�,

Xr�q � �

k�q

r

Xrk. (2)

3. Experimental Results

A. Experimental Setup

To validate the theoretical findings and simulationsproposed in part I,1 we use a 1.55-�m cw multire-ceiver HDL �Fig. 1�. A fiber erbium cw laser sourcethat delivers 1 W is used as a transmitter �95% oflaser intensity� and local oscillator �LO� �5% of laser

intensity�. Figure 2 presents the layout of the lidar.The laser light is linearly p polarized and is sentthrough the atmosphere via a fiber collimator, a po-larization splitter, a ��4 wave plate, and a telescope.The ��4 wave plate changes the linear polarizationinto a left circular polarization. The transmittedbeam is Gaussian with a spatial width of 1.5 cm at1�e of the amplitude and is focalized on a remote hardtarget, located at 20 m from the transmitter, whichallows us to assume a far-field geometry. The targetis a rough steel plate �20% reflection� that rotates at1500 rpm. It is turned at 45 deg to avoid specularreflection, which results in a 4.5-MHz Doppler fre-quency shift. Backscattering from the target resultsin a right circular polarization. Eventually, the ��4wave plate changes the polarization of the backscat-tered light into a linear s polarization. The polar-ization splitter is followed by the receiver. Thereceiver is made of three fiber collimators that arelocated on the image plane �see Fig. 2�b��. As thereceiver has a diameter larger than the outgoingbeam diameter, the absence of correlation betweenthe collimators relies on the independence of specklefrom the rough target because the separation of thecollimators is greater than the outgoing beam diam-

Fig. 1. Schematic of a one-to-many HDL �one transmitter tomany �r� receivers�.

Fig. 2. Experimental setup. �a� 1.55-�m cw multireceiver HDL.�b� Receiving bloc made of three receiver–detector units �zoom ofdashed box in �a�.

20 December 2002 � Vol. 41, No. 36 � APPLIED OPTICS 7511

eter. A fiber splitter divides the LO into three partsof the same intensity. The HDL signal from eachreceiving collimator is mixed with a LO beam in aphotomixer. The raw HDL signals are digitized at100-MHz sampling frequency. A 500-kHz high-passnumerical filter is used to prevent any low-frequencymodulation owing to electronic interferences. Thena 20-MHz low-pass filter is applied to reduce noisecontribution �the Doppler shift is centered approxi-mately 4.5 MHz� as well as a decimation factor of 5.The resulting sampling frequency or processingbandwidth is 20 MHz. Every measurement set con-tains 400 realizations for both HDL signal and noise.

B. HDL Signal Key Parameters for a Good SignalDetection Procedure

Figure 3 displays HDL signals and the correspondingspectra for various CNR values: �5 dB �Figs. 3�a�and 3�b��, �1 dB �Figs. 3�c� and 3�d��, and 11 dB �Figs.3�e� and 3�f ��. The changes in the CNR are obtainedby variation of outset intensity of the laser. TheCNR is estimated from measurements of noise se-quences, systematically recorded after sequences ofreturn signals from the rough target. The HDL sig-nals are characterized by a Gaussian power spectrumand a near constant-level white noise �Fig. 3�. Thekey parameters of the HDL signals are the spectralwidth ws and the CNR. The average HDL spectralwidth at 1�e2 of the power spectrum is estimated fromthe whole data set and is found equal to 40 kHz �i.e.,0.002 Fs�, and the CNR is computed from noisesamples and the HDL signals.

Qualitatively, one can note that at �1 dB, the HDLsignal in Fig. 3�c� displays mostly noise for time be-tween 0 and 20 �s and heavy speckle afterward.The peaks and fading segments in the HDL signal are

related to the HDL signal statistical properties,driven by the number of independent samples � inthe range gate. The quantity � is defined as8

� � p� 2��p2. (3)

The quantity p� is the statistical mean of the averageHDL signal power p, and �p

2 is the variance of p.�1�2 measures the relative amplitude of the statisti-cal fluctuations of the signal. As we will see hereaf-ter, it includes the random fluctuations of the returnsignal from the remote hard target due to the speckleeffect and the random fluctuations of the noise. Itcan be shown that � is given by1

1�

�1M � CNR

1 � CNR�2

�1N �1 � � CNR

1 � CNR�2� , (4)

where M is the number of independent time specklesin the atmospheric return. It can be interpreted asthe number of speckles within the range gate. M isrelated to � by the equation1 M � �1 4��2. Thecoherence time �c of the HDL signals is determined bythe inverse relative root variance technique,8,9 i.e., byuse of Eq. �3�. The number of independent cells M inthe return signal for a range gate �T � NTs is deter-mined from � �see Eq. �4��. Figure 4 displays a log–log plot of M as a function of �T for CNR � �5, �1,and 11 dB �Figs. 4�a�, 4�b�, and 4�c�, respectively�. Mis calculated from 400 HDL and noise signals. Theerrors bars indicate the relative uncertainty �1 � ��on the estimation of M. For large range gates, M ��T��c,8 which leads to �c by use of linear regression.The coherence time ranges from 4.5 to 5.6 �s. As weuse a cw HDL with high coherence time and as theexperiment is conducted in laboratory conditions

Fig. 3. Examples of signals and associated spectra, respectively,for various CNR values: �a� and �b� CNR � �5 dB, �c� and �d�CNR � �1 dB, �e� and �f � CNR � 11 dB.

Fig. 4. Log–log plots of the number of speckle cells M in theatmospheric return as a function of the range gate �T � NTs for �a�CNR � �5 dB, �b� CNR � �1 dB, �c� CNR � 11 dB. The estimatesof M as well as the experimental uncertainties are represented byerror bars. The solid curves represent the fit between M2 and�T2. This leads to an approximate relation M � �1 �T2��c

2.The corresponding correlation time �c and mean regression error�M are indicated.

7512 APPLIED OPTICS � Vol. 41, No. 36 � 20 December 2002

�negligible turbulence�, the coherence time of thebackscattered signal is set mostly by the transversevelocity of the scattering surface.10,11 The variationin the estimates of M and �c caused by change in thevalue of the CNR is less than 20%.

C. HDL Performance by Use of Simultaneous GoodActual Signals

Figure 5 presents simultaneous HDL signals de-tected on each of the three detectors for CNR � 11 dB.It can be seen that the segments of heavy speckle andfadings of the three HDL signals are uncorrelated.The correlation coefficient between any two HDL sig-nals �si and sj� is Cij � sisj��si

2sj2�1�2. The correla-

tion coefficients shown in Table 1 are estimated on400 shots, for different CNR values, from an averageon a 1-�s range gate. This processing range gate islong enough for accurate detection and short enoughnot to average over the speckle effect �the coherencetime is 5 �s�. The correlation coefficients are allsmaller than 0.10, matching the usual criterion usedfor uncorrelated HDL signals.3

The HDL performance is computed for differentCNR values ��5, �1, 4, and 11 dB� and for variousrange gates. The aim is to confirm the theoreticalresults presented in part I. To achieve this objec-tive, we generate numerically Zrnic synthetic HDL

signals4 with characteristics similar to the actual1.55-�m cw HDL to compute the one-to-one probabil-ity X �X � X1

1 � X1�1�, and Eq. �2� is used to compute

Xr�q from X.In practice, three receiver collimators are avail-

able, so the validation is conducted for X1�1, X2

�1,X3

�1, X2�2, X3

�2, and X3�3 from 400 HDL signals

detected on each collimator. Figures 6 and 7 displaythe values of Tth and � and the probabilities Xr

�q asa function of � �� refers to one HDL shot and onecollimator� for CNR � �5 and �1 dB, respectively.These quantities are computed with ws � 0.002 Fs�i.e., 40 kHz� and a probability of false alarm PFA �1%. One can note the very good agreement �lessthan 5% difference� on a large � range �from 1 to 103�between the values of Xr

�q computed from the actualHDL signals �circles, squares, and triangles� andfrom the Zrnic synthetic HDL signals4 �solid curves�and Eq. �2� �dashed curves�. The accurate estima-tion of Xr

�q �with r � 1� by use of Eq. �2� demon-strates the validity of the assumption of decorrelated

Fig. 5. Examples of simultaneous HDL signals from the threedetectors for CNR � 11 dB.

Fig. 6. Experimental results for CNR � �5 dB �the HDL spectralwidth ws � 0.002 Fs, i.e., 40 kHz� and probability of false alarmPFA � 1%: �a� threshold value Tth �solid curve� and parameter ��dashed curve� as a function of � � N CNR, �b� probabilitiesXr

�1, �c� Xr�2 and �d� X3

�3 as functions of � � N CNR. Circles,case r � 1; squares, r � 2; triangles, r � 3. The probabilities arecompared with those computed numerically from Zrnic syntheticHDL signals with similar characteristics when �q; r� � �1; 1� �solidcurve� and by use of Eq. �2� when r � 1 �dashed curves�.

Table 1. Correlation Coefficients Cij between Two Simultaneous HDLSignals �si, sj� Delivered by the Three Receivers for Various CNRs,

Estimated on 400 Shotsa

CNR �dB�

Correlation Coefficients Cij

C12 C13 C23

11 �0.012 0.068 �0.0014 0.041 0.015 �0.008

�1 0.077 0.025 0.039�5 0.017 0.076 0.024

aThe HDL signals are averaged on a 1-�s range gate.

20 December 2002 � Vol. 41, No. 36 � APPLIED OPTICS 7513

HDL signals between the three receiver–detectorunits, as also shown in Table 1.

Similar to what is shown in the Guerit et al.1 com-panion paper, increasing the number of receiver–detector units leads to a significant increase of theprobability Xr

�q at a low CNR �see Figs. 6 and 7�. Ithas to be noted that Figs. 8 and 9 of part I1 displayedthe HDL performance as a function of � for fixedvalues of �, whereas in the present study, � varieswith � �see Figs. 6�a� and 7�a��. Figure 6�b� �Fig.7�b�� shows that X1

�1 � 100% for � � 70 �100�, whichis coherent with the threshold value determined fromthe simulations conducted by Rye and Hardesty5

�� � 60 for getting HDL signals with certainty, i.e.,all estimates good—that is, a good detection proba-bility that tends to 100%� and with the observationsmade by Frelhich et al.6 using a 2-�m pulsed HDL.When several receiver–detector units are considered,the threshold value for � can be lowered to 20 in Fig.6�b� and 40 in Fig. 7�b� for �q; r� � �1; 2�. The thresh-old value � � 10 obtained for �q; r� � �1; 3� �Fig. 6�b��can roughly be compared with the threshold � � 6obtained by Frelhich et al.6 when they accumulatedfive consecutive shots in similar CNR conditions.For �q; r� � �2; 2�, �2; 3�, and �3; 3�, the criterionbecomes � larger than 90, 30, and 95 in Fig. 6, re-spectively, and 100, 50, and 100 in Fig. 7, respec-tively. For practical use, Table 2 extracts from Figs.6 and 7 the values of Xr

�q computed for CNR � �5,

�1, 4, and 11 dB and for N � 60 or �T � 3 �s �ws �40 kHz, i.e., 0.002 Fs�.

4. Conclusion

The present study has been dedicated to the experi-mental validation of the findings presented in theGuerit et al.1 companion paper on the effectiveness ofindependent realizations to improve HDL perfor-mance �to produce the best possible velocity or powerestimates or both� at a low CNR by use of a 1.55-�mcw HDL with three receiver–detector units. Theprinciple of the two studies �i.e., part I and thepresent study� is to increase the chances of gettingheavy speckles in HDL signals by use of manyreceiver–detector units on a single- or several-shotbasis. The HDL signal selection procedure is basedon Rye and Hardesty’s study.5 The actual HDL dataallow us to investigate a range of effective photo-counts for one shot and one collimator, � � N CNR,between 1 and 103. The experimental results are invery good agreement �better than 95%� with the the-oretical findings: �i� The probabilities of good detec-tion by use of several receiver–detector unitscomputed from synthetic HDL signals and Eq. �2�match accurately the probabilities obtained from theactual HDL data; �ii� the probability of detecting sev-eral good HDL signals for accumulation increasessignificantly with the number of HDL signals de-tected simultaneously even for effective photocount� � 10; �iii� the comparison with the criterion � � 60for getting HDL signals with nearly 100% probabilityof good detection is relevant when one receiver–detector unit is used; and �iv� this criterion becomes� � 10 when three receiver–detector units are used.

So, the technique presented in part I to set thenumber of detected HDL signals needed to meet agiven specification a priori on the probability of gooddetection and the number of good signals has beenvalidated in the details. Future papers will addressthe case of distributed aerosol targets and will con-sider additional receiver–detector units for actual at-mospheric applications.

The authors thank A. Delaval, X. Favreau, A. M.Dabas, and J. P. Cariou for fruitful discussions.They are grateful to C. Boitel and D. Goulard for

Fig. 7. Same as Fig. 6 for CNR � �1 dB.

Table 2. Probability Xr>q Computed from the Actual HDL Dataa

CNR�dB�

X1�1

�%�X2

�1

�%�X3

�1

�%�X2

�2

�%�X3

�2

�%�X3

�3

�%�

�5 86.4 98.3 99.7 74.6 95.4 64.2�1 93.7 99.4 99.7 88.0 98.6 82.7

4 97.8 99.9 100 95.6 99.7 93.511 99.7 100 100 99.5 100 99.2

aProbability Xr�q to obtain at least one, two, or three good HDL

signals considering one, two, or three receiver–detector units op-erated simultaneously, computed from the actual HDL data by useof a 3-�s range-gate length �i.e., N � 60�, ws � 0.002 Fs �i.e., ws �40 kHz and Fs � 20 MHz� for CNR � �5, �1, 4, and 11 dB. Theseparameters correspond to ��; �� approximately equal to �19; 2.4�,�48; 2.4�, �151; 2.4�, and �755; 2.4�, respectively.

7514 APPLIED OPTICS � Vol. 41, No. 36 � 20 December 2002

technical assistance. The research has been con-ducted at the Laboratoire de Meteorologie Dynamiqueand the Office National d’Etude et Recherche Aeronau-tique. This research has also been supported by Cen-tre National d’Etudes Spatiales.

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