Download - Practical considerations for the design of CO_2 lidar systems

Practical considerations for the design of CO2 lidar systems

Jay A. Fox, Cynthia R. Gautier, and Jeffrey L. Ah

A 10.6-,um single laser lidar system has been utilized to monitor the amplitude, standard deviation, and

correlation of returns from foliage, hillside, and man-made targets as a function of the lidar system divergenceand mode shape, the receiver field of view and receiver/transmitter alignment tolerance, the repetition rate,and the sampling time. Studies of the dependence of the system sensitivity on signal averaging and signalcorrelation demonstrate performance comparable with that achieved with reported dual laser lidar systems.

1. Introduction

It is well known that differential absorption lidar(DIAL) is extremely useful for the remote sensing andquantitative measurement of gaseous constituents ofthe atmosphere. Most of the recently reported directdetection studies have dealt, either directly or indi-rectly, with improvements of the accuracy of DIALsystems.1 -7 The experimental work has generally in-volved the analysis of large data sets obtained overcomparatively long intervals of time (10-20 min) andhas utilized multiple lasers operating at relatively lowpulse repetition rates (10 Hz). These experimentshave yielded statistically useful results, but little infor-mation was obtained that would be useful for the de-sign of more compact lidar systems with optimizedsensitivity.

This paper attempts to address this need by present-ing data bearing on the basic design parameters of adirect detection DIAL lidar system. Consideration isgiven to the optimum useful magnitude of both thetransmitter divergence and receiver field of view. Inaddition, the relative importance of transmitter/re-ceiver alignment is explored as well as the possibility ofutilizing multitransverse-mode beams to enhance sys-tem performance. The effect of varying the pulserepetition rate as well as the data collection interval isalso presented. Finally, the possibility of using a sin-gle tunable laser source is discussed. It will be shownthat for applications requiring minimum size and

Jeffrey Ahl is with Science Applications International Corpora-tion, McLean, Virginia 22102; the other authors are with U.S. ArmyCenter for Night Vision and Electro-Optics, Fort Belvoir, Virginia22060.

Received 18 July 1987.

weight and operating from a stationary platform, itmay be beneficial to use such a system. In fact, datawill be presented that suggest that signal averagingwith a single-laser system may be superior to thatpreviously reported with multilaser lidars.

11. Experimental Apparatus

The CO2 laser lidar system is shown schematically inFig. 1 and consists of a CO2 TEA laser, a variablemagnification beam expander, a beam steering mirror(not shown), an 18-cm (7-in.) aperture Dall-Kirkhamtelescope, HgCdTe detectors for monitoring the trans-mitted and received beam intensities, a pyroelectricarray for monitoring far-field beam patterns, a dual-channel 200-MHz digitizer, and a computerized dataacquisition system. This system has monitored back-scatter returns from foliage and hillside targets atranges exceeding 3.5 km, with carrier-to-noise ratiosexceeding 10, dependent on atmospheric absorptivity.

The system utilized a grating tuned Laser Science,Inc. model 150G TEA laser yielding 120-mJ pulses in amultitransverse-mode beam. An intracavity apertureallowed single-transverse-mode operation with -60-mJ output energy. Laser pulses exhibited a 150-nsduration gain switched spike and a 1-2-gs tail. Thesingle-mode beam had a measured divergence of 3mrad and the multimode beam exhibited a divergenceof 5 mrad. Virtually no triggering jitter was observedfrom the thyratron triggered power supply. The laserwavelength was monitored with a spectrum analyzer,and the laser was typically operated on the 10P(22)transition to minimize the effects of absorbing atmo-spheric species.

The output of the laser was directed through a beamexpander with stepwise selectable magnifications of 1,2, 4, and 6. A portion of the resulting beam was thenfocused through a 2-m focal length lens onto a 128-element pyroelectric array, with an element width of0.1 mm and an element-to-element gap of 0.015 mm.

1 March 1988 / Vol. 27, No. 5 / APPLIED OPTICS 847

Fig. 1. Schematic of the TEA CO2 laser lidar system.

Thus, the far-field beam profile could be observed witha 50-grad pixel resolution. Monitoring revealed thatthe laser exhibited <100,grad of pointing angle fluctu-ations, and the beam profile was observed to be ex-tremely uniform on a shot-to-shot basis, even whenoperating multimode.

The transmitted energy was monitored by splittingoff a fraction of the transmitted beam and focusing iton a HgCdTe detector. Particular care was taken inminimizing the effects of ghost reflections from the ARcoated side of all beam splitters. The focused spot sizewas -1/4 of the detector diameter, ensuring that theentire beam was monitored. The transmitted energytypically exhibited a standard deviation of between 1%and 2% for a 180-shot burst, as measured independent-ly by both a pyroelectric energy meter and by the lidardata acquisition system.

The laser beam was transmitted coaxially with the16-cm (6.3-in.) clear aperture, f/2.5 receiver telescope.The backscattered radiation was imaged on a 0.5-mmGe-immersed HgCdTe detector with a field of view of 5mrad. The detectivity of the detector at 10 kHz was2.5 X 1010 cm Hz 1/2 W- 1 .

The detector outputs were low pass filtered with abandwidth of 300 kHz and digitized at 100 MHz withan 8-bit digitizer (Tektronix 7612). The resultingwaveforms (2048 points/record) were stored in RAMon an IBM AT computer equipped with 3.5 Mbytes ofEMS memory. Although the laser was capable ofoperation at repetition rates of up to 150 Hz, the sys-tem was limited to a repetition rate of 40 Hz by the dataacquisition system.

The data were peak detected and a statistical analy-sis was performed in real time. The mean, normalizedstandard deviation, and autocorrelation were comput-ed as described by Killinger et al.

8 Both the standarddeviation and the autocorrelation as a function of thenumber of pulses averaged were also computed.

To simulate the performance of a rapidly tunable,single-laser lidar system, the data set was separatedinto an odd and even data set representing the twosimulated wavelengths. The ratio of these two datasets was then computed and the resulting data set wasanalyzed to determine the mean, normalized standard

deviation, and correlation as a function of the numberof pulses averaged.

All data were acquired at the Laser Test Range atFort A. P. Hill, VA, against a variety of targets includ-ing weathered plywood boards, bare and foliated hill-sides, and treetop foliage, at ranges between 0.6 and 3.5km.

111. Sources of Signal Variance

The minimum signal variance that can be achievedin a single-wavelength lidar system will be determinedby several independent noise sources, including:

(1) speckle noise,(2) physical motion of the target (principally due to

wind),(3) atmospheric turbulence effects, including beam

steering,(4) atmospheric absorptivity fluctuations,(5) laser pointing angle and beam profile fluctua-

tions, and(6) detector, electronics, and digitization noise.While most of these items will be discussed in detail

in later sections, a few general comments about each ofthem may prove useful now.

Flamant et al.9 have shown that the speckle noise ofthe receive signal is reduced when using a multilongi-tudinal-mode beam compared with that obtained witha single-longitudinal mode. It is shown in the Appen-dix that, for a laser such as the one used in our experi-ment, the use of multitransverse modes will also lead toa decrease in the speckle noise. It is calculated thatthe noise improvement will be approximately a factorof 2 and the expected minimum speckle-limited stan-dard deviation will be -0.5%.

Physical motion of nonrigid targets such as trees canresult in a random fluctuation in the target reflectivity.These fluctuations will occur on a relatively long timescale, ranging from 0.1 to 10 s. As we shall demon-strate in a later section, these effects are probably notimportant contributors to the overall single-shot (i.e.,unaveraged) noise levels typically encountered in thissystem. Fluctuations in the effective target reflectiv-ity can also result because of laser pointing angle andbeam profile variations. The profile of the transmit-ted beam was monitored with a 50-grad resolutionpyroelectric array, and no beam steering or modeshape changes were observed.

Kjelaas et al.10 have reported on the frequency spec-trum of atmospheric turbulence-induced noise.While their data were taken for a 660-m path length,the frequency spectrum should scale as vL, where Lis the path length, and v is the perpendicular compo-nent of the wind velocity. For a crosswind speed of 2m/s and a target range of 1 km, their results predictthat the coherence will fall off so rapidly above 80 Hzthat the signal variance caused by turbulence will beprimarily uncorrelated at laser repetition rates greaterthan that frequency.

Additional noise may also be introduced by atmo-spheric absorptivity changes that occur relativelyslowly. Small amplitude fluctuations will contribute

848 APPLIED OPTICS / Vol. 27, No. 5 / 1 March 1988

to the noise variance at frequencies below a few hertz.Larger amplitude changes (exceeding 50%) have beenobserved to occur on a time scale of several minutes.

Throughout these experiments, both the carrier-to-noise ratio and transmitter energy variance were moni-tored. Most of the data analyzed exhibited CNRsexceeding 100:1 at 1 km and 40:1 at 2 km, and thereforedid not represent the dominant noise source in themeasurement. The transmitter standard deviationranged between 1% and 2%, matching values deter-mined with a pyroelectric energy meter. Electronicand digitization noise were measured by injecting areproducible signal into the detector preamp. Thecomputed standard deviation was below 1% and thuswas not a substantial contributor to the observed lidarsignal variance.

A. Transmitter/Receiver Alignment

One important consideration in constructing a lidarsystem is maintaining the relative alignment betweenthe transmitted beam and the receiver field of view. Itis obvious that the receiver must image the targetilluminated by the transmitted beam. However, ifthere is any misalignment between the receiver and thetransmitter, there will be a reduction in the receivedsignal, which will eventually give rise to an increase inthe noise level. Of course, a designer would alwayswant to construct a lidar in which the transmitter andreceiver were aligned as well as possible; but it is im-portant to know the effect of misalignment so that areasonable tolerance can be specified. We have per-formed an experiment that is designed to investigatethis issue.

Treetop foliage at a range of 2 km was irradiatedwith a 3-mrad divergence, single-transverse-modebeam and the normalized return signals were mea-sured. The transmitted beam was then moved rela-tive to the receiver by known amounts which weremeasured in the far field with the pyroelectric array.The results can be seen in Fig. 2. Note that the stan-dard deviation of the returns is almost unaffected bytransmitter movements as large as 1.5 mrad eventhough a substantial portion of the beam has beenmoved out of the field of view of the receiver as evi-denced by the fact that the return has decreased toonly -60% of the value at perfect alignment. Thus,although the carrier-to-noise ratio is affected by trans-mitter/receiver misalignment, the sensitivity (signalvariance) of the system has not been substantiallydegraded. Therefore, the receiver field of view cansafely be reduced to a value only slightly larger thanthe transmitter spot size on target.

B. Beam Size

One of the principal lidar system design consider-ations is selection of the proper transmitter divergenceand receiver field of view. As discussed above, thereceiver field of view should be selected to be slightlylarger than the transmitted spot size on the target.Selection of the transmitter divergence is subject tothe following considerations. Changes in beam size

1. U.1Z

NORMALIZED RETURN / 0.10

1.0 - 3 8 - -8 / 0.08

in\ w > / ~ ~~~~~~~~~~~~~~~ 0.06

0.5 - 0.04

STANDARD DEVIATION

6 -0.02

I l l n inn

To

To

:ait

-3 -2 -1 0 1 2 3"_

TRANSMITTER OFFSET (mrad

Fig. 2. Dependence of the normalized lidar return signal and stan-dard deviation as a function of the relative transmitter/receiveroffset angle for a foliage target at 2 km and a 3-mrad TEMoo trans-

mitter beam.

0.1

0.09

0.08

0.07

0.06

0.05

0.04

0.03

0.02 -

0.01

02 4

TRANSMITTER DIVERGENCE (mrad)

Fig. 3. Uncorrelated noise level from a foliage target at 2 km as afunction of the transmitter divergence monitored at 40 Hz with afixed 5-mrad receiver field of view. The continuous line represents

a curve fit.

are expected to affect the lidar signal variance in sever-al ways. (1) Increases in the beam size on the targetwill reduce the speckle noise by increasing the numberof independent speckle cells averaged by the receiver.(2) Increasing the area of the irradiated target spot sizewill enhance the averaging of spatial reflectivity varia-tions. This will minimize the effects of target motionor beam steering produced by either atmospheric tur-bulence or laser pointing jitter. (3) Increasing thereceiver field of view or the transmitter divergence willimprove the transmitter/receiver overlap and will min-imize the effect of variations in atmospheric absorptiv-ity.

The effect of varying the irradiated spot size wasmonitored by reducing the divergence of the transmit-ted beam by factors of 1, 2, 4, and 6. Typical resultsare shown in Fig. 3 for a multimode beam with a 5-mrad divergence, illuminating a foliage target 2 kmaway at a repetition rate of 40 Hz. As expected, thesignal variance is smaller for the larger divergencebeam. The theoretical speckle limit of 0.8%, assumingsix uncorrelated modes, is substantially lower than theobserved uncorrelated noise level. This is the case for


l

c

=1

e!

CD

Table . Standard Deviation (%) for Returns from Diffuse Targets

RangeTargets (km) Multimode Single-mode MM/SM

Trees 1 2.6 + 0.3 3.2 ± 0.2 0.81 ± 0.112 4.4 ± 0.2 4.9 + 0.4 0.75 I 0.07

Plywood 1 3.1 i 0.5 4.1 + 0.5 0.76 + 0.15

both single-mode and multimode data taken at rangesof 0.7-3 km. Autocorrelation was also measured dur-ing this experiment and there was no discernible de-pendence of the values on the beam divergence.

C. Transverse Modes

Several recent lidar systems have been designed thatutilize single-transverse-mode TEA lasers, due to aconcern that fluctuations in the profile of a multimodelaser would significantly increase the system variance.These profile fluctuations could be due to either varia-tions in the mixture of the intensities of the individualtransverse modes on a shot-to-shot basis, or to changesoccurring during a single-laser pulse. Measurementsdetailed in this section, however, demonstrate thatsystem variance with a multimode laser is at least aslow as that resulting from a single-mode laser of thesame divergence, and that the additional energy out-put (approximately a factor of 2) available with a mul-timode laser may significantly extend the operationalrange of the lidar system.

As noted previously, the laser spatial mode structurecould be selected in a reproducible manner by means ofa variable diameter intracavity aperture, and theshape of the resulting beam could be monitored bymeans of the pyroelectric array. Measurements wereperformed on both treetop foliage and a 24-m (8-ft)square painted plywood target. The divergences ofthe single-mode and multimode transmitter beamswere measured to be -3 and 5 mrad, respectively.

Typical results comparing single-mode vs multi-mode performance are displayed in Table I. All datahave been corrected for differences in the carrier-to-noise ratios for the single-mode and multimode (MM)beams. It can be seen that use of the MM beamreduces the standard deviations for signals returningfrom a foliage target by as much as 25%, while thereduction for a plywood target is up to 40%.

The reduction in the magnitude of the standarddeviation could be due to two effects: (1) The irradiat-ed target size for the multimode beam is -60% largerthan for the single-mode beam. (2) The number of

Table Ill. Short-Term Fluctuations of the Normalized Return and StandardDeviation

Data collection Standardtime Average deviation(s) return (%)

3 0.87 i 0.01 3.4 ± 0.36 0.86 0.01 3.0 0.1

12 0.86 ± 0.01 3.3 0.424 0.85 0.01 3.2 + 0.2

uncorrelated frequencies of the multimode beam islarger than for the single-mode beam.

As shown in Fig. 3, for a foliage target the standarddeviation decreases by -25% when the divergence of amultimode beam is increased from 3 to 5 mrad. Asthis is the same enhancement achieved by changingfrom a single-mode to a multimode beam, it appearsthat the additional speckle noise reduction due totransverse mode frequency decorrelation is not signifi-cant. This is consistent with the earlier observationthat the uncorrelated noise level is substantially abovethe computed speckle noise limit.

Data taken with a plywood target also show a 25%reduction in standard deviation when switching from asingle-mode to a multimode beam. As the targetdepth is insufficient to produce decorrelation of thetransmitted frequencies, this result is consistent withthe interpretation of the results from the foliage tar-gets.

D. Sampling Time

A possible area of concern to the lidar user might bethe variation with time of return signals reflected fromtopographic targets. Both long- and short-term fluc-tuations could have a deleterious effect on lidar utility.During the months of September and December 1986,data were taken to investigate any long-term changes.The results are given in Table II. A variety of targetswere used at 1- and 2-km ranges. A burst of 160 shotsat a repetition rate of 40 Hz was fired every minute fordurations of 13-17 min. As can be seen from the table,variations in the return signals are quite small (2-3%),while the standard deviations did not change morethan -10%. Similar results were obtained during themonths of May and June.

The effect of short-term variations was also investi-gated. A foliage target at a distance of 1800 m wasirradiated with bursts of 120 shots for times extendingfrom 3 to 24 s. Table III illustrates the results of thisexperiment. Apparently, both the magnitude and the

Table II. Long-Term Fluctuations of the Normalized Return and Standard Deviation

StandardRange Normalized deviation

Target (km) return (%) Autocorrelation Notes

Treetop foliage 2 0.84 ± 0.03 2.9 ± 0.2 0.20 ± 0.12 13-min duration, Sept. 1986

Plywood 1 1.05 + 0.02 4.2 + 0.3 0.40 ± 0.11 15-min duration, Sept. 1986

Shrubs 2 1.02 ± 0.02 4.9 ± 0.5 0.12 ± 0.09 17-min duration, Dec. 1986


Table IV. Repetition Rate Dependence of the Lidar Returns

StandardRepetition Normalized deviation

rate return (%) Autocorrelation

40 0.94 ± 0.03 4.35 ± 0.77 0.440 ± 0.05120 0.91 + 0.01 4.56 ± 0.38 0.407 ± 0.08110 0.93 ± 0.02 4.06 ± 0.35 0.174 ± 0.1535 0.91 ± 0.01 4.49 + 0.67 0.149 i 0.044

standard deviation of the reflected return signals areunaffected by any atmospheric or other variations thatmight have occurred during these time intervals. Asabove, this result was typical of others obtained overthe May through December experimental period.

E. Repetition Rate

As noted previously, although the laser was capableof operating at a repetition rate of up to 150 Hz, dataacquisition limitations gave a practical upper limit of40 Hz. Nevertheless, this rate was great enough toessentially avoid effects of slow changes in atmospher-ic conditions as noted by others, where it has beensuggested that single-laser lidars may be practical ifthis effect can be mitigated. Most of the direct detec-tion lidar studies have dealt with multilaser systems togive pulses that are emitted closely enough together intime that they are affected by the same atmosphericfluctuations.7 However, it has been pointed out5 thateven this method cannot remove the effects of atmo-spheric turbulence. Indeed, these authors report tem-poral correlations that are relatively low (<0.5) forpulses that are emitted within 50 gus of each other.Warren 1 has shown that the sensitivity of a lidar sys-tem can be improved by only a factor of 1.5 if the pulseshave correlations this great. It is conceivable that forsome applications the increased sensitivity may not beworth the additional complexity, size, and weight of amultilaser system. As the following results will dem-onstrate, the potential performance of a single-laserlidar can be even better than that suggested by the 1.5factor.

Table IV shows the results of an experiment in whichbursts of 120 shots were fired against a plywood target1 km from the transmitter. A multimode beam wasused and the pulse repetition rate was varied from 5 to40 Hz. It can be seen that both the normalized returnfrom the target and the standard deviation are unaf-fected by the change in repetition rate, however theautocorrelation decreases by more than a factor of 2 forpulse separation times of 0.1 s or more. It should benoted that the autocorrelation measured at 40 Hz withthis single-laser system is in agreement with that mea-sured by Menyuk et al.,1 even though they were using atwo-laser system with the pulses separated by only 5-7As.

IV. Signal Averaging

A. Autocorrelation

The autocorrelation coefficient is an important pa-rameter in determining the utility of a lidar system. If

the pulse-to-pulse correlation is high, the ultimate sen-sitivity of the device is maximized."1 On the otherhand, it is frequently necessary to decrease the single-shot measurement error by pulse averaging. Howev-er, unless the correlation is low, the expected reductionin error by the square root of the number of measure-ments N will not occur. Instead, the relationship be-tween , the single-shot error, and UEN, the error afteraveraging N pulses, has been shown to be2

-N-11/

OaN = +/ (1 -jIN)pj

where pj is the temporal autocorrelation coefficient fora delay time T-, and j is the time interval betweensuccessive pulses. Thus, the pulses must be decorre-lated (p = 0) to gain the maximum benefit from averag-ing.

Menyuk and Killinger3 have presented pioneeringautocorrelation measurements for their direct detec-tion lidar. We present an extension of this importantwork for conditions that may be of more utility to thelidar designer. For example, the lidar used in thisinvestigation had a much lower percentage single-shotstandard deviation of normalized returns (5% vs 20%)and the data were taken at considerably higher repeti-tion rates (40 vs 10 Hz). In addition, the earlier resultswere based on a few large sets of shots (6000-12,000)extending over 10-20 min.

This technique, while yielding a statistically usefuldata base, has the added complication of being affect-ed by slowly varying atmospheric conditions. Indeed,during one of the two direct detection data collectionperiods recently reported by Menyuk et al., such acircumstance did occur and the rate of single-pulsesignal averaging was changed. However, for manyapplications, e.g., moving clouds of pollutants and/or amoving lidar platform, it would be desirable to mini-mize the duration of the burst of shots to, at most, a fewseconds. Then these slowly varying changes wouldnot be as important. In fact, Menyuk et al.1 implythat, when the atmospheric extinction is essentiallyconstant throughout the measurement period, single-laser systems would be as useful as multilaser lidars.

If the user is to rely on one or more short bursts, it isimportant that the statistical nature of the autocorre-lation value be appreciated. Although Menyuk andKillinger3 allude to the possibility of p changing fromburst to burst, to the best of our knowledge, no one hasever presented data that explicitly demonstrate thispossibility and show the typical ranges of values to beexperienced. Figure 4 gives a reasonably typical illus-tration of the manner in which the autocorrelation canchange with time. Each point represents a burst of180 shots with a repetition rate of 40 Hz. The laser wasoperating in a TEMoo mode and the target was treetopfoliage. Note the large deviations from shot to shot.The average value and the standard deviation of thisdata set are 0.165 + 0.088. During the period of thisexperiment, the transmission through the atmospherewas monitored by measuring the normalized return


I

TIME Imin)

Fig. 4. Variation of the autocorrelation with time for a foliagetarget at 1700 m and a 0.025-s measurement interval.

0.4-FOLIAGE

0.3 AVE = 0.23 0 .12

0 0.2

0.1

s 0-+---= I II0

OA

2 PLYWOOD

t; 0.3 _AVE = 0.44 t 0.13

0.2

0.1

0 0 0.2 0.4 0.6 0.8 1.0

AUTOCORRELATION

Fig. 5. Histogram of the autocorrelation for foliage targets at 1 kmand plywood targets at 1 km. Data taken at 40 Hz, 3-mrad TEMoo

beam, and 5-mrad receiver FOV.

from the target. The returns did not change by morethan 5% and averaged less than a 2% deviation from theaverage. Any changes that were evident did not ap-pear to be correlated with changes in the autocorrela-tion.

Figure 5 shows the results of another set of shotstaken six months earlier against both foliage and aplywood target. The targets were near one anotherand were located 1 km from the transmitter. Eachevent represents a burst of 120 shots at a pulse repeti-tion rate of 40 Hz. Once again, the large statisticaldeviation is present. In this case, note the differencebetween the autocorrelation values measured usingreturns from the two types of target. Apparently,either beam steering and/or target motion serves todecorrelate the pulses reflected from the foliage.Speckle averaging from the optically deep foliagecould also play a role in this phenomenon.

Finally, although this point was not specifically in-

0.5

0.5 -{

0.3 I0.2

0 IL I800 100 1200 1400 1600

RANGE {ml

Dependence of the autocorrelation with range for foliagetargets.

0.09

0.08 H

0.07 _-

0.06

0.05

0.04

0.03

0.02

0.01

00 1000 12M 140 1600

RANGE (m}

Fig. 7. Dependence of the lidar return signal standard deviationwith range for foliage targets.

vestigated, a perusal of the data strongly suggests thatthe autocorrelation is a function of range. For exam-ple, Fig. 6 contains results that indicate that the auto-correlation decreases with range. Indeed, for our sys-tem, it appears to vanish for ranges longer than 2.5 km,although this result is not part of the data set present-ed. The reader is cautioned against taking the exactvalues too literally, since they were the result of com-paratively few bursts and show substantial scatter.Nevertheless, the general trend is evident. It has beensuggested5 that turbulence is strongly range depen-dent and will cause an increase of the standard devi-ation of the lidar return with range as R 11 1 2 formoderate turbulence levels. An increase has been ob-served for the same data set (see Fig. 7), althoughinsufficient data exist to ascertain the functional formof the increase. It is therefore reasonable to concludethat the observed decrease in autocorrelation withrange is at least partially due to turbulence.

B. Pulse Ratios

As noted earlier, our system and data analysis proce-dure is designed to simulate a rapidly tunable, single-laser lidar system, wherein the principle observable isthe ratio of received power at two wavelengths (1/12).The standard deviation of each of these signals hasbeen reported earlier to vary between 3% and 5% for


o S o

0 0

0 0_l~~~~~~~~

u

Z

06

4

03

2 ~~~~-RAW DATA

0 0.1 0.2 0.3 0.4 0.5 0.6

AUTOCORRELATION

Fig. 8. Histogram of the autocorrelation for a foliage target for rawand ratioed data.

ranges up to 2 km. If the two signals I, and I2 wereindependent, the standard deviation of the ratio wouldbe a2_ times larger than the single-wavelength standarddeviation. However, if turbulence and/or target ef-fects represent a sizable portion of the measurementnoise and affect both transmitted wavelengths equally,a significiant correlation of the two signals is expected.As shown by Killinger and Menyuk, 7 the variance ofthe ratio will be given by a2/y = 2o-2(1 - pt). For largevalues of the correlation coefficient (p > 0.5), the stan-dard deviation of the ratio can be less than that for theindividual returns.

Measurements of the autocorrelation of the lidarreturn signal were performed on several hundred datasets. As displayed in Fig. 8, the autocorrelation of theraw data varied uniformly between 0 and 0.6. Overthis range, the standard deviation of the signal ratioswill range from 1.4 to 0.9 times the individual signalstandard deviation. Thus, ratioing the signals doesnot substantially increase the system sensitivity. Thevariation in autocorrelation magnitude occurred on aminute by minute time scale, with no apparent relationto atmospheric visibility or to visual turbulence level.

The rate of decay of the autocorrelation varied ran-domly throughout these tests. At times, the autocor-relation would decay to near zero in less than the 0.025-s measurement interval, while at other times the auto-correlation remained above 0.25 for intervalsapproaching 0.5 s. Again, there was no apparent de-pendence on the atmospheric visibility.

C. System Averaging Performance

The typical minimum standard deviation achiev-able with a well-designed lidar system is in the range of5%, however, many applications require deviationssubstantially less than this value. One means of re-ducing the system standard deviation is by averagingthe received signal. If the sequential return signalsare uncorrelated, the signal will average down as thesquare root of the number of samples averaged. How-ever, as noted earlier, a substantial shot-to-shot corre-lation is observed when operating at high repetitionrates. Grant12 has suggested that is caused by measur-ing nearly the same speckle pattern from pulse to

0.05

0.04

0.03

0.01

I0 5 10 15N NUMBER OF PULSES AVERAGED)

20 25

Fig. 9. Standard deviation as a function of the number of pulsesaveraged, raw and ratioed data, for an extreme case of high correla-

tion.

pulse. He speculates that the decorrelation by atmo-spheric turbulence is not complete, so that each mem-ber of the pulse set is not independent.

An extreme case of the effect of this correlation onsignal averaging can be seen in Fig. 9, where the signalstandard deviation is reduced by only 10% rather thanby the expected 500% when averaging twenty-fiveshots. As noted earlier, Menyuk et al.

4 have deter-mined the maximum sensitivity enhancement achiev-able by signal averaging. In the limit of a constantautocorrelation and for large N, their expression forthe maximum enhancement reduces to cr/oN = 14.For the maximum observed autocorrelation of 0.6, thisequation implies that the maximum achievable reduc-tion in standard deviation is a factor of 1.3. In most ofour data sets, the autocorrelation declined to valuesbelow 0.2 after ten shots, allowing a reduction in stan-dard deviation by a factor of 2.4.

The reduction in signal averaging efficiency can beunderstood by considering the overall signal varianceas being due to the sum of a correlated noise source a,and an uncorrelated noise source o-. The signal vari-ance is then given by6

U2

= (2 + O¢), and the autocorre-lation coefficient is p = oc/2 For a correlation of 0.6,the correlated standard deviation is 77% of the totalstandard deviation. Thus, even if all the uncorrelatednoise could be removed by signal averaging, the overallnoise level would be reduced only by a factor of (1/0.77)= 1.3 to the correlated noise level (assuming a constantcorrelation). Thus, it is important to reduce the corre-lated noise level.

If the uncorrelated noise can be removed by averag-ing, it should be possible to remove the cross-correlat-ed noise by ratioing the multiwavelength returns. Inour system, this is simulated by treating the odd andeven pulse returns as two independent data sets. Thissimulates a dual-wavelength single-laser lidar systemoperating on a single wavelength and removes the ef-fects of differential target albedo and atmospheric ab-sorptivity.

The autocorrelation of the ratioed data set has beenmonitored, and a histogram of the frequency of occur-


0 0 00*00 0oee *e.@eS 0 e@Oe@0

RAW DATA

I _ARR~ODDT

0 00 0

n'7

ax

0.02

n

rence of a given level is shown in Fig. 8 (negative valueshave been treated as zero). The mean value of thecorrelation of the ratioed data set is -0.01 + 0.08. Thestandard deviation of this result is consistent with theexpected value of 1N for the 180-point data sets.These data demonstrate that the ratioed data set isentirely uncorrelated to within the statistical noiselimits. Confirmation of this result is seen in Fig. 9, inwhich the rate of averaging for both the original dataset and the ratioed data set is shown. The ratioed dataset averages down approximately as Ad, even for rawdata sets which do not average down at all.

This result is in disagreement with those of Killingeret al.", 3 -7 Their results showed that signal averagingfor both the initial data and the ratioed data averagedsimilarly in most cases, and significantly slower thanV7N. There are several significant differences betweenthe two lidar systems utilized which may contribute tothis discrepancy.

In Killinger's system, two lasers were utilized withan almost speckle-limited optical system. Turbu-lence-induced beam steering, laser pointing jitter, andslight variations in the intensity pattern of the twolasers will result in a reduction in the cross correlationof the two signals. This effect will be enhanced by therelatively small beam divergence (400 grad) utilized.This is confirmed by their measurements of the auto-correlation and cross correlation for zero time delay.While their system obviously exhibits a zero time delayautocorrelation of unity, the reported cross correlationdegrades to the range of 0.3-0.4 for single-wavelengthmeasurements. Examining the signal standard devi-ations of both systems as a function of number ofpoints averaged, shown in Table V, reveals that theratioed data for the single-laser system averaged downas N-0.5 for both the nine- and sixteen-shots averagedcases, while the two-laser system data averaged downconsiderably more slowly (as N-0 .4 for nine shots, andas N-0

.36 for sixteen shots).

This degradation may be due either to the pulse-to-pulse variation in a single-laser beam profile or to avariation between the two lasers. We believe that it ismost likely the latter. In a laser transmitter, the laserspot will be affected by nonuniformities in the plasmadischarge due to small misalignments of the elec-trodes, nonuniform preionization, and variations inelectrode profile and surface quality. For the case ofmultiple shots from a single-transmitter laser, theseparameters remain unchanged and will not alter thebeam profile, while for multiple transmitters, a built-in bias in the beam profile is inherent in the design.Thus, multiple shots from a single laser will exhibit agreater uniformity than individual shots from multipletransmitters, and the cross correlation of the single-laser system is expected to be substantially higher.Wavelength tuning of the single-laser system is notexpected to alter this result as existing tuning sys-tems" 2 have demonstrated a pointing error and beamshape uniformity of better than 2%. The portion ofthe correlated noise that cannot be removed throughratioing will persist for time periods of hundreds of

Table V. Factor by Which the Standard Deviation of Ratioed DataDecreases as a Function of the Number of Points Averaged

Standard deviationimprovement after

Nine shots Sixteen shots

Present work 2.94 + 0.36 4.31 + 1.07Menyuk et al.

4 2.4 2.7

milliseconds, comparable with the rapid decay portionof the autocorrelation decay time, or -10-100 ms.

V. Conclusions

It is hoped that the results presented in this paperwill provide useful input for the design of future directdetection lidar systems. A number of practical issuesthat directly impact on lidar construction have beeninvestigated as well as more basic considerations ofmethods of error reduction. For example, it has beenshown that the size of transmitted lidar beams shouldbe as large as is practical commensurate with targetsize and range, and should fill the receiver field of view.It has also been shown that the latter requirement doesnot pose serious alignment constraints. Further, ithas been demonstrated that even a single-laser lidarsystem is capable of comparatively low noise and re-producible performance over periods of time that easi-ly allow statistically useful data to be collected. Pulserepetition rates of from 5 to 40 Hz yield usable results,although for some scenarios such as rapidly movingpollutant clouds and/or moving lidar platforms, thehighest available rate should be used.

The possibility of noise reduction by means of thespectral diversity of multitransverse-mode beamscompared with the single-transverse-mode case wasinvestigated. Although the theoretical improvementwas too small to be evident in this system, it was shownthat using multimode beams is practical, reproducible,and probably even desirable from the point of view ofachieving the most efficient energy extraction from thetransmitter, and thereby minimizing the system size,weight, and power requirements.

Noise reduction by signal averaging was also ad-dressed. It was demonstrated that the correlationbetween pulses limits averaging efficiency and is alsosubject to large short-term fluctuations as well as beingboth target and range dependent. Specifically, it wasshown that the correlation decreases with range and isless for optically deep targets. Ratioing data fromsuccessive shots was shown to essentially remove thecorrelation and noise reduction by the square root ofthe number of shots obtained.

Finally, the possibility of using a single-laser lidarshould be noted. We have shown that this single-laser40-Hz system produces pulses with correlations thatare not significantly different from those produced byreported multilaser lidars. Of greater importance, ithas been shown that using a single laser actually resultsin better signal averaging performance than observedfor existing dual laser lidar systems. Noise levels be-low 1% have been consistently achieved for the ratioeddata. Of course, the added complexity of a rapidly


tunable system'3"14 has not been addressed in the cur-rent device, and it is entirely possible that this additionwill give rise to increased noise levels. However, evenif this feature results in slightly reduced performancelevels, the potential benefits of lower cost, complexity,size, and weight might make this a desirable choice forsome applications.

Appendix

For a monochromatic Gaussian beam distributionon the target plane, Wang and Pruitt' 5 have computedthe speckle coherence area at the receiver plane as

A,

where X is the transmitted wavelength, L is the dis-tance between the receiver and the target plane, and Dis the diameter of the irradiated area at the 1/e intensi-ty point.

The normalized signal variance due to speckle willbe given by the reciprocal of the number of indepen-dent speckle cells falling on the receiver aperture. Forthe monochromatic case, this is just 2

= (Ad/Ac). Forthe experimental apparatus used for this paper, thedivergence of the single-transverse-mode beam was 3mrad at 10 um, and the receiver size has a clear aper-ture of 16 cm. Thus, the monochromatic speckle vari-ance is 3.5 X 10-4, equivalent to a standard deviation of1.9%, representing the lower detection limit for a sin-gle-longitudinal-mode, single-transverse-mode sys-tem.

For a multilongitudinal-mode laser, Flamant et al.9have shown that the variance of lidar return signals isdependent on the optical depth and structure of thetarget (e.g., treetop foliage, hillside shrubbery, andtarget boards). Specifically, it was demonstrated thatthe frequency diversity of the beam gave rise to areduction of the variance obtained when multilongitu-dinal-mode beams were transmitted compared withthe single-longitudinal-mode case. For two transmit-ted frequencies, the correlation coefficient of the twospeckle pattern amplitudes is given by = exp[-(6ko-/~J2)2], where o- is the standard deviation of the targetdepth, and k is the difference in transmitted frequen-cies.

The FWHM gain bandwidth of the 1.2-atm TEACO2 laser that was utilized is -5.3 GHz.' 6 In typicaloperating conditions, this laser will generate longitudi-nal modes across a frequency spectrum of -600 MHz.For a laser cavity length of 75 cm, the longitudinalmodes are separated by 200 MHz (6k = 0.04 cm-'),allowing four modes to oscillate simultaneously. Thespeckle patterns for these modes will be uncorrelated ifo- > 50 cm. For a typical terrain target, the targetdepth exceeds several meters, therefore the specklenoise standard deviation of our system will be reducedby a factor of ~4j or 2 for the multilongitudinal case.Thus, speckle noise-limited performance for multilon-gitudinal, single-transverse-mode operation would re-sult in a receive signal standard deviation of slightly<1%.

For a multitransverse-mode beam, additional fre-quencies, given by' 6

fmnq = [q + (m + n + )cos'( g9)/r](c/2L),

are present in the transmitted beam (assuming a near-ly planar resonator). For the resonator configurationutilized in this work (R, = -, R2 = 10 m), the transversemodes are separated by 17 MHz (6k = 0.0036 cm-').As transverse modes up to TEM22 were observed, therewere five unique, equally spaced frequencies emittedper longitudinal mode. For a sufficiently deep target,a > 4 m, the speckle patterns will be decorrelated andthe multitransverse-mode speckle noise will be ap-proximately a factor of 2 lower than for the comparablesingle-transverse-mode case, leading to a speckle-lim-ited minimum signal standard deviation of 0.5%.

References1. N. Menyuk, D. K. Killinger, and C. R. Menyuk, "Error Reduc-

tion in Laser Remote Sensing: Combined Effects of Cross Cor-relation and Signal Averaging," Appl. Opt. 24, 118 (1985).

2. H. Ahlberg, S. Lundqvist, M. S. Shumate, and U. Persson,"Analysis of Errors Caused by Optical Interference Effects inWavelength-Diverse CO2 Laser Long-Path Systems," Appl.Opt. 24, 3917 (1985).

3. N. Menyuk and D. K. Killinger, "Assessment of Relative ErrorSources in IR DIAL Measurement Accuracy," Appl. Opt. 22,2690 (1983).

4. N. Menyuk, D. K. Killinger, and C. R. Menyuk, "Limitations ofSignal Averaging Due to Temporal Correlation in Laser Re-mote-Sensing Measurements," Appl. Opt. 21, 3377 (1982).

5. N. Menyuk, D. K. Killinger, and W. E. DeFeo, "Laser RemoteSensing of Hydrazine, MMH, and UDMH Using a Differential-Absorption CO2 Lidar," Appl, Opt. 21, 2275 (1982).

6. D. K. Killinger and N. Menyuk, "Remote Probing of the Atmo-sphere Using a CO2 DIAL System," IEEE J. Quantum Electron.QE-17, 1917 (1981).

7. D. K. Killinger and N. Menyuk, "Effect of Turbulence-InducedCorrelation on Laser Remote Sensing Errors," Appl. Phys. Lett.38, 968 (1981).

8. N. Menyuk, D. K. Killinger, and C. R. Menyuk, "Signal Averag-ing Limitations in Heterodyne- and Direct-Detection Laser Re-mote Sensing Measurements," in Optical and Laser RemoteSensing, A. Mooradian and D. K. Killinger, Eds. (Springer-Verlag, Berlin, 1983).

9. P. H. Flamant, R. T. Menzies, and M. J. Kavaya, "Evidence forSpeckle Effects on Pulsed CO2 Lidar Signal Returns from Re-mote Targets," Appl. Opt. 23, 1412 (1984).

10. A. G. Kjelaas, P. E. Nordal, and A. Bjerkestrand, "Scintillationand Multiwavelength Coherence Effects in a Long-Path LaserAbsorption Spectrometer," Appl. Opt. 17, 277 (1978).

11. R. E. Warren, "Effect of Pulse-Pair Correlation on DifferentialAbsorption Lidar," Appl. Opt. 24, 3472 (1985).

12. W. B. Grant, "He-Ne and cw CO2 Laser Long-Path Systems forGas Detection," Appl. Opt. 25, 709 (1986).

13. J. A. Fox and J. L. Ahl, "High Speed Tuning Mechanism for CO2Lidar Systems," Appl. Opt. 25, 3830 (1986).

14. A. Crocker, R. M. Jenkins, and M. Johnson, "A Frequency Agile,"Sealed-Off C02 TEA Laser," J. Phys. E 18, 133 (1985).

15. J. Y. Wang and P. A. Pruitt, "Laboratory Target ReflectanceMeasurements for Coherent Laser Radar Applications," Appl.Opt. 23, 2559 (1984).

16. J. T. Verdeyen, Laser Electronics (Prentice-Hall, EnglewoodCliffs, NJ, 1981).


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