Multishot laser altimeter: design and performance

Multishot laser altimeter: design and performance

Xiaoli Sun, James B. Abshire, and Frederic M. Davidson

The maximum measurement range of a laser altimeter can be extended by averaging the measurementsfrom multiple laser shots at the same target. We present the principles of operation and design of such amultishot laser altimeter, which uses a Si avalanche photodiode detector. As an example, theperformance of a spaceborne multishot altimeter containing components similar to those of thesingle-shot Mars Observer Laser Altimeter are given under operating conditions that would beencountered near Saturn. With 100-shot averages, we show that the multishot laser altimeter is capableof accurate ranging at fly-by distances of 10,000 km from an icy satellite. With 100-shot averages, theminimum optical signal level at a 90% correct-measurement probability under nighttime background is9.8 detected signal photons per pulse as compared with 76 photons per pulse with a single shot.

Introduction

Laser altimetry is a valuable technique for measuringsurface topography from aircraft and spacecraft.'Direct detection laser altimeters measure the roundtrip time delay between the transmission of a shortlaser pulse and the detection of the much weakersurface reflection. There are two principal advan-tages of laser altimeters over their conventional radarcounterparts. Laser altimeters can better resolvesurface height and slope variations because of theirmuch narrower transmitter optical beamwidths.Laser altimeters are also insensitive to the effects ofcoherent interference, or speckle, at the receiver,because even modest-sized (20-50 cm diameter) re-ceiver telescopes perform considerable aperture aver-aging. As a result, laser altimeters are capable ofmeasuring range to an accuracy of 1 m or less on asingle shot.1 In contrast, microwave-frequency an-tennas used in conventional radar altimeters aretypically a few tens of wavelengths in diameter.Because the spatial extent of the interference isroughly the same size as the antenna, the antennasare unable to perform much aperture averaging of thereturn signal. Consequently radar altimeters must

X. Sun and F. M. Davidson are with the Department of Electricaland Computer Engineering, The Johns Hopkins University, Balti-more, Maryland 21218. J. B. Abshire is with NASA GoddardSpace Flight Center, Experimental Instrumentation Branch, Green-belt, Maryland 20771.

Received 9 June 1992.0003-6935/93/244578-08$06.00/0.© 1993 Optical Society of America.

average the results of a number of individual pulsetransmissions to achieve comparable range accura-cies.

Recent advances in rugged semiconductor-laser-pumped solid-state lasers,2 lightweight telescopes,3and very-low-noise Si avalanche photodiodes (APD's)have made it possible to design laser altimeters forplanetary missions. The Mars Observer Laser Altim-eter (MOLA) has been developed recently to profilethe surface topography of Mars continuously for 2years.4 The MOLA is designed for a single-shotmeasurement probability of 90% from a 400-kmorbit. Several types of planetary missions requirealtimeter measurements at significantly longer ranges.For these applications, achieving a high single-shotmeasurement probability in a lightweight, compactinstrument is difficult.

An alternative approach for long-distance altimetryis to attempt many altimeter measurements, eachwith a low correct-detection probability, and thenselect the valid range measurements by aligning andaveraging the recorded data. This paper describesthe design and performance analysis of such a mul-tishot laser altimeter.

As an example, the performance of a multishotlaser altimeter similar to the MOLA is calculated.The multishot altimeter uses a Q-switched Nd:YAGlaser ( = 1.064 [um) that emits 40-mJ optical pulsesof 20-ns duration at a repetition rate of 10 Hz, a SiAPD with a 30% quantum efficiency that has beenenhanced for operation at X = 1.064 plm, and a0.5-m-diameter receiver telescope with roughly a 1mrad field-of-view. When one averages over 100

4578 APPLIED OPTICS / Vol. 32, No. 24 / 20 August 1993

laser shots for each range measurement, this systemis shown to be capable of accurate altimetry measure-ment of the surface features of an icy satellite nearSaturn at fly-by distances of about 10,000 km undernighttime background, as compared with 3,600 kmwith a single-shot laser altimeter. The minimumdetected optical signal level at a 90% correct-measure-ment probability is 9.8 detected signal photons perpulse with 100 shots as compared with 76 photons perpulse, the level required by the MOLA with a singleshot under similar conditions.

Laser Altimeter Design and Principles of OperationA block diagram of MOLA is shown in Figure 1. Themultishot laser altimeter is similar to MOLA exceptfor the signal processing at the receiver. Figure 2illustrates the principle of operation of the multishotlaser altimeter. The figure shows a series of N noisyAPD output signals over the range-gate interval, onefor each firing of the laser. The threshold-crossingtimes, tk, indicate the instance of the kth thresholdcrossing on the jth laser shot. The tk's are consid-ered to be statistically independent. If the rangegate interval is TRG seconds and the received laser-pulse width is Tp, the low-pass filter (LPF) shouldlimit the maximum number of threshold-crossingtimes to TRG/Tp.

As shown in Fig. 2, many of the threshold crossingtimes are due to noise spikes in the APD output.These are false alarms and are distributed uniformlyin time. The threshold-crossing times resulting fromthe reflected laser pulse will occur, with a certainprobability, at nearly the same times within the rangegate, as indicated by the vertical dashed line. Thealtimeter estimates the laser-pulse round trip time tobe at the point where the largest number of thresholdcrossings have been observed.

A block diagram of the receiver of the multishotlaser altimeter is shown in Figure 3. Received lightis focused onto the active area of a low-noise Si APD.The photocurrent output from the APD is amplifiedand filtered by an LPF. For simplicity, we havemodeled the LPF as an ideal integrator that inte-grates the input signal over the expected optical pulsewidth, Tp. The equivalent noise bandwidth of thefilter is B = (2Tp)-' Hz. The LPF output is com-pared against a fixed threshold by the high-speedcomparator.

The circuit following the AND gate is used to recordthe threshold-crossing times measured in clock ticksat which the filtered APD output exceeds the fixedthreshold. The bandwidth of the LPF is such thatthere can be at most one threshold crossing every Tpseconds. The clock frequency is selected to be suffi-

Fig. 1. Block diagram of the Mars Observer Laser Altimeter.

20 August 1993 / Vol. 32, No. 24 / APPLIED OPTICS 4579

FalseAlarms

Voltage

1 st shot -

2nd shot -

Nth shot -

to

Detected4/•~ Signal

tN2

IT

Threshold

Time

to + TRGtD

TargetReflection

Fig. 2. Sample photodetector output signals from the multishot laser altimeter.

ciently high that the clock period, AT, is much shorterthan the received pulsewidth, i.e., AT << Tp. TheAND gate allows only the threshold-crossing timeswithin the range gate of the altimeter to be recorded.

The threshold-crossing time memory acts as amultishot timer. It stores the system clock settingfor each positive transition of the AND gate. Eachtime the AND gate output is HIGH because of athreshold crossing, the contents of the counter areread out and stored in the shift register stack. Theremainder of the diagram indicates logic that resetsthe counter and fires the transmitter laser at a givenpulse-repetition rate.

Performance Analysis

Maximum Likelihood ReceiverThe optimal receiver of a multishot laser altimetershould be a maximum likelihood estimator of thelaser-pulse round trip delay time. The joint probabil-ity of the threshold-crossing times recorded over the

N separate laser firings may be written as

Ml M2 MN

P[(tjk)] = H P(tlk) II P(t 2 k) ... 7 P(tNk), (1)k=1 k=1 k=1

where P(tjk) is the probability of the kth thresholdcrossing on jth laser shot and M. is the total number ofthreshold crossings on the jth shot with j = 1,2, . . , N. When a laser pulse is absent, P(tjk) =Pfa - probability of false alarm (noise only) and whena laser pulse is present, P(tjk) = PD =_ probability ofdetection (signal + noise). By taking the logarithm,Eq. (1) may be rewritten as

N M

ln{P[(tjk)] = ln[P(tjk)]j=1 k=1

N N

= ln(Pfa) E (Mj - nJtD) + ln(PD) E nJtD'j=1 j=1


Fig. 3. Block diagram of a multishot laser altimeter.

where n tD = 1, 0 is the number of threshold crossingsresulting from the received light pulse in the jth lasershot. In this analysis, the range of the target isassumed to be fixed and the received light pulses areassumed to arrive in the same time interval for alllaser shots. The threshold-crossing time resultingfrom the return light pulse in each shot is denoted astD. If the target moves within the observation time,a predictable correction for the relative motion be-tween target and spacecraft over N laser firings mustbe made.

If we define the total number of threshold crossingsas

N

M = , z m, (3)j=1

and the total number of threshold crossings resultingfrom detected laser pulses as

N

NtD = E njtD (4)J=1

then the log likelihood function of the thresholdcrossing times [Eq. (2)] can be rewritten as

l(tD) = ln{P[(tjk)]1 = (M - NtD)lf(Pfa) + NtD ln(PD).

Because PD > Pfa and n(PD) > ln(Pfa), maximizingthe log likelihood function [Eq. (5)] is equivalent tofinding the time, tD, such that NtD has the largestvalue. In other words, a maximum-likelihood mul-tishot laser altimeter receiver locates the time inter-val that contains the maximum number of thresholdcrossings in the successive laser shots. The lengthof this time interval is equal to the received laser-pulse width.

Probability of a Correct Range Measurement

Range measurement of a multishot laser altimeter isaffected by both misses and false alarms in detectingthe received light pulses. Both the miss and falsealarm probabilities depend on the received signalenergy, background light, APD parameters, amplifierthermal noise levels, and threshold levels. Using aGaussian probability density model, we can write theprobabilities of detection and false alarm as

PD = J exp[-(x

Rx1Pf.a= J exp[- (x

72=7h r

- )2 /2r,2]dx,

- )2 /2 o2 ]dX,

(6a)

(6b)

(5) where x represents the integrated electron charge


output from the APD and Xth represents the thresholdlevel. Assuming the received optical-pulse shape isrectangular, the means and the variances of theGaussian distributions can be written as5

result of noise alone is given by

NVnm |) = m f Pm(l - f m'

x = qG(X + o)Tp + ITp + GIbTp, (7

x = qGX0Tp + ITp + GIbTp, (71

cr12

= q2 G2 F(X8 + Xo)Tp + qG2FIbTp + qIhTp

2KT,,+ R Tp, (7

Oo2 = q2 G2FXoTp + qG2FIbTp + qIsTp + R TP

(7(

where the APD excess noise factor is given by

F = keffG + (1 - keff)(2 - 1/G). (7i

a) kr)The maximum probability of m such crossings

) resulting from noise alone occurring anywhere withinthe range-gate interval is given by the union bound

c) P.(m' N) < Kfa( )Pfam (-Pfa)Nm, (10)

where Kfa = (TRG/Tp)pfa is the average number ofthreshold crossings caused by noise alone in onerange-gate interval. 6

1) The altimeter will correctly locate the return lightpulse if n > 0 and n > m'. A measurement probabil-ity can be defined as Pmea = 1 - Prob(m' 2 n).Consequently, a lower bound on the probability of a

') correct altimeter measurement can be expressed as

In Eqs. (7), q is the electron charge; X = qqPs/hv,where iQq is the APD quantum efficiency, hv is thephoton energy, and P, is the peak optical power of thereceived optical pulse; and Xo = TqPB/hv, where PB isthe power of the background light within the receiveroptical filter bandwidth, G is the average APD gain,keff is the hole-to-electron-ionization coefficient ratioof the APD, I, and Ib are the surface leakage currentand the bulk leakage current of the APD, respec-tively, and RL is the APD load resistance, which isassumed to have an equivalent noise temperature ofT (K).

The Gaussian model of Eqs. (6a) and (6b) is only anapproximation of the true distributions of the APDoutput. 5 Because the computation times requiredwhen the more exact models were used were exces-sively long, we used the Gaussian approximation inthe numerical computations presented in this paper.

The performance of the altimeter can be evaluatedby calculating the probability of choosing the correctarrival time of the received laser pulses. In thesecalculations, we have assumed that the altimetertime resolution is equal to the received optical-pulsewidth. On any set of N laser fringes, the altimeterwill correctly locate the return light pulse within therange-gate interval if the number of threshold cross-ings resulting from signal at some point, tD, exceedsthe number of such threshold crossings at any otherpoint resulting from noise alone. The probabilitythat n such crossings in N laser firings occur as aresult of optical pulses reflected by the target is givenby

P(n IN) = ()PD( - PD)Nn (8)

where 0 n N. The probability that m thresholdcrossings in N laser firings occur at a given time as a

Pmeas 2 1 - Pr(n = 0) - Pr( < n < mi')N

=1- (1 -PD)N n=1

N

x mm' =n

Ranging Accuracy

The rms error in the range measurement can bewritten as

1 crtUr = Nt (12)

where c is the speed of light and ct is the standarddeviation of the random threshold-crossing time ineach shot. As an approximation, the average valueof NtD, ND = PDN, may be substituted into Eq. (12).It has been shown7 that, for this case,

rt 2= Tp2

G2F(XOTp + XSTth) + G2FIbTp/q + ITp/q+ 2KTTp

x

(13)

where Tth is the average value of the threshold-crossing times, which satisfies 0 < Tth < T Asignal-to-noise ratio (SNR) at the threshold crossingtime may be defined as

SNRth

G2 (XSTp)2

2KTT,G2F(XoTp + XSTth) + G2FIbTp/q + jTp/q + RqTP

(14)

[ )pDn(l -pD)NfnKfa


0 < m < N.

( N)pfm (1-pfa mN-m']inP)Pfam' lPfJ

The rms error in threshold-crossing time can bewritten as

(t = Tp/ SNRth- (15)

The value of t is affected by the threshold settingbecause the shot-noise output from the photodetectoris signal dependent. Although Eq. (13) suggests thatthe threshold level should be as low as possible, thenumber of false alarms also increases as the thresholdlevel is decreased. Normally, the threshold level isset to below one half the average pulse height in amultishot laser altimeter for a reasonable detectionprobability. Under this condition, an upper boundfor Ut 2 is obtained by substituting Tth = Tp/2 into Eq.(13)

The finite clock rate of the range counter (time-interval unit) also causes a quantization error in therange measurement. The resultant uncertainty inthreshold-crossing time is less than a clock period, At,and it does not improve by averaging the results.The overall range measurement error is, therefore

c(J < At +2

at

A-tD= (P

2 JSNRthPDN(16)

Altimeter Performance Calculationsand Numerical Results

This section presents performance calculations for atypical space-borne laser altimeter. The altimeterparameters are given in Table 1.

Signal and Background Levels

The optical pulse energy at the altimeter receiver canbe computed as

rdiffE = Et~sQ, 'f (17)

where Et is the transmitted laser-pulse energy, ts isthe system optical transmitter and receiver through-put efficiencies, rdiff is the diffuse surface reflectivityof the target, and fl is the solid angle subtended bythe receiver telescope, here taken as fl = r(+/2)2/R2,with + the receiver telescope aperture diameter and Rthe range from the transmitter to the target. It isassumed that the receiver field of view completelycovers the illuminated target area. The signal photo-electron emission rate, Xs, required to compute PD isgiven by

lTqErA= T,,hv

_ -qq Et (+/2)2

h T Isrdiff R2

The optical power of background light entering the'receiver is given by

PB = Iol.ANls[r( 2O ) ]f- , (19)

where Io, is the solar illumination level on the target

Table 1. Laser Altimeter and Target Parameter Values Used in theNumerical Example

Parameter Value

Laser altimeter parametersLaser wavelength X = 1.064 pumLaser-pulse energy Et = 40 mJLaser-pulse width T = 20 nsLaser beam divergence angle OD = 0.25 mradReceiver telescope diameter ( 0.5 mReceiver telescope FOV OFOV = 0.85 mradReceiver optical bandwidth AX = 2 nmOptics transmission = 50%

throughputTarget parameters

Target surface reflectivity rdiff = 0.5 (ice),0.2 (terrain)

Daytime solar illumination Isolr = 7.965intensity (mW m-2 nm-)

Day-night solar illumination 1000:1ratio

Reflected laser-pulse width T, = 180 nsRange-gate interval TRG = 667 .s (100 km)

Si APD parametersIonization coefficient ratio keff = 0.0065Average APD Gain G = 100 to 600APD load resistance RL = 100 kflEquivalent noise tempera- Tn = 750 K

tureQuantum efficiency 'qq = 30%

(enhanced for X = 1.064 pLm)iq = 5% (RCA-C30902S)

Bulk leakage current Ib = 50 pA(enhanced for X = 1.064 plm)

Ib = 0.5 pA (RCA-C30902S)Surface leakage current I = 12 nA

in Watts m-2 nm-1 , AX is the receiver optical filterbandwidth in nanometers, and OFOV is the receiverfield of view in radians. Because the solid angle ofthe receiver, Q, is inversely'proportional to the squareof the range, the received background light power isindependent of the range. The average backgroundphotoelectron emission rate is given by

'iqPB Ilq OFOV 2 ( 2\o = hv =jyIsolarA6s\ r 2 rdiff 2 . (20)

The ratio of solar illumination between day and nightis assumed to be 1000:1.

Performance Calculations

For a given target scenario, the value of Pmeas can becalculated as a function of range and threshold levelby substituting Eqs. (18) and (20) into Eqs. (6) and (7)and then Eq. (11). As an example, we have calcu-lated the performance of a laser altimeter operatingin the vicinity of Saturn on targets with rdiff = 0.5 (icysurface) under sunlit (daytime) illumination. Therange gate was set to TRG = 667 l.Lsec (100 km) and theaverage APD gain was fixed at G = 200. The valuesof other parameters are given in Table 1.

Table 2 shows a sample of the calculation results.In Table 2, nthre is the comparator threshold level


expressed in terms of the number of primary detectedphotons, and Kfa = (TRG/Tp)Pfa, as in Eq. (10), is theexpected number of threshold crossings during onerange-gate interval resulting from noise alone.There is always an optimal threshold level underwhich the receiver correct-measurement probability,Pmeas, is maximized. In an actual design, the receiv-er's threshold-crossing level can be adjusted close tothe optimal value by monitoring the value of Kfa.

The useful range of the altimeter can be defined asthe maximum range for which Pmeas exceeds a certainlevel. For this paper, we have selected Pma, 0.90.The variation of useful range with average APD gainwas also studied and found to be relatively insensi-tive, provided the optimal value of nthre was used.It turned out that, for the receiver parameters se-lected and N = 10 shots, the choice G = 200 maxi-mized the altimeter useful range at approximatelyRma = 5000 km.

The useful range of the altimeter can be extendedby increasing the number of laser firings. Figure 4plots Pmeas versus range with nthre close to its optimalvalues for N = 10, 30, and 100 shots and an averageAPD gain of G = 200 under both day and night solarilluminations. Increasing N to 100 shots extendsthe useful range to slightly more than 9000 km underdaytime solar illumination of a target near Saturn.It was also found, though not shown in Table 3, thatincreasing the number of laser firings from 100 to 300extends the useful range by about 2000 km. Theuseful range extends to slightly more than 10,000 kmwith N = 100 under nighttime background light.The increase in range at night is due to a reduction inthe number of detected photons per pulse width

1.0

0.8 .

en

CLE

0.6-

0.4-

0.2-

0.0 0 l , I . . . .0 . . . . . .0 5000 10000 15000 20000

Range (km)

Fig. 4. Probability of a correct measurement, Pmeas, as a functionof range at optimal threshold values. The photodetector used wasan Si APD enhanced for 1.064-pm wavelength. The APD gainwas fixed to G = 200. The range gate was set to 667 ps (100 km)and the target reflection coefficient was rdiff = 0.5 (ice). Otherparameter values are listed in Table 1.

resulting from background light from about 40 underdaytime illumination to about 0.04 under nighttimeconditions. However, the dominant noise sourcehere is the APD bulk leakage current, which corre-sponds to about 60 noise photoelectrons per receivedpulse width duration. At this distance from the sun,the bulk leakage current and the receiver-amplifierthermal noise limit the useful range of the multishotlaser altimeter. The minimum received optial signal

Table 2. Miss Probabilities l-PD and Measurement Probabilities Pmeas for a Multishot Laser Altimeter with the Threshold Setting nthro as a Parametera

nthre 170 180 190 200Pfa 0.363 0.188 0.0782 0.0255Kfa 1300 700 290 96

Range (km) X8TP 1 -PD Pmeas 1 PD Pmes 1 - PD Pmeas 1 - PD Pmeas

N = 10 shots3500 79.6 0.00544 1.000 0.0161 1.000 0.0410 1.0004000 61.0 0.0294 0.990 0.0716 1.000 0.150 0.9994500 48.2 0.0809 0.928 0.169 0.975 0.304 0.9765000 39.0 0.153 0.758 0.285 0.848 0.456 0.8415500 32.2 0.232 0.525 0.396 0.609 0.580 0.591N = 30 shots5000 39.0 0.0693 1.000 0.153 1.000 0.285 1.0005500 32.2 0.115 0.993 0.232 0.999 0.396 0.9996000 27.1 0.164 0.950 0.308 0.982 0.490 0.9776500 23.2 0.212 0.834 0.376 0.908 0.567 0.8807000 19.9 0.257 0.656 0.435 0.754 0.628 0.695N = 100 shots7500 17.3 0.297 0.999 0.485 1.000 0.676 0.9978000 15.2 0.333 0.990 0.527 0.992 0.714 0.9738500 13.5 0.364 0.956 0.561 0.960 0.744 0.9019000 12.0 0.391 0.877 0.591 0.881 0.769 0.7719500 10.8 0.415 0.755 0.615 0.757 0.789 0.611

aNumber of laser firings are (a) N =10 shots, (b) N = 30 shots, and (c) N = 100 shots. The photodetector used was assumed to be a SiAPD enhanced for operating at = 1.064 pm. The APD gain was G = 200, target reflectivity rdiff = 0.50 (icy surface), and backgroundnoise XOT = 39.7 (under daytime background light). Other parameter values are listed in Table 1.


"S - Day

I ' '

I I I -- Nih

I 'SI

I I

I I I

I I %

10s sots '% %

30 ots 00 shots

a - ^ os-s - -t

................

Table 3. Maximum Operational Range of the Multishot Laser AltimeterUnder Pmeas > 0.90 with the Enhanced Si APD, and RCA-C30902S SiAPD, and a Hypothetical Intermediate APD for Day and Night Target

Background Lighta

Rma, (km) (Day/Night)

"i(%) Ib (pA) 10 Shots 30 Shots 100 Shots

30 50 4500/5000 6500/7000 8500/10,00015 5 4000/5500 5500/8000 7000/11,0005 0.5 3000/5000 4000/7000 6000/10,000

aOther parameter values used are listed in Table 1. Optimalaverage APD gains were used in each case.

power for Pmeas 2 0.90 is 9.8 detected signal photonsper pulse with 100 laser shots under nighttimebackground light. As a comparison, the single-shotMOLA requires 76 detected signal photons to achievePmeas 2 0.90 under similar conditions.

We also used a shorter range gate, TRG = 133 Rus (20km), in the calculations under day and night targetillumination at the Saturn distance. The shorterrange gate increases the useful range by about 500km under both conditions.

The value of the target reflection coefficient, rdiff =0.5, used in Figure 4 is consistent with reflection froman icy or light-colored target planet. Darker targetsurfaces are more accurately described by rdiff = 0.2.Because the received signal is inversely proportionalto the square of the range, the useful range of thealtimeter decreases as the square root of the reflec-tion coefficients.

We also calculated the performance of the mul-tishot laser altimeter with a commercially availablelow-noise Si APD (RCA-C30902S), which has a muchlower bulk leakage current but also has a lowerquantum efficiency at 1.064 pum wavelength, as listedin Table 1. Table 3 shows the calculation resultswhen using this APD and a hypothetical intermediateAPD with qq = 15% and Ib = 5pA. The rangingperformance at night is improved slightly, but thedaytime performance is degraded because of thelower detector quantum efficiency. For these lowervalues of bulk leakage current, the altimeter perfor-mance becomes limited by the sunlight during day-time and by the circuit thermal noise during night-time. The optimal value of the average APD gainwas higher, G = 600, in this case to compensate thelower quantum efficiency. The APD excess noise

Table 4. Maximum Range of the Multishot Laser Altimeter Versus PulseWidth with the Enhanced Si APD Under Pmeas 2 0.90a

Rmas (km) (Day/Night)

Tp (ns) 10 Shots 30 Shots 100 Shots

90 5500/6000 7000/8000 10,000/11,000180 4500/5000 6500/7000 8500/10,000360 4000/4500 5500/6000 7500/8500720 3500/4000 4500/5000 6500/7500

aOther parameter values used are listed in Table 1.average APD gains were used in each case.

Optimal

also increases as the average APD gain increases.As a result, the overall altimeter performance atnight does not improve much for the much lower APDbulk leakage currents.

Table 4 shows the effects of received laser-pulsewidth on the maximum useful range of the altimeter.The wider the received pulse, the longer the requiredreceiver integration time and the greater the circuitthermal noise contribution. As a result, the maxi-mum useful range decreases as the received laser-pulse width increases.

References1. J. L. Bufton, "Laser altimetry measurements from aircraft and

spacecraft," Proc. IEEE 77, 463-477 (1989).2. G. Gaither, "Design of the Mars observer laser altimeter laser

transmitter," in Conference on Lasers and Electro-Optics, Vol.10 of 1991 OSA Technical Digest Series (Optical Society ofAmerica, Washington, D.C., 1991), pp. 520-521.

3. L. Ramos-Izquierdo and J. L. Bufton, "Optical system design ofthe Mars Observer laser altimeter," in Conference on Laser andElectro-Optics, Vol. 10 of OSA Technical Digest Series (OpticalSociety of America, Washington, D.C., 1991), pp. 448-450.

4. J. B. Abshire, S. S. Manizade, B. H. Schaefer, R. K. Zimmerman,J. S. Chitwood, and J. C. Caldwell, "Design and performance ofthe receiver for the Mars Observer Laser Altimeter," in Confer-ence on Lasers and Electro-Optics, Vol. 10 of OSA TechnicalDigest Series (Optical Society of America, Washington, D.C.,1991), pp. 520-522.

5. X. Sun, F. M. Davidson, L. Boutsikaris, and J. B. Abshire,"Receiver characteristics of laser altimeters with avalanchephotodiodes," IEEE Trans. Aerosp. Electron. Syst. 28,268-275(1992).

6. M. L. Skolnik, Introduction to Radar Systems (McGraw-Hill,New York, 1962), p. 31.

7. F. M. Davidson and X. Sun, "Slot clock recovery in optical PPMcommunication systems with avalanche photodiode photodetec-tors," IEEE Trans. Commun. 37, 1164-1172 (1989).


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Multishot laser altimeter: design and performance