Laser-ranging scanning systemto observe topographical deformations of volcanoes

Tetsuo Aoki, Masao Takabe, Kohei Mizutani, and Toshikazu Itabe

We have developed a laser-ranging system to observe the topographical structure of volcanoes. Thissystem can be used to measure the distance to a target by a laser and shows the three-dimensionaltopographical structure of a volcano with an accuracy of 30 cm. This accuracy is greater than that of atypical laser-ranging system that uses a corner-cube reflector as a target because the reflected light jittersas a result of inclination and unevenness of the target ground surface. However, this laser-rangingsystem is useful for detecting deformations of topographical features in which placement of a reflector isdifficult, such as in volcanic regions. © 1997 Optical Society of America

Key words: Laser ranging, laser altimeter.

1. Introduction

In volcanic regions heavy landslides often occur be-cause of topographical instability caused by steepslopes and stratified structures. Therefore, it is im-portant to detect signs of geographical deformationsto predict the occurrence of landslides. We have de-veloped a laser-ranging ~laser radar! system that canbe used to determine the topographical deformationsof volcanoes by measuring the distance from volca-noes precisely and by detecting time variations of thedistances. This laser-ranging system emits laserpulses toward the target and receives reflected light.It then precisely measures the time interval betweenthe emitted and reflected light. Since the wave-length of light is shorter than that of radio waves,laser radar has a great advantage over radar becauseof its high angular resolution. In recent years, highresolution radar such as synthetic aperture radar hasbeen developed, but the resolution of laser ranging isstill higher. In the case of satellite laser ranging,each satellite carries a corner-cube reflector that isused as a target for the laser. Therefore very highprecision, as high as 1 cm, can be achieved with sat-ellite laser ranging for distances greater than 1000km.1 This system can also be used on an airplane asan altimeter2 to measure cross-sectional topographic

The authors are with the Communications Research Laboratory,Ministry of Posts and Telecommunications, Nukui-kita, Koganei,Tokyo 184, Japan.Received 12 June 1995; revisedmanuscript received 22 July 1996.0003-6935y97y061239-06$10.00y0© 1997 Optical Society of America

data on flood plains,3 the sea state,4 and a crest fieldgeoid.5 The accuracy is worse when one measuresground distances because of the inclination angle ofthe ground to the laser light and the unevenness ofthe ground. The laser-ranging system is useful,however, for measuring distances in areas in which itis dangerous to place corner-cube reflectors.We report on the development of the system and

the initial test results obtained at Mt. Bandai ~Fuku-shima Prefecture! in Japan.

2. Measurement Algorithm

The basic concepts of the measurement technique areshown in Fig. 1. This laser-ranging system consistsof a telescope and a laser attached to an altazimuthmount. We measured the round-trip time of a shortlaser pulse emitted toward the target and reflectedback. The distance toward target R was then calcu-lated as follows:

R 5 cTy2, (1)

where T is the round-trip time of the light and c is thevelocity of light. To measure a two-dimensionalarea, the telescope is raster scanned horizontally andvertically. We calculated a topographical map of thetarget in a rectangular coordinate system ~X, Y, Z! byusing the following coordinate transformation:

X 5 R sin f cos u, Y 5 R cos f cos u, Z 5 R sin u,

(2)

where f is the azimuth angle and u is the elevationangle.

20 February 1997 y Vol. 36, No. 6 y APPLIED OPTICS 1239

3. Measurement System

A diagram and photograph of the measurement sys-tem is shown in Figs. 2 and 3, and system specifica-tions are listed in Table 1. The pulse laser source isa second-harmonic Nd:YAG laser ~532-nm wave-length! fired at 10 Hz. This laser light is divided bya beam splitter that directs part of the beam onto aPIN diode, which starts the time interval counter andsynchronizes it with the laser emission. The rest of

Fig. 1. Concept of the laser-ranging scanning system.

Fig. 2. Block diagram of the laser-ranging scanning system.GPIB, general-purpose interface bus.

Fig. 3. Photograph of the laser-ranging scanning system.

1240 APPLIED OPTICS y Vol. 36, No. 6 y 20 February 1997

the laser beamwas expanded by a Galileo-type trans-mitting telescope of 7-cm diameter and was directedtoward the target. The beam divergence was esti-mated to be less than 2 3 1024 rad from direct mea-surement of the beam at a distant place. The lightreflected from the target, such as a crest field, wascollected by a Schmidt–Cassegrain-type receivingtelescope of 20-cm diameter. The field of view waslimited to 0.004 rad by an aperture and a bandpassfilter was used to reduce the background light, whichmade possible daytime observation. Because scat-tered light from the nearby atmosphere or aerosol isincluded in the return signal, the signal is gated sothat only light from the distant target was measured.The collected light was detected by a highly sensitivehigh-speed photomultiplier tube with a microchannelplate. The return signal was amplified by a high-speed low-noise amplifier and was applied to a con-stant fraction discriminator ~CFD!. The CFD can beused to detect the constant fraction of the input signalindependent of the amplitude of the signal, so it elim-inates the effect of time walk of the received pulse.This operates as follows: An incoming signal is splitinto two paths. In one, the signal is attenuated byfactor a. In the other, the signal is delayed by factord. These two signals are combined in a differentialamplifier fromwhich we get the zero crossing point ata constant fraction of the signal. This technique ismost useful when the return pulse does not spread.In this experiment the return pulse spreads appre-ciably and the pulse width varies according to theslant angle of the slope, so the effect of the spread ofthe pulse width should be considered. The system-atic offsetRoff that we obtained as a result of using theCFD is given by

Roff 5~a 1 1!W 1 d

22 W 5

d 2 ~1 2 a!W2

, (3)

where W is the received pulse width. In this exper-iment, we chose a to be 0.2, and, as shown in Section4, W varies from 4 to 8 ns. This means that, whenwe receive a spread signal, we underestimate thedistance by at least 10 cm. This systematic offsetvaries from place to place, but is probably not domi-nant when one detects the deformation of the topo-graphical structure because the deformation isdetected at the same place ~i.e., with almost the samespread of received light!.The return signal stops the time interval counter

that gives an accurate measure of the round-trip timeof emitted light. The total jitter in measured timethat originates from electronics is 50 ps ~rms!, i.e., 8mm. Measurements are repeated ten times for eachpoint to reduce the measuring error, and all the dataare sent to a personal computer through a general-purpose interface bus. Each one-point measure-ment takes approximately 1 s. The round-trip timeis averaged on the computer and stored on a harddisk with directional information of the telescopetaken from the encoder of the telescope mount. Themeasurement system is loaded into a van that we

Table 1. Characteristics of the Laser-Ranging System

Transmitting part Laser Nd:YAG laser SHGa ~532 nm!Output power 150 mJPulse width 5 nsPulse rate 10 HzTransmitting telescope 7-cm Galileo typeLaser beam footprint 1 m at 7 kmLaser divergence Less than 2 3 1024 rad

Receiving part Receiving telescope Meade 20-cm Schmidt–Cassegrain typeAmplifier Hewlett-Packard 8447FDetector Photomultiplier with microchannel plate,

Hamamatsu PMT R2809U with 7%quantum efficiency, 150-ps rise time

CFD Tennelec TC454Time interval counter SRSa SR620Telescope mount Shinwa Kouki Model 1Axis encoder Heidenhein VRZ404Scan step size 0.005°

aSHG, second-harmonic generation; SRS, Stanford Research Systems.

jack up during measurement. The control unit ispositioned outside the van to prevent any unneces-sary oscillation of the measurement system. Figure

Fig. 4. Distance to a perpendicular wall with a square pillar on it.

4 shows an example of a measured profile of the wallwith a square pillar on it. The thickness of the pillarwas 39.5 cm, which agrees well ~better than 1 cm!with the measured thickness shown in Fig. 4.

4. Measurements

Measurements were carried out in Fukushima Pre-fecture, 16–20 May 1994. The target was Mt. Ban-dai ~1819m!, which is a dormant volcano that has noterupted since 1888, at which time it destroyed manyvillages and killed hundreds of people. Its slopes aresteep and scree covered and there are no trees. Be-cause it is prone to landslides, it makes a suitabletarget for this kind of measurement. The linear dis-tance from the location where the measurementswere taken to Mt. Bandai is approximately 7 km. Aview ofMt. Bandai as seen from this location is shownin Fig. 5; the areas that we measured are marked inthe figure.

A. Error Estimation

We assume that the total error from the measure-ments arises from several factors: jitter that occurswhen the return light pulse is converted to an electric

Fig. 5. View of Mt. Bandai from the observation point.

20 February 1997 y Vol. 36, No. 6 y APPLIED OPTICS 1241

signal, pointing error, speckle effect, and atmosphericbeam dancing. The effect of speckle is not negligiblecompared with the effect of the pointing error becausethe latter is smaller than the beam footprint.6 How-ever, at each point distance is measured ten timesand then averaged, so the effect of speckle is reduced.The effect of atmospheric beam dancing is difficult tospeculate, but, based on Ref. 7, we estimate it to beless than 10 cm. This is also less than the pointingerror and is negligible. Thus the total error of themeasured distance can be estimated by

DR 5 @~DRP!2 1 ~DRu!

2 1 ~DRf!2#1y2, (4)

where DRP is the error that occurs when one convertsthe measured light to an electric signal, DRu and DRf

are the errors that originate from pointing errors inthe azimuth and elevation directions, respectively.We measured a distance to a perpendicular wall toestimate DRP: errors that originate from pointingerrors are negligible in this situation. The mea-sured distance was 580.056 6 0.017 m. Therefore,we estimated DRP to be around 2 cm. The secondand third terms of Eq. ~4! are pointing errors ~repe-tition error!. Because the observation point is infront of themountain, the third term is negligible ~thedistance does not change much when the telescopemoves slightly in the azimuth direction!. On theother hand, the second term is not negligible and isestimated as follows:

DRu 5 tan~S 1 u!RDu, (5)

where angle S is the slope angle, as shown in Fig. 1,u is the elevation angle, and Du is the repetition errorof the elevation angle ~see Fig. 6!. For example, if weassume that S 5 65°, u 5 2°, R 5 7000 m, and Du 50.001°, then DR can be estimated to be 25 cm. Toevaluate Eq. ~5!, we measured the distances to sevendifferent points on the volcano slope. At each pointthe distance was measured ten times and the wave-form of the return pulse was recorded by a high-speed

Fig. 6. Error estimation from beam divergence.

1242 APPLIED OPTICS y Vol. 36, No. 6 y 20 February 1997

digital oscilloscope ~HP54720D!. In this case thevariation of measured distance is not independent ofthe second or third term because the telescope isstationary while the distance is measured ten times.Therefore, by averaging ten measurements at eachpoint, we get a good estimate of R. Then we repeatthe measurements for all seven points. This wholesequence is repeated ten times. We assume that, byaveraging ten measurements at a stationary place,DRP becomes negligible and Eq. ~4! approximates to

DR 5 DRu 5 tan~S 1 u!RDu, (6)

where DR is the dispersion of ten measured and av-eraged distances at each position. On the otherhand, the full width at half-maximum of return pulseW, which was recorded by a digital oscilloscope, is thesum of two terms and is approximated by

W 5 W0 1 WS 5 W0 1 ~2yc!tan~S 1 u!Ra, (7)

whereW0 is the intrinsic pulse width that originatesfrom the laser and receiver electronics, WS is thepulse width that originates from the inclination of theslope, and a is the divergence angle of the transmit-ted laser. From Eqs. ~6! and ~7! we get

W 5 W0 12c

a

DuDR. (8)

Table 2 shows the pulse width and repetition errorsat the seven points. By fitting a regression line, weget

W~ns! 5 3.3 1 0.094DR~r 5 0.90!. (9)

Thus we get

ayDu 5 1.41 (10)

from Eqs. ~8! and ~9!. We estimated Du to be around4.4 3 1025 rad ~half of the step size of the encoder ofthe mount; see Table 1!. Therefore, the divergenceangle of the laser was estimated to be 6.2 3 1025 rad.

Table 2. Correlation between the Width of the Return Pulse andRepetition Error

Point Number 1 2 3 4 5 6 7

Pulse width ~ns!a 8.0 4.5 7.2 7.4 4.3 8.4 3.7Error ~cm! 44 9 32 34 24 62 10

aFull width at half-maximum of each pulse.

Table 3. Correlation between Slope Angles

PointNumber 1 2 3 4 5 6 7

R 7094.9 7222.3 7193.3 7292.1 7127.3 7147.2 7170.1tan~S 1 u! 1.41 0.28 1.01 1.06 0.77 1.97 0.32Swidth

a 52.3 13.4 42.9 44.3 35.0 60.5 14.8S2points

b 56.2 33.7 47.8 52.3 22.2 9.4 40.3

aSlope angle estimated from the width of the return pulse.bSlope angle estimated from the distance between two points.

Fig. 7. Histogram of the received pulse. Ab-scissa is the difference between the distance de-rived from each single pulse and the averageddistance at each point. The ordinate representsthe number of pulses.

Fig. 8. Part of the measured topographical map. The abscissa is the azimuth angle and the ordinate is the elevation angle measuredfrom the observation point.

Fig. 9. Bird’s-eye view of the measuredregion.

20 February 1997 y Vol. 36, No. 6 y APPLIED OPTICS 1243

From this estimation we calculated the slope anglesof each point. It is difficult to evaluate this resultbecause direct measurement of the slope angle is im-possible. Therefore, we estimated the slope anglebased on measurements of the distance between twoclose points, one is at the same point as that listed inTable 2; the other is 0.005° above the point. Theseresults are shown in Table 3. Except for point 6,these two values are consistent. For point 6, thereturn pulse shows a double peak. Therefore wesuspect that there was something like a rock at thatpoint which is why we obtained such a large pulsewidth and a large distance error.Figure 7 shows the distance dispersion for each

measured point. Abscissa shows the difference be-tween the measured distance from one pulse at eachpoint and themean distance ~average of tenmeasure-ments!. The data are fitted accurately by a Gauss-ian function. The full width at half-maximum of thegraph is 0.28 m. Therefore, in this experiment thetopography of the volcano was measured with an ac-curacy of approximately 30 cm. Thus, we can detectdeformations of geographical features of the volcanothat are greater than 30 cm by analyzing the timevariation of the topographical map.

B. Topographical Map

Several areas of Mt. Bandai were measured from 17through 20 May during the daytime. These mea-sured areas aremarked in Fig. 5. Themeasurementrange was 10° azimuth and 0.4° elevation. The stepsize of the raster scan is 0.01°, which corresponds to1.2m at the target. Themeasurements took approx-imately 18 h. Figure 8 shows a detailed view of oneof the small areas. The total range of the measuredareas of Mt. Bandai viewed from the observation lo-cation is from 6900 to 7400 m in linear distance, from0 to 1250 m in tangential distance, and from 300 to

1244 APPLIED OPTICS y Vol. 36, No. 6 y 20 February 1997

400 m in height. Figure 9 shows a bird’s-eye view ofthe measured area, which we transformed fromspherical coordinates to rectangular coordinates withEq. ~3!. The uneven conditions of the craggy cliff atthe crest can be seen clearly.

5. Conclusions

We have developed a laser-ranging scanning systemthat can be used to map deformations of the geo-graphical structure of volcanoes. This system con-sists of a Nd:YAG laser, a transmitting telescope, areceiving telescope, and an altazimuth mount. Itcan be used to raster scan a volcano and to obtain athree-dimensional structure. The total system errorin distance is approximately 30 cm. The error andthe width of the return pulse show good correlation.To make practical use of this system, we need toimprove the system’s accuracy by stabilizing thepointing system.

References1. J. J. Degnan, “Satellite laser ranging: current status and fu-

ture prospects,” IEEE Trans. Geosci. Remote Sensing GE-23,398–413 ~1985!.

2. W. B. Krabill, J. G. Collins, L. E. Link, R. N. Swift, and M. L.Butler, “Airborne laser topographic mapping results,” Photo-gramm. Eng. Remote Sensing 50, 685–694 ~1984!.

3. S. C. Cohen, J. J. Degnan, J. L. Bufton, J. B. Garvin, and J. B.Abshire, “The geoscience laser altimetryyranging system,”IEEE Trans. Geosci. Remote Sensing GE-25, 581–592 ~1987!.

4. B.M. Tsai and C. S. Gardner, “Remote sensing of sea state usinglaser altimeters,” Appl. Opt. 21, 3932–3940 ~1982!.

5. J. L. Bufton, “Laser altimetry measurements from aircraft andspacecraft,” Proc. IEEE 77, 463–477 ~1989!.

6. C. S. Gardner, “Target signatures for laser altimeters: ananalysis,” Appl. Opt. 21, 448–453 ~1982!.

7. T. Chiba, “Spot dancing of the laser beam propagated throughthe turbulent atmosphere,” Appl. Opt. 10, 2456–2461 ~1971!.