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Advances in Space Research 52 (2013) 262–271

Lunar laser topography by LALT on board the KAGUYAlunar explorer – Operational history, new topographic data, peak

height analysis of laser echo pulses

Hiroshi Araki a,⇑, Hirotomo Noda b, Seiichi Tazawa c, Yoshiaki Ishihara d, Sander Goossens e,Sho Sasaki b

a National Astronomical Observatory of Japan, 2-21-1 Mitaka, Tokyo 181-8588, Japanb National Astronomical Observatory of Japan, 2-12 Mizusawa, Ohshu, Iwate 023-0861, Japan

c National Astronomical Observatory of Japan, Hilo, HI 96720, USAd National Institute of Advanced Industrial Science and Technology, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan

e CRESST/Planetary Geodynamics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA

Available online 7 March 2013

Abstract

In this paper we review the lunar laser ranging conducted by the laser altimeter (LALT) on board the KAGUYA lunar explorer(2007–2009). Five aspects of LALT measurements are described: (1) General operational history, (2) Laser shot and data statistics,(3) Revisions to LALT topographic data, (4) Variations in laser output energy, and (5) Peak height analysis of laser echo pulses. LALTwas able to range to the lunar surface despite some troubles with respect to laser output energy in the middle of the KAGUYA mission.The time series topographic data set was revised (Ver. 2) by incorporating new lunar gravity model based on KAGUYA and other his-torical lunar satellite’s orbit data, along with other improvements, for example by incorporating the accurate position of the laser col-limator on board the KAGUYA; however, more than half of the acquired range data could not be converted properly due to problemswith orbit accuracy during the extended phase of the mission. The spherical harmonic coefficients and the basic lunar figure parametersderived from LALT_LGT_TS agree very well with LRO-LOLA and the Chang’E-1 LAM model. It is possible that partial failure to thelaser diode was responsible for the gradual degradation of laser power (0.835 mJ per million shots) and the rapid decrease that occurredover April 9–14, 2008. The laser power also proved to be extremely sensitive to the temperature of the laser oscillator. The peak heightratio – that is peak height telemetry data divided by calculated ratio – is about 19% on average using the mean slope and albedo datafrom LALT and Spectral Profiler on KAGUYA space craft, respectively, which suggests the performance of peak height measurement ismore than 1/5 for more than 70 km altitude, if compared with calculated one. The peak height ratio may be better if we take the effect ofsmall scale topography within a footprint into account.� 2013 COSPAR. Published by Elsevier Ltd. All rights reserved.

Keywords: KAGUYA; LALT; Laser; Lunar topography; Operational history; Peak height

1. Introduction

The Japanese lunar explorer KAGUYA was launchedfrom the JAXA Tanegashima Space Center on September

0273-1177/$36.00 � 2013 COSPAR. Published by Elsevier Ltd. All rights rese

http://dx.doi.org/10.1016/j.asr.2013.02.018

⇑ Corresponding author. Tel.: +81 422343938; fax: +81 422343596.E-mail addresses: araki.hiroshi@nao.ac.jp (H. Araki), hirotomo.

noda@nao.ac.jp (H. Noda), tazawa.seiichi@nao.ac.jp (S. Tazawa),ishihara.yoshiaki@aist.go.jp (Y. Ishihara), sander.j.goossens@nasa.gov(S. Goossens), sasaki.sho@nao.ac.jp (S. Sasaki).

14, 2007 and conducted several scientific observations fromthe lunar polar orbit until the controlled collision onto thelunar surface at 18:25 (UT), June 10, 2009 (Kato et al.,2011). The laser altimeter (LALT) on board KAGUYAbegan nominal observation on December 30, 2007, andcompleted laser ranging just several seconds before thelunar impact (Fig. 1). Because KAGUYA was in a polarorbit, the LALT was able to perform altimetry of the wholeof the Moon from the main orbiter and compile lunar

rved.

H. Araki et al. / Advances in Space Research 52 (2013) 262–271 263

global topographic data, or a grid model, with the aid oforbit ephemeris and attitude data.

We finished constructing a lunar global topographicmodel using LALT data on March 31, 2008, and discov-ered a new flat feature around 30–60 harmonic degrees ofthe topographic spectrum (Araki et al., 2009). We also con-firmed for the first time that there is no constantly solarilluminated area on the Moon up to 470 � 470 m2 resolu-tion, based on the solar illumination geometry calculatedfrom the same topographic data (Noda et al., 2008; Busseyet al., 2010). The relatively shallow lunar internal structure,including the crustal thickness, was investigated using atopographic model derived from LALT observations bythe end of October 2008, and an accurate lunar gravitymodel newly derived from KAGUYA gravimetry con-firmed that the crustal thickness under Mare Moscovienseis extremely thin (Ishihara et al., 2009). A double-impacthypothesis for the formation of Moscoviense basin wasalso proposed based on the fact that the topographyaround Mare Moscoviense shows triple and offset ringedfeatures (Ishihara et al., 2011). The accuracy of the lunartopographic model obtained by LALT has been estimatedto be better than 70 m statistically by making a comparisonwith LLR (lunar laser ranging) landmark positions andcrossover analysis (Fok et al., 2011).

The first version of the lunar global topographic datasets – including time series range and topographic data,global and polar topographic grid model, and normalizedcoefficients of spherical harmonic expansion – werereleased on November 1, 2009 via the JAXA website(http://l2db.selene.darts.isas.jaxa.jp/index.html.en). Thegrid model and normalized coefficients of the spherical har-monic expansion of lunar topography and gravity were

Fig. 1. The last range data acquired by LALT (left) and

made public on the NAOJ-RISE website (http://www.miz.nao.ac.jp/rise-pub/en).

We aim to review operational and performance historyof LALT with improved topographic products other thanresearch highlights as stated above. This paper is structuredas follows; the operational history of LALT and relatedtopics are reported in Section 2; laser output energy is dis-cussed in Section 3; a peak height analysis of echo pulses ispresented in Section 4; and a conclusion is given inSection 5.

2. Operational history of LALT

LALT was designed to measure the distance to the sur-face of the Moon from the KAGUYA spacecraft by trans-mitting Q-switched Nd and Cr-doped yttrium–aluminumgarnet (Cr-doped Nd:YAG) laser pulses every second (Tsu-bokawa et al., 2002). Q-switching is a technique for obtain-ing energetic short pulses from a laser by modulating theintracavity losses. The laser beam divergence was 0.4 mrad,resulting in a typical laser spot size on the lunar surface of40 m from the orbiter altitude of 100 km. The range datawere calibrated for thermal variations in the internal clockfrequency and for instrument delay. Errors related to dataquantization, thermal variations in the clock and electron-ics, and instrument delay measurement to the normal planetarget were estimated to be 0.55 m (Araki et al., 2008).

An initial operation test which includes the first increaseof high-voltage for generating laser pulse was carried outon November 25, 2007 for the first high-voltage increase,and additional operations were conducted on December11, 12 and 25 to adjust the APD (avalanche photodiodes)sensitivity for the echo pulse intensity and thermal

the impact point of KAGYA on the Moon (right).

Table 1Operational history of LALT.

Items Nominal mission Extended mission

Period �2008.04.14 �2008.07.28 �2008.10.31 �2008.12.26 (Ex1) �2009.02.11 �2009.06.10 (Ex2)

LALT obs. Normal Inter- mittent Inter-mittent Inter-mittent Stopped NormalMain orbiter AMD

12 hAMD12 h

AMD6 h

AMD6 h

Thrustermode

Thrustermode

Tracking data Normal Normal Normal Insufficient Insufficient InsufficientEvent "

Obs. start2007.12.30

"Laser power down

"RW failed (1)

"S/C tracking reduced

"RW failed (2)

"Alt. 50 km LALTre-started

"Obs. end2009.06.10

264 H. Araki et al. / Advances in Space Research 52 (2013) 262–271

environment of LALT in orbit. After these experiments,LALT began laser ranging on December 30, 2007, andcompleted its altimetry by the end of the KAGYA mission(Fig. 1). In the rest of this section, the operational historyof LALT, with some important events, is presented in Sec-tion 2.1, the reprocessing of LALT topographic data is dis-cussed in Section 2.2, and the revised lunar figure model isdetailed in Section 2.3.

2.1. Operation history and laser shot statistics

Key events for LALT and main orbiter tracking aresummarized in Table 1. For the first three and a halfmonths of the mission, the observation status was quitegood; however, over April 9–14, 2008, the laser powerdropped by around 5 mJ (�6%) by April 14, and we hadto operate LALT intermittently during the remaining nom-inal mission phase in order to avoid a possible further lossof power and to investigate the cause of this phenomenon.

One of the four reaction wheels (RW) of the main orbi-ter failed at the end of July 2008, resulting in a doubling offrequent AMD events (angular momentum de-saturation)from one event every 12 h to one every 6 h, leading tonot only the loss of LALT observation time but also

Fig. 2. Successful laser shot numbers for the entire observation period. Nomperiod is by dashed line.

degrading the orbit accuracy that was necessary for accu-rate topography. The number of tracking station andobservation time available for Doppler tracking werereduced after the end of the nominal mission phase, result-ing in a second negative influence for orbit determination.LALT observations had to be stopped for one and a halfmonths after the failure of a second RW on December26, 2008, to avoid contamination from the orbiter’s thrus-ter, which had to operate continuously to control the atti-tude of the orbiter. After the second RW failure, thealtitude of the main orbiter was controlled down to50 km for observations of the lunar magnetic field, andwas maintained at 50 km ± 30 km until the final impactphase. LALT restarted 1-Hz laser ranging on February11, 2009, which lasted until the end of the KAGUYA mis-sion (June 10, 2009).

The number of successful LALT laser shots per monthuntil mission end is shown in Fig. 2. LALT attained 2.2millions shot retrievals per month from January to March,2008. The shot retrievals dropped to less than 1 million permonth after April 14, 2008 when intermittent operationbegan. LALT was able to acquire range data normallywithout any negative influence from thruster contamina-tion from February 11 to June 10, 2009.

inal mission period is designated by solid circle and the extended mission

H. Araki et al. / Advances in Space Research 52 (2013) 262–271 265

2.2. Reprocessing of LALT topographic data

LALT acquired more than 22 million range measure-ments over the one-and-a-half year mission period. Accu-rate orbital and attitude data for the KAGUYA mainorbiter are necessary for a topographic conversion fromrange data; however, the quality of the orbital datadeclined during the extended mission period as a result ofless frequent orbiter tracking (Section 2.1).

We are attempting to extract accurate topographic datafrom the LALT range data collected during the extendedmission, but unfortunately this has turned out to be a verydifficult task; attitude data especially in the thruster stabil-ization period are severely perturbed even for short periodto be recovered through topographic data matching withsome other Digital Terrain Model (DTM). Even if weintroduce crossover analysis using LALT data, the orbitaldata accuracy remains one order or more worse than dur-ing the nominal mission (Goossens et al., 2011). Thus wehave concluded that lunar topographic products shouldbe made from data collected during the nominal missionperiod.

Lunar topography is reproduced by simple vector calcu-lations using the SPICE toolkit with spacecraft orbit, atti-tude, and laser ranged data (Araki et al., 2009; http://naif.jpl.nasa.gov/naif/toolkit.html). We use Generic Map-ping Tools (GMT) commands and SHTOOLS codes formaking topographic grid models and performing sphericalharmonic expansion, respectively (Wessel and Smith, 1991;http://www.ipgp.fr/�wieczor/). The products of LALT aresummarized in Table 2. The first version of these productswas released via the JAXA website (http://www.jaxa.jp/press/2009/11/20091102_kaguya_e.html).

The second version of the time series topographic dataset (LALT_LGT_TS) was re-released by JAXA to the pub-lic on October 7, 2011. The three revisions to the secondversion of the data set were:

(1) Error correction of the LALT laser direction unit vec-tor: When making a comparison with LISM-TCDTM (Lunar Imager SpectroMeter – Terrain Cam-era, Digital Terrain Model), the unit vector – which

Table 2List of LALT products.

Product ID General description

LALT_RD Time series range data of LALT. Time tag is not inLALT_LGT_TS Lunar global time series topographic data. Time tag (

position, range, and other data are includedLALT_GGT_NUM Lunar global gridded topographic dataLALT_GGT_MAP A special format of LALT_GGT_NUM for the browLALT_GT_NP_NUM Lunar north polar gridded topographic data. The cen

or moreLALT_GT_NP_IMG Binary data for LALT_GT_NP_NUMLALT_GT_SP_NUM Lunar south polar gridded topographic data. The cen

or moreLALT_GT_SP_IMG Binary data for LALT_GT_SP_NUMLALT_SH Spherical harmonic coefficients of the Lunar topogra

defines the laser beam direction of LALT, was foundto have a periodic error of about 0.01% in length, cor-responding to about 10 m in radial topography. Thehorizontal difference was found to be less than 1 m.The error was fixed for the second version of theLALT_LGT_TS data sets. The bore-sight vector tospacecraft body frame is (�0.00064577182324,�0.00061086523820, +0.99999960491113) describedin SPICE-IK kernel by the measurement of the align-ment mirror on LALT-TR during its final assemblyto the KAGUYA orbiter. The accuracy of these val-ues is less than 0.01�(less than 17.5 m for the altitudeof 100 km).

(2) SGM100i-based orbit: We introduced a high-preci-sion SGM100i-based orbit of the main orbiter inplace of the SGM100g-based one that was used forfirst version of the data sets. SGM100i is the mostrecent and most accurate lunar gravity model derivedfrom SELENE lunar gravimetry based on 2-way, 4-way, and same beam VLBI tracking (Goossenset al., 2011). The error of the new orbit data is abouthalf (�25 m) of the SGM100g-based model in orbitoverlap analysis (Goossens et al., 2011). However,the total topographic position error was not reducedmarkedly, even after the improvement in orbit,because the attitude then became the largest errorcomponent (�175 m at most; Araki et al., 2008).

(3) LALT position in KAGUYA main orbiter: Weincorporated the LALT position in the main orbitercoordinates with the SPICE IK file for the secondversion of the product. The distance between theorbiter’s center of gravity and LALT (the top of thelaser transmit collimator) is about 1.5 m. Thus theradial distance between the lunar center of gravityand the Seleno-located laser bounced point isexpected to be about 1.5 m longer than in the previ-ous result, while the lunar radius is converselyexpected to be about 1.5 m shorter compared withthe first version.

The topographic difference in LALT_LGT_TS betweenthe first and the second versions is shown in Fig. 3. The

Resolution File

UT but the orbiter time (TI) 1 s ASCIIUT and TI), longitude, latitude, height, the orbiter’s 1 s ASCII

1/16� ASCIIsing system in KAGUYA project 1/16� Binary

ter is the north pole and the region is 10� in latitude 1/32� �1/128�

ASCII

– Binaryter is the south pole and the region is 10� in latitude 1/32� �

1/128�ASCII

– Binaryphic model up to 359� – ASCII

Fig. 3. Topographic difference in LALT_LGT_TS between Ver. 1 and 2 for 1 month.

266 H. Araki et al. / Advances in Space Research 52 (2013) 262–271

mean difference in the radial component of about 1.5 m ormore is a direct consequence of the shift in the laser firingpoint. The periodic difference of less than 300 m is due tothe improvement in orbit accuracy.

The number of topographic data points used for theLALT product (Ver. 2) is summarized in Table 3. In orderto make the LALT_LGT_TS data sets, some outliers witha height of less than �10 km, more than 11 km and along atrack height difference of more than 1.6 km (filter_1 inTable 3) were excluded. The height reference is a spherewith a radius of 1737.4 km and an origin centered toCOM (center of mass). Furthermore, in order to prepareraw data for the grid model, bad topographic arcs thatexhibited large differences from a known polar topographicmodel were removed from LALT_LGT_TS; a differenceless than ±100 m is allowed generally (filter_2 in Table 3).In total, 189 pieces of data were excluded by filter_1, and106,122 by filter_2, as described in Table 3.

2.3. Revised lunar figure model

We are currently revising our spherical harmonic modelSTM359_grid-02 to STM359_grid-04 (tentative name)using an LALT_GGT_NUM grid model; it is due to bereleased in the near future (Table 2). The grid model is

derived from selected LALT_LGT_TS data (Ver. 2)through filter_2 (Table 3). They are interpolated and re-sampled to 0.0625� by the 0.0625� gridded model, then con-verted into spherical harmonic coefficients (Araki et al.,2009).

Resultant coefficients up to 10� and orders are tabulatedin Table 4; they are almost the same as for our releasedmodel STM359_grid-02. It is reasonable that (l,m) = (0,0)coefficient of the grid-04 model is about 2 m smaller thanthe previous grid-02 model because the LALT position inthe KAGUYA main orbiter has been taken into consider-ation (Section 2.2).

The global figure parameters of the Moon are summa-rized in Table 5. The LALT topographic model agrees verywell with the model of LOLA (Lunar Orbiter Laser Altim-eter, Smith et al., 2010, http://pds-geosciences.wustl.edu/lro/lro-l-lola-3-rdr-v1/lrolol_1xxx/data/lola_shadr/lro_ltm04_720_sha.tab) and CLTM-s01 (Chang’E-1 LunarTopography Model s01, Ping et al., 2009).

3. Laser output energy

LALT was able to range to the lunar surface at the endof the mission period as described in Section 2.1; however,there were some unclear phenomena with respect to laser

Table 3LALT laser shot and retrievals statistics and data number used for each LALT product. See text for further explanations (chapter 2.1, 2.2, 2.3, 4.1).

Mission phase Shot num. Returned pulse [RD] Success rate (%) Filter_1 [for peak analysis] Filter_1 [LGT_TS] Filter_2 [GGT&SH]

Nominal 10,977,487 10,340,899 94.20 10,340,710 10,340,710 10,234,588Extended 11,786,702 11,720,597 99.44 11,720,307 – –Total 22,764,189 22,061,496 96.91 22,061,017 10,340,710 10,234,588

Table 4Spherical harmonic coefficients of STM359_grid-04 (tentative name) up to degree 10.

l m C(m) S (m) l m C (m) S (m) l m C (m) S (m)

0 0 1,737,153.73 – 6 1 107.91 �130.12 8 8 �22.46 72.001 0 137.79 – 6 2 �27.24 �78.37 9 0 –17.40 –1 1 �1,024.78 �422.399 6 3 �58.11 �55.63 9 1 82.81 20.622 0 �667.84 – 6 4 �91.49 �132.38 9 2 8.45 �30.742 1 �769.83 �17.07 6 5 �31.24 �156.38 9 3 �9.86 11.522 2 108.77 384.09 6 6 13.46 116.65 9 4 �101.87 �57.343 0 62.85 – 7 0 79.09 – 9 5 �68.01 �110.193 1 552.75 87.44 7 1 147.35 52.84 9 6 22.43 �20.713 2 438.46 188.55 7 2 64.41 10.80 9 7 �24.89 �37.303 3 405.67 �6.02 7 3 17.09 71.84 9 8 94.65 �116.334 0 215.70 – 7 4 0.02 29.93 9 9 22.17 19.224 1 �224.09 �48.00 7 5 �29.21 90.03 10 0 �62.38 –4 2 �327.38 �101.47 7 6 �80.01 33.70 10 1 31.26 9.884 3 �198.64 �286.35 7 7 21.80 �15.68 10 2 �12.31 31.534 4 �191.05 111.14 8 0 54.60 – 10 3 3.88 �69.295 0 �114.93 – 8 1 �134.02 25.51 10 4 �22.15 52.525 1 29.70 �33.34 8 2 �4.11 40.30 10 5 10.43 53.215 2 179.59 143.93 8 3 2.73 49.43 10 6 �3.82 31.385 3 18.20 209.51 8 4 113.07 �15.66 10 7 34.28 38.515 4 36.80 10.77 8 5 46.33 74.65 10 8 30.24 14.645 5 121.72 �76.58 8 6 �6.45 �20.73 10 9 41.17 �0.146 0 21.91 – 8 7 16.38 14.20 10 10 100.69 12.57

Table 5Lunar figure parameters obtained by KAGUYA-LALT, LRO-LOLA, and Chang’E-1 LAM topography.

Model STM_359-grid04 STM_359-grid02 LOLAa CLTM-s01b

Mean radius (km) 1,737.15373 1,737.15629 1,737.15152 1,737.103Equatorial radius (km) 1,737.90040 1,737.90326 1,737.89843 1,737.646Polar radius (km) 1,735.66039 1,735.66235 1,735.65769 1,735.843COM-COF (km) 1.93461 1.93182 1.93541 1.93566COM-COF (deg., east lon.) 202.40 202.41 202.38 202.33COM-COF (deg., lat.) 7.09 7.10 7.12 7.03

a http://pds-geosciences.wustl.edu/lro/lro-l-lola-3-rdr-v1/lrolol_1xxx/data/lola_shadr/lro_ltm04_720_sha.tab.b Ping et al., 2009.

H. Araki et al. / Advances in Space Research 52 (2013) 262–271 267

output energy: (1) a gradual degradation of laser energyover the entire mission period, (2) a decrease in laser energyover a relatively short period, (3) a variation in the laserenergy within a very short time.

Virtual output energy converted for a constant highvoltage for Q-switching (2.5 kV) is shown in Fig. 4 with fit-ted line equation in order to show the change in perfor-mance of the laser without the influence of the highvoltage variation. The gradual decrease (1) is clearlyobserved at a rate of 0.835 mJ per million shots on average(Fig. 4), regardless of the LALT operation status beingcontinuous or intermittent; The relatively rapid laserenergy decrease (2) is about 5 mJ from April 9 to April14, 2008 (when the laser shot number was around 8

million), and also the relatively high decrease in convertedenergy of about 8 mJ during the first 2 millions shots.

Change (2) was relatively rapid but not consecutive; thusthe cause of (2) is not considered to be damage to the laseroptics in the laser oscillator, but partial failure to the laserdiode (LD) and/or pyro-electric trouble in the Q-switch.Partial failure to the LD in a vacuum environment is con-sidered to be more probable because the Q-switch was keptto 21–22 �C as a countermeasure against the pyro-electriceffect. The range success rate in the extended mission phaseis extremely high (99.44%; Table 3). This is because 85% ofrange measurements in the extended mission phase werecarried out from about 50 km altitude. Even in the nominalmission phase in which average altitude was 100 km, the

Fig. 4. Laser output energy for the entire operational period. The opendiamonds represent raw telemetry data averaged per day and the filledsquares are converted for a constant voltage for Q-switching (2.5 kV). Theregression line is also added for the converted energy data.

268 H. Araki et al. / Advances in Space Research 52 (2013) 262–271

success rate was 96.86% (averaged raw shot energy is72.7 mJ) before change (2), then the success rate was downto 87.04% (averaged raw shot energy is 64.0 mJ). This isprobably due to range failures on the crater’s limb and/or low albedo region such as mares.

We show an example of rapid change (3) is in Fig. 5.Laser output energy is generally very sensitive to the ther-mal environment. Despite the temperature of the laseroscillator being controlled to within 21 or 22 �C,a ± 4 mJ change in about one hour was found with onlya ± 1 �C temperature variation.

4. Peak height analysis of LALT echo pulses

In addition to the ranging capability, LALT had anoptional capability to measure the peak height of echopulses from the lunar surface. The peak height measure-ment is realized by the peak holding capability of APD out-put voltage in the detection unit. This function is limitedwhen the peak height is less than several tens of mV by

Fig. 5. Relation between output energy (black solid line, �75 mJ

the non-linearity of the peak holding circuit. If accuratepeak height data are available and compared with theoret-ical values from a known slope and the albedo of the foot-print area, it may be possible to obtain information onsurface roughness within a footprint area on the Moon.The roughness information is applicable for the classifica-tion and mapping of geological units on the Moon. Unfor-tunately, we could not perform the accuracy check of thepeak height data due to their optional capability but onlythe linearity check of the detection circuit between inputand output pulse height. Thus, at first we had to checkthe performance of peak height measurement on the orbit,rather than obtaining information on the small scale topog-raphy within a footprint. The technique and results of thiscomparison are described and discussed in this section.Here, we used slope data from LALT_LGT_TS (Ver. 2)and surface albedo data from the global reflectance modelderived from LISM-SP (Spectral Profiler) in KAGUYA forthe calculation of theoretical peak height.

4.1. Formulation and data selection

We calculated the theoretical peak height of LALT andcompared it with the corresponding peak height measure-ments. The theoretical peak heights (Vpk) are calculatedas a function of five elements of telemetry data: TAPD, Eout,

h, h, and q and Eqs. (1)–(3):

V pk ¼ fpkF APDðT APDÞ � W ðEOUT ; h; h; qÞ ð1Þ

W ¼ EOUT

Dtþ 2 � ðhT h=cÞ � tan h� cos h � qT T T RT IF D2

R

4h2ð2Þ

F APDðT APDÞ ¼ F 25�

APD C0 þ C1T APD þ C2T 2APD þ C3T 3

APD

�

þC4T 4APD

�ð3Þ

Parameters used in Eqs. (1) and (2) are as follows; forEq. (1), FAPD is APD sensitivity, TAPD is APD tempera-ture, W is the mean echo power, and fpk is a factor toobtain the peak height Vpk from the mean echo signal(FAPDW); for Eq. (2), Eout is the output energy of LALT,h is the ranging distance, h is the averaged surface slope

) and laser oscillator temperature (gray solid line, 21–22 �C).

Fig. 6. Raw telemetry data (Raw) more than 19 mV and calculated peak height value (Calc.) for an output power more than 60 mJ using ()()()(1)–(3) areplotted in the left and right figures, respectively. Black dots are data from the nominal mission period (Nom), light gray dots are data from the extendedperiod (Ex1) from Nov. 1 to Dec. 26, 2008, and dark gray dots are data from the extended period (Ex2) from Feb. 11 to Jun. 10, 2009. Nom area isoverlapped by Ex1. The data numbers are summarized in Table 6.

H. Araki et al. / Advances in Space Research 52 (2013) 262–271 269

with respect to the laser incidence direction derived fromLALT_LGT_TS (Ver. 2), q is the diffuse reflectivity(albedo) in the footprint area at 1064 nm, Dt is the full timewidth of the output laser pulse (=34 ns) that is twice of17 ns as full-width half maximum pulse assuming the beamprofile is approximately Gaussian, hT is the full beam diver-gence angle after laser collimator in 1/e2 definition of thepeak height (=0.4 mrad), c is light speed in a vacuum(=299, 792, 458 m/s), TT is transmittance of the laser colli-mator (=0.9), TR is transmittance of the receiving telescope(=0.85), TIF is transmittance of the interference filter(=0.8), and DR is effective aperture of the receiving tele-scope (=0.1 m).

Equation (2) is based on the assumption that lunar sur-face illuminated by laser footprint is Lambertian, flat, andinclined with respect to the laser incidence direction. Emit-ted laser pulse width is enlarged when reflected by inclinedsurface from Dt to DT(=Dt + 2�(hTh/c)�tanh). If we take theecho pulse is Gaussian and its full width (2 � 3r) equals toDT, fpk is 3

ffiffiffiffiffiffiffiffi2=p

pffi 2:39 (see Appendix for further explana-

tion). q data are derived from a 1-degree resolution reflec-tivity map of the Moon made by the LISM-SPspectrometer on board KAGUYA (Yokota et al., 2011)for 1064 nm and the laser ranging condition (laser beamincident equals the emission angle, and phase angle is 0�).They are obtained from the original data by using the pro-cedure described in Yokota et al. (2011).

APD sensitivity FAPD in (1) is approximated as (3)based on pre-flight testing, where F 25�

APD is the APD sensitiv-ity (=725 kV/W) for reverse voltage 260 V at 25 �C,C0 = 1.55177, C1 = �3.78505 � 10�2, C2 = 1.14309 �10�3, C3 = �2.79829 � 10�5, C4 = 3.18765 � 10�7 (Taza-wa et al., 2011).

For the peak height analysis, all ranging measurementspassed filter_1 (see Section 2.2 and Table 3) were usedregardless of topographic accuracy because the error issmall (2 or 3 km at most) compared with the resolutionof a lunar reflectivity map (30.3 km); however, for the peakanalysis, we only used data for an output power of more

than 60 mJ, a peak height of more than 19 mV, and withlatitudes on both sides of less than 80�, taking into consid-eration the accuracy of these telemetry data and the lunarreflectivity model.

4.2. Results and discussion

The peak height raw telemetry data (Raw) and the cal-culated peak height value (Calc.) using Eqs. (1)–(3) areplotted in Fig. 6, with the range data on the horizontal axis.The “Raw/Calc.” ratios are plotted in Fig. 7, not only for“Global” (without polar regions with latitudes of morethan 80�) but also for three typical geological region onthe Moon: Feldspathic Highlands Terrain (FHT), Procella-rum KREEP Terrain (PKT), and South Pole-Aitken basin(SPA). Statistics of (Raw/Calc.) data are summarized inTable 6.

Two points should be noted from Fig. 7 and Table 6;

(1) “Raw/Calc.” ratio is evidently dependent on rangefor less than �70 km,

(2) “Raw/Calc.” ratio is �19% on average except forPKT (�14%) in the “Nom” and “Ex1” period.

As for (1), this is probably due to the limit of the capa-bility (non-linearity) of the peak detection system when thedistance is too small (Tazawa et al., 2011); and for (2), thereason the “Raw/Calc.” ratio in “Nom” and “Ex1” (�19%)is smaller than one is explained by the performance of peakheight detection of LALT and/or the shape degradation ofthe echo pulse due to small scale topography in the LALTfootprint area (diameter is 40 m at 100 km altitude). Theseresults suggest that the performance of peak height mea-surement is more than 1/5 for more than 70 km altitude,if compared with calculated one, which may be better whentaking the effect of small scale topography within a foot-print into account; however, further discussion is difficultbecause there is no peak height calibration datum. Themedian slopes at the �17 m effective baseline are reported

Fig. 7. “Raw/Calc.” ratio with range data. The upper left figure is for “Global,” the upper right is for FHT, the lower left is for PKT, and the lower right isfor SPA. See Fig. 6 caption for color index. The data numbers are summarized in Table 6.

Table 6Summary of the peak height analysis of LALT echo pulses; data number and average “Raw/Calc.” ratio with standard deviation for each geologicalregion. “Nom” is for nominal mission from Dec. 30, 2007 to Oct. 30, 2008. “Ex1” is for the extended mission from Nov. 1 to Dec. 26, 2008. “Ex2” is fromFeb. 11 to Jun. 10, 2009. FHT is between �15 and +30� in latitude and between �180 and �105� in longitude. PKT is between +15 and +60� in latitudeand between �75 and 0� in longitude. SPA is between �80 and �40� in latitude and between +150 and +225� in east longitude. “Global” means from �80to +80� in latitude.

Mission phase Global FHT PKT SPA

Nom Data Num. 4,979,826 447,584 115,566 132,078Raw/Calc. 0.185 ± 0.068 0.182 ± 0.059 0.143 ± 0.057 0.184 ± 0.068

Ex1 Data Num. 951,814 89,984 965 66,151Raw/Calc. 0.191 ± 0.060 0.190 ± 0.057 0.188 ± 0.053 0.186 ± 0.056

Ex2 Data Num. 6,691,482 347,078 475,497 241,945Raw/Calc. 0.103 ± 0.042 0.080 ± 0.041 0.108 ± 0.033 0.088 ± 0.034

Total Data Num. 12,623,122 884,646 592,028 440,174Raw/Calc. 0.142 ± 0.069 0.143 ± 0.073 0.115 ± 0.041 0.132 ± 0.070

270 H. Araki et al. / Advances in Space Research 52 (2013) 262–271

as 7.5� and 2.0� in the highland and mare region, respec-tively, from LRO-LOLA topography (Rosenburg et al.,2011). Even if we assume the roughness in the LALT foot-print area as �7�, “Raw/Calc. “is �0.3 (PKT) or �0.4(other three regions), still smaller than one. As for small“Raw/Calc. “data in PKT, this may also be the other sideof the small scale topography in the mare regions differentfrom the highland (Rosenburg et al., 2011), which shouldbe studied further with high-resolution images and reflec-tion data of the Moon. In summary, it is difficult to obtainsmall scale topographic information within the footprintfrom peak height data of LALT due to the lack of calibra-tion data; however, it should be noted that this can be

another approach for the small scale topography if thepeak height calibration data were available withoutmulti-beam system such as LRO-LOLA.

5. Conclusion

The operational history of LALT was described in thispaper for the first time. LALT maintained its ranging capa-bility until the end of the KAGUYA mission despite trou-ble with the laser output energy. However, not all of theranging data were converted into topographic data(10,340,710 for LALT_LGT_TS from 22,061,496 rangedata) because orbit accuracy could not be improved during

H. Araki et al. / Advances in Space Research 52 (2013) 262–271 271

the extended mission period owing to less frequent orbitertracking.

New time series topographic data (LALT_LGT_TS)were released on October 7, 2011 using SGM-100i-basedKAGUYA orbit data with several improvements. Spheri-cal harmonic coefficients are due to be released in the nearfuture, and the figure parameters derived from these coeffi-cients are in very good agreement with the LOLA andCLTM models.

A rapid decrease in laser energy over April 9–14, 2008,and a continuous degradation of laser output energy at arate of 0.835 mJ/million shots are assumed to be causedby a partial failure of the laser diode. A variation of just±1� in the laser oscillator was found to be enough to causea variation of ±4 mJ in laser energy.

Peak height data of LALT with a large uncertainty wasfound to be generally smaller than the calculated values(“Raw/Calc.” �19%), which suggests the performance ofpeak height measurement is more than 1/5 for more than70 km altitude, if compared with calculated one. The ratio“Raw/Calc.” may be better when taking the effect of smallscale topography within LALT footprint into account. Thedifference in the ratio between the PKT and other regionsmay also depend on their small scale topographies. Theseare open problems to be resolved by future lunar explora-tions and/or investigations.

Acknowledgments

We thank Dr. Yokota, Dr. Matsunaga and the LISM-SP science team members for offering us their lunar reflec-tivity data sets prior to publication. We also express ourgratitude to Prof. M. Wieczorek for SHTOOLS on hiswebsite. Comments and suggestions of the anonymousreviewers have been very helpful for the improvement ofour manuscript.

Appendix A. fpk value

In order to obtain fpk value, we suppose the echo pulsedetected by LALT is Gaussian for simplicity whose width(1 standard deviation) is r and the peak power is Wp. Thentotal echo energy is expressed as Eecho ¼

ffiffiffiffiffiffi2pp

W pr – (a1).On the other side, Eecho can be written by the mean power“W” and full time width “Dt” as Eecho = W�Dt. If

Dt = 2 � 3r, Eecho = 6�Wr – (a2). Thus, we can obtainW p=W fpk ¼ 3

ffiffiffiffiffiffiffiffi2=p

pfrom (a1) and (a2).

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