JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 102, NO. El0, PAGES 23,761-23,773, OCTOBER 25, 1997

The NEAR laser ranging investigation M.T. Zuber l

Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology Cambridge

D.E. Smith

Laboratory for Terrestrial Physics, NASA/Goddard Space Flight Center, Greenbelt, Maryland

A.F. Cheng, T.D. Cole Johns Hopkins University Applied Physics Laboratory, Laurel, Maryland

Abstract. The objective of the Near-Earth Asteroid Rendezvous (NEAR) laser ranging investigation is to obtain high integrity profiles and grids of topography for use in geophysical, geodetic and geological studies of asteroid 433 Eros. The NEAR laser rangefinder (NLR) will determine the slant range of the NEAR spacecraft to the asteroid surface by measuring precisely the round trip time of flight of individual laser pulses. Ranges will be converted to planetary radii measured with respect to the asteroid center of mass by subtracting the spacecraft orbit determined from X band•Doppler tracking. The principal components of the NLR include a 1064 nm Cr:Nd:YAG laser, a go!d-coated aluminum Dall-Kirkham Cassegrain telescope, an enhanced silicon avalanche photodiode hybrid detector, a 480-MHz crystal oscillator, and a digital processing unit. The instrument has a continuous in-flight calibration capability using a fiber-optic delay assembly. The singie shot vertical resolution of the NLR is <6 m,..and the absolute accuracy of the global grid will be -10 m with respect to the asteroid center of mass. For the current mission orbital scenario, the laser spot size on the surface of Eros will vary from -4-11 m, and the along- track resolution for the nominal pulse repetition rate of 1 Hz will be approximately comparable to the spot size, resulting in contiguous along-track profiles. The across-track resolution will depend on the orbital mapping scenario, but will likely be <500 m, which will define the spatial resolution of the global topographic model. Planned science investigations include global-scale analyses related to collisional and impact history and internal density distribution that Utilize topographic grids as well as spherical harmonic topographic models that will be analyzed jointly with gravity at commenstirate resolution. Attempts will be made to detect possible subtle time variations in internal structure that may be present if Eros is not a single coherent body, by analysis of low degree and order spherical harmonic coefficients. Local- to regional-scale analyses will utilize high-resolution three-dimensional topographic maps of specific surface structures to address surface geologic processses. Results from the NLR investigation will contribute significantly to understanding the origin, structure, and evolution of Eros and other asteroidal bodies.

Introduction

Much of our understanding of the formation and early evolution of the solar system has come from the study of asteroids and meteorites [Binzel et al., 1989]. Near-Earth asteroids have become the object of increasing focus because of their proximity to Earth and the likelihood that they are the immediate progenitors for most meteorites [Wetherill and Chapman, 1988]. Interest in near-Earth asteroids has been further heightened by the realization of their potential for catastrophic terrestrial impacts [Alvarez et al., 1980].

1Also at Laboratory for Terrestrial Physics, NASA/Goddard Space Flight Center, Greenbelt, Maryland.

Copyright 1997 by the American Geophysical Union.

Paper number 97JE00890. 0148-0227/97/97JE-00890509.00

Knowledge about asteroids has been derived from remote, Earth-based observations, two flybys by the Galileo spacecraft [Belton eta!., 1992], selected data from the asteroid-like Martian moons [Veverka and Burns, 1980; Thomas et al., 1992], analyses of relationships to meteorites [Wetherill and Chapman, 1988; Binzel and Xu, 1993], and theoretical modeling of asteroidal dynamics [Wisdom, 1983, 1985], structure, and thermal evolution [Bell et al., 1989]. The Near-. Earth Asteroid Rendezvous (NEAR) Mission [Cheng et al., this issue] holds the promise of dramatically improving our understanding of a near-Earth asteroid that has been well- studied by Earth-based observations [cf. Icarus, Volume 28, May, 1976].

The sizes and shapes of asteroids contain important information concerning the thermal, collisional and dynamical histories of these bodies and their internal structures. For asteroids with diameters less than 100 km, like

23,761

23,762 ZUBER ET AL.: NEAR LASER RANGING INVESTIGATION

433 Eros, shape is believed to be controlled by collisions and impact cratering, with only a minor contribution due to self- gravitation [Catullo et al., 1984; Bell et al., 1989]. However, questions such as the collisional and fragmentation history as evidenced by asteroidal shape and regolith properties, and the extent of possible chemical differentiation of the interior remain enigmatic. Analysis of high-resolution altimetry data, in combination with gravity, magnetics, and data from imaging sensors on NEAR will provide valuable insight into these fundamental questions.

Sizes and Shapes of Small Satellites and Asteroids

The modest sizes of even the largest near-Earth asteroids dictate that details of their surface shapes cannot be unambiguously resolved from Earth-based observations. Consequently, a variety of novel techniques have been developed to infer the sizes and gross shapes of these bodies [Binzel et al., 1989]. Detailed numerical representations of the shapes of the best studied minor planetary bodies have principally utilized limb, terminator, and photogrammetric measurements derived from imagery [Batson et al., 1989; Magnusson et al., 1989; Millis and Dunham, 1989; Stooke and Keller, 1990; Duxbury, 1991; Simonelli et al., 1993; Thomas, 1993] and radar techniques [Ostro, 1989; Ostro et al., 1988, 1990a, 1990b, 1991, 1995; Hudson, 1993; Hudson and

Ostro, 1994, 1995]. These models invoke assumptions about the natuce of solid-body tides, rotation, and self-gravity in constraining surface slopes [Thomas, 1993].

Perhaps the best studied small bodies are the Martian moons, Phobos (with radial axes of 13.05 km x 11.10 km x 9.30 km) and Deimos (7.8 km x 6.0 km x 5.1 km). Studies of these bodies have made use of an extensive database of Mariner

9 and Viking Orbiter imagery [Duxbury and Callahan, 1988, 1989; Batson et al., 1989, 1992; Duxbury, 1989, 1991; Thomas, 1993]. Several analyses of these bodies used interpolation between control points to generate digital shape models for mosaicking and re-projection of image data.

The shape of asteroid 951 Gaspra has also been constrained (radial axes of 9.25 km x 5.25 km x 4.45 km) [Thomas et al., 1994] utilizing control point techniques [Davies et •ll., 1994] and Galileo imagery [Belton et al., 1992], and it was shown that this asteroid has a more irregular shape than is characteristic of other well-imaged small bodies. Subsequent to the Gaspra encounter, Galileo flew by the asteroid 243 Ida and used a similar approach [Davies et al., 1996] to determine the radial axes (14.95 km x 6.35 km x 4.65 km) and shape [Thomas et al., 1996] of this body, and recognized the first asteroidal satellite, 0.7-kin radius Dactyl.

In the particular case of 433 Eros, size and shape have been estimated from measurements of angular dimensions [Heintz, 1975], stellar occultations [O'Leary et al., 1976], color and polarization measurements [Zellner, 1976; Zellner and Gradie, 1976], radar [Campbell et al., 1976; Jurgens and Goldstein, 1976], and thermal radiometric observations [Morrison, 1976: Lebofsky and Rieke, 1979]. All of theses studies yielded average radii at photometric maxima in the 10 to 20-km range, with corresponding long and short radial axes generally estimated to be --18.5 km x -8 km. More recently, Ostro et al. [1990b] reanalyzed radar echo spectra originally collected by Jurgens and Goldstein [1976] utilizing advanced processing techniques and determined radial extrema of Eros' polar silhouette to be 17.5 km x 8 km. On the basis of these studies

it would appear that Eros is a highly elongate body. However, the observations do not rule out the possibility that the asteroid may actually be a "rubble pile," consisting of two or more small, gravitationally bound bodies [G. Shoemaker, personal communication, 1994].

Science and Measurement Objectives

The objective of the NEAR laser ranging experiment is to produce high-resolution and high-accuracy profiles and grids of topography that will contribute significantly to understanding the shape, internal structure, and evolution of Eros. This objective represents the essential influence on the designed measurement capability of the NEAR laser rangefinder (NLR) [Cole et al., 1995]. The accuracy and geodetic control of the topographic measurements produced by the NLR will enable quantitative analyses ranging from global-scale questions such as collisional history and internal density distribution, to local- to regional-scale analyses such as the nature of specific surface structures and the nature of the asteroid regolith. As discussed in more detail later, the single- shot range precision of the NLR (taking into account random and systematic error sources)will be less than 6 m, and the absolute vertical accuracy, which is mainly governed by the radial orbit error of the NEAR spacecraft, will be of the order of 10 m with respect to the asteroid center of mass. The along- track spatial resolution of the instrument will be -4-11 m, and the across-track resolution will be determined by the orbit and mission duration, but should be 500 m or better. All NLR measurements will be in a center of mass reference frame, allowing precise registration of these data to observations from other NEAR sensors.

The NEAR Laser Rangefinder

Instrument Description

The NLR [Cole et al., 1995, 1997], shown in Figure 1, uses a direct-detection, bistatic transmitter - receiver design. Instrument parameters are given in Table 1. The transmitter contains a chromium and neodymium-doped yttrium-aluminum- garnet (Cr:Nd:YAG) laser rod pumped by a gallium arsenide (GaAs) laser diode array. The transmitter employs a U-shaped cavity design [Culpepper et al., 1995] in which the YAG slab is side-pumped. A lithium-niobate (LiNbO3) Q-switch controls the pulsing of the laser by changing the polarization state of recirculating laser light within the cavity. This Q- switched, solid-state laser emits 12-ns wide pulses with an energy of 15 mJ at a wavelength of 1064 nm. A 9.3x Galilean beam expander reduces the exit beam divergence to the desired level of 235 grad. The NLR is a facility instrument designed and built at the Johns Hopkins University (JHU)/Applied Physics Laboratory [Cole et al., 1995]. The laser transmitter was procured from the McDonnell-Douglas Space Systems Division, St. Louis, and has heritage with the NASA Mars Observer Laser Altimeter (MOLA) [Zuber et al., 1992] and the Ballistic Missile Defense Organization Clementine [Nozette et al., 1994; Zuber et al., 1994] and Brilliant Pebbles lasers. The

laser receiver, processor, and power supplies were derived using previously flight proven designs from the JHU/Applied Physics Laboratory.

The instrument receiver employs direct, incoherent detection of laser photons that will be backscattered from the

ZUBER ET AL.: NEAR LASER RANGING INVESTIGATION 23,763

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SUPPLY (MVPS)

Figure 1. Photograph of the NEAR laser rangefinder showing major subsystems [Cole et al., 1995]. The cover on the 8.89-cm-diameter telescope (far right) is shown closed.

asteroid surface. This backscattered laser signal is collected by an 8.89-cm-diameter gold-coated aluminum Dall-Kirkham Cassegrain telescope designed and built by the Optical Corporation of America in Garden Grove, California. A baffle surrounds the receiver telescope to reject stray sunlight that might otherwise focus on the detector. The NLR receiver uses a door over the entrance aperture and was designed to prevent contamination from propellant burns during the NEAR cruise phase. The release mechanism uses redundant pyrotechnic wire cutters with a tempered beryllium (BeO) wire. The door, which is shown in the closed configuration in Figure 1, contains six fused silica windows to permit NLR operation at orbital altitudes of at least 50 km in the unlikely event of a door release failure. A 7-nm-wide spectral bandpass filter rejects

solar background. The signal is directed onto an enhanced silicon avalanche photodiode (SiAPD)hybrid detector that includes temperature compensation and transimpedance amplification. This detector configuration permits automatic bias adjustment to maintain constant gain throughout the thermal range of the NLR. The detector is characterized by an 800-gm-diameter active area, which greatly exceeds the •-100 gm diameter of the focused return pulse.

Inside the receiver is an analog electronics package that contains the SiAPD detector, a transimpedance amplifier, a video amplifier, a lowpass (30-MHz) Bessel filter, and a voltage comparator circuit. The purpose of the analog electronics is to convert the received optical laser energy into digital stop pulses that are used to compute the round-trip time

Table 1. NEAR Laser Rangefinder Instrument Parameters

Parameter Value

Mass 4.9 kg Average power 15.1 W Volume (1 x w x h) 0.374 x 0.229 x 0.216 m 3 Laser wavelength 1064 nm Pulse energy 15.3 mJ Pulse energy jitter < ! % Pulse width 12 ns

Pulse width jitter I ns Pulse repetition frequencies 0, 1/8, I (nominal), 2, 8 Hz Beam divergence 235 grad Telescope diameter, m 0.0889 Effective aperture, f 0.0762 m, f/3.4 Spectral receiver bandwidth 7 nm Temporal receiver bandwidth 30 MHz

-9 Receiver integration time 7x10 s APD dark voltage 150 mV, rms APD responsivity 775 kV W -• Optical receiver FOV 2.9 mrad Receiver threshold levels 8 (2" x 16 mV) T-0 gate time resolution 500 ns Range gate time resolution 41.667 ns Data rates variable, fi'om 6.4 to 51 bits s -• Range accuracy <2 m Range resolution 0.3148 m Maximum range >200 km Required shots (lifetime) 3.15x 107 ( 1 year operation at I Hz) Spot size (35 to 50 km orbits) -4-11 m Boresight, TX-to-RX < 10 grad, <25 grad Threshold levels 8 (2" * 16 mV)

TX - RX alignment shift 345 grad previbration to postvibration Thermal control +_2øC

Beam centroid jitter (shot to shot) ( 50 •rad Beam centroid wander 4.81 •rad Calibration power jitter <5% Calibration timing jitter 0.3148 m

23,764 ZUBER ET AL.: NEAR LASER RANG1NG INVESTIGATION

of flight measurements. The Bessel filter integrates returned pulses that have dilated in time in response to target surface topology. The filter thus optimizes the probability of detection for high surface slopes and, in addition, limits the high-frequency noise response of the analog electronics. The comparator determines whether an input signal has sufficient energy to generate a "stop" signal. This device operates using any of eight detection threshold levels defined based on a Neyman-Pearson technique. The selected th/'eshold level i s used to eliminate the background and electronic noise floor and can be set by a direct command from the ground, or autonomously using an auto-acquisition sequence.

The digital electronics, denoted the digital processing unit or DPU, is a single-board design which supports the timing, data acquisition and formatting, and the telemetry interface functions. Timing is accomplished using a 480-MHz oscillator, with a time of flight applications-specific integrated circuitry (ASIC)chip, under control from an Actel 1020A gate array and an RTX2010 microcontroller. The oscillator frequency defines the 31.48-cm range resolution which is the least significant bit in the 21-bit range word.

Instrument Operation

The NLR will measure the slant range of the NEAR spacecraft to the asteroid surface from the round-trip time of flight of individual laser pulses. A schematic of the ranging process is shown in Figure 2. The instrument generates a laser pulse with a peak optical power and duration at a time -192 gs after the "fire" command. A T-0 gate is employed to eliminate noise that typically occurs at laser pulse generation. A range gate isolates subsequent bounces and provides tighter control in the placement of the T-0 gate. Together the two gates effectively disable the receiver until the transmitted and received pulse times are recorded, and serve to eliminate all self-generated electronic noise that occurs prior to the arrival of the calibration pulse, -558 ns after the transmitted pulse.

The transmitted pulse is reflected from the asteroid surface and detected by the NLR above the solar background and electronic noise threshold. The received pulse has a lower power and a longer duration than the transmitted pulse due to its interaction with the nonideally reflecting surface of Eros. The range from the spacecraft to the surface (R) is simply determined from

AT R=c• (1)

2

where AT is the time of flight of the pulse times and c is the speed of light.

The percentage of the incoming laser energy that is reflected from the asteroid surface depends mainly on the albedo and roughness of the surface. When the number of photons collected by the SiAPD detector exceeds the specified threshold value established by the electronic comparator, the time of flight ASIC is stopped. By reading the 21-bit ASIC counter, the total time of flight is measured leading to the computation of range.

The operation of the NLR can be traced through the instrument block diagram in Figure 3. The ranging process initiates when a "fire" command is issued by the DPU for a prescribed pulse repetition frequency. Each transmitted pulse is simultaneously coupled into a 100-m-long fiber-optic delay line (FODA) as it traverses through the transmitter (TX) cavity to the output optics. The output of the FODA is directly routed to the receiver (RX) optics and thereby provides complete end- to-end timing calibration of the NLR. Consequently, for each transmitted pulse, both a calibrated return pulse as well as a backscattered signal are obtained. The TOF ASIC is a chip that supports an l 1-bit calibration counter as well as the 21-bit counter and therefore provides both the "fixed" calibration range and the slant range to the asteroid's surface for every transmitted pulse.

By correcting for the position of the spacecraft with respect to the center of the asteroid via determination of the spacecraft orbit from the X band Doppler tracking data, the measured

-558 ns ,•Fiber-optic delay (average)

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• ' '•' GATE ! Ground bounce

Backscattered pulse (dilated)

- -- •_ t i0 - 192 ms ]!

• OPTiCAL•PUi• E FIRE.COMMAND (IN•I• PI.K,SE)

Figure 2. Schematic of the laser ranging process, showing optical power on the vertical axis and time on the horizontal axis. In practice, the NLR uses T-0 and range gates to eliminate spurious system noise, such as ground bounces, that occur at laser pulse generation and before the arrival of the calibration pulse 558 ns after pulse transmission. The backscattered laser pulse will have a lower amplitude and will be spread in time compared to the transmitted pulse due to its interaction with the nonideally scattering surface.

ZUBER ET AL.' NEAR LASER RANGING INVESTIGATION 23,765

Htr AD590 SPACECRAFT PWR (33.5 VDC)

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UNIT (D Pk•l

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48 MHz

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RTX 2010

Figure 3. Block diagram of the NLR instrument. TX corresponds to the transmitter, and RX corresponds to the receiver. LR is the laser resonator assembly, LPS is the laser power supply, FODA is the fiber-optic delay assembly, DPU is the digital processing unit, LVPS is the low voltage power supply, and MVPS is the medium- voltage power supply. The operation of the instrument is discussed in the text.

ranges will be transformed into a discrete set of radii referenced to the asteroid center of mass. Altimetric and tracking data from NEAR will be reduced simultaneously in the same reference frame in order to maximize the accuracy of both the topography and gravity data sets.

Along-Track Resolution

The size of the laser footprint on the surface of Eros will depend on the spacecraft altitude. Given the spacecraft orbits of 35 km or 50 km from center of Eros, the laser beam

divergence of 235 grad and approximate radial dimensions of Eros of 18 km x 7.5 km x 6.5 km, the spot size on the surface will vary from about •-4-11 m. For a nominal spacecraft velocity of •-5 m s -1 the along-track resolution will be comparable to the spot size for the expected 95% probability of successful ranging at these orbital altitudes.

Across-Track Resolution

The current NEAR mission scenario [Cheng et al., this issue] calls for mapping in a range of orbital altitudes at varying inclinations and viewing geometries to satisfy spacecraft communication and power (i.e., solar array orientation) constraints, as well as instrument observation

requirements and desires. The configurations span the range from advantageous to non-optimal for the NLR. For example, as shown in Figure 4, some orbital configurations will enable the instrument to obtain global coverage in a spacecraft nadir-

pointing orientation. During these sequences the NLR will have opportunities to sample the entire surface, though perhaps non-uniformly. The higher altitude (40- and 50-km) mapping orbits are particularly favorable because these will be at higher inclinations and will include a few months in polar or near-polar orbits. During this time the Radio Science (RS) investigation [Yeomans et al., this issue] will obtain global gravity, and the multispectral imager (MSI) and near-infrared spectrograph (NIS) [Veverka et al., this issue] will be able to obtain a global distribution of images. In contrast, the spacecraft will spend some time in a 35-km orbit in which the subspacecraft point will be constrained to remain within a narrow band of equatorial latitudes. The NEAR X ray/gamma ray spectrometer (XRS/GRS [Trombka et al., this issue]) will have priority during this phase and plans to point at a slowly varying angular offset of 5ø-10 ø from nadir to optimize the ground coverage and solar illumination geometry. The mapping configurations shown in Figure 4 do not encompass the extent of expected coverage, but rather illustrate the possibilities for obtaining both global moderate resolution coverage and very high resolution coverage for selected areas.

For geophysical problems such as the determination of the internal density structure of the asteroid, it is desirable to have topographic information at the same resolution as gravity data. Simulations indicate that it is reasonable to expect a gravitational field derived from radio tracking of the NEAR spacecraft around Eros up to degree and order 15 [Smith et al., 1995b; Yeomans et al., this issue], which corresponds to a

23,766 ZUBER ET AL.: NEAR LASER RANGING INVESTIGATION

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Figure 4. Plots of the subsurface point of the NEAR spacecraft for three different phases of the mapping mission: (a) 35-km orbit, (b) 50-km orbit, and (c) 40-km orbit. The orbit configurations shown do not encompass the full extent of expected mapping coverage but illustrate opportunities for both moderate- resolution global and high-resolution topographic mapping of Eros. Pluses represent sampling at 10-min intervals and do not correspond to the nominal pulse repetition rate of the NLR, which is 1 Hz.

half-wavelength (block size) resolution of 3 km. For orbits with near-polar inclinations the topographic resolution will exceed the gravity resolution within a month if mapping occurs continuously. Ideally, a month of continuous ranging with continuous Deep Space Network (DSN) tracking during the initial period of topographic mapping is desirable in order to get the best possible orbits, which will be beneficial in the determination of both topography and gravity fields.

As discussed below, higher (meter-scale) spatial resolution

coverage will be required to address interesting geological questions such as the origin of surface grooves, if they exist on Eros. The shapes of impact craters and the morphology of the surface and its relationship to regolith thickness are other areas of anticipated study.

Laser Ranging Rate

The NLR has the capability to range at four nonzero pulse repetition rates: 1/8, 1, 2, and 8 Hz. The 1/8 Hz rate has a

ZUBER ET AL.' NEAR LASER RANGING INVESTIGATION 23,767

corresponding data rate of 6.4 bits S -I, and the maximum rate is 51 bits s -• This rate is intended to enable the NLR to range continuously, without impacting downlink of data from other NEAR instruments at times when other data rate-intensive

sensors, such as the MSI, are in modes that require high downlink bandwidths. By having this low rate, the NLR instrument will undergo less stress associated with the number of power cycles.

The nominal rate for topographic mapping is 1 Hz, and this produces approximately contiguous along-track profiles. Solid-state lasers that are being used in spaceborne planetary altimetry are expected to deliver tens of millions to hundreds of millions of shots. Thus far, no spaceborne lasers have actually demonstrated close to the anticipated lifetimes: the MOLA laser accumulated 180,000 shots in space, the Clementine laser expended 600,000 shots [Zuber et al., 1994; Smith et al., 1997], and the Shuttle laser altimeter (SLA) laser accumulated 2.9 million shots (J.B. Garvin, J. L. Bufton, J. B. Blair, S. B. Luthcke and J. A. Marshall, Observations of the

Earth's topography from the Shuttle Laser Altimeter (SLA): Laser pulse echo recovery measurements of terrestrial surfaces and clouds, submitted to Science, 1997, hereafter referred to as

submitted paper]. However, this performance specification is supported by several laboratory tests of diode laser arrays (R. Afzal, personal communication, 1995). In order to preserve laser life, it is desirable to pulse the NLR at a nominal 1-Hz rate until a global map of the asteroid is obtained.

When the performance of the laser in orbit is understood and after data for a global map suitable for geophysics are collected, the laser pulse repetition rate will be intermittently increased in order to collect data to address interesting short - wavelength geological questions. The 2-Hz data rate will be used for oversampling in the along-track direction for detailed geological studies.

Due to thermal considerations, the 8-Hz ranging rate is sustainable for a period of 2s. As discussed below, at this pulse repetition frequency, the laser spot will be visible in the field of view of the MSI when ranging on the dark side of Eros. This mode allows in-orbit alignment of these instruments and will enable accurate registration of altimetry and imaging data.

Instrument Performance

Characterization of the topography of Eros using the NLR will require an adequate signal-to-noise level. Assessment of the instrument performance is determined using a link analysis, in which instrument, mission, and target parameters are used to evaluate the probability of obtaining a successful range measurement. The performance requirement for the NLR is to maintain a single-shot detection probability of_>0.95 at the maximum orbital altitude (42 km) for an asteroid surface reflectivity ranging from 0.05 to 0.2.

The most important parameter in the system performance is the mean detected signal level (N r, in photoelectrons), which, for the assumption of LambertJan scattering surface, is given by

Nr Etr I Ar rtar ) where E t is the transmitted laser energy, q is the quantum efficiency of the detector, hv is the photon energy, A,. is the effective receiver telescope area, z is the range of the NEAR spacecraft to the surface of Eros, ,c2t• •. is the target scattering angle, /"tar is the target reflectance, and tsys is the system

Table 2. Parameters Assumed in NEAR Laser Rangefinder Link Analysis

Parameter Symbol V al ue Transmit laser energy E t, mJ 15 SiAPD quantum efficiency r I, pe ph -• 0.4

I -19

Photon energy hv, J ph- 1.87x10 Receiver telescope area A, m 2 0.00456 Range to Eros z, km 42 System transmission t 0.75

sys

Target scattering angle i•u .•

Target reflectance r 0.15 [ar

transmission. Typical values for these parameters are given in Table 2, though most were varied. Four separate link analyses were performed for the NLR. On the basis of nominal values, we estimate that --3000 backscattered photoelectrons per pulse will be received at the stop detector when the spacecraft is in a nadir-pointing configuration and ranging to a flat (--1 ø slope on the scale of the laser footprint) surface. This constitutes considerable signal margin. In addition, we note that recent results from the Shuttle Laser Altimeter-1 Mission (J. B. Garvin, et al., submitted, 1997) indicate that the formalism used in that investigation for predicting signal/noise in practice significantly underestimated the number of received photons for this Earth-orbital sensor. The same formalism has been used in the calculation presented here. For the expected instrument performance and mission mapping scenario, the instrument has more than adequate signal/noise to fulfill the objectives of the experiment.

Sources of Range Error

To produce topographic profiles and gridded topography, from spacecraft to surface ranges, a number of corrections need be made. Here we focus on effects that are expected to induce meter-scale or larger errors in absolute topographic height.

The largest correction in the laser ranging measurements is generally associated with uncertainty in the knowledge of the spacecraft orbit [Zuber et al., 1992]. The orbital accuracy of the NEAR spacecraft around Eros should be recoverable at approximately the 5 to 10-m level with respect to the asteroid center of mass [Smith et al., 1995b; Yeomans et al., this issue]. For comparison, the topography of Venus is known to many tens of meters [Ford and Pettengill, 1992], the Moon is known to --100 m [Zuber et al., 1994; Smith et al., 1997], and Mars has vertical errors of 500 m [Smith and Zube•; 1996].

Another source of range error arises from the uncertainty in the spacecraft orientation. The NEAR spacecraft has been designed to achieve excellent pointing capability. The three- axis angular stability is anticipated to be 50 grad over 1 g, and 3-axis attitude control and knowledge are expected to be 1.7 mrad and 50 grad, respectively. The spacecraft attitude as a function of time relative to the J2000 inertial reference frame

will be given in terms of quaternions and distributed to the science team as SPICE kernels. These data will be used to

determine the orientation of the NLR boresight as a function of time. The precise orientation of the MSI relative to the spacecraft attitude (more precisely, the reference frame defined by the Inertial Measurement Unit) will be determined from analyses of star fields taken during cruise. Subsequently, the relative co-alignment of MSI and NLR will be determined at Eros by imaging the laser spot over the darkside of the asteroid. The spacecraft attitude quaternions can then be used to determine the NLR boresight direction to within about 50 grad. We note that the boresight alignments of MSI and NLR

23,768 ZUBER ET AL.: NEAR LASER RANGING INVESTIGATION

were measured during spacecraft integration to assure that NLR •ots fall within the MSI high-resolution field. Verification that the co-alignment was maintained after launch cannot be done until the NEAR spacecraft enters Eros orbit.

Because the NLR will make use of a leading edge detector, spreading of the laser pulse will also necessitate a "time walk" correction. Time walk occurs because the spreading of the return pulse due to scattering on the incident surface delays the time at which the accumulated photons exceed the prescribed threshold, thus causing an error in the timing of the returned pulse. The amount of pulse spreading is dependent on electronic system effects (-0.05 m) and biases due to curvature of the beam wavefront (<1 m), pointing jitter (-1 m), RMS surface roughness (<1 m), slope effects (1-10 m), instrument pointing uncertainty (1-10 m), and variations in surface albedo (1-2 m RMS) [Harding et al., 1994]. Thresholding minimizes but does not eliminate the time walk effect.

Because the various error sources are independent, it is appropriate to take the root sum square of the errors. Such an estimate indicates that the topographic field is expected to be accurate in a global sense to approximately 10 m with respect to Eros' center of mass.

Off-Nadir Pointing

Another source of range error arises from the deviation of the spacecraft from a nadir-pointing orientation. Deviations from nadir pointing are detrimental for altimetry due to increased spreading of the returned pulse which results in lower signal/noise and greater time walk. However, off-nadir pointing is desirable for some NEAR instruments at certain times, such as the XRS/GRS and MSI instruments. While non-

optimal, the NLR does have the ability to range while in a non-nadir-pointing mode. In order to understand the ability of the NLR to collect meaningful data in an off-nadir configuration, we have estimated the amount of range error induced due to increased pulse spreading for pointing angles, at. Based on the current mission scenario and the best estimate

of the shape of Eros, values of at greater than 19.8 ø would cause the instrument to point off the asteroid. Our simulation, which (necessarily) assumes Gaussian laser pulses, was modified from the approach of Gardner [1992] and takes into account all of the contributions to pulse spreading discussed above. The calculation assumes the maximum spacecraft orbital mapping altitude (50-km), a footprint-scale RMS surface roughness of 1 m, and a surface reflectivity of 0.15. To the best of our knowledge, these represent reasonable and in some cases, conservative estimates. Figure 5 plots the RMS range error as a function of at for footprint-scale surface slopes, q•, ranging from 0 to 40 ø. The calculation demonstrates how range error increases with increasing at and qb. The results show that for off-nadir-pointing angles of up to the 20 ø allowable maximum, the instrument will meet the

design specification and science requirement of 6 m range precision for surface slopes of up to 40 ø. Whether successful ranges are obtained from topographic extremes will also depend on signal/noise considerations.

Maximum Ranging Distance and Contribution to Spacecraft Navigation

Though designed to range continuously (detection probabilities >0.95) at orbital altitudes of-50 km, the NLR also has the capability to range to the asteroid from greater distances at lower probabilities of detection. This attribute

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Figure 5. RMS range error as a function of off-nadir pointing angle, at, for footprint-scale surface slopes, q•, ranging from 0 to 40 ø. The calculation demonstrates how range error increases with increasing at and q•. Assumptions are discussed in the text.

makes the NLR useful for spacecraft navigation in the asteroid approach phase of the NEAR mission. The maximum ranging distance Rmax can be expressed [Cole et al., 1995]

1

max SNRpNEP (3)

where SNRp is the power signal-to-noise ratio for successful operation and NEP is the noise equivalent power of the receiver. Figure 6 plots the received signal photoelectrons per pulse (Figure 6a) and the probability of successful ranging (Figure 6b) as a function of spacecraft-asteroid range. The calculation demonstrates that successful ranges can be obtained to distances of 223 km at a probability of detection of 0.2, corresponding to one successfully detected shot every 5 S.

Calibration

Ground calibration of the NLR was performed via functional and end-to-end system tests that are discussed in detail by Cole et al. [1997]. In the functional tests, optical pulses from the capped laser were transmitted through a fiber-optic cable to a trigger generator to produce an electrical pulse. This pulse triggered a pulse generator to provide a delayed optical pulse to simulate the round-trip time of laser pulses from the NEAR spacecraft to the surface of Eros. Figure 7a presents data for a functional test using the backscattered laser pulse in which the receiver is sequenced through the range of threshold settings. The results illustrate range walk typical of a leading-edge detection scheme.

ZUBER ET AL.: NEAR LASER RANGING INVESTIGATION 23,769

a)

0

o

/

15

12

9

6

3

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t

.

0 70 140 210 280 350

b) I ,

0.2 0

70 140 210 280 350 Range (km)

Figure 6. (a) Received signal photoelectrons per pulse and (b) probability of detection, both as a function of spacecraft-asteroid range. Signal-to-noise considerations dictate that successful ranges can be obtained at distances of 223 km from Eros at a probability of detection of 0.2, corresponding to one shot every 5 s for a 1- Hz ranging rate. If the instrument performs in accordance with this expectation, which is conservative, then the NLR will be useful for spacecraft navigational purposes during the asteroid approach phase of the NEAR mission.

The flee-air test represented an end-to-end test of NLR system. The test was conducted during August 8-9, 1995 in a 213-m long hallway at the JHU/Applied Physics Laboratory. Sand-blasted aluminum (a Lambertian scatterer) and silicic rock surfaces were used as ranging targets. With the instrument configured to pulse at a 1-Hz rate, ranges were accurately determined to both targets at varying distances, as verified by a 30.5-m-long surveyor's rule. The test also characterized the range walk of the system (Figure 7b) and verified the system attenuation.

The NLR is the first spaceborne laser altimeter to incorporate a continuous in-flight calibration capability. This calibration will be used to evaluate the functionality throughout the cruise phase, subsequent to launch, and will permit characterization of range walk due to threshold level changes and temperature- and time-related oscillator drift. Approximately five cruise calibration tests are planned in transit to Eros, and results will be used to correct range observations collected while in orbit. At the time this paper was revised, the instrument had been tested in space twice and each time demonstrated identical functionality to prelaunch tests.

Data Products

Profiles

A high priority of the NLR investigation is the rapid release and distribution of data to the scientific community and the public. As a valuable initial product, the NLR Science Team

will produce Experimental Data Records (EDR) that have an approximate horizontal resolution comparable to the laser spot size. For this product we will subtract initial orbits produced by the NLR Science Support Team from the range profiles to convert them to rough topographic profiles. We will produce initial orbits on a timescale of-1 week after receipt of spacecraft tracking and required ancillary information (SPICE kernals) and create the profiles from the ranges within a month. This data product is intended as a "quick-release" (albeit imperfect) version of the data that will be easily accessible. The format of these data files will be of the form: lat, lon, height above preliminary reference surface.

When updated orbits and spacecraft state information become available later in the mission, we will compute more precise profiles, which we term Corrected Data Records (CDR). The CDRs will be profiles which use final precision orbits so these profiles will have the same horizontal resolution but higher vertical (and horizontal) integrity than the EDRs. The CDRs will be the final archived profile product.

Grids

As soon as data coverage permits, we will produce a global grid of topography that will be referenced the best available ellipsoid. As more detailed observations become available, we will produce refined grids that will be referenced to an updated reference surface that we will produce (see below). Grids of intermediate resolution could be generated on an as-needed basis.

Our preferred gridding algorithm [Smith amt Wessel, 1990]

23,770 ZUBER ET AL.: NEAR LASER RANGING INVESTIGATION

175--

174-

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172-

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168

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165

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15117

1586

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Figure 7. (a) Functional test of the NLR using simulated backscattered pulse. Calibration counts (range) are denoted by triangles, and simulated ranges by squares. The calibration curve indicates a range walk of -4 m from threshold levels 2-7. For levels 0 and 1 the range values overflowed, indicating insufficient power level for ranging. (b) Results of free-air test on the APL campus, August 8-9, 1995. The plots show range counts (vertical axis) versus distance in feet (horizontal axis).

fits observations to a spherical cap. The algorithm then performs a bilinear interpolation to produce each grid point and for each point also provides a formal radial error estimate. The grid can be generated at any desired resolution, but the algorithm can also be instructed to choose the best resolution that is allowed by the data in a statistical sense. We will release this grid as soon as the data used in its generation are validated. As more data are collected, we will produced denser, updated grids, as well as higher resolution regional grids in areas of interest.

Spherical Harmonic Topographic Model

For regional-scale studies, we will perform a spherical harmonic expansion of the topographic data, producing the highest possible resolution model. For geophysical analyses, we will also produce a model with commensurate resolution to the gravity field [Yeomans et al., this issue].

Reference Surface

With approximately the first month of data collected in a high-inclination orbit, we will produce a global reference surface that will supersede all current ellipsoids. If the shape of Eros turns out to be distinctly elliptical, then we will compute a best fit ellipsoid. However, if Eros has a complex (e.g., jagged) shape, then we will choose a spherical harmonic surface to as many degrees and orders as are required to describe the global figure of the asteroid. There is a practical reason for choosing a reference surface that is more complex than an ellipsoid that is especially relevant to small, irregular planetary bodies: if the reference surface does not well approximate the shape of the body, it is difficult to map images onto it. This problem is evident in the mapping of digital images on Phobos (T. Duxbury, personal communication, 1993), and we will work closely with members of the NEAR imaging team to be responsive to the kind of surface that is needed for the accurate positioning of images on the surface.

Small-Scale Surface Features

The NLR and MSI/NIS Science Teams will jointly produce a topographic map of one or more specific surface features with overlaid eight-color imagery plus 64-color data at lower spatial resolution. The density of the topographic grid will depend on the number of transects obtained, and the relative topographic accuracy will be about 5 m. In addition, the teams will produce a database containing NLR crater transects with simultaneous MSI images.

Other Topographic Results

In addition to the basic products listed above, we will produce a global hypsometric distribution of the topography of Eros, a topographic power spectrum, and a topographic error map and an error spectrum. The basis of our formal error estimation will be the variance-covariance matrix of the

spherical harmonic topography solution. Our error analysis will provide a quantitative measure of the accuracy and integrity of the topographic field.

Geophysical Modeling of the Structure, Origin, and Evolution of 433 Eros

An essential component of the NLR investigation will be the interpretation of the topographic field in combination with gravity to investigate the global shape, internal structure, rotational dynamics, and geologic evolution of Eros.

Global Shape

The shape of Eros holds the record of that asteroid's impact and collisional record. We will analyze the fundamental topographic parameters (ellipsoidal axes, spherical harmonic coefficients) to characterize fundamental aspects of the shape over the wavelength spectrum. This characterization will provide information on the extent to which these exogenic processes have controlled the surficial evolution of Eros. Comparison of Eros' fundamental shape to that of other small

ZUBER ET AL.: NEAR LASER RANGING INVESTIGATION 23,771

bodies should also clarify in a quantitative sense the influence of low gravity and impact history in controlling macroscale surface evolution.

Mean Density

From NLR altimetry, we expect to resolve the volume of Eros to 1 part in 10 3 and from the tracking data, the asteroid mass will be determined to 1 part in 10 6 [Smith et al., 1995b; Yeomans et al., this issue]. Thus the measurement of Eros' mean density will be limited by the accuracy of the topographic field, though our global topographic grid will be 1-2 orders more accurate than that of any other asteroidal body [Williams et al., 1988; Duxbury, 1991; Thomas, 1993; Smith et al., 1995a]. Determination of the mean density of Eros at the level expected from NEAR can be used together with compositional information from NEAR spectral sensors to understand the constitution of the asteroid interior.

Internal Structure and Dynamics

Analysis of the topography and gravity fields will elucidate the internal structure of Eros. For example, comparison of the magnitudes and orientations of the topographic and gravitational field moments will provide insight into the internal distribution of mass. Such analysis will indicate whether or not there is an offset in the center of mass (COM)

and center of figure (COF) of Eros. The COM/COF relationship will provide information whether possible internal density differences are uniformly distributed, in a spatial sense. Along with information from the NEAR magnetometer [Acuna et al., this issue], it may be possible to detect whether the asteroid contains any significant metallic component in the interior. Combination of data of the NEAR geophysical and compositional sensors will permit insight into the nature of the asteroid parent body and possible genetic relationships to meteorites. Joint analysis of low-degree and-order terms of the spherical harmonic gravity and topography fields holds the potential to measure librations and obliquity changes [Zuber and Smith, 1997] that will quantify rotational dynamics and address questions such as whether the asteroid underwent a collision in its recent history.

'Temporal Variations?

The analysis plan presented thus far assumes that Eros is a single, coherent body. However, we do not rule out the possibility that Eros actually consists of two or more bodies gravitationally bound and covered by a thick regolith. Information on the COM/COF relationship and the moments will yield some insight into this question. However, additional information can be gained by looking for temporal variations in the gravity and topography fields in the attempt to detect if there is any subtle shifting of internal material. Any changes that may occur would be most apparent in low- degree and-order terms of the fields that are continuously sampled by the spacecraft in orbit. To discern whether or not Eros is solid or unconsolidated asteroidal body, we will compute independent topography models of Eros for subsets of the data. These models will be compared to similar models of time-varying gravity that will be produced by the Doppler tracking data. Given Eros' small size, it should be possible to collect enough data to recompute new global topography and gravity fields from which there is the possibility of detecting

statistically significant variations on timescales in the range of a week to a month. In the event that Eros is composed of more than one solid object, the anticipated orbital and topographic results proposed herein would require major reconsideration.

High-Resolution Profiles of Surface Features

Due to its small size relative to the solid planets and major satellites, Eros represents a natural laboratory to test ideas and models about impact, eject emplacement, and regolith processes under very low gravity. For example, understanding of the properties and thickness of the regolith, the unconsolidated surficial layer that contains the record of accretional and postaccretion collision could be enhanced by measurement of surface roughness at a range of spatial scales, such as that provided by meter-scale altimetry. Another key investigation will be to analyze processes that produce and modify small-scale topographic features such as craters and grooves (if present) from measurements of their widths and depths [Thomas, 1979]. In particular, high-precision altimetry will be combined with high spatial resolution color imaging from MSI. The ranging data will provide unambiguous determinations of topography, in contrast to image-derived topography which cannot be unambiguously distinguished from albedo variations. The imaging sensors will provide geologic context. The MSI spatial resolution is slightly higher than that of the NLR. As described above, the NLR altimetric transect consists of a series of laser spots on the asteroid surface which are close to contiguous or which' may overlap given the current mission design. The degree of overlap is currently uncertain, primarily because of the uncertainty in the mass of Eros. An image taken during an NLR transect will unambiguously reveal, for example, whether the feature being profiled is a crater or a groove, and if it is a crater, whether the transect passed through the center or close to the rim.

The NLR and MSI/NIS Science Teams have planned two specific joint experiments to exploit the synergistic capabilities of the instruments. In the first, one or more individual surface features will be selected by the Science Team early in the mission for targeted observations by the NLR, MSI, and the NIS. The goal will be to collect a large number of NLR transects with simultaneous MSI/NIS observations, so as

to be able to construct a three-dimensional topographic model of the feature and to overlay multispectral images and 64-color observations by NIS. From observations at 20-km range, we will obtain a topographic grid from altimetry with 5-m spot sizes and with relative topographic accuracy of-5 m. These data will be combined with eight-color imaging at 1.9 m x 3.2 m per pixel and NIS 64-color data at 130 m x 260 m resolution. We will analyze the structure and morphology of the feature, and relate these to the mineralogy. We will explore stratigraphic relations, and attempt to infer geologic processes.

The second experiment will be a statistical study of crater morphology using MSI and NLR data. MSI images will be used to identify times when the NLR spot passes over a crater. The image data will also determine the portion of the crater that was transected by NLR. From the NLR transects over a large number of craters, we will determine the average depth-to- diameter ratio and the average profile shapes as functions of

23,772 ZUBER ET AL.: NEAR LASER RANGING INVESTIGATION

crater diameter. From these measurements, we hope to learn how cratering dynamics on asteroids with low gravity may differ from that on much larger planetary bodies, such as the Moon, where detailed quantitative analyses of impact crater morphology have been performed [Pike, 1977].

The crater shape results produced from joint NLR and imaging data will enable improvements in the stereo and photoclinometric topography for small objects such as Phobos and Gaspra. These profiles will enable improved quantitative characterization of surface morphology of those bodies.

Synergy With Other Data Sets

A key aspect in the synergistic interpretation of NEAR instrument data sets is the capability to measure the boresight co-alignment of MSI and NLR in-flight at Eros. The MS1 has been designed such that its 1050-nm filter passband includes the 1064-nm radiation from the NLR. The MS! sensitivity is adequate to detect a NLR laser spot in a single image when the NLR operates in the 8-Hz mode over the darkside of the asteroid; thus when the MSI obtains an image during an NLR transect, it will be known precisely which imager pixels are illuminated by the laser. The in-flight determination of the relative alignment between the NLR and MSI will make it possible to directly correlate elevations with surface features, which considerably enhances both geological analysis and geodetic positioning on the surface. The NLR spot diameter at 235 grad is larger than, but comparable to, the MSI pixel size of 95 x 161 grad. During routine operations at Eros, when NLR is in its 1-Hz pulse repetition rate and the MS! is imaging the dayside, the NLR does not interfere with MSI observations in any way. This is because NLR fires its laser pulses at times when the MSI electronic shutter is normally closed (i.e., the MSI CCD is not integrating the image). However, it is possible to operate the MSI such that its shutter is open when NLR fires in its 1-Hz mode, and in this case only, when the MSI is in its 1050 nm filter, the laser pulse makes a small contribution to the detected brightness from the specific pixels illuminated by the NLR. The magnitude of this contribution will be measured in flight. The laser wavelength is outside the passbands of the other seven MSI filters.

All NLR topographic data sets will be produced in an areocentric, COM reference frame and will be easily comparable to data from the other NEAR sensors. For example, analysis of topography along with data t¾om other geophysical investigations, magnetics and gravity from Radio Science, will enable analyses of the interior structure of the asteroid. On the surface, the XRS/GRS requires a model for the shape of the entire asteroid, including the darkside, which will be provided by the NLR. Finally, NLR altimetric data will provide high-resolution detail to enhance the interpretation of asteroid shape data obtained from Earth-based astronomical observations.

Summary

The high-accuracy, geodetically referenced observations provided by the NEAR Laser Rangefinder will make significant contributions to the shape, internal structure, and evolution of 433 Eros and to near-Earth asteroids in general. In addition to providing a high-resolution topographic field of Eros, the data

will facilitate interpretation of observations from other NEAR spectral and geophysical sensors, and will assist in navigation of the NEAR spacecraft. In addition, the data will further increase the value of many Earth-based observations of the shapes of asteroids.

Acknowledgments. We appreciate input fi'om A. Reiter and R. Afzal concerning detector and transmitter performance, respectively, M. Boies and A. El-Dinary for providing details of instrument specifications and test results, J. Garvin for information on observed surface roughness of planetary surfaces, G. Neumann for generating the predicted orbital coverage plots, and P. Thomas and an anonymous reviewer for comments on the manuscript. In addition we thank R. Binzel and J. Abshire for helpful discussions and D. Harding and J. Bufton for providing an algorithm that we adapted to calculate range errors due to pulse spreading. The NLR investigation is supported by NASA's Near Earth Asteroid Rendezvous Project.

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A.F. Cheng, and T.D. Cole, Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723-6099. (e-mail: andrew_cheng @jhuapl.edu; timothy_cole @jhuapl.edu)

D.E. Smith, Laboratory for Terrestrial Physics, Code 920, NASA/Goddard Space Flight Center, Greenbelt, MD 20771. (e-mail: ds mi th @ tharsis. gsfc. nasa. g o v)

M.T. Zuber, Department of Earth, Atmospheric, and Planetary Sciences, 54-518, Massachusetts Institute of Technology, Cambridge, MA 02139-4307. (e-mail: zuber@mit.edu)

(Received April 5, 1996; revised February 13, 1997; accepted March 24, 1997.)