NLR Calibration Description Introduction The Near Laser Rangefinder (NLR) is the first laser altimeter to employ continuous, in-flight calibration using a fiber-optic delay assembly (FODA), which is a spooled 109.5 m fused silica fiber-optic cable. Part of each optical pulse formed within the laser resonator is injected into the FODA, which injects a delayed optical signal directly into the receiver. This allows end-to-end calibration for each emitted pulse even when no target surface is available. Data Format The NLR Experiment Data Records (EDR) take the form of Flexible Image Transport Standard (FITS) files, in which each packet makes up one record. The NLR FITS files are organized such that all the normal format packets from any Coordinated Universal Time (UTC) day are compiled into one file, while all the high rate packets from the same day are compiled into another file. The FITS file naming convention is as follows: for the normal format FITS file, LyydddNT.FIT is used where L=laser, and yyddd represents digits giving date of observation in two-digit-year and day-of-year format; correspondingly, for the high rate format FITS file LyydddHT.FIT is used. An example is L96116HT.FIT for data obtained at 2 Hz on April 25, 1996. The orbital mission phase employed only normal format packets. In these packets, the spacecraft mission elapsed time (MET) is recorded at the time of the first major frame in the packet. A normal rate packet contains up to 56 observations, so that the last observation may occur up to 55 seconds after the nominal packet time in the case of 1 Hz data. While the NLR packets contain basic information on the instrument status, additional information on the state of the instrument is returned in the spacecraft housekeeping packets. The SDC merges this additional information with that from the NLR packets to produce the NLR FITS files. A full listing of the data values in the NLR FITS files with complete definitions is given in Cheng, et al. (2000). Laboratory Calibration of Range Measurement The absolute calibration of NLR range measurements, or the relation between measured TOF and range, was established in laboratory tests prior to launch (Cole, et al. 1997). Two separate measurements were obtained: first, a determination of the total system delay in commanded threshold TH = 2, and second, a determination of how this delay varies with TH (threshold-based range walk). The total system delay is the time between the arrival of a laser pulse and the electronic registration of counts, and it was determined by comparing the time delay of an optical pulse through the FODA in two cases: 1) FODA separate from the NLR (529.2 ns delay); and 2) FODA integrated with the NLR receiver at commanded threshold TH = 2 (558.33 ns delay). The total system delay Tsd was measured as the increase in the time delay when connected to NLR, or 29.13 ns. This measurement was confirmed, and the threshold-based range walk was measured, during the absolute calibration tests performed on August 8-9, 1995 ("hall shot test", Zuber, et al. 1997). We conclude that the total system delay is 29 ns, with a (conservative) uncertainty corresponding to half a count, which is 1 ns or 15.6 cm in range. In-flight Calibration Results The measurements of total system delay and threshold-based range walk yield the conversion from range counts to range R in meters measured by NLR R = 0.3122838 * counts - corr ( TH ) - 4.37 (1) where the last term accounts for the total system delay of 29 ns, and where the correction is listed in Table 1 below and accounts for the threshold-based range walk. The threshold-based range walk corrections in Table 1 were obtained from in-flight calibration tests. The calibration counts for all shots with a given TH are averaged from a given test, omitting shots without valid calibrations (e.g., FAILSAFE data, also data with range gate values that suppress the calibration pulse). Each entry in Table 1 is the average of >1000 valid calibrations. The difference in average calibration counts between the given threshold and TH = 2 yields the range correction in Table 1, using the conversion 0.3122838 m per count. The TH = 2 correction is zero by definition. No calibration pulses are detected for TH = 7 so no range correction is shown, and none is shown for TH = 0 which is at the noise level and which was not used for mapping. Since TH=7 was used for very low altitude flybys, a nominal 4.0 meters was assigned to corr(TH=7) in calibrating the resulting science data. The second column of Table 1 shows the threshold-based range walk corrections from the combined data sets obtained in the flight tests performed 4/19/99 and 8/13/99. The values in the second column will be adopted for initial analyses. The third column shows, for comparison, the corrections obtained from the combined data sets obtained in all flight tests from launch through 1998. The changes in these corrections over the > 3 yr time span are regarded as a conservative estimate of the uncertainties in the corrections. The uncertainty in range walk correction corresponds to less than 11 cm in range. Table 1 Range corrections in meters vs. TH: TH corr (TH) corr (TH) 4/99 & 8/99 previous tests 1 -0.37 -0.36 2 0 0 3 0.40 0. 51 4 0.84 0.92 5 1.38 1.38 6 2.17 2.15 7 4.0 (nominal) Calibrated Level 2 products The level 2 data products comprise the along-track time series of the NLR instrument's science data in physical units, produced using precision orbits, ancillary timing and attitude information supplied by the NEAR SDC and instrument data derived from in-flight analysis. Each level 2 data product is a text format table corresponding to a daily level 1 EDR file and is described by a detached label. The file naming convention is LyydddNv.TAB, where L=laser, and yyddd contains the two-digit year and the three-digit Julian day of observation. The letter v stands for processing version. Each Level 2 product begins with 2 header lines or records, followed by data. The first record lists the name of the source FITS file and the SPICE kernels used to compile the information included in the table. The SPICE files de403s.bsp, naif0007.tls, and pck0006.tpc used are constants in the analysis and are not listed in the header. The files listed in the first line of the header are, in order: aggregated NLR telemetry filename; SPICE Orientation file for NEAR; SPICE spacecraft position for NEAR; Additional SPICE position file for NEAR; SPICE on-board time (SCLK) to ET mapping; SPICE file for 433 Eros ephemeris; SPICE Orientation file for 433 Eros; SPICE Instrument kernel file for NLR. The second line/record of the header lists brief table headings. These are for convenience only and should not be construed as object names. Precision orbit data for the NEAR-Shoemaker spacecraft is provided by the NASA-GSFC analysis team and is archived in the form of SPICE-format spacecraft ephemeris (SPK) files. The MET time associated with each shot, with minor frame given in decimal seconds, is converted to Ephemeris Time in seconds past J2000 (ET) using the most recent time conversion (SCLK) file. The spacecraft position at the ET shot time is interpolated from the SPK file. The spacecraft orientation SPICE file (CK) is resampled at 1-second intervals of whole seconds and convolved with a 9-point, centered, finite-impulse-response filter to reduce high-rate gyro noise. Coefficients of the filter (unnormalized) are given below. The noise reduction allows slow-scanning ground tracks to move more smoothly across the surface, and only slightly affects positional accuracy during high-rate slews. Table 2 Orientation filter convolution coefficients vs. convolution index: Index Coefficient -4 0.19 -3 0.69 -2 1.31 -1 1.81 0 2.0 1 1.81 2 1.31 3 0.69 4 0.19 The filtered spacecraft orientation matrix transforms vectors from the J2000 inertial reference frame to the instrument deck (NEAR_SC_BUS_PRIME) frame. In this frame, observations are taken in the positive X-direction. A fixed boresight offset with respect to this frame is assumed. The NLR laser boresight orientation was obtained from a least-squares relocation of the NLR bounce points (Neumann, et al. 2001), that minimized altimetric errors at crossovers. The Euler angles of the boresight are provided as a SPICE instrument kernel (IK) file, from which a transformation matrix from NEAR to NLR frame is derived. The J2000-to-NLR frame matrix is calculated from the smoothed CK by matrix composition. The one-way time-of-flight from the laser range is added to the laser fire time to obtain the bounce point time, and the calibrated one-way range vector is projected from the spacecraft state at this time along the boresight to obtain the surface bounce point position in inertial coordinates with respect to the asteroid center-of-mass. The inertial position is then rotated to the asteroid body-fixed coordinate system using satellite/planet position and orientation files (PCK). The asteroid-located radius vector is given in both radial coordinates and as a Cartesian position vector. The angle subtended by the bounce point to spacecraft position vector and the radius vector is calculated. This angle is loosely termed the EMISSION_ANGLE, assuming a spherical body. Normally an emission angle greater than 90 degrees would indicate a missed shot, but due to the irregular shape of 433 Eros, emission angles >120 degrees were obtained. The off-pointing angle from the asteroid center (OFF_NADIR angle) is also given. Lastly, the potential due to gravity and rotation at the shot location is calculated (Cheng, et al. 2001) assuming a uniform density of 2670 kg m^-3 and the NLR shape model NLR125AR.IMG. Since the asteroid is irregularly shaped, a simple topographic datum does not exist. The potential field represents the work required to transport a particle of unit mass from the shot point to another fixed position with respect to the rotating body. The potential divided by an average gravitational acceleration can be interpreted as a proxy for topographic height in geophysical analyses. References Cole, T., M. Boies, A. El-Dinary, A.F. Cheng, M. Zuber, and D.E. Smith, The Near Earth Asteroid Rendezvous Laser Altimeter, Space Science Reviews, 82, 217-253, 1997. Cheng, A,F, Cole, T.D., Zuber, M.T., Smith, D.E., Guo, Y. and Davidson,F., In-Flight Calibration of the Near Earth Asteroid Rendezvous Laser Rangefinder, Icarus, 148, 572-586, 2000. Cheng, A.F., Barnouin-Jha, O., Prockter, L., Zuber, M.T., Neumann, G., Smith, D.E., Garvin, J., Robinson, M., Veverka, J., and Thomas, P., Small Scale Topography of 433 Eros from Laser Altimetry and Imaging, Icarus, in press, 2001. Neumann, G.A., Rowlands, D.D., Lemoine, F.G., Smith, D.E., and Zuber, M.T., Crossover analysis of Mars Orbiter Laser Altimeter data, Journal of Geophysical Research, in press, 2001. Zuber, M., D.E. Smith, A.F. Cheng, and T.D. Cole, The NEAR Laser Ranging Investigation, Journal of Geophysical Research, 102, 23761-23773, 1997.