KPL/IK Mars Polar Lander MARDI Instrument Kernel. =============================================================================== This SPICE System Instrument Kernel (IK) file contains external and internal and FOV geometry characteristics for the Mars Polar Lander (MPL) Mars Descent Imager (MARDI) Instrument. Version and Date -------------------------------------------------------- Version 3.0, August 3, 1999, by Boris Semenov, NAIF/JPL Added "floor" target calibration section and updated camera mounting alignment based on "floor" target processing results. Version 2.0, July 27, 1999, by Boris Semenov, NAIF/JPL Added grid target calibration section and some of the camera parameters based on the calibration results. Version 1.0, July 17, 1999, by Boris Semenov, NAIF/JPL Initial Release. References -------------------------------------------------------- 1. MARDI ICD, Document MSP-96-1008, rev A, July 7, 1998. 2. MSSS MPL WWW Server, July 1999. 3. MPL Frames Kernel; latest version. 4. ``Kernel Pool Required Reading'' 5. MARDI Grid Target Calibration results, provided by Mike Caplinger, MSSS, July 1999. 6. MARDI "Floor" Target Calibration results, provided by Mike Caplinger, MSSS, July 1999. Implementation Notes -------------------------------------------------------- User programs that need I-kernel data must `load' the I-kernel file, normally during program initialization. Loading the kernel using SPICELIB routine LDPOOL causes the data items and their associated values present in the kernel to become associated with a data structure called the ``kernel pool''. Then a user's program can obtain the value(s) for any data item using the SPICELIB routines GDPOOL, GIPOOL and GCPOOL. See [4] for details. This file was created and can be updated with a text editor or word processor. Naming Conventions -------------------------------------------------------- All names referencing values in this I-kernel start with the characters `INS' followed by the NAIF MPL spacecraft ID number (-116) followed by the NAIF three digit MARDI instrument reference number (200). The remainder of the name is an underscore character followed by the unique name of the data item. For example, the focal length of the camera is specified by INS-116200_FOCAL_LENGTH The upper bound on the length of the name of any data item is 32 characters. If the same item is included in more then one file, or if the same item appears more than once within a single file, the latest value supersedes any earlier values. MARDI Overview -------------------------------------------------------- From [2]: Mars Surveyor '98 Lander Descent Imager MARDI This investigation proposes to develop and operate a descent imaging system for the Mars Surveyor '98 Lander. It will acquire and analyze close-up pictures of surface features at and in the immediate vicinity of the Mars Surveyor '98 landing site, in order to provide geologic and geographic context for the results of other lander investigations, to provide near-realtime planning information for lander operations, and to study specific attributes of the geology and geomorphology of Mars. Observational goals will include studies of: 1) surface morphology (e.g., nature and distribution of landforms indicating past and present environmental processes); 2) local and regional geography (e.g., context for other lander instruments--precise location, detailed local relief); and 3) relationships to features seen in orbiter data. The Mars Surveyor '98 Descent Imager (MARDI) includes a single camera head consisting of optics, focal plane assembly and support electronics, and housing. The design is derived from a Planetary Instrument Definition and Development Program (PIDDP) project to radically shrink the mass and power requirements of small spacecraft cameras. The system design uses highly-integrated devices to minimize mass and parts count. The camera uses a megapixel, electronically-shuttered CCD, and other electronics parts, tested for flight applications as part of the PIDDP effort. A digital signal processor (DSP) is used for system control and high-level operation of the detectors, with minimal requirements on the spacecraft central processing unit (CPU). Small gate arrays are used for time-critical digital functions and glue logic. The analog processing chain uses analog ASICs for clock generation, and square-root encoding to eliminate the need for gain settings. MARDI provides panchromatic images of the landing site over a 73.4 FOV with a resolution of 1.25 mrad/pixel (12.5 cm/pixel from 100 m). It can use either spacecraft altitude as determined by the lander altimeter, or continuous operation and a software sieving algorithm operating under software control from the lander CPU, to acquire fully nested images at scale ratios of 2:1. Assuming operations begin about 10 seconds after parachute deployment (upon aeroshell jettison), 10 images covering areas from 8 km to 9 m across and at resolutions of 7.5 to 0.009 m/pixel would be acquired, compressed, and stored in the spacecraft DRAM for later transmission to Earth. The anticipated results of this investigation include: 1) detailed knowledge of the local and regional setting of the Mars Surveyor '98 landing site, including geologic and topographic maps, 2) a specific link between the landing site and the rest of Mars as seen from orbit, and 3) serendipitous discovery of geomorphic processes at scales between those seen from orbit and those seen from the surface. Mars Surveyor '98 Lander Descent Imager (MARDI) Instrument Parameter Table ---------------------------------------------------------------- Mass and Volume: ---------------- Optics 50 gm 5 X 5 X 5 cm (5 X 5 X 4 cm assembled) FPA 150 gm 4.6 X 5 X ~3 cm DAS 100 gm 4.6 X 5 X ~1.7 cm Power Supply 120 gm 3.5 X 5 X 1.3 cm (4.6 X 5 X 1.3 ass.) Total 420 gm 5 X 5 X 10 cm (assembled) ---------------------------------------------------------------- Power: 2W imaging, 0.1W standby ---------------------------------------------------------------- Optics: ------- Type 9-element refractive FOV 73.4 degrees IFOV 1.25 mrad (7.5 m @ 6 km, 12.5 cm @ 100 m altitude) f/ratio f/2 Focal Length 7.135 mm ---------------------------------------------------------------- Detector: --------- Type Kodak KAI-1001: 1024 X 1024 (1018 X 1008 photoactive), 9 micron pixels, 20% fill factor, interline transfer electronic shuttering Noise 30 e- Full-well > 30,000 e- Exposure Time 250 microseconds SNR 27:1 (worst-case = aphelion, albedo 0.1, i = 70° ) Bandpass Panchromatic 500 to 800 nm ---------------------------------------------------------------- Electronics: ------------ Microprocessor Motorola DSP 56166 @ 60 MHz, 4096 Bytes Program RAM, 4096 Bytes Data RAM Communications 2 synchronous ports @ 1 Mbps/port Signals: RS-422 receive, transmit, clock Frame Time 2 sec per image (limited by bandwidth to S/C) Compression 2:1 lossless Huffman first-difference (realtime in DSP), 10:1 lossy "fast" discrete cosine transform (DCT) (near-realtime inS/C CPU), > 10:1 lossy "zerotree" wavelet (post-landing S/C CPU) ---------------------------------------------------------------- Data Return 10 images at factors of 2:1 in resolution ----------- between 7 m/pixel and 9 mm/pixel and covering areas from 8 km to 9 m across. ---------------------------------------------------------------- MARDI Grid Target Calibration Results -------------------------------------------------------- From [5]: "To calibrate its geometric parameters prior to mounting on the spacecraft, MARDI was used to image a grid target with major spacing 4x4 inches and minor spacing 1x1 inch. The target plane was approximately normal to the camera boresight. The distance from MARDI to the target plane was 41.5 inches. The distance from the floor to the MARDI boresight was 58.25 inches; from the floor to the left corner of grid target 41.4 inches; from the floor to the right corner of grid target 40.8 inches. The lower left corner of grid target was 27.4 inches left of the MARDI boresight (approximate.) Assuming that the center of the projection is at sample 515, line 511 (0-based) in the image, then the surrounding 1" grid points are at sample line ------ ---- 509 492 528 492 528 511 509 511 509 530 528 530 The deltas between these points are all 19 pixels. So one inch maps to 19 pixels at the center of the field at a distance of 41.5 inches. One inch at 41.5 inches is 24.1 mrad, so the IFOV is 1.27 mrad. This is in good agreement with the measured EFL for MARDI of 0.276", which for the 9-micron pixels of the MARDI detector translates to an IFOV of 1.28 mrad. (Note that all measurements here were limited to 1-pixel accuracy at best.) Since MARDI has a wide field of view, it suffers from a significant amount of barrel distortion. We now solve for the radial distortion parameter kappa as described in "A Versatile Camera Calibration Technique for High-Accuracy 3D Machine Vision Metrology Using Off-the-Shelf TV Cameras and Lenses", Roger Y. Tsai, IEEE Journal of Robotics and Automation, Vol. RA-3, No. 4, August 1987, pages 323-344. This maps distorted to undistorted pixel coordinates as follows: Ru = Rd * (1 + kappa * Rd^2) distortion_factor = 1 + kappa * (Xd^2 + Yd^2); Xu = Xd * distortion_factor Yu = Yd * distortion_factor On the grid target, the center pixel is at 28", 14.25" in the grid coordinate system. The 0-based and left-handed pixel coordinates (samp, line) can be mapping into the "sideways" right-handed coordinate system just by transposition -- i.e., (line, samp) is used rather than (samp, line). The two input files with the (samp,line) coordinates of the grid in the image, and the undistorted and distorted grid coordinates in pixels relative to the image center, are given below. We then plot rd/ru against rd^2, where rd=xd^2+yd^2 and ru=xu^2+yu^2, and fit a line to this dataset, forcing the Y intercept to be 1. The result of the fit is Ru = Rd*(1+7.6417e-7*Rd^2) So, summarizing: pixel size 9 microns measured EFL 0.276" or 7.0104 mm kappa 7.6417e-7 It should be noted that all images taken in flight by MARDI, regardless of their frame size, will be centered on the nominal center pixel. RAW DATA The distorted image pixel coordinates (samp, line) of the 4x4-inch grid: X Y Z Px Py ----- ----- --- --- --- 0.0 0.0 0.0 297 66 0.0 101.6 0.0 357 61 0.0 203.2 0.0 420 56 0.0 304.8 0.0 485 53 0.0 406.4 0.0 551 54 0.0 508.0 0.0 615 57 0.0 609.6 0.0 679 61 0.0 711.2 0.0 741 68 101.6 0.0 0.0 289 118 101.6 101.6 0.0 351 112 101.6 203.2 0.0 416 108 101.6 304.8 0.0 482 106 101.6 406.4 0.0 550 106 101.6 508.0 0.0 617 109 101.6 609.6 0.0 683 114 101.6 711.2 0.0 747 121 101.6 812.8 0.0 807 128 203.2 0.0 0.0 281 173 203.2 101.6 0.0 345 167 203.2 203.2 0.0 412 164 203.2 304.8 0.0 480 162 203.2 406.4 0.0 550 163 203.2 508.0 0.0 620 164 203.2 609.6 0.0 687 169 203.2 711.2 0.0 753 176 203.2 812.8 0.0 814 183 304.8 0.0 0.0 273 233 304.8 101.6 0.0 338 228 304.8 203.2 0.0 407 225 304.8 304.8 0.0 478 223 304.8 406.4 0.0 550 224 304.8 508.0 0.0 621 226 304.8 609.6 0.0 691 230 304.8 711.2 0.0 758 236 304.8 812.8 0.0 821 243 406.4 0.0 0.0 267 297 406.4 101.6 0.0 333 294 406.4 203.2 0.0 403 291 406.4 304.8 0.0 476 290 406.4 406.4 0.0 549 290 406.4 508.0 0.0 623 293 406.4 609.6 0.0 695 297 406.4 711.2 0.0 762 301 406.4 812.8 0.0 826 306 508.0 0.0 0.0 262 365 508.0 101.6 0.0 330 363 508.0 203.2 0.0 401 361 508.0 304.8 0.0 474 361 508.0 406.4 0.0 549 362 508.0 508.0 0.0 623 363 508.0 609.6 0.0 695 366 508.0 711.2 0.0 764 369 508.0 812.8 0.0 830 374 609.6 0.0 0.0 398 434 609.6 101.6 0.0 326 435 609.6 203.2 0.0 473 435 609.6 304.8 0.0 259 436 609.6 406.4 0.0 548 436 609.6 508.0 0.0 623 437 609.6 609.6 0.0 697 439 609.6 711.2 0.0 766 441 609.6 812.8 0.0 832 444 711.2 0.0 0.0 258 507 711.2 101.6 0.0 325 509 711.2 203.2 0.0 397 510 711.2 304.8 0.0 472 511 711.2 406.4 0.0 548 512 711.2 508.0 0.0 623 512 711.2 609.6 0.0 696 514 711.2 711.2 0.0 766 515 711.2 812.8 0.0 832 515 812.8 0.0 0.0 257 579 812.8 101.6 0.0 325 582 812.8 203.2 0.0 397 584 812.8 304.8 0.0 471 586 812.8 406.4 0.0 829 586 812.8 508.0 0.0 546 587 812.8 609.6 0.0 622 588 812.8 711.2 0.0 694 588 812.8 812.8 0.0 764 588 914.4 0.0 0.0 259 649 914.4 101.6 0.0 326 654 914.4 203.2 0.0 397 657 914.4 304.8 0.0 471 659 914.4 406.4 0.0 545 661 914.4 508.0 0.0 619 661 914.4 609.6 0.0 692 660 914.4 711.2 0.0 761 659 914.4 812.8 0.0 825 656 1016.0 0.0 0.0 263 718 1016.0 101.6 0.0 329 723 1016.0 203.2 0.0 398 727 1016.0 304.8 0.0 471 730 1016.0 406.4 0.0 544 731 1016.0 508.0 0.0 616 732 1016.0 609.6 0.0 688 730 1016.0 711.2 0.0 756 728 1016.0 812.8 0.0 820 723 1117.6 0.0 0.0 267 782 1117.6 101.6 0.0 332 788 1117.6 203.2 0.0 400 793 1117.6 304.8 0.0 471 796 1117.6 406.4 0.0 542 798 1117.6 508.0 0.0 614 797 1117.6 609.6 0.0 683 795 1117.6 711.2 0.0 750 792 1117.6 812.8 0.0 812 786 1219.2 0.0 0.0 273 841 1219.2 101.6 0.0 336 849 1219.2 203.2 0.0 403 854 1219.2 304.8 0.0 471 857 1219.2 406.4 0.0 541 859 1219.2 508.0 0.0 610 859 1219.2 609.6 0.0 678 856 1219.2 711.2 0.0 743 851 1219.2 812.8 0.0 804 845 1320.8 0.0 0.0 281 897 1320.8 101.6 0.0 341 904 1320.8 203.2 0.0 406 910 1320.8 304.8 0.0 472 914 1320.8 406.4 0.0 540 915 1320.8 508.0 0.0 607 914 1320.8 609.6 0.0 672 911 1320.8 711.2 0.0 736 906 1320.8 812.8 0.0 796 899 The undistorted and distorted pixel coordinates translated to right-handed image-center-relative form: Xu Yu Xd Yd ---- ------- ---- ---- -532 -270.75 -446 -219 -532 -194.75 -451 -159 -532 -118.75 -456 -96 -532 -42.75 -459 -31 -532 33.25 -458 35 -532 109.25 -455 99 -532 185.25 -451 163 -532 261.25 -444 225 -456 -270.75 -394 -227 -456 -194.75 -400 -165 -456 -118.75 -404 -100 -456 -42.75 -406 -34 -456 33.25 -406 34 -456 109.25 -403 101 -456 185.25 -398 167 -456 261.25 -391 231 -456 337.25 -384 291 -380 -270.75 -339 -235 -380 -194.75 -345 -171 -380 -118.75 -348 -104 -380 -42.75 -350 -36 -380 33.25 -349 34 -380 109.25 -348 104 -380 185.25 -343 171 -380 261.25 -336 237 -380 337.25 -329 298 -304 -270.75 -279 -243 -304 -194.75 -284 -178 -304 -118.75 -287 -109 -304 -42.75 -289 -38 -304 33.25 -288 34 -304 109.25 -286 105 -304 185.25 -282 175 -304 261.25 -276 242 -304 337.25 -269 305 -228 -270.75 -215 -249 -228 -194.75 -218 -183 -228 -118.75 -221 -113 -228 -42.75 -222 -40 -228 33.25 -222 33 -228 109.25 -219 107 -228 185.25 -215 179 -228 261.25 -211 246 -228 337.25 -206 310 -152 -270.75 -147 -254 -152 -194.75 -149 -186 -152 -118.75 -151 -115 -152 -42.75 -151 -42 -152 33.25 -150 33 -152 109.25 -149 107 -152 185.25 -146 179 -152 261.25 -143 248 -152 337.25 -138 314 -76 -270.75 -76 -257 -76 -194.75 -77 -190 -76 -118.75 -78 -118 -76 -42.75 -77 -43 -76 33.25 -76 32 -76 109.25 -75 107 -76 185.25 -73 181 -76 261.25 -71 250 -76 337.25 -68 316 0 -270.75 -5 -258 0 -194.75 -3 -191 0 -118.75 -2 -119 0 -42.75 -1 -44 0 33.25 0 32 0 109.25 0 107 0 185.25 2 180 0 261.25 3 250 0 337.25 3 316 76 -270.75 67 -259 76 -194.75 70 -191 76 -118.75 72 -119 76 -42.75 74 -45 76 33.25 75 30 76 109.25 76 106 76 185.25 76 178 76 261.25 76 248 76 337.25 74 313 152 -270.75 137 -257 152 -194.75 142 -190 152 -118.75 145 -119 152 -42.75 147 -45 152 33.25 149 29 152 109.25 149 103 152 185.25 148 176 152 261.25 147 245 152 337.25 144 309 228 -270.75 206 -253 228 -194.75 211 -187 228 -118.75 215 -118 228 -42.75 218 -45 228 33.25 219 28 228 109.25 220 100 228 185.25 218 172 228 261.25 216 240 228 337.25 211 304 304 -270.75 270 -249 304 -194.75 276 -184 304 -118.75 281 -116 304 -42.75 284 -45 304 33.25 286 26 304 109.25 285 98 304 185.25 283 167 304 261.25 280 234 304 337.25 274 296 380 -270.75 329 -243 380 -194.75 337 -180 380 -118.75 342 -113 380 -42.75 345 -45 380 33.25 347 25 380 109.25 347 94 380 185.25 344 162 380 261.25 339 227 380 337.25 333 288 456 -270.75 385 -235 456 -194.75 392 -175 456 -118.75 398 -110 456 -42.75 402 -44 456 33.25 403 24 456 109.25 402 91 456 185.25 399 156 456 261.25 394 220 456 337.25 387 280" MARDI "Floor" Target Calibration Results -------------------------------------------------------- After the camera was mounted on the lander, it shot calibration image(es) of five "floor" targets the location of which was measured by theodolites. From [6]: "MARDI geometric calibration theodelitically-measured points, units are inches, coord system is "RHR" (Lander - BVS) X Y Z ------- ------- ------- 1 19.8521 71.0912 83.9699 2 77.2928 47.6703 86.1238 3 37.0116 43.1353 84.4329 4 26.8374 16.9590 84.6925 5 9.6749 43.1755 84.2135 Coordinates in MARDI image (upper left 0,0, image 1032x944 "calibration" mode with dark and isolation pixels) X Y ------- ------- 1 975 542 2 362 52 3 542 475 4 187 840 5 759 892" Using "... the distortion function to map the five points measured at LMA into undistorted pixel coordinates ... the transformed points as measured in pixel samp,line: X Y ------- ------- 1 1049.21 546.851 2 334.308 -30.718 3 542.041 474.942 4 132.739 894.096 5 796.779 951.078 or if image-center-relative coordinates are preferred, X Y ------- --------- 1 533.213 34.8505 2 -181.692 -542.718 3 26.040 -37.0578 4 -383.261 382.096 5 280.779 439.078" MARDI Location and Mounting Alignment -------------------------------------------------------- The following nominal MARDI location and mounting alignment information is provided in the Appendix B "MARDI position on Lander" of [1]: CENTER OF [MARDI] MOUNTING SURFACE ---------------------------------- X = 26.56+/-.25 Y = 26.09+/-.25 Z = 41.15+/-.25 CANT ANGLE ---------- ANGLE ABOUT X = -19.28 deg \__ -22.00 ANGLE ABOUT Y = -11.42 deg / degrees ANGLE ABOUT Z = 27.37 deg A set of Euler angles that would rotate the lander frame to the MARDI mounting plate frame can be derived from these cant angles using the following algorithm: Step 1: find direction of the intersection of the lander YZ and XZ planes with the MARDI mounting plate plane using corresponding cant angles: X' = ( cos(-11.42), 0.0, sin(-11.42)) Y' = ( 0.0, cos(-19.28), sin(-19.28)) Step 2: compute cross product of these vectors which will be the direction of the normal to the MARDI mounting plane N = X' x Y' (sanity check -- angle between N and lander Z axis should be close to 22 degrees; i.e. equal to the total cant angle given above) Step 3: compute cross product of the normal and lander Z axis (0,0,1) which will give the direction of an axis laying in the lander XY plane a rotation by 22 degrees about which will take lander XY plane into MARDI mounting plate orientation RAXIS = N x Z Step 4: knowing rotation axis and rotation angle about it, compute corresponding rotation matrix (using SPICE's AXISAR routine) and euler rotation angles (using SPICE's M2EUL routine); Euler rotation order 3-2-3 seem to match geometry well and will allow the last rotation to "consume" cant about Z. By applying this algorithm we compute the following rotational angles: M = [ -32.6251 ] [ 21.9956 ] [ 59.9951 ] Z Y Z where M is a matrix rotating vectors from LANDER to an intermediate frame, orientation of which is specified by the set of cant angles given above. In order to transform from this intermediate frame to the camera frame we need an additional rotation of +90 degrees about +Z axis. This rotation will bring X and Y axes of the intermediate frame to be along the directions of increasing image samples and lines correspondingly. So, the final set of nominal rotation angles is: M = [ 57.3749 ] [ 21.9956 ] [ 59.9951 ] Z Y Z where where M is a matrix rotating vectors from LANDER frame to MARDI frame. In other words, nominally LANDER frame can be transformed to the MARDI frame by three subsequent rotations, first of +59.9951 degrees about Z axis, second by +21.9956 degrees about new position of Y axis and third by +57.3749 degrees about final position of Z axis. Using the result of "floor" target calibration data and nominal rotation angles as a starting point, someone can solve for the actual rotation between the lander and camera frames. The input data for such solution would be the locations of the five targets and the location of the camera focal point in the lander frame with respect to the lander center (coordinates provided in the table were computed using MPL structures SPK file): X,m Y,m Z,m ------- ------- ------- 1 0.50424 1.80572 2.13284 2 1.96324 1.21083 2.18754 3 0.94009 1.09564 2.14460 4 0.68167 0.43076 2.15119 5 0.24574 1.09666 2.13902 MARDI FP 0.69188 0.69052 1.12747 and undistorted sample/line coordinates of the targets as measured in the calibration image (see "MARDI Floor Target Calibration Results" section above): sample line ------- -------- 1 533.213 34.850 2 -181.692 -542.718 3 26.040 -37.057 4 -383.261 382.096 5 280.779 439.078 Depending on chosen solution method different values of adjusted angles can be computed; the solution performed by NAIF resulted in: M = [ 57.143282 ] [ 21.711773 ] [ 58.197535 ] Z Y Z With this set of alignment angles, estimated target coordinates match actual ones within 2 pixels for targets 1, 2, 4 and 5 and give almost exact match for the target 3. The keywords ``INS-116200_EULER_ANGLES'' and ``INS-116200_EULER_AXIS'' contain the angle values and the indexes of the corresponding rotation axes ( 1 -- 'X', 2 -- 'Y', 3 -- 'Z'): INS-116200_EULER_ANGLES = ( 57.143282, 21.711773, 58.197535 ) INS-116200_EULER_AXES = ( 3, 2, 3 ) Note that the keywords above are NOT enclosed between \begindata -- \begintext tokens and, therefore, they are NOT available to SPICE System toolkit. This is done to encourage use of the SPICE Frames subsystem that provides a more flexible interface to instrument mounting alignment information. Refer to the latest MPL Frames Kernel file for details. MARDI Optics Geometry -------------------------------------------------------- The following nominal MARDI first order optical parameters are provided in [2] (see "MARDI Overview" section of this file): --------------------------------------------------- parameter value --------------------------------------------------- Focal Length, mm 7.135 f/ratio f/2 FOV Angular Size, rad 1.281 x 1.281 (73.4 deg) IFOV, rad/pixel 0.00125, 0.00125 Radial distortion coeff. - --------------------------------------------------- The following actual MARDI first order optical parameters values are provided in [5]. These values were derived during processing of the pre-flight calibration data, (see "MARDI Grid Target Calibration Results" section of this file): --------------------------------------------------- parameter value --------------------------------------------------- Focal Length, mm 7.0104 f/ratio f/2 FOV Angular Size, rad 1.281 x 1.281 (73.4 deg) IFOV, rad/pixel 0.00128, 0.00128 Radial distortion coeff. 7.6417e-7 --------------------------------------------------- The values in the keywords are given in the same units as in the actual values table above. \begindata INS-116200_FOCAL_LENGTH = ( 7.0104 ) INS-116200_F/RATIO = ( 3.5052 ) INS-116200_FOV_ANGULAR_SIZE = ( 1.28107167, 1.28107167 ) INS-116200_IFOV = ( 0.00128, 0.00128 ) INS-116200_ALPHA0 = ( 0.00000076417 ) \begintext MARDI FOV Geometry -------------------------------------------------------- The following nominal MARDI detector geometry parameters are provided in [2] (see "MARDI Overview" section of this file): --------------------------------------------------- parameter value --------------------------------------------------- Detector Array Size 1024 x 1024 Detector Array Center 511.5,511.5 Pixel Size, mm 0.009 Number of pixels/mm 111.1111111 --------------------------------------------------- The following actual MARDI detector geometry parameters are provided in [5] (see "MARDI Grid Target Calibration Results" section of this file): --------------------------------------------------- parameter value --------------------------------------------------- Detector Array Size 1032 x 1024 Detector Array Center 516,512 Pixel Size, mm 0.009 Number of pixels/mm 111.1111111 --------------------------------------------------- The values in the keywords are given in the same units as in the actual values table above. \begindata INS-116200_PIXEL_SAMPLES = ( 1032 ) INS-116200_PIXEL_LINES = ( 1024 ) INS-116200_CENTER = ( 516, 512 ) INS-116200_PIXEL_SIZE = ( 0.009 ) INS-116200_K = ( 111.11111111 ) \begintext Platform ID -------------------------------------------------------- The MARDI instrument is mounted on the MPL spacecraft body. Therefore the value for the platform ID keyword below is -116000. \begindata INS-116200_PLATFORM_ID = ( -116000 ) \begintext