KPL/IK Mars Polar Lander SSI Instrument Kernel. =============================================================================== This SPICE System Instrument Kernel (IK) file contains external, internal and FOV geometry characteristics for the Mars Polar Lander SSI camera. Version -------------------------------------------------------- Version 2.1, November 8, 1999 by Boris Semenov, NAIF/JPL Included backlash correction tables and updated some UofA model parameters based on the latest SSI Pointing Spreadsheet ([1]). Version 2.0, August 15, 1999 by Boris Semenov, NAIF/JPL Included CAHVOR model parameters. Version 1.0, August 18, 1998 by Boris Semenov, NAIF/JPL Initial Release. CAHV model parameters, fiducial mark location and backlash correction tables are not included in this version. References -------------------------------------------------------- 1) Camera model Excel spreadsheet by SSI team of University of Arizona (Mike Burkland, Jon Weinberg, Mark Lemmon, et al); version 19f, Oct-Nov, 1999; 2) CAHV Camera model parameters by MIPL/JPL (Justin Maki, et al). Camera Models Overview -------------------------------------------------------- Two different models exist for SSI camera: -- Camera model created at UofA by UofA SSI Team (Mike Burkland, Jon Weinberg et al) as the result of extensive camera calibrations at UofA before the camera was mounted on the Mars Polar Lander; this model in implemented in SSI pointing spreadsheet maintained by UofA team; -- Camera model created at JPL by MIPL team (Justin Maki, Allan Runkle, Jean Lorre, Todd Litwin) to support processing of SSI images in MIPL software; this model is also known as CAHV camera model. Supposedly: the first model was obtained as the result of bigger number of more accurate calibrations; the set of parameters in the first model can be explained in a clearer way; the first model's algorithm is more straight forward; and it can be easier implemented in a software. Therefore this IK file provides the set of parameters from the first model in the file's data sections. The set of parameters from the second model and some values derived from these parameters to perform correlation between two models are provided in the description sections of the IK file and aren't available for SPICE System Toolkit software. SSI External Geometry -------------------------------------------------------- The camera head was mounted on a deployable mast. It had two degrees of rotational freedom -- first in azimuth and second in elevation. There are four different frames associated with SSI camera: - MVACS frame; - SSI Camera Head frame; - SSI Left Eye frame; - SSI Right Eye frame; Refer to the latest version of Mars Polar Lander Frames Kernel File for more information regarding these frames. Also refer to the comment area of the latest Mars Polar Lander Structures SPK for more information regarding relative offsets between origins of these frames. Camera Base And Camera Head Locations The SSI Base Center coordinates, given in respect to the Mars Polar Lander frame, in meters. The SSI Base center is the origin of MVACS coordinates and located at the intersection of the camera azimuth axis and the lander deck: \begindata INS-116110_SSI_BASE = ( -0.530091 -0.232458 0.799530 ) \begintext The SSI Camera Head center coordinates for stowed and deployed positions, given in respect to the MVACS frame, in meters. The SSI Camera Head center is the origin of the SSI Camera Head frame and is located at the intersection of the camera azimuth and elevation axes: \begindata INS-116110_SSI_HEAD_STWD = ( 0.000 0.000 0.17570 ) INS-116110_SSI_HEAD_DPLD = ( 0.000 0.000 0.79375 ) \begintext AZ and EL Drives: Motor Step Sizes and Ranges and Hard Stop Positions The drawing below shows SSI camera head hard stop positions and rotation ranges in AZIMUTH and ELEVATION: Camera Head TOP (+Zmvacs) View: Camera Head Side (-Y) View: ------------------------------- --------------------------- Camera Head shown in camera shown in AZ_ANGLE=0, in AZ_ANGLE=0 position EL_ANGLE=0 position. ^ +X mvacs ^ +Zssi = +Zmvacs | | | | +Yssi = +Ymvacs | | (into page) ______|______ _|_ | * | * | / |*\ <------------o | | X----------> +Ymvacs |_______\_____| \___/ +Xssi = +Xmvacs +Z mvacs \ direction ,^ (out of page) \ ^ of rotation |--' direction \ ,' | of rotation \ | AZ Hard Stop EL Hard Stop position (*) position (**) (*) As seen from above camera head rotates counterclockwise from its hard stop position (AZIMUTH motor step 0; AZIMUTH angle -23.0 deg for stowed and -143.31 deg for deployed) through its AZIMUTH angle zero position (AZIMUTH motor step 41.589 for stowed and 259.137 for deployed) towards its maximum AZ motor step position (AZIMUTH motor step 650). The azimuth motor step count and azimuth angle both increase when rotating counterclockwise as seen from above. AZIMUTH angle is measured counterclockwise from the MVACS +X axis direction. (**) As seen from camera head -Y side, camera rotates counterclockwise from its EL hard stop position (ELEVATION motor step 0, ELEVATION angle -94.51 deg for stowed and ELEVATION angle -94.51 deg for deployed) through position when it looks straight down (ELEVATION ANGLE -90 deg) through zero ELEVATION ANGLE position (ELEVATION motor step 170.896 for stowed and ELEVATION motor step 170.896 for deployed) towards its maximum EL motor step position (ELEVATION motor step 332); elevation motor step count and elevation angle both increase when rotating counterclockwise as seen from -Y camera head side (clockwise as seen form +Y camera head side). AZIMUTH and ELEVATION motor step sizes (0.553027 degrees), in radians, and motions speeds, in seconds/step. \begindata INS-116110_AZ_STEP_SIZE = 0.00965214 INS-116110_EL_STEP_SIZE = 0.00965214 INS-116110_EL_SPEED = 0.05 INS-116110_AZ_SPEED = 0.05 \begintext Camera hard stop positions, given in respect to MVACS frame, and ranges in AZIMUTH and ELEVATION. All angles are provided in radians and motor steps. \begindata INS-116110_STWD_AZ_OFFSET_STEPS = -41.58929833 INS-116110_STWD_AZ_OFFSET_ANGLE = -0.40142573 INS-116110_DPLD_AZ_OFFSET_STEPS = -259.13749179 INS-116110_DPLD_AZ_OFFSET_ANGLE = -2.50123135 INS-116110_STWD_EL_OFFSET_STEPS = -170.89585108 INS-116110_STWD_EL_OFFSET_ANGLE = -1.64951068 INS-116110_DPLD_EL_OFFSET_STEPS = -170.89585108 INS-116110_DPLD_EL_OFFSET_ANGLE = -1.64951068 INS-116110_AZ_RANGE_STEPS = 650 INS-116110_AZ_RANGE_ANGLE = 6.27389100 INS-116110_EL_RANGE_STEPS = 332 INS-116110_EL_RANGE_ANGLE = 3.20451048 \begintext Hard stop values that Justin Maki used in computing pointing for the CAHVOR model are a little different. The are provided in the comments below for completeness sake: INS-116110_DPLD_AZ_OFFSET_STEPS = -259.02899771 INS-116110_DPLD_AZ_OFFSET_ANGLE = -2.50018415 INS-116110_DPLD_EL_OFFSET_STEPS = -170.93201508 INS-116110_DPLD_EL_OFFSET_ANGLE = -1.64985974 SSI Internal Geometry -------------------------------------------------------- University Of Arizona Camera Model parameters The UofA model defines the following SSI camera internal geometry parameters: - half stereo separation distance (half baseline), W [meters] - half toe-in angle (positive toward center), GAMMA [radians] - distance from nodal point to elevation axis long optic axis, V [meters] - distance from nodal point to focal plane, H [meters] - pixel spacing, PIXEL_SPACING [meters] - hight of optic axis above elevation axis, G [meters] - boresight elevation error (relative to LEFT telescope), BRST_ERROR [radians] - Scale factor, SCALE_FACTOR [radians/pixel] - absolute image rotation, IMAGE_ROTATION [radians] Set of these parameters is defined for each of two telescopes -- LEFT and RIGHT. The drawing below (camera TOP view) illustrates meaning of some of the quantities: left right boresight boresight | / \ | GAMMAl |<->/ \<->| GAMMAr | / central \ | | / look vector \ | __ _|/ ____________|___________ \|_ __ | |_/_| | |_\_| | | / | \ | | / | \ | | / | \ | ---*------------------o-----------------*------ Vl / Wl Wr \ / Vr \ right nodal o left nodal pt. | o point / |______________________________________| \ \ Hl/ \ / left \ / Hr \ / right focal \ / focal plane \ / plane Actual values obtained as the result of calibration data processing done by University of Arizona SSI Team (half toe-in angles and boresight elevation errors are given for the filter 5, [1]): \begindata INS-116110_LEFT_W = 0.075 INS-116110_LEFT_GAMMA = -0.01719 INS-116110_LEFT_V = 0.0623 INS-116110_LEFT_H = 0.02359 INS-116110_LEFT_PIXEL_SPACING = 0.000023 INS-116110_LEFT_G = 0.012 INS-116110_LEFT_BRST_ERROR = 0.0 INS-116110_LEFT_SCALE_FACTOR = 0.000975 INS-116110_LEFT_IMAGE_ROTATION = 0.00340 INS-116110_RIGHT_W = 0.075 INS-116110_RIGHT_GAMMA = 0.01533 INS-116110_RIGHT_V = 0.0623 INS-116110_RIGHT_H = 0.02359 INS-116110_RIGHT_PIXEL_SPACING = 0.000023 INS-116110_RIGHT_G = 0.012 INS-116110_RIGHT_BRST_ERROR = 0.00270 INS-116110_RIGHT_SCALE_FACTOR = 0.000975 INS-116110_RIGHT_IMAGE_ROTATION = -0.00096 \begintext For the filter 0 the values are (disabled, not-avialble to SPICE readers): INS-116110_LEFT_GAMMA = -0.01749 INS-116110_LEFT_BRST_ERROR = 0.0 INS-116110_LEFT_IMAGE_ROTATION = 0.00333 INS-116110_RIGHT_GAMMA = 0.01611 INS-116110_RIGHT_BRST_ERROR = 0.00148 INS-116110_RIGHT_IMAGE_ROTATION = -0.00123 For the filter 11 the values are (disabled, not-avialble to SPICE readers): INS-116110_LEFT_GAMMA = -0.01798 INS-116110_LEFT_BRST_ERROR = 0.0 INS-116110_LEFT_IMAGE_ROTATION = 0.00333 INS-116110_RIGHT_GAMMA = 0.01490 INS-116110_RIGHT_BRST_ERROR = 0.00215 INS-116110_RIGHT_IMAGE_ROTATION = -0.00123 CAHVOR Camera Model Parameters Parameters below are only a subset of parameters defined the CAHVOR camera model developed at JPL. This subset is sufficient to describe SSI telescopes boresight directions relative to the lander and camera head: - camera focal center location in the lander frame (C); - direction of the symmetry axis of the lens in the lander frame (A); - horizontal pixel coordinate of the intersection of A and FOV (Hc); - vertical pixel coordinate of the intersection of A and FOV (Vc); - "horizontal" focal length (Hs); - "horizontal" focal length (Vs); Values of these parameters for the left and right telescopes are given below: INS-116110_LEFT_CAHV_C = ( -0.466541 -0.189455 -0.015339 ) INS-116110_LEFT_CAHV_A = ( -0.843807 0.368680 0.389955 ) INS-116110_LEFT_CAHV_HC = 127.440445 INS-116110_LEFT_CAHV_VC = 135.833588 INS-116110_LEFT_CAHV_HS = 1019.158081 INS-116110_LEFT_CAHV_VS = 1020.090576 INS-116110_RIGHT_CAHV_C = ( -0.523778 -0.330018 -0.019969 ) INS-116110_RIGHT_CAHV_A = ( -0.835564 0.396039 0.380770 ) INS-116110_RIGHT_CAHV_HC = 131.901886 INS-116110_RIGHT_CAHV_VC = 127.836227 INS-116110_RIGHT_CAHV_HS = 1023.501587 INS-116110_RIGHT_CAHV_VS = 1024.295166 These values were analytically derived by processing of a pair of images of a dotted target. These images were taken when camera head was in the 305 azimuth motor steps and 130 elevation motor steps position. The image size defined in CAHV model was 256 rows by 256 columns with the nominal image center at the row 127.5 and column 127.5. Image upper, left pixel was marked 0,0 with X (the horizontal coordinate) increasing to the right and Y (the vertical coordinate) increasing down. To correlate this model with UofA model set of parameters defined in UofA model had to be derived from the CAHV model. After that derived parameters had to be compared with UofA values. For that the direction A of the CAHV model defined relative to the lander frame was transformed to the camera head frame and adjusted to align with the boresight vectors (from the center of the FOVs though focal points); after that toe-in and boresight error angles similar to those defined in UofA model were computed. The algorithm included the following steps: 1) Compute AZ and EL angles with respect to the MVACS frame from motor step counts for the deployed position of the camera head: AZ = ( AZST + AZHS ) * AZSS + AZBC EL = ( ELST + ELHS ) * ELSS + ELBC (AZST/ELST are motor step counts at which picture was taken; AZHS/ ELHS are motor step counts for AZ/EL hard stop positions, AZSS/ELSS are motor step sizes and AZBC/ELBC are backlash correction values.) 2) Compute transformation combining three rotations, first by 180 degrees about Y (to align LANDER frame with MVACS frame), second Z about axis by computed azimuth and third about Y by negative of computed elevation: M = [ -EL ] * [ AZ ] * [ 180 ] Y Z Y 3) Apply this transformation to A vectors: AL' = M * AL AR' = M * AR 4) Compute toe-in angles in horizontal and vertical planes (in rad): TLH = atan( AL'(2) / AL'(1) ) TRH = atan( AR'(2) / AR'(1) ) TLV = atan( AL'(3) / sqrt( AL'(1)**2 + AL'(2)**2 ) ) TRV = atan( AR'(3) / sqrt( AR'(1)**2 + AR'(2)**2 ) ) 5) Compute pixel horizontal and vertical angular sizes from Hs and Vs: PLH = atan( 1. / HSL ) PLV = atan( 1. / VSL ) PRH = atan( 1. / HSL ) PRV = atan( 1. / VSR ) 6) Apply image center correction to toe-in angles (HCN and VCN are pixel coordinates of the nominal center): TLH' = TLH + ( HCL - HCN ) * PLH TLV' = TLV + ( VCL - VCN ) * PLV TRH' = TRH + ( HCR - HCN ) * PRH TRV' = TRV + ( VCR - VCN ) * PRV UofA model values computed from CAHV model parameters this combination of inputs are: INS-116110_LEFT_GAMMA = -0.02051062 INS-116110_LEFT_BRST_ERROR = 0.01215903 INS-116110_RIGHT_GAMMA = -0.03249310 INS-116110_RIGHT_BRST_ERROR = -0.03031232 Relative directions of the left and right telescopes in UofA and CAHV models: UofA CAHV DIFFERENCE -------- -------- ---------------- ABS(GAMMAL-GAMMAR) 0.032520 0.032670 approx. 0.15 pix ABS(BSERRL-BSERRR) 0.002700 0.002181 approx. 0.53 pix Note that this comparison did NOT account for radial distortion implemented in the CAHVOR model when adjustment of the toe-in angles was done. SSI FOV Geometry -------------------------------------------------------- Both telescopes have CCD arrays of the same size. Few side pixel lines are not used therefore real CCD size is smaller than nominal one (2 pixel lines at the top and 6 pixel lines at the bottom of the 256x256 image were neglected). Pixel dimensions are given in meters. \begindata INS-116110_NOM_PIXEL_SAMPLES = 256 INS-116110_NOM_PIXEL_LINES = 256 INS-116110_PIXEL_SAMPLES = 256 INS-116110_PIXEL_LINES = 248 INS-116110_PIXEL_DIMENSIONS = ( 0.000023 0.000023 ) \begintext There are two different pixel numbering nomenclatures: - IDL System: lower left corner pixel is (0,0), top right corner pixel is (247,255); - MIPL System: top left corner pixel is (1,1), lower right corner pixel is (248,256) Depending on pixel numbering nomenclature coordinates of the look vector origin are (sample,line): \begindata INS-116110_IDL_CCD_CENTER = ( 127.5 123.5 ) INS-116110_MIPL_CCD_CENTER = ( 128.5 124.5 ) \begintext SSI Target Locations. -------------------------------------------------------- SSI Calibration target and fiducial mark locations are provided in the most recent version of the Lander Structures SPK file. Values in this file are given FYI only. From [1]: ID Location Description X, m Y, m Z, m ---- ----------------------- ------ ------- ------ I1 by solar panel mount 0.086 -0.510 0.800 I2 behind solar panel mount 0.289 -0.506 0.800 I3 near center of deck 0.129 -0.075 0.799 I4 near TEGA -0.509 0.160 0.799 Same in keyword assignments (disabled, not-avialble to SPICE readers): INS-116110_FMARK_I1 = ( 0.086 -0.510 0.800 ) INS-116110_FMARK_I2 = ( 0.289 -0.506 0.800 ) INS-116110_FMARK_I3 = ( 0.129 -0.075 0.799 ) INS-116110_FMARK_I4 = ( -0.509 0.160 0.799 ) SSI Camera Head Rotation Backlash Correction Tables -------------------------------------------------------- The four keywords below contain forward and backward motion backlash correction values for the AZIMUTH and ELEVATION angles defining SSI camera head orientation. Forward motion in each angle correspond to increasing motor step count, backward motion to decreasing motor step count. I.e. if camera head moved from position 244 AZ steps and 152 EL steps to 200 AZ steps and 180 EL steps, it moved "backward" in azimuth and "forward" in elevation. Each of the tables contains multiple pairs of numbers. In each pair the first number is motor step counts and the second number is the correction value for the corresponding angle. The correction values are given below as provided in [1] in degrees. The "active" backlash correction tables are the "smoothed" ones from the spreadsheet. The "original" tables are provided at the end in the description section. \begindata INS-116110_EL_BKWD_CORRECTION = ( 328 -0.603671 326 -0.240415 324 -0.226158 322 -0.155260 320 -0.177991 318 -0.244910 316 -0.300599 314 -0.340786 312 -0.358389 310 -0.355362 308 -0.347209 306 -0.344426 304 -0.351653 302 -0.353265 300 -0.350849 298 -0.341841 296 -0.327706 294 -0.311374 292 -0.295774 290 -0.293601 288 -0.295214 286 -0.310131 284 -0.319556 282 -0.332032 280 -0.331447 278 -0.329519 276 -0.323684 274 -0.318461 272 -0.318852 270 -0.322905 268 -0.329644 266 -0.326862 264 -0.322248 262 -0.308601 260 -0.294344 258 -0.273739 256 -0.264731 254 -0.260606 252 -0.266246 250 -0.273718 248 -0.288147 246 -0.298670 244 -0.303944 242 -0.298232 240 -0.280801 238 -0.257023 236 -0.231413 234 -0.215081 232 -0.201922 230 -0.196210 228 -0.189887 226 -0.186983 224 -0.177609 222 -0.173117 220 -0.169480 218 -0.170115 216 -0.166234 214 -0.166870 212 -0.162378 210 -0.167042 208 -0.162673 206 -0.170632 204 -0.164066 202 -0.164213 200 -0.150444 198 -0.150225 196 -0.137188 194 -0.133918 192 -0.126008 190 -0.130916 188 -0.130575 186 -0.129013 184 -0.126597 182 -0.124791 180 -0.117858 178 -0.111413 176 -0.108265 174 -0.112196 172 -0.114296 170 -0.118106 168 -0.119840 166 -0.123283 164 -0.123430 162 -0.123333 160 -0.120673 158 -0.118622 156 -0.116816 154 -0.112447 152 -0.110885 150 -0.112253 148 -0.115452 146 -0.118773 144 -0.120873 142 -0.124805 140 -0.124464 138 -0.124733 136 -0.122194 134 -0.122342 132 -0.120902 130 -0.121904 128 -0.124248 126 -0.130865 124 -0.139435 122 -0.147273 120 -0.154134 118 -0.159774 116 -0.166879 114 -0.175571 112 -0.185972 110 -0.196007 108 -0.202136 106 -0.207532 104 -0.207313 102 -0.210878 100 -0.214321 98 -0.223501 96 -0.228287 94 -0.236125 92 -0.237371 90 -0.237762 88 -0.237543 86 -0.239155 84 -0.243086 82 -0.243844 80 -0.249728 78 -0.249753 76 -0.252220 74 -0.248461 72 -0.254712 70 -0.256079 68 -0.260011 66 -0.258327 64 -0.259573 62 -0.261429 60 -0.262186 58 -0.260258 56 -0.253814 54 -0.243829 52 -0.225055 50 -0.204451 48 -0.184944 46 -0.182162 44 -0.197202 42 -0.231406 40 -0.275377 38 -0.323498 36 -0.357580 34 -0.371155 32 -0.363856 30 -0.352163 28 -0.344741 26 -0.345865 24 -0.354191 22 -0.366057 20 -0.377679 18 -0.383441 16 -0.381391 14 -0.371162 12 -0.355806 10 -0.328732 8 -0.291770 6 -0.239305 4 -0.172679 2 -0.108740 0 0.000000 ) INS-116110_EL_FRWD_CORRECTION = ( 0 0.000000 2 -0.351659 4 -0.413280 6 -0.534226 8 -0.583029 10 -0.588620 12 -0.583223 14 -0.573066 16 -0.560712 18 -0.548724 20 -0.541131 22 -0.533537 24 -0.524845 26 -0.518350 28 -0.520278 30 -0.533925 32 -0.558558 34 -0.589051 36 -0.618811 38 -0.635021 40 -0.639513 42 -0.641074 44 -0.615537 46 -0.560336 48 -0.476204 50 -0.391706 52 -0.301349 54 -0.233697 56 -0.190948 58 -0.184087 60 -0.175761 62 -0.170364 64 -0.163870 66 -0.161037 68 -0.157838 70 -0.156836 72 -0.155835 74 -0.155199 76 -0.154930 78 -0.150632 80 -0.147067 82 -0.141305 84 -0.139205 86 -0.135639 88 -0.135736 90 -0.135101 92 -0.135198 94 -0.134562 96 -0.134659 98 -0.135123 100 -0.133022 102 -0.131288 104 -0.126991 106 -0.123792 108 -0.118029 110 -0.117028 112 -0.114927 114 -0.116855 116 -0.116952 118 -0.119247 120 -0.117879 122 -0.114680 124 -0.108917 126 -0.102056 128 -0.097759 130 -0.094926 132 -0.093924 134 -0.090725 136 -0.087893 138 -0.084328 140 -0.080030 142 -0.075000 144 -0.070702 146 -0.066771 148 -0.063572 150 -0.060007 152 -0.059372 154 -0.058736 156 -0.062129 158 -0.061494 160 -0.063788 162 -0.062786 164 -0.065447 166 -0.062248 168 -0.062345 170 -0.058779 172 -0.058144 174 -0.052015 176 -0.051380 178 -0.049646 180 -0.051574 182 -0.052037 184 -0.055064 186 -0.055161 188 -0.054891 190 -0.054622 192 -0.056184 194 -0.059211 196 -0.065167 198 -0.076250 200 -0.085869 202 -0.095853 204 -0.106204 206 -0.115823 208 -0.122878 210 -0.133595 212 -0.171045 214 -0.232299 216 -0.311864 218 -0.387767 220 -0.460007 222 -0.505148 224 -0.528683 226 -0.532442 228 -0.536567 230 -0.539228 232 -0.541156 234 -0.542717 236 -0.545378 238 -0.552067 240 -0.551797 242 -0.550796 244 -0.547597 246 -0.544764 248 -0.538635 250 -0.539099 252 -0.541393 254 -0.543321 256 -0.544150 258 -0.540951 260 -0.536654 262 -0.529060 264 -0.531355 266 -0.536578 268 -0.546929 270 -0.554351 272 -0.559574 274 -0.550882 276 -0.542556 278 -0.536428 280 -0.536525 282 -0.536622 284 -0.538550 286 -0.535351 288 -0.530321 290 -0.520896 292 -0.510007 294 -0.495456 296 -0.480904 298 -0.468916 300 -0.463520 302 -0.464349 304 -0.472869 306 -0.469304 308 -0.459147 310 -0.447891 312 -0.426016 314 -0.377773 316 -0.306093 318 -0.242835 320 -0.197522 322 -0.201647 324 -0.271690 326 -0.394834 328 -0.601840 ) INS-116110_AZ_BKWD_CORRECTION = ( 644 -1.032811 642 -0.979613 640 -0.951501 638 -0.924305 636 -0.910292 634 -0.901772 632 -0.900393 630 -0.902860 628 -0.903678 626 -0.896806 624 -0.875652 622 -0.830328 620 -0.763032 618 -0.679255 616 -0.613057 614 -0.540267 612 -0.498239 610 -0.483677 608 -0.477904 606 -0.458947 604 -0.463611 602 -0.463880 600 -0.437782 598 -0.425966 596 -0.439419 594 -0.442435 592 -0.433915 590 -0.437480 588 -0.426763 586 -0.390228 584 -0.368525 582 -0.357258 580 -0.351485 578 -0.365487 576 -0.373996 574 -0.361631 572 -0.338280 570 -0.312731 568 -0.281140 566 -0.253394 564 -0.225099 562 -0.194607 560 -0.171805 558 -0.145157 556 -0.121806 554 -0.113835 552 -0.110259 550 -0.126459 548 -0.126728 546 -0.139082 544 -0.161874 542 -0.198398 540 -0.205808 538 -0.228599 536 -0.253038 534 -0.262646 532 -0.262915 530 -0.256043 528 -0.233241 526 -0.208791 524 -0.183243 522 -0.145609 520 -0.114018 518 -0.098357 516 -0.073907 514 -0.048908 512 -0.033796 510 -0.028572 508 -0.025546 506 -0.022519 504 -0.021140 502 -0.018663 500 -0.012890 498 -0.002173 496 0.011291 494 0.009923 492 0.013499 490 0.014329 488 0.021200 486 0.028072 484 0.043733 482 0.046760 480 0.044293 478 0.046221 476 0.038811 474 0.035795 472 0.039921 470 0.050088 468 0.047072 466 0.052846 464 0.059718 462 0.061646 460 0.066320 458 0.072093 456 0.075669 454 0.075400 452 0.077878 450 0.078158 448 0.076790 446 0.078168 444 0.082843 442 0.084222 440 0.084502 438 0.086430 436 0.086161 434 0.083145 432 0.087270 430 0.093593 428 0.096619 426 0.100745 424 0.104870 422 0.113390 420 0.118064 418 0.124387 416 0.127414 414 0.131539 412 0.126326 410 0.125507 408 0.123590 406 0.120574 404 0.119206 402 0.120585 400 0.120316 398 0.120046 396 0.120876 394 0.121156 392 0.116492 390 0.113476 388 0.112658 386 0.112938 384 0.110471 382 0.111850 380 0.111032 378 0.109114 376 0.108296 374 0.106379 372 0.100616 370 0.096502 368 0.095683 366 0.094315 364 0.092398 362 0.091030 360 0.090212 358 0.087745 356 0.084729 354 0.083361 352 0.081444 350 0.077330 348 0.071018 346 0.064706 344 0.059493 342 0.052083 340 0.042475 338 0.035614 336 0.032049 334 0.028484 332 0.028764 330 0.031241 328 0.030423 326 0.027407 324 0.024940 322 0.023023 320 0.021655 318 0.022485 316 0.020568 314 0.018650 312 0.017832 310 0.014816 308 0.006856 306 -0.000554 304 -0.005218 302 -0.007135 300 -0.010700 298 -0.011519 296 -0.011239 294 -0.013705 292 -0.018369 290 -0.020835 288 -0.022753 286 -0.023571 284 -0.022192 282 -0.025758 280 -0.026027 278 -0.027395 276 -0.029861 274 -0.037821 272 -0.040837 270 -0.043303 268 -0.044671 266 -0.048236 264 -0.051252 262 -0.055916 260 -0.061678 258 -0.070737 256 -0.078147 254 -0.081712 252 -0.083629 250 -0.089392 248 -0.088562 246 -0.084986 244 -0.085255 242 -0.088271 240 -0.089090 238 -0.090458 236 -0.095671 234 -0.099785 232 -0.101153 230 -0.102521 228 -0.102790 226 -0.101412 224 -0.102230 222 -0.104697 220 -0.107712 218 -0.109630 216 -0.114293 214 -0.117859 212 -0.122522 210 -0.124989 208 -0.130751 206 -0.133767 204 -0.135684 202 -0.137052 200 -0.137321 198 -0.140887 196 -0.145001 194 -0.145270 192 -0.147737 190 -0.149654 188 -0.152120 186 -0.152390 184 -0.155955 182 -0.154027 180 -0.155944 178 -0.156763 176 -0.157581 174 -0.157850 172 -0.159218 170 -0.161685 168 -0.162503 166 -0.162223 164 -0.164140 162 -0.167156 160 -0.166876 158 -0.168244 156 -0.174556 154 -0.178121 152 -0.179489 150 -0.180857 148 -0.181126 146 -0.183043 144 -0.184960 142 -0.186877 140 -0.187696 138 -0.188515 136 -0.187136 134 -0.182461 132 -0.181632 130 -0.182450 128 -0.182170 126 -0.176946 124 -0.177765 122 -0.180232 120 -0.179951 118 -0.175826 116 -0.172799 114 -0.170871 112 -0.166746 110 -0.163170 108 -0.161242 106 -0.158216 104 -0.152992 102 -0.147218 100 -0.142544 98 -0.138418 96 -0.134842 94 -0.131267 92 -0.128789 90 -0.127960 88 -0.129328 86 -0.133442 84 -0.134261 82 -0.134530 80 -0.137546 78 -0.138364 76 -0.137535 74 -0.136156 72 -0.137524 70 -0.137793 68 -0.138612 66 -0.138881 64 -0.140798 62 -0.139969 60 -0.137492 58 -0.135564 56 -0.134185 54 -0.133905 52 -0.131977 50 -0.127302 48 -0.124825 46 -0.125643 44 -0.127561 42 -0.128928 40 -0.133043 38 -0.138256 36 -0.140722 34 -0.144288 32 -0.145656 30 -0.145925 28 -0.146743 26 -0.148111 24 -0.145085 22 -0.141509 20 -0.139581 18 -0.135455 16 -0.130231 14 -0.122810 12 -0.113741 10 -0.100827 8 -0.082968 6 -0.063462 4 -0.042308 2 -0.023901 0 0.000000 ) INS-116110_AZ_FRWD_CORRECTION = ( 0 0.000000 2 -0.074255 4 -0.107128 6 -0.161790 8 -0.214804 10 -0.279904 12 -0.350496 14 -0.405708 16 -0.458723 18 -0.517230 20 -0.555962 22 -0.575469 24 -0.620243 26 -0.651834 28 -0.658157 30 -0.661733 32 -0.684535 34 -0.700745 36 -0.715857 38 -0.735363 40 -0.761461 42 -0.773826 44 -0.772458 46 -0.779330 48 -0.789498 50 -0.802412 52 -0.821918 54 -0.849115 56 -0.853789 58 -0.858464 60 -0.858195 62 -0.856278 64 -0.853262 66 -0.858486 68 -0.859315 70 -0.861243 72 -0.867566 74 -0.868944 76 -0.877464 78 -0.880491 80 -0.884616 82 -0.887643 84 -0.891219 86 -0.889301 88 -0.889582 90 -0.889862 92 -0.885198 94 -0.883281 96 -0.884110 98 -0.884390 100 -0.884121 102 -0.880556 104 -0.882484 106 -0.879468 108 -0.877551 110 -0.876732 112 -0.880857 114 -0.883884 116 -0.889108 118 -0.893783 120 -0.899007 122 -0.906428 124 -0.911652 126 -0.915228 128 -0.919353 130 -0.919633 132 -0.916068 134 -0.913601 136 -0.914980 138 -0.917457 140 -0.921583 142 -0.925708 144 -0.925439 146 -0.926268 148 -0.924900 150 -0.924082 152 -0.924362 154 -0.924642 156 -0.926021 158 -0.930695 160 -0.932623 162 -0.931805 164 -0.933183 166 -0.931266 168 -0.926602 170 -0.919741 172 -0.914528 174 -0.907118 176 -0.899708 178 -0.892847 180 -0.893127 182 -0.893407 184 -0.895884 186 -0.891770 188 -0.888204 190 -0.891231 192 -0.890413 194 -0.885749 196 -0.885480 198 -0.885760 200 -0.878349 202 -0.876981 204 -0.877261 206 -0.875894 208 -0.874526 210 -0.872608 212 -0.869593 214 -0.862732 216 -0.855871 218 -0.851756 220 -0.845994 222 -0.838583 224 -0.837215 226 -0.837496 228 -0.832832 230 -0.828168 232 -0.825152 234 -0.821038 236 -0.815825 238 -0.807865 240 -0.803201 242 -0.796340 244 -0.788380 246 -0.782618 248 -0.782349 250 -0.780432 252 -0.779613 254 -0.779893 256 -0.782370 258 -0.779904 260 -0.776339 262 -0.772224 264 -0.768110 266 -0.762348 268 -0.761529 270 -0.755767 272 -0.751652 274 -0.745890 276 -0.742874 278 -0.734365 280 -0.730800 282 -0.723389 284 -0.719824 286 -0.714611 288 -0.712694 290 -0.709678 292 -0.710508 294 -0.711886 296 -0.709969 298 -0.708601 300 -0.711079 302 -0.713007 304 -0.711089 306 -0.708074 308 -0.708903 310 -0.705338 312 -0.701773 314 -0.698757 316 -0.697938 318 -0.692176 320 -0.692456 322 -0.688341 324 -0.682030 326 -0.674619 328 -0.671054 330 -0.666940 332 -0.669417 334 -0.672993 336 -0.677668 338 -0.679596 340 -0.680974 342 -0.681255 344 -0.684830 346 -0.686209 348 -0.684841 350 -0.682924 352 -0.681556 354 -0.674695 356 -0.670581 358 -0.670861 360 -0.671141 362 -0.667576 364 -0.666757 366 -0.664840 368 -0.659627 370 -0.653865 372 -0.649750 374 -0.644537 376 -0.642620 378 -0.642351 380 -0.640983 382 -0.636319 384 -0.636599 386 -0.636330 388 -0.634962 390 -0.633594 392 -0.634973 394 -0.635253 396 -0.635533 398 -0.637461 400 -0.637741 402 -0.639120 404 -0.636104 406 -0.631989 408 -0.626227 410 -0.617718 412 -0.610857 414 -0.602348 416 -0.594938 418 -0.588626 420 -0.587807 422 -0.584242 424 -0.584522 426 -0.587000 428 -0.592223 430 -0.595799 432 -0.599925 434 -0.604599 436 -0.603781 438 -0.605159 440 -0.608735 442 -0.612311 444 -0.615338 446 -0.621111 448 -0.622490 450 -0.622770 452 -0.621402 454 -0.622232 456 -0.619765 458 -0.617848 460 -0.618677 462 -0.620056 464 -0.619237 466 -0.622264 468 -0.626939 470 -0.629416 472 -0.637936 474 -0.646456 476 -0.654426 478 -0.659650 480 -0.665973 482 -0.670098 484 -0.678618 486 -0.689335 488 -0.698404 490 -0.706924 492 -0.714894 494 -0.722865 496 -0.723145 498 -0.726172 500 -0.730846 502 -0.732225 504 -0.733604 506 -0.740475 508 -0.746798 510 -0.748726 512 -0.756147 514 -0.762470 516 -0.769342 518 -0.777312 520 -0.784733 522 -0.789408 524 -0.793533 526 -0.800405 528 -0.807826 530 -0.816346 532 -0.824317 534 -0.831189 536 -0.834764 538 -0.839439 540 -0.841916 542 -0.841647 544 -0.841378 546 -0.844405 548 -0.845234 550 -0.842767 552 -0.840301 554 -0.838384 556 -0.832072 558 -0.828507 560 -0.836477 562 -0.838405 564 -0.832094 566 -0.830177 568 -0.829907 570 -0.829638 572 -0.832115 574 -0.847776 576 -0.857395 578 -0.862619 580 -0.862349 582 -0.868672 584 -0.867304 586 -0.867035 588 -0.868963 590 -0.871440 592 -0.870622 594 -0.872000 596 -0.878872 598 -0.879152 600 -0.882728 602 -0.892896 604 -0.900867 606 -0.902795 608 -0.910216 610 -0.915989 612 -0.921213 614 -0.930831 616 -0.942098 618 -0.951716 620 -0.960236 622 -0.966009 624 -0.971783 626 -0.974809 628 -0.977287 630 -0.978116 632 -0.979495 634 -0.983620 636 -0.990492 638 -0.999561 640 -1.011377 642 -1.021728 644 -1.032811 ) \begintext These are "original" (non-smoothed) backlash correction tables for AZ. INS-116110_AZ_BKWD_CORRECTION = ( 644 -1.038304 642 -0.962218 640 -0.938318 638 -0.917164 636 -0.901503 634 -0.902321 632 -0.892153 630 -0.895718 628 -0.910270 626 -0.913835 624 -0.906414 622 -0.857794 620 -0.789948 618 -0.683650 616 -0.577352 614 -0.487533 612 -0.526804 610 -0.425999 608 -0.473509 606 -0.504540 604 -0.458667 602 -0.432020 600 -0.449318 598 -0.474855 596 -0.374050 594 -0.399588 592 -0.499284 590 -0.464397 588 -0.432256 586 -0.391876 584 -0.346003 582 -0.316609 580 -0.355880 578 -0.375924 576 -0.363010 574 -0.416014 572 -0.359154 570 -0.294055 568 -0.259168 566 -0.235267 564 -0.258058 562 -0.220424 560 -0.152578 558 -0.106705 556 -0.121257 554 -0.124822 552 -0.103668 550 -0.112726 548 -0.088825 546 -0.202254 544 -0.126168 542 -0.165439 540 -0.226682 538 -0.271446 536 -0.239305 534 -0.240124 532 -0.287635 530 -0.274720 528 -0.272792 526 -0.204946 524 -0.126114 522 -0.165385 520 -0.146977 518 -0.084624 516 -0.046991 514 -0.047809 512 -0.043135 510 -0.021980 508 -0.009066 506 -0.020871 504 -0.032676 502 -0.028001 500 -0.015087 498 0.003321 496 0.007995 494 0.020910 492 0.039317 490 -0.021926 488 0.021200 486 0.012142 484 0.055269 482 0.073676 480 0.056378 478 0.036334 476 -0.000190 474 0.064909 472 0.036625 470 0.041299 468 0.056960 466 0.050648 464 0.049830 462 0.065491 460 0.075659 458 0.066600 456 0.074021 454 0.078696 452 0.083371 450 0.074312 448 0.078987 446 0.075422 444 0.071857 442 0.090264 440 0.097685 438 0.085881 436 0.076822 434 0.081497 432 0.088918 430 0.082606 428 0.106507 426 0.108435 424 0.096630 422 0.109544 420 0.103233 418 0.149106 416 0.131808 414 0.128243 412 0.124678 410 0.123859 408 0.123041 406 0.127715 404 0.118657 402 0.109599 400 0.117020 398 0.129934 396 0.126369 394 0.117311 392 0.113746 390 0.118420 388 0.106615 386 0.111290 384 0.113218 382 0.115146 380 0.106088 378 0.113509 376 0.107197 374 0.103632 372 0.111053 370 0.096502 368 0.084697 366 0.086625 364 0.099539 362 0.104214 360 0.086916 358 0.077857 356 0.082532 354 0.087207 352 0.089135 350 0.080076 348 0.068271 346 0.061960 344 0.055648 342 0.057576 340 0.054011 338 0.031220 336 0.013922 334 0.021343 332 0.039750 330 0.036185 328 0.032620 326 0.026308 324 0.017250 322 0.024671 320 0.023853 318 0.023034 316 0.019469 314 0.021397 312 0.015085 310 0.014267 308 0.018941 306 0.004390 304 -0.018401 302 -0.021967 300 -0.009052 298 0.009355 296 -0.013436 294 -0.022494 292 -0.020566 290 -0.021385 288 -0.013964 286 -0.025768 284 -0.032080 282 -0.024659 280 -0.014491 278 -0.031789 276 -0.027115 274 -0.038919 272 -0.036991 270 -0.054290 268 -0.046868 266 -0.039447 264 -0.045759 262 -0.054817 260 -0.069369 258 -0.070187 256 -0.068259 254 -0.091050 252 -0.091869 250 -0.087194 248 -0.079773 246 -0.097071 244 -0.086903 242 -0.073989 240 -0.088541 238 -0.094852 236 -0.101164 234 -0.093743 232 -0.100055 230 -0.109113 228 -0.101692 226 -0.108003 224 -0.095089 222 -0.093161 220 -0.113206 218 -0.114024 216 -0.123082 214 -0.104675 212 -0.116480 210 -0.131031 208 -0.137343 206 -0.135415 204 -0.133487 202 -0.131559 200 -0.140617 198 -0.144182 196 -0.136761 194 -0.151313 192 -0.152131 190 -0.141963 188 -0.156515 186 -0.146347 184 -0.163645 182 -0.153477 180 -0.159789 178 -0.146875 176 -0.155933 174 -0.167738 172 -0.157570 170 -0.161135 168 -0.153714 166 -0.168266 164 -0.171831 162 -0.156170 160 -0.170721 158 -0.168793 156 -0.166865 154 -0.178670 152 -0.187729 150 -0.188547 148 -0.175633 146 -0.173705 144 -0.180016 142 -0.197314 140 -0.198133 138 -0.185219 136 -0.177797 134 -0.184109 132 -0.190421 130 -0.174760 128 -0.181072 126 -0.181890 124 -0.182709 122 -0.164301 120 -0.178853 118 -0.193404 116 -0.180490 114 -0.162082 112 -0.149168 110 -0.169213 108 -0.172778 106 -0.162610 104 -0.152442 102 -0.134035 100 -0.143093 98 -0.143912 96 -0.139237 94 -0.131816 92 -0.116155 90 -0.125213 88 -0.131525 86 -0.135090 84 -0.138655 82 -0.136727 80 -0.129306 78 -0.132871 76 -0.150169 74 -0.142748 72 -0.132580 70 -0.122412 68 -0.139711 66 -0.151515 64 -0.146841 62 -0.133926 60 -0.131998 58 -0.135564 56 -0.139129 54 -0.137201 52 -0.127033 50 -0.130598 48 -0.125923 46 -0.115756 44 -0.124814 42 -0.131126 40 -0.140184 38 -0.132763 36 -0.136328 34 -0.150879 32 -0.143458 30 -0.158010 28 -0.139602 26 -0.137674 24 -0.154972 22 -0.150298 20 -0.142876 18 -0.121722 16 -0.128034 14 -0.134346 12 -0.124178 10 -0.105770 8 -0.076377 6 -0.063462 4 -0.045055 2 -0.026647 0 0.000000 ) INS-116110_AZ_FRWD_CORRECTION = ( 0 0.000000 2 -0.100805 4 -0.121959 6 -0.145860 8 -0.167014 10 -0.273312 12 -0.365877 14 -0.447456 16 -0.498823 18 -0.443072 20 -0.538384 22 -0.658415 24 -0.641117 26 -0.596353 28 -0.666946 30 -0.696340 32 -0.690028 34 -0.658997 36 -0.710364 38 -0.747997 40 -0.771898 42 -0.787559 44 -0.789487 46 -0.772189 48 -0.741158 50 -0.806257 52 -0.838398 54 -0.854059 56 -0.869720 58 -0.877141 60 -0.829630 62 -0.861771 64 -0.852712 66 -0.860134 68 -0.862062 70 -0.855750 72 -0.865918 74 -0.862352 76 -0.891746 78 -0.868955 80 -0.898349 82 -0.881051 84 -0.882979 86 -0.906880 88 -0.886835 90 -0.888763 92 -0.882451 94 -0.884379 96 -0.883561 98 -0.877249 100 -0.892910 102 -0.883852 104 -0.883033 106 -0.865735 108 -0.886889 110 -0.877831 112 -0.874266 114 -0.878940 116 -0.886361 118 -0.902022 120 -0.903950 122 -0.897639 124 -0.905060 126 -0.923467 128 -0.928142 130 -0.921830 132 -0.918265 134 -0.906460 136 -0.905642 138 -0.915809 140 -0.928724 142 -0.930652 144 -0.927087 146 -0.926268 148 -0.914463 150 -0.932871 152 -0.923812 154 -0.922994 156 -0.927669 158 -0.915864 160 -0.939764 162 -0.947186 164 -0.932634 166 -0.923576 168 -0.922757 170 -0.930178 172 -0.923867 174 -0.898329 176 -0.897510 178 -0.885705 180 -0.893127 182 -0.889561 184 -0.899729 186 -0.898911 188 -0.898092 190 -0.872554 192 -0.871736 194 -0.914863 196 -0.894818 198 -0.874773 200 -0.871208 202 -0.873136 204 -0.877811 206 -0.887979 208 -0.876174 210 -0.864369 212 -0.866297 214 -0.868225 216 -0.872899 218 -0.841868 220 -0.830064 222 -0.845724 224 -0.839413 226 -0.835848 228 -0.835029 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