PDS_VERSION_ID                = PDS3                                          
RECORD_TYPE                   = STREAM                                        
OBJECT                        = TEXT                                          
  PUBLICATION_DATE            = 2016-04-22                                    
  DESCRIPTION                 = "                                             
  This file is intended as documentation of the Field(s) Of View (FOV(s))     
  for the detectors and/or slits and/or apertures comprising the instrument   
  on the New Horizons (NH) spacecraft that generated the data archived in     
  this data set.                                                              
                                                                              
  This file is a NH Project LORRI SPICE Instrument Kernel (IK),               
  current at the time of delivery of this data set, with an attached PDS      
  label prepended.  It is only provided as a convenience to the user          
  to visualize the FOVs of the instrument.  This file will not be updated     
  in this PDS data set as part of any SPICE kernel updates, and should        
  therefore not be used as a SPICE kernel in any scientific investigation.    
                                                                              
  Specifically, the references in the IK are not relevant to the graphic      
  visualization of the FOV and will not be provided with this data set or     
  archived elsewhere; therefore the references should be ignored in the       
  context of the intended scope of this file as described above.              
                                                                              
  As a SPICE IK, this file has much more information than just the            
  FOV description (e.g. references to project documentation), but in the      
  context of this PDS data set only the FOV description is relevant.  For     
  a more complete understanding of the geometry and timing issues of the      
  New Horizons mission, the user is directed to the SPICE PDS data set        
  for the mission, with a data set ID of NH-J/P/SS-SPICE-6-V1.0.              
                                                                              
  See further caveats in the PDS NOTE field of this document.                 
  "                                                                           
                                                                              
  NOTE                        = "                                             
  See also the PDS DESCRIPTION field of this document.                        
                                                                              
  CAVEATS:                                                                    
                                                                              
  This file is the NH LORRI SPICE Instrument Kernel (IK),                     
  current at the time of delivery of this data set, with an attached PDS      
  label prepended.  It is only provided as a convenience to the user          
  to visualize the FOVs of the instrument.  This file will not be updated     
  in this PDS data set as part of any SPICE kernel updates, and should        
  therefore not be used as a SPICE kernel in any scientific investigation.    
                                                                              
  Specifically, the references in the IK are not relevant to the graphic      
  visualization of the FOV and will not be provided with this data set;       
  therefore the references should be ignored in the context of this file.     
                                                                              
  If the user wishes to do any data analysis requiring NAIF/SPICE IKs,        
  they should not use this file, but rather get the most recent IK from       
  the NH SPICE data set and use that.                                         
                                                                              
  - This file is included in the /DOCUMENT/ directory of most if not          
    all volumes for this instrument as a convenience to the user              
    because, in some of its sections, it documents the geometry of the        
    LORRI instrument Field(s) Of View (FOV(s)).  Other sections of            
    this IK (e.g. the references) will have limited use in that scope.        
                                                                              
  - The original name of the source of this file was                          
                                                                              
      NH_LORRI_V###.TI                                                        
                                                                              
    where ### is a version number.                                            
                                                                              
  - The format of this file, starting five lines after this                   
    TEXT OBJECT, is a SPICE Kernel Pool text file                             
                                                                              
    - The Instrument Kernel itself is (or will be) formally archived          
      with the New Horizons SPICE dataset.                                    
                                                                              
    - See the SPICE documentation for details of that format                  
                                                                              
      - http://naif.jpl.nasa.gov/                                             
                                                                              
    - Even without understanding that format, the Instrument Kernel,          
      and especially its comments, are human readable.  Comments are          
      any line for which one of the following three statements is true:       
                                                                              
      1) The line is before the first data marker line in the file            
      2) The line is in a section of lines between a text marker line and     
         a data marker line with no intervening text or data marker lines     
      3) The line is in a section of lines between the last text marker and   
         the end of the file with no intervening text or data marker lines    
                                                                              
      - a data marker line has the single token '\begindata' on it with       
        all other characters on the line being whitespace                     
                                                                              
      - a text marker line has the single token '\begintext' on it with       
        all other characters on the line being whitespace                     
                                                                              
    - N.B. Because padding and a carriage return have been added to           
           each line of this file, it may or may not be functional            
           as a valid SPICE kernel.                                           
"                                                                             
END_OBJECT                    = TEXT                                          
END                                                                           
########################################################################      
##################### SPICE IK Starts after next line ##################      
########################################################################      
KPL/IK                                                                        
                                                                              
                                                                              
LORRI Instrument Kernel                                                       
==============================================================================
                                                                              
   This instrument kernel (I-kernel) contains references to the mounting      
   alignment, internal and FOV geometry for the New Horizons LOng Range       
   Reconnaissance Imager (LORRI).                                             
                                                                              
                                                                              
Version and Date                                                              
----------------------------------------------------------                    
                                                                              
   The TEXT_KERNEL_ID stores version information of loaded project text       
   kernels. Each entry associated with the keyword is a string that consists  
   of four parts: the kernel name, version, entry date, and type. For example,
   the LORRI I-kernel might have an entry as follows:                         
                                                                              
         TEXT_KERNEL_ID += 'NEWHORIZONS_LORRI V2.0.1 01-MAR-2016 IK'          
                                    |           |         |       |           
                                    |           |         |       |           
                KERNEL NAME <-------+           |         |       |           
                                                |         |       V           
                                VERSION <-------+         |      KERNEL TYPE  
                                                          |                   
                                                          V                   
                                                     ENTRY DATE               
                                                                              
   LORRI I-Kernel Version:                                                    
                                                                              
           \begindata                                                         
                                                                              
           TEXT_KERNEL_ID += 'NEWHORIZONS_LORRI V2.0.1 01-MAR-2016 IK'        
                                                                              
           NAIF_BODY_NAME += ( 'NH_LORRI' )                                   
           NAIF_BODY_CODE += ( -98300 )                                       
                                                                              
           NAIF_BODY_NAME += ( 'NH_LORRI_1X1' )                               
           NAIF_BODY_CODE += ( -98301 )                                       
                                                                              
           NAIF_BODY_NAME += ( 'NH_LORRI_4X4' )                               
           NAIF_BODY_CODE += ( -98302 )                                       
                                                                              
           \begintext                                                         
                                                                              
   Version 2.0.1 -- March 1, 2016 -- Howard Taylor, JHU/APL                   
                                                                              
            --   Added discussion on adapting coefficients of the OOC         
                 distortion model (Ky and EM5) to comply with the LORRI       
                 instrument frame.                                            
            --   Changed the pixel size to the measured value rather          
                 than the assumed value. This affected values for the         
                 focal length, f-number, and coefficients in both the         
                 OOC and SIP distortion models [15].                          
            --   Changed the sense of the sign of two coefficients            
                 ( Ky, EM5) in the Owen and O'Connell distortion model        
                 due to differences in the direction of the +Y-axis used      
                 in the published model compared to the LORRI instrument      
                 frame.                                                       
            --   Fixed values for INS-9830X_OOC_EM_SIGMA.  The exponent       
                 had been omitted unintentionally.                            
            --   Added keywords INS-9830X_APERTURE_DIAM_UNITS                 
            --   changed the reference for the INS*_OOC_CCD_CENTER keywords   
                 from unit reference to zero reference pixel values.          
            --   Text updated in Optical Distortion model section that        
                 incorrectly described the detector size to include the       
                 dark columns.                                                
            --   Removed references to pixel pitch for consistency,           
                 replacing with equivalent term:  pixel size.                 
            --   Clarified representation of mathematical equations           
                 in the SIP distortion section.                               
            --   Added section relating Owen & O'Connell model to the         
                 SIP reverse transform.                                       
            --   Updated plate scale (IFOV) values based on updated           
                 estimate for focal length.                                   
                                                                              
   Version 2.0.0 -- August 18, 2015 -- Howard Taylor, JHU/APL                 
                                                                              
            --   Redefined the units of two keywords to maintain              
                 internal consistency and to make them consistent with        
                 the Owen and O'Connell distortion model.  The units on       
                 the FOCAL_LENGTH keyword were changed from m to mm. The      
                 units of the APERTURE_DIAMETER keyword were changed          
                 from cm to mm.                                               
            --   Added distortion model coefficients for OOC and SIP          
                 distortion models.                                           
            --   Fixed begin data and begin text tags in platform id section. 
                                                                              
   Version 1.0.0 -- February 21, 2007 -- Lillian Nguyen, JHU/APL              
                                                                              
            --   Updated the diagrams to match those in the frames kernel,    
                 nh.tf.                                                       
            --   Promoting to version 1.0.0 denoting approval of kernel set   
                 by instrument teams.                                         
                                                                              
   Version 0.0.3 -- January 4, 2007 -- Lillian Nguyen, JHU/APL                
                                                                              
            --   Added field of view information for the 1x1 and 4x4 binning  
                 modes.                                                       
            --   Added optical and CCD geometry parameters, and reference     
                 vector.                                                      
                                                                              
   Version 0.0.2 -- October 4, 2006 -- Lillian Nguyen, JHU/APL                
                                                                              
            --   Removed the 3-letter frame NH_LOR.                           
                                                                              
   Version 0.0.1 -- January 25, 2006 -- Lillian Nguyen                        
                                                                              
            --   Frame definition and frame diagram modified after            
                 review by instrument team.                                   
                                                                              
   Version 0.0.0 -- January 5, 2006 -- Lillian Nguyen                         
                                                                              
            --   Draft Version. NOT YET APPROVED BY INSTRUMENT TEAM.          
                                                                              
                                                                              
References                                                                    
----------------------------------------------------------                    
                                                                              
            1.   LOng-Range Reconnaissance Imager (LORRI) Specification       
                 Document, 7400-9000 Rev A.                                   
                                                                              
            2. ``Kernel Pool Required Reading''                               
                                                                              
            3.   Spacecraft to LORRI Interface Control Document (ICD),        
                 7399-9048, Rev B.                                            
                                                                              
            4.   APL New Horizons web site,                                   
                 http://pluto.jhuapl.edu/spacecraft/overview.html.            
                                                                              
            5.   New Horizons Spacecraft Frames Kernel.                       
                                                                              
            6.   New Horizons Mission Science Definitions (MSD),              
                 NH7399-9000v1.6.                                             
                                                                              
            7.   LOng-Range Reconnaissance Imager (LORRI) User's Manual,      
                 7400-9601, dated Jan. 10, 2006.                              
                                                                              
            8.   LORRI_orientation_1-9-06, received on 1/23/2006 by e-mail    
                 from Hal Weaver along with a description of the LORRI frame  
                 relative to the spacecraft frame. Also a phone conversation  
                 with Hal clarifying the diagrams in the document.            
                                                                              
            9.   Discussions with Howard Taylor regarding LORRI instrument    
                 frame definition and LORRI keywords, 12/21/2006.             
                                                                              
           10.   Response to LORRI OpNav action items, forwarded in an e-mail 
                 from Howard Taylor on 12/21/2006.                            
                                                                              
           11.   Owen, Jr., W. M. and O'Connell, D., "New Horizons LORRI      
                 Geometric Calibration of August 2006", JPL Interoffice       
                 Memorandum 343L-11-002, 06/08/2011                           
                                                                              
           12.   Email exchange between Bill Owen and Hal Weaver containing   
                 updated distortion coefficients of [11] using ACO-7 Wishing  
                 Well data, 04/16/2015.                                       
                                                                              
           13.   Shupe, David L, et. al. "The SIP Convention for Representing 
                 Distortion in FITS Image Headers", Astronomical Data Analysis
                 Software and Systems XIV, ASP Conference, Vol 347, 2005,     
                 P. L. Shopbell, M. C. Britton, and R. Ebert, eds.            
                                                                              
           14.   Analysis results from Brian Carcich for Hal Weaver, which    
                 derived SIP coefficients from Bill Owen's latest model       
                 coefficients on 04/16/2015 at                                
                 https://www.spaceops.swri.org/~brian/for_hal/sip             
                                                                              
           15.   Email exchange between Bill Owen and Hal Weaver detailing    
                 how to scale his published coefficients for the updated      
                 pixel size. 01/27/2016                                       
                                                                              
Contact Information                                                           
----------------------------------------------------------                    
                                                                              
   Lillian Nguyen, JHU/APL, (443)-778-5477, Lillian.Nguyen@jhuapl.edu         
   Howard Taylor, JHU/APL, (443)-778-5682, Howard.Taylor@jhuapl.edu           
   Brian Carcich, Latchmoor Services LLC, Williamsburg, VA, USA               
                                                                              
                                                                              
Implementation Notes                                                          
----------------------------------------------------------                    
                                                                              
   This file is used by the SPICE system as follows: programs that make use of
   this instrument kernel must ``load'' the kernel, normally during program   
   initialization. Loading the kernel associates data items with their names  
   in a data structure called the ``kernel pool''. The SPICELIB routine       
FURNSH,                                                                       
   CSPICE routine furnsh_c, and IDL routine cspice_furnsh load SPICE kernels  
   as shown below:                                                            
                                                                              
   FORTRAN (SPICELIB)                                                         
                                                                              
           CALL FURNSH ( 'kernel_name' )                                      
                                                                              
   C (CSPICE)                                                                 
                                                                              
           furnsh_c ( "kernel_name" )                                         
                                                                              
   ICY (IDL)                                                                  
                                                                              
           cspice_furnsh, 'kernel_name'                                       
                                                                              
   In order for a program or subroutine to extract data from the pool, the    
   SPICELIB routines GDPOOL, GCPOOL, and GIPOOL are used. See [2] for details.
                                                                              
   This file was created and may 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 New Horizons spacecraft ID number (-98)         
   followed by a NAIF three digit ID code for the LORRI instrument.           
                                                                              
   The remainder of the name is an underscore character followed by the unique
   name of the data item. For example, the LORRI boresight direction in the   
   LORRI frame (``NH_LORRI'' -- see [5] ) is specified by:                    
                                                                              
           INS-98300_BORESIGHT                                                
                                                                              
   The upper bound on the length of the name of any data item is 32           
   characters.                                                                
                                                                              
   If the same item is included in more than one file, or if the same item    
   appears more than once within a single file, the latest value supersedes   
   any earlier values.                                                        
                                                                              
                                                                              
LORRI description                                                             
----------------------------------------------------------                    
                                                                              
   From [4]:                                                                  
                                                                              
   ``The instrument that provides the highest spatial resolution on New       
   Horizons is LORRI - short for Long Range Reconnaissance Imager - which     
   consists of a telescope with a 8.2-inch (20.8-centimeter) aperture that    
   focuses visible light onto a charge coupled device (CCD). LORRI has a      
   very simple design; there are no filters or moving parts. Near the time    
   of closest approach, LORRI will take images of Pluto's surface at          
   football-field sized resolution, resolving features approximately 100      
   yards or 100 meters across.''                                              
                                                                              
   From [1]:                                                                  
                                                                              
   ``The Long Range Reconnaissance Imager, LORRI, is a modest aperture        
   (200 mm), narrow-angle camera capable of producing high-resolution         
   imagery.  The LORRI will provide imagery of Pluto-Charon, beginning 90     
   days prior to encounter. From 75 days regarding before closest approach,   
   LORRI will provide resolution of Pluto beyond that achievable using HST.   
     .                                                                        
     .                                                                        
     .                                                                        
   LORRI imager consists of a 208 mm aperture Ritchey-Chretien telescope      
   made of silicon carbide.  The telescope is f/12.75, and feeds an           
   unfiltered, 1024 x 1024 frame transfer CCD.  The effective band-pass is    
   primarily limited by the CCD response to 350 to 850 nm.  There is a long   
   composite baffle running the length of the instrument, and smaller         
   baffles at the outside of the secondary and inside of the primary.  The    
   assembly is mounted to the spacecraft via 3 titanium legs.                 
     .                                                                        
     .                                                                        
     .                                                                        
   LORRI operations consist of imaging at Jupiter, Pluto/Charon, and one to   
   three Kuiper Belt Objects.  Additionally, various calibration images and   
   functional tests will be performed.''                                      
                                                                              
   From [3]:                                                                  
                                                                              
   ``The LOng Range Reconnaissance Imager (LORRI) is intended to complement   
   the PERSI/MVIC wide angle, medium resolution imagers.  LORRI is            
   controlled independently of PERSI/MVIC. It will provide higher resolution  
   imagery with a much narrower field-of-view and contributes a measure of    
   redundancy to the mission.  Its boresight is aligned to within 0.1 deg of  
   PERSI/MVIC to support coordinated operations when operated in their        
   "framing mode".  The long-range capability of LORRI will permit the        
   receipt of high-resolution observations of Pluto-Charon at least 75 days   
   before their encounter and of the Kuiper-Belt Objects (KBOs).              
     .                                                                        
     .                                                                        
     .                                                                        
   LORRI is a panchromatic visible imager with an angular resolution of 5     
   microrad/pixel and a field-of-view (FOV) of 0.2912 deg x 0.2912 deg.  It   
   consists of a 20-cm aperture, f/13 telescope imaging onto a CCD focal      
   plane. The combined mass of the telescope structure, mirrors, supporting   
   electronics, and aperture door is 8.593 Kg.  To reduce unwanted stray      
   light, the telescope is heavily baffled.  LORRI is fixed mounted inside    
   the spacecraft structure within a baffle tube protruding through the       
   spacecraft structure.  An aperture door provides contamination protection  
   during ground operation, launch, and early cruise.''                       
                                                                              
                                                                              
LORRI Frame                                                                   
----------------------------------------------------------                    
                                                                              
   The following diagrams are reproduced from [8] and [9].                    
                                                                              
   When viewed by an observer looking out LORRI's boresight, the spacecraft   
   axes on the sky will look like:                                            
                                                                              
   Diagram 1                                                                  
   ---------                                                                  
                  Sky View Looking out from LORRI                             
                 _________________________________                            
                |                                 |                           
                |                                 |                           
                |                ^ +Y             |                           
                |                |   sc           |                           
                |                |                |                           
                |                |                |                           
                |                |                |                           
                |       <--------o                |                           
                |     +Z           +X  (out)      |                           
                |       sc           sc           |                           
                |                                 |                           
                |                                 |                           
                |                                 |                           
                |                                 |                           
                |_________________________________|                           
                                                                              
                                                                              
   The LORRI optics inverts images in both the Y and Z directions, so that the
   projection of these spacecraft axes onto the LORRI CCD will look like the  
   following: (Note that we are looking INTO the LORRI telescope in the       
   diagram below, whereas above we were looking outwards, hence the position  
   of the +Z axis does not appear to have changed when in fact it has         
flipped).                                                                     
                                                                              
   Diagram 2                                                                  
   ---------                                                                  
                   Looking in at the LORRI CCD                                
                 _________________________________                            
                |                                 |       Spacecraft Axes     
                |                                 |                           
                |                                 |              ^ +Y         
                |                                 |              |   sc       
  increasing  ^ |                                 |              |            
   columns    | |                   p             |              x-----> +Z   
              | |    p            +X  (in)        |        +X (in)         sc 
              | |  +Z  <---------x  sc            |          sc               
              | |    sc          |                |                           
              | |                |                |                           
              | |                |                |                           
              | |                |    p           |                           
              | |                V  +Y            |                           
              | |                     sc          |                           
                O_________________________________|                           
                 ------------------------>                                    
          [0,0]=[column, row]            increasing rows                      
                                                                              
                                                 p       p                    
   Note that in Diagram 2, the axes are labeled Z   and Y   to clarify        
                                                 sc      sc                   
   that although these are still spacecraft coordinates, they are the         
   projections of the spacecraft axes from Diagram 1 onto the LORRI CCD, not  
   the actual spacecraft axes. The actual spacecraft axes are depicted to the 
   right of Diagram 2. The origin in the CCD view is at the bottom left, and  
   the CCD storage area and serial register are to the left.                  
                                                                              
   The LORRI IDL display further inverts the image in Diagram 2 about the     
   diagonal originating at [0,0]:                                             
                                                                              
   Diagram 3                                                                  
   ---------                                                                  
                        LORRI IDL Display                                     
                 _________________________________                            
                |                                 |       Spacecraft Axes     
                |                                 |                           
                |                                 |              ^ +Z         
                |                                 |              |   sc       
  increasing  ^ |                                 |              |            
        rows  | |                    p            |              o-----> +Y   
              | |    p             +X  (out)      |        +X (out)        sc 
              | |  +Y  <---------x   sc           |          sc               
              | |    sc          |                |                           
              | |                |                |                           
              | |                |                |                           
              | |                |    p           |                           
              | |                V  +Z            |                           
              | |                     sc          |                           
                O_________________________________|                           
                 ------------------------>                                    
          [0,0]=[column, row]            increasing columns                   
                                                                              
                                                                              
                                                                              
   Also provided here are the same set of three diagrams using the LORRI      
   instrument axes, X , Y , Z , rather than the spacecraft axes.              
                     L   L   L                                                
                                                                              
   Diagram 1a                                                                 
   ----------                                                                 
                  Sky View Looking out from LORRI                             
                 _________________________________                            
                |                                 |                           
                |                                 |      Spacecraft Axes      
                |                                 |                           
                |                                 |             ^ +Y          
                |                                 |             |   sc        
                |                                 |             |             
                |                                 |       <-----o             
                |                o--------->      |      +Z      +X  (out)    
                |                |          Y     |        sc      sc         
                |                |           L    |                           
                |                |                |                           
                |                |                |                           
                |                V X              |                           
                |                   L             |                           
                |_________________________________|                           
                                                                              
                                                                              
   Diagram 2a                                                                 
   ----------                                                                 
                   Looking in at the LORRI CCD                                
                 _________________________________                            
                |                                 |                           
                |                   p             |                           
                |                ^ X              |                           
                |                |  L             |                           
  increasing  ^ |                |                |                           
   columns    | |                |                |                           
              | |                |                |                           
              | |                x---------> p    |                           
              | |                           Y     |                           
              | |                            L    |                           
              | |                                 |                           
              | |                                 |                           
              | |                                 |                           
              | |                                 |                           
                O_________________________________|                           
                 ------------------------>                                    
          [0,0]=[column, row]            increasing rows                      
                                                                              
   As in Diagram 2, the axes in Diagram 2a are the projections of the LORRI   
   instrument axes through the optics onto the LORRI CCD.                     
                                                                              
   Diagram 3a                                                                 
   ---------                                                                  
                        LORRI IDL Display                                     
                 _________________________________                            
                |                                 |                           
                |                   p             |                           
                |                ^ Y              |                           
                |                |  L             |                           
  increasing  ^ |                |                |                           
        rows  | |                |                |                           
              | |                |                |                           
              | |            p   o---------> p    |                           
              | |           Z (out)         X     |                           
              | |            L               L    |                           
              | |                                 |                           
              | |                                 |                           
              | |                                 |                           
              | |                                 |                           
                O_________________________________|                           
                 ------------------------>                                    
          [0,0]=[column, row]            increasing columns                   
                                                                              
                                                                              
   Taken from [9], we have the following coordinate system definition for the 
   LORRI frame:                                                               
                                                                              
   The -Z axis in instrument coordinates is defined to be the boresight and   
   is approximately aligned with the spacecraft -X axis. The Y axis in        
   instrument coordinates is approximately aligned with the spacecraft -Z axis
   and is in the direction of increasing rows. The X axis in instrument       
   coordinates is approximately aligned with the spacecraft -Y axis and is in 
   the direction of increasing columns.                                       
                                                                              
                                                                              
LORRI Field of View Parameters                                                
----------------------------------------------------------                    
                                                                              
   From [10] and updated in [12], the LORRI FOV is 0.29121706 deg square.     
                                                                              
   Since LORRI's angular separation in Y is 0.29121706 deg, looking up the +Y 
   axis in the instrument frame we have: (Note we are arbitrarily choosing    
   vectors that terminate in the Z=-1 plane.)                                 
                                                                              
                             X    ^                                           
                              inst|                                           
                                  |                                           
                                  |                                           
                                  |        _.-|                               
                                  |    _.-'   |    o                          
                                  |_.-'  0.14560853                           
                                  x-------------->                            
                            Y (in) `~._       |   -Z                          
                             inst      `~._   |     inst                      
                                           `~.|                               
                                                                              
                                  |--- 1.0 ---|                               
                                                    Plane X = 0               
                                                                              
   Since LORRI's field of view is square, a similar computation yields the    
   Y component.                                                               
                                                                              
   These FOV values for LORRI are given in the keywords below:                
                                                                              
           \begindata                                                         
                                                                              
           INS-98300_FOV_FRAME                 = 'NH_LORRI'                   
           INS-98300_FOV_SHAPE                 = 'RECTANGLE'                  
           INS-98300_BORESIGHT                 = ( 0.0, 0.0, -1.0 )           
           INS-98300_FOV_CLASS_SPEC            = 'ANGLES'                     
           INS-98300_FOV_REF_VECTOR            = ( 1.0, 0.0, 0.0 )            
           INS-98300_FOV_REF_ANGLE             = ( 0.14560853 )               
           INS-98300_FOV_CROSS_ANGLE           = ( 0.14560853 )               
           INS-98300_FOV_ANGLE_UNITS           = 'DEGREES'                    
                                                                              
           \begintext                                                         
                                                                              
   And are duplicated for the 1x1 and 4x4 binning mode frames:                
                                                                              
           \begindata                                                         
                                                                              
           INS-98301_FOV_FRAME                 = 'NH_LORRI_1X1'               
           INS-98301_FOV_SHAPE                 = 'RECTANGLE'                  
           INS-98301_BORESIGHT                 = ( 0.0, 0.0, -1.0 )           
           INS-98301_FOV_CLASS_SPEC            = 'ANGLES'                     
           INS-98301_FOV_REF_VECTOR            = ( 1.0, 0.0, 0.0 )            
           INS-98301_FOV_REF_ANGLE             = ( 0.14560853 )               
           INS-98301_FOV_CROSS_ANGLE           = ( 0.14560853 )               
           INS-98301_FOV_ANGLE_UNITS           = 'DEGREES'                    
                                                                              
           INS-98302_FOV_FRAME                 = 'NH_LORRI_4X4'               
           INS-98302_FOV_SHAPE                 = 'RECTANGLE'                  
           INS-98302_BORESIGHT                 = ( 0.0, 0.0, -1.0 )           
           INS-98302_FOV_CLASS_SPEC            = 'ANGLES'                     
           INS-98302_FOV_REF_VECTOR            = ( 1.0, 0.0, 0.0 )            
           INS-98302_FOV_REF_ANGLE             = ( 0.14560853 )               
           INS-98302_FOV_CROSS_ANGLE           = ( 0.14560853 )               
           INS-98302_FOV_ANGLE_UNITS           = 'DEGREES'                    
                                                                              
           \begintext                                                         
                                                                              
LORRI Optics Parameters                                                       
----------------------------------------------------------                    
                                                                              
   From [10] and updated in [12] and [15], LORRI has the following optics     
   parameters:                                                                
                                                                              
      -----------------------------------------------------------------       
      parameter                 1x1 binning mode      4x4 binning mode        
      -----------------------------------------------------------------       
      Focal length (mm)       2618.4775964615382691   2618.4775964615382691   
      f-number                  12.59                   12.59                 
      IFOV (microrad/pixel)      4.963571               19.854284             
      Aperture diameter (mm)   208                     208                    
      -----------------------------------------------------------------       
                                                                              
   The focal length indicated in the table above is the result of a           
   transformation of the updated parameters by way of a scaling               
   operation.  It is given to full precision to preserve the                  
   relationship to the published values.  Check the Owen and O'Connell        
   distortion section below for more details.                                 
                                                                              
   These parameters are captured in the following keywords in the same units  
   as in the table.                                                           
                                                                              
           \begindata                                                         
                                                                              
           INS-98301_FOCAL_LENGTH       = ( 2618.4775964615382691 )           
           INS-98301_FOCAL_LENGTH_UNITS = 'mm'                                
           INS-98301_F/NUMBER            = ( 12.59 )                          
           INS-98301_IFOV                = ( 4.963571 )                       
           INS-98301_APERTURE_DIAMETER   = ( 208 )                            
           INS-98301_APERTURE_DIAM_UNITS = ( 'mm' )                           
                                                                              
           INS-98302_FOCAL_LENGTH       = ( 2618.4775964615382691 )           
           INS-98302_FOCAL_LENGTH_UNITS = 'mm'                                
           INS-98302_F/NUMBER            = ( 12.59 )                          
           INS-98302_IFOV                = ( 19.854284 )                      
           INS-98302_APERTURE_DIAMETER   = ( 208  )                           
           INS-98302_APERTURE_DIAM_UNITS = ( 'mm' )                           
                                                                              
           \begintext                                                         
                                                                              
LORRI Optical Distortion Specifications                                       
----------------------------------------------------------                    
                                                                              
   This section provides parameters for two sets of optical distortion        
   models for both formats (1x1 and 4x4) of the LORRI camera.  The first      
   model has been used by the New Horizons (NH) Optical Navigation (OPNAV)    
   teams during the NH mission (based on [11] and personal                    
   communication with Bill Owen; there are two OPNAV teams on NH:             
   "PNAV", led by KinetX, is the "Primary" OPNAV team on NH, and "INAV",      
   led by JPL, is the "Independent" OPNAV team on NH).                        
   This is the same camera model used by the Deep Impact camera and           
   Cassini OPNAV.  The second model is used by the LORRI team and is          
   commonly used within the astronomical community (based on [13]).           
   The parameters for the SIP model have been derived by Brian                
   Carcich using parameters from the Owen & O'Connell model.                  
                                                                              
                                                                              
   Owen & O'Connell Distortion Model                                          
   ----------------------------------                                         
                                                                              
   The following distortion model has been used by the NH OPNAV team          
   for this camera during the mission (based on [11]; according to Bill       
   Owen, NH INAV and PNAV used the same camera model as for Deep Impact       
   and Cassini OPNAV).                                                        
                                                                              
   In the following discussion, the terms 'sample' and 'line' are used        
   by the author and retained for ease of comparison to the published         
   work.  In all cases in this document, sample is equivalent to column       
   and line is equivalent to row.                                             
                                                                              
      A 3d vector (P) in the camera frame is mapped into sample and           
      line (S,L) coordinates by:                                              
                                                                              
          ( X )    FL    ( P(1) )                                             
          (   ) = ------ (      )                                             
          ( Y )   P(3)   ( P(2) )                                             
                                                                              
              2    2    2                                                     
             R  = X  + Y                                                      
                                                                              
         ( dX )   ( X*R*R  X*Y X*X ) ( EM2 )                                  
         (    ) = (                ) ( EM5 )                                  
         ( dY )   ( Y*R*R  Y*Y X*Y ) ( EM6 )                                  
                                                                              
          ( S )   ( Kx   Kxy ) ( X + dX )   ( S0 )                            
          (   ) = (          ) (        ) + (    )                            
          ( L )   ( Kyx  Ky  ) ( Y + dY )   ( L0 )                            
                                                                              
      where FL is the camera focal length in mm; EM(i) are coefficients       
      of the cubic radial distortion and detector misalignment; the           
      matrix K provides a mapping from millimeters to pixels in the           
      focal plane; and (S0,L0) are the focal plane coordinates as sample      
      and line of the optical axis.                                           
                                                                              
      The values of X and Y are computed from vector P by way of the          
      gnomonic projection.  These values represent the non-distorted          
      location in instrument coordinates measured in millimeters.  The        
      values for dX and dY indicate the amount of the distortion introduced   
      by the optics and electromagnetic configuration of the detector.        
                                                                              
      The values of S and L represent the pixel location associated with      
      point P as affected by the distortion as would be observed in an        
      image.                                                                  
                                                                              
      The undistorted pixel location associated with X and Y can be           
      computed by setting the distortion parameters, EM(i), to 0.             
                                                                              
    Adapting Owen and O'Connell Model Parameters To LORRI Instrument Frame    
    ----------------------------------------------------------------------    
                                                                              
      The +Y axis defined in OOC model is opposite to the direction of        
      the +Y axis defined in the LORRI instrument kernel.  To make use        
      of the OOC model equations without modification and remain              
      consistent with the LORRI instrument frame, the parameters Ky and       
      EM5 must be negated.                                                    
                                                                              
      The need to change the sign on Ky is apparent by inspection when        
      pushing the four corners of the detector through the OOC model.         
      The need to negate EM5 is not as obvious. The derivation below          
      supports work by Brian Carcich, who originally identified the need      
      to negate EM5, as well as Ky.                                           
                                                                              
      Starting from the distortion portion of the OOC model:                  
                                                                              
        (  dX  )     (   X*R^2    X*Y   X^2  )    (  EM2 )                    
        (      )  =  (                       )    (  EM5 )                    
        (  dY  )     (   Y*R^2    Y^2   X*Y  )    (  EM6 )                    
                                                                              
      The +Y axis in the OOC model (Y) is opposite the +Y axis in the         
      LORRI Instrument frame (Y_L), while the +X axes agree in                
      direction. So a change in Y in the OOC model (dY) will be a             
      negative change in Y in the LORRI frame (dY_L).                         
                                                                              
         Y =  -Y_L                                                            
        dY = -dY_L                                                            
                                                                              
      Substituting these into the previous equation:                          
                                                                              
        (  dX   )     (   X*R^2     -X*Y_L     X^2   )  (  EM2 )              
        (       )  =  (                              )  (  EM5 )              
        ( -dY_L )     (  -Y_L*R^2   (Y_L)^2   -X*Y_L )  (  EM6 )              
                                                                              
      Then rewrite this equation in terms of distortion changes in dX         
      and dYL by distributing the negative sign from the left to the          
      right side:                                                             
                                                                              
        (  dX  )     (   X*R^2       -X*Y_L      X^2      )  (  EM2 )         
        (      )  =  (                                    )  (  EM5 )         
        ( dY_L )     ( (-)-Y_L*R^2  (-)(Y_L)^2  (-)-X*Y_L )  (  EM6 )         
                                                                              
      And simplifying:                                                        
                                                                              
        (  dX  )     (   X*R^2    -X*Y_L        X^2  )  (  EM2 )              
        (      )  =  (                               )  (  EM5 )              
        ( dY_L )     (  Y_L*R^2   -(Y_L)^2    X*Y_L  )  (  EM6 )              
                                                                              
      The structure of this equation is very similar to the OOC model         
      but with the Y component of the left-hand matrix negated. By            
      absorbing  the negative sign into EM5, the equation will look           
      exactly like the OOC model but in terms of the LORRI frame:             
                                                                              
        (  dX  )     (   X*R^2      X*Y_L      X^2   )  (  EM2 )              
        (      )  =  (                               )  ( -EM5 )              
        ( dY_L )     (   Y_L*R^2    (Y_L)^2    X*Y_L )  (  EM6 )              
                                                                              
      So by changing the sign on EM5 and Ky, code for the OOC model           
      can be reused for to get distortion deltas in the LORRI frame.          
      Based on this relationship, the sign of two coefficients (Ky, EM5)      
      in this model have been changed from the published material[11] to      
      remain consistent with the LORRI instrument frame.                      
                                                                              
    Initial results (2006)                                                    
    ----------------------                                                    
                                                                              
      The following NH LORRI optical distortion parameters for this           
      model were derived using data collected in 2006 and were provided       
      by Bill Owen, NH INAV (from [11]) assuming a pixel scale of 13um.       
                                                                              
      *** Values for Focal Length, EM2, EM5, EM6, KMAT(1,1) and ***           
      *** KMAT(2,2) in the following table below are now        ***           
      *** obsolete. See below for updated results.              ***           
                                                                              
        Description         Value       Sigma       Units                     
      -------------------  -----------  --------    --------                  
      Focal Length         2619.008      0.021       mm                       
      EM2                  2.696E-05     0.016E-05   mm^{-2}                  
      EM5                 -1.988E-05     0.091E-05   mm^{-1}    **            
      EM6                 -2.864E-05     0.099E-05   mm^{-1}                  
                                                                              
      other parameters computed analytically assuming a pixel scale           
      of 13um:                                                                
                                                                              
      KMAT(1,1) =  76.9231                                                    
      KMAT(1,2) =   0.0                                                       
      KMAT(2,1) =   0.0                                                       
      KMAT(2,2) =  76.9231   // sign differs from published material **       
      S0        = 511.5      // zero reference                                
      L0        = 511.5      // zero reference                                
                                                                              
      ** The sign of two coefficients (Ky, EM5) in this model have been       
      changed from the published material[11] due to the difference in        
      the definition of the LORRI +Y axis for the model compared to the       
      LORRI instrument frame. All references to these two coefficients        
      in this document have had their sign flipped to remain consistent       
      with the LORRI instrument frame.                                        
                                                                              
      The values for S0 and L0 are referenced to the center of the first      
      pixel of the first line as 0, rather than 1 as is used in the Owen      
      and O'Connell literature. This was done to remain consistent with       
      the LORRI coordinate system.                                            
                                                                              
    Updated results (2013)                                                    
    ----------------------                                                    
                                                                              
      Some of the coefficients for this model were updated [12] using         
      the image data from the Wishing Well star cluster collected             
      during Annual Check Out 7 (ACO-7), which executed between May and       
      August 2013.  These results were derived assuming a pixel size          
      of 13um.                                                                
                                                                              
        Description         Value       Sigma       Units                     
      -------------------  -----------  --------    --------                  
      Focal Length         2619.082      0.020       mm                       
      EM2                  2.716E-05     0.016E-05   mm^{-2}                  
      EM5                 -1.903E-05     0.083E-05   mm^{-1}     **           
      EM6                 -2.880E-05     0.080E-05   mm^{-1}                  
                                                                              
    Results used by the LORRI Team in this kernel                             
    ---------------------------------------------                             
                                                                              
      After consulting with the CCD manufacturer, E2V Technologies,           
      the pixel size was determined to be 12.997 +/- 0.003 um rather          
      than the assumed size of 13 um.  To account for the change in           
      pixel size, the coefficients published in [12] were scaled              
      appropriately [16].  The scale factor is defined as                     
                                                                              
        T = 12.997 um / 13.000 um                                             
                                                                              
      the scaled coefficients are calculated as:                              
                                                                              
      scaled Focal Length = original focal length * T                         
      scaled KMAT(1,1)    = original KMAT[1,1] / T                            
      scaled KMAT(2,2)    = original KMAT[2,2] / T                            
      scaled EM2          = original EM2 / T ^ 2                              
      scaled EM5          = original EM5 / T                                  
      scaled EM6          = original EM6 / T                                  
                                                                              
      The table below captures the scaled coefficients to full precision      
      to preserve the relationship to the published values in [12].           
                                                                              
        Description         Value                                             
      -------------------  -----------                                        
      Focal Length         2618.4775964615382691                              
      KMAT(1,1)              76.9408555820574094                              
      KMAT(2,2)              76.9408555820574094        // sign change **     
      EM2                     2.7172539725122498E-05                          
      EM5                    -1.9034392552127415E-05    // sign change **     
      EM6                    -2.8806647687927984E-05                          
                                                                              
   Notice that there are several differences in convention in this            
   distortion model when compared to what is adopted in the other             
   portions of this document:                                                 
                                                                              
      - the keywords in the next section include "_OOC_" for Owen and         
        O'Connell to distinguish these distortion parameters from the         
        "_SIP_" distortion keywords in the next section.                      
                                                                              
      - the units for INS*_OOC_FOCAL_LENGTH keyword are always                
        expressed in millimeters.  The units for focal length were            
        previously expressed in meters.  These units have been adjusted       
        to millimeters to remain consistent throughout the document.          
                                                                              
      - the INS*_OOC_CCD_CENTER keywords listed below follow the LORRI        
        pixel naming scheme which labels the center of the first              
        pixel of the first row as pixel (0,0). This differs from the          
        convention indicated in [11], which labels the center of the          
        first pixel of the first row as pixel (1,1).                          
                                                                              
   The FOCAL_LENGTH keyword is defined below.  It is also presented           
   with the _OOC_ term in the keyword to indicate that it is associated       
   with the Owen and O'Connell distortion model.  Also note that there        
   is no focal length associated with the SIP distortion model.               
                                                                              
   The updated values for this data is provided in the keywords below:        
                                                                              
      \begindata                                                              
                                                                              
         INS-98301_OOC_FOCAL_LENGTH       = 2618.4775964615382691             
         INS-98301_OOC_FOCAL_LENGTH_SIGMA = 0.020                             
                                                                              
         INS-98301_OOC_KMAT         = (                                       
                                        76.9408555820574094,                  
                                        0.0,                                  
                                        0.0,                                  
                                        76.9408555820574094                   
                                      )                                       
                                                                              
         INS-98301_OOC_EM           = (                                       
                                        2.7172539725122498E-05,               
                                       -1.9034392552127415E-05,               
                                       -2.8806647687927984E-05                
                                      )                                       
         INS-98301_OOC_EM_SIGMA     = (                                       
                                        0.016E-05,                            
                                        0.083E-05,                            
                                        0.080E-05                             
                                      )                                       
                                                                              
         INS-98301_OOC_CCD_CENTER   = ( 511.5, 511.5 )                        
                                                                              
      \begintext                                                              
                                                                              
   The equivalent coefficients for 4x4 mode can be derived from the 1x1       
   mode coefficients.  The only coefficients affected by the effectively      
   larger pixel area are given in the last equation from the model:           
                                                                              
          ( S )   ( Kx   Kxy ) ( X + dX )   ( S0 )                            
          (   ) = (          ) (        ) + (    )                            
          ( L )   ( Kyx  Ky  ) ( Y + dY )   ( L0 )                            
                                                                              
    The parameters S, L, S0 and L0 are all given in pixel coordinates and     
    are thus affected.  Specifically, 4x4 mode has 256 columns and 256        
    rows rather than the 1024 columns and 1024 rows for 1x1 mode.             
    Because of this, the values for S0 and L0 must be updated to reflect      
    the new pixel dimensions.  The parameters in the K matrix also needs      
    to be adjusted to account for the effectively larger pixel size           
    since they convert from mm to pixel space.                                
                                                                              
    The 4x4 binning mode combines 4 pixels in each of the X and Y             
    directions.  This has the effect of creating a pixel that is four         
    times the size in both directions, yielding an effective pixel size       
    of 4 * 12.997 um = 51.998 um.  From [11], the Kx and Ky elements of the   
    K matrix are computed as the inverse of the pixel size in units of        
    mm^{-1}.  The updated values for 4x4 mode are listed in the table below:  
                                                                              
      KMAT(1,1) =  19.2352138955143523                                        
      KMAT(1,2) =   0.0                                                       
      KMAT(2,1) =   0.0                                                       
      KMAT(2,2) =  19.2352138955143523 // sign change **                      
      S0        = 127.5                // zero reference                      
      L0        = 127.5                // zero reference                      
                                                                              
    ** The sign of two coefficients (Ky, EM5) in this model have been         
    changed from the published material[11] due to the difference in          
    the definition of the LORRI +Y axis for the model compared to the         
    LORRI instrument frame. All references to these two coefficients          
    in this document have had their sign flipped to remain consistent         
    with the LORRI instrument frame.                                          
                                                                              
    The values for S0 and L0 are referenced to the center of the first        
    pixel of the first line as 0, rather than 1 as is used in the Owen        
    and O'Connell literature. This was done to remain consistent with         
    the LORRI coordinate system.                                              
                                                                              
      \begindata                                                              
                                                                              
         INS-98302_OOC_FOCAL_LENGTH       = 2618.4775964615382691             
         INS-98302_OOC_FOCAL_LENGTH_SIGMA = 0.020                             
                                                                              
         INS-98302_OOC_KMAT         = (                                       
                                        19.2352138955143523,                  
                                        0.0,                                  
                                        0.0,                                  
                                        19.2352138955143523                   
                                      )                                       
                                                                              
         INS-98302_OOC_EM           = (                                       
                                        2.7172539725122498E-05,               
                                       -1.9034392552127415E-05,               
                                       -2.8806647687927984E-05                
                                      )                                       
         INS-98302_OOC_EM_SIGMA     = (                                       
                                        0.016E-05,                            
                                        0.083E-05,                            
                                        0.080E-05                             
                                      )                                       
                                                                              
         INS-98302_OOC_CCD_CENTER   = ( 127.5, 127.5 )                        
                                                                              
      \begintext                                                              
                                                                              
    This small fragment of SPICE-based FORTRAN code illustrates how           
    these parameters can be loaded into an application and used to            
    compute sample and line for a 3d vector defined in the camera frame,      
    NH_LORRI_1X1:                                                             
                                                                              
      C                                                                       
      C     Retrieve loaded camera distortion parameters.                     
      C                                                                       
            CALL GDPOOL ( 'INS-98301_OOC_FOCAL_LENGTH', 1, 1, N, FL,   FND1 ) 
            CALL GDPOOL ( 'INS-98301_OOC_KMAT',         1, 4, N, KMAT, FND2 ) 
            CALL GDPOOL ( 'INS-98301_OOC_EM',           1, 3, N, EM,   FND3 ) 
            CALL GDPOOL ( 'INS-98301_OOC_CCD_CENTER',   1, 2, N, CNTR, FND4 ) 
      C                                                                       
      C     Given 3d vector VECTOR in the camera frame, 'NH_LORRI_1X1',       
      C     compute ideal X and Y in sample/line space.                       
      C                                                                       
            CALL VSCLG ( FL / VECTOR(3), VECTOR, 2, XYIDL )                   
      C                                                                       
      C     Construct XYR2 matrix.                                            
      C                                                                       
            R2 = XYIDL(1)**2 + XYIDL(2)**2                                    
                                                                              
            XYRMAT(1,1) = XYIDL(1) * R2                                       
            XYRMAT(2,1) = XYIDL(2) * R2                                       
            XYRMAT(1,2) = XYIDL(1) * XYIDL(2)                                 
            XYRMAT(2,2) = XYIDL(2) * XYIDL(2)                                 
            XYRMAT(1,3) = XYIDL(1) * XYIDL(1)                                 
            XYRMAT(2,3) = XYIDL(1) * XYIDL(2)                                 
     C                                                                        
     C      Compute delta X and Y.                                            
     C                                                                        
            CALL MXVG ( XYRMAT, EM, 2, 3, XYDLT )                             
     C                                                                        
     C      Compute line sample, SL (sample is the first element,             
     C      line is the second element.)                                      
     C                                                                        
            CALL VADDG( XYIDL, XYDLT, 2, XY )                                 
            CALL MXVG ( KMAT, XY, 2, 2, SLREL )                               
            CALL VADDG( SLREL, CNTR, 2, SL )                                  
                                                                              
                                                                              
   Simple Imaging Polynomial (SIP) Distortion Model                           
   ------------------------------------------------                           
                                                                              
   The use of the Simple Imaging Polynomial distortion model is               
   prevalent in the astronomy community and is supported by a large           
   number of freely available software packages.  It extends the World        
   Coordinate System standard for FITS images to provide non-linear           
   geometric distortion using polynomials in FITS headers and is              
   described in [13]:                                                         
                                                                              
        Values u and v are the distorted locations in relative pixel          
        coordinates with origin at CRPIX1, CRPIX2, which are the center       
        pixel sample and line locations.  Values x and y are                  
        "intermediate world coordinates" in degrees with origin at            
        CRVAL1, CRVAL2, which are Right Ascension and Declination in the      
        case of LORRI images. Then f(u,v) and g(u,v) are the quadratic        
        and higher order terms of the distortion polynomial:                  
                                                                              
          ( x ) = ( CD1_1  CD1_2 ) ( u + f(u,v) )                             
          ( y )   ( CD2_1  CD2_2 ) ( v + g(u,v) )                             
                                                                              
        A_p_q an B_p_q are defined as the polynomial coefficients for         
        polynomial terms u^p * v^q, respectively.  From this:                 
                                                                              
                      ----                                                    
                      \                                                       
            f(u, v) = /    A_p_q * u^p * v^q,   p + q <= A_ORDER              
                      ----                                                    
                      p,q                                                     
                                                                              
                      ----                                                    
                      \                                                       
            g(u, v) = /    B_p_q * u^p * v^q,   p + q <= B_ORDER              
                      ----                                                    
                      p,q                                                     
                                                                              
        For example, for a third order polynomial:                            
        f(u,v) = A_2_0 * u^2 + A_0_2 * v^2 + A_1_1 * u * v +                  
                 A_2_1 * u^2 * v + A_1_2 * u * v^2 + A_3_0 * u^3 +            
                 A_0_3 * v^3                                                  
                                                                              
        The values for u and v represent the distorted pixel location         
        resulting from the effects caused by the optics, measured             
        relative to the center of the detector.                               
                                                                              
        The CDi_j keywords encode skew as well as rotation and scaling.       
        The CD matrix values together with the higher-order distortion        
        polynomials define a unique transformation from pixel                 
        coordinates to the plane-of-projection.                               
                                                                              
        The polynomials for the reverse transformation are also provided      
        for fast inversion.  Pixel coordinates U,V are the location if        
        the optics didn't cause any distortion and can be found from:         
                                                                              
          ( U ) =     -1  ( x )                                               
          ( V )     CD    ( y )                                               
                                                                              
        then the distorted pixel coordinates (u,v) can be computed from       
        the undistorted pixel coordinates (U,V) by:                           
                                                                              
                               ----                                           
                               \                                              
         u = U + F(U,V) = U +  /    AP_p_q * U^p * V^q,  p + q <= AP_ORDER    
                               ----                                           
                               p,q                                            
                                                                              
                               ----                                           
                               \                                              
         v = V + G(U,V) = V +  /    BP_p_q * U^p * V^q,  p + q <= BP_ORDER    
                               ----                                           
                               p,q                                            
                                                                              
   Relating the Owen & O'Connell Distortion Model to the SIP Model            
   ---------------------------------------------------------------            
                                                                              
   With some substitution, the Owen & O'Connell distortion model              
   equations can be rewritten in the form of the SIP reverse                  
   transformation.  To do so requires recognizing that the values of U        
   and V in the SIP model represent the undistorted pixel location as         
   computed using the gnomonic projection, meaning that the distortion        
   produced from the optics are not present.  The SIP values of U and V       
   are in units of pixels and can be related to the values X and Y, in        
   units of millimeters, from the Owen & O'Connell model by multiplying       
   by the effective scale factor                                              
                                                                              
        U = Kx * X              V = Ky * Y                                    
        X = U / Kx              Y = V / Ky                                    
                                                                              
   The following derivation is provided for the sample (ie: column) component 
   of the Owen & O'Connell model.  The derivation for the line (ie: row)      
   component follows directly.  From the Owen and O'Connell model:            
                                                                              
        dX = X * R ^ 2 * EM2 + X * Y * EM5 + X * X * EM6                      
                                                                              
    Substituting for R ^ 2:                                                   
                                                                              
        dX = X * ( X ^ 2 + Y ^ 2 ) * EM2 + X * Y * EM5 + X * X * EM6          
                                                                              
    simplifying:                                                              
                                                                              
        dX = X ^ 3 * EM2 + X * Y ^ 2 * EM2 + X * Y * EM5 + X * X * EM6        
                                                                              
    From the Owen & O'Connell model:                                          
                                                                              
        S = Kx * ( X + dX ) + Kxy ( Y + dY ) + S0                             
                                                                              
    Rearranging, simplifying and recalling that for LORRI, Kxy = 0:           
                                                                              
        S - S0 = Kx * ( X + dX )                                              
                                                                              
    Recall that the S - S0 represents the distorted, relative pixel           
    location, which is equivalent to the parameter u in the SIP model.        
                                                                              
        u = Kx * ( X + X ^ 3 * EM2 + X * Y ^ 2 * EM2 +                        
                                     X * Y * EM5 + X * X * EM6 )              
                                                                              
    Substituting for X = U / Kx   and  Y = V / Ky                             
                                                                              
        u = U + EM2 / Kx ^ 2 * U ^ 3 + EM2 / Ky ^ 2 * U * V ^ 2 +             
                EM5 / Ky * U * V + EM6 / Kx * U ^ 2                           
                                                                              
    This equation is now in the form of the SIP reverse transform:            
                                                                              
        u = U + F ( U, V )                                                    
                                                                              
    The components of F( U, V) are available by inspection:                   
                                                                              
        AP_3_0 = EM2 / ( Kx ^ 2 )                                             
        AP_1_2 = EM2 / ( Ky ^ 2 )                                             
        AP_1_1 = EM5 / Ky                                                     
        AP_2_0 = EM6 / Kx                                                     
                                                                              
    Following similar methods, the derivation for the line (ie: row)          
    component follows:                                                        
                                                                              
        dY = Y * ( X ^ 2 + Y ^ 2 ) * EM2 + Y * Y * EM5 + X * Y * EM6          
        dY = X ^ 2 * Y * EM2 + Y ^ 3 * EM2 + Y * Y * EM5 + X * Y * EM6        
        L = Kyx * ( X + dX ) + Ky ( Y + dY ) + L0       (recall: Kyx = 0)     
        L - L0 = Ky * ( Y + dY )                                              
        v = Ky * ( Y + X ^ 2 * Y * EM2 + Y ^ 3 * EM2 +                        
                                     Y * Y * EM5 + X * Y * EM6 )              
        v = V + EM2 / Kx ^ 2 * U ^ 2 * V + EM2 / Ky ^ 2 * V ^ 3 +             
                EM5 / Ky * V ^ 2 + EM6 / Kx * U * V                           
                                                                              
    This equation is now in the form of the SIP reverse transform:            
                                                                              
        v = V + G ( U, V )                                                    
                                                                              
    The components of G( U, V) are available by inspection:                   
                                                                              
        BP_2_1 = EM2 / ( Kx ^ 2 )                                             
        BP_0_3 = EM2 / ( Ky ^ 2 )                                             
        BP_0_2 = EM5 / Ky                                                     
        BP_1_1 = EM6 / Kx                                                     
                                                                              
                                                                              
   Definition of SIP Distortion Model Coefficients:                           
   ------------------------------------------------                           
                                                                              
   The parameters listed below were derived by Brian Carcich starting         
   from the parameters listed in the Owen & O'Connell distortion model.       
   In the list of keywords below, all unmentioned polynomial coefficients     
   are assumed to be 0.                                                       
                                                                              
   The SIP coefficients for 1x1 mode are captured in variables below:         
                                                                              
           \begindata                                                         
                                                                              
            INS-98301_SIP_A_ORDER  =                    3                     
            INS-98301_SIP_A_3_0    = -4.5683524653106E-09                     
            INS-98301_SIP_A_2_1    =  3.6773993329229E-13                     
            INS-98301_SIP_A_1_2    = -4.5506608174421E-09                     
            INS-98301_SIP_A_0_3    = -4.8263827227450E-16                     
            INS-98301_SIP_A_2_0    =  3.7132883452972E-07                     
            INS-98301_SIP_A_1_1    =  2.4489911491959E-07                     
            INS-98301_SIP_A_0_2    = -3.8995992016687E-10                     
            INS-98301_SIP_B_ORDER  =                    3                     
            INS-98301_SIP_B_3_0    = -4.8263374371619E-16                     
            INS-98301_SIP_B_2_1    = -4.5505047160943E-09                     
            INS-98301_SIP_B_1_2    =  3.6773991492864E-13                     
            INS-98301_SIP_B_0_3    = -4.5685088916275E-09                     
            INS-98301_SIP_B_2_0    = -2.5764535470748E-10                     
            INS-98301_SIP_B_1_1    =  3.7063022991452E-07                     
            INS-98301_SIP_B_0_2    =  2.4536068067188E-07                     
            INS-98301_SIP_AP_ORDER =                    3                     
            INS-98301_SIP_AP_3_0   =  4.5900372459772E-09                     
            INS-98301_SIP_AP_1_2   =  4.5900372459772E-09                     
            INS-98301_SIP_AP_1_1   = -2.4738992578302E-07                     
            INS-98301_SIP_AP_2_0   = -3.7439988768003E-07                     
            INS-98301_SIP_BP_ORDER =                    3                     
            INS-98301_SIP_BP_2_1   =  4.5900372459772E-09                     
            INS-98301_SIP_BP_0_3   =  4.5900372459772E-09                     
            INS-98301_SIP_BP_0_2   = -2.4738992578302E-07                     
            INS-98301_SIP_BP_1_1   = -3.7439988768003E-07                     
                                                                              
           \begintext                                                         
                                                                              
    The equivalent set of distortion parameters for LORRI in 4x4 mode         
    were computed from the 1x1 set of parameters listed above:                
                                                                              
           \begindata                                                         
                                                                              
            INS-98302_SIP_A_ORDER  =                    3                     
            INS-98302_SIP_A_3_0    = -7.3093639444970E-08                     
            INS-98302_SIP_A_2_1    =  5.8838389330992E-12                     
            INS-98302_SIP_A_1_2    = -7.2810573079073E-08                     
            INS-98302_SIP_A_0_3    = -7.7222124763245E-15                     
            INS-98302_SIP_A_2_0    =  1.4853153381189E-06                     
            INS-98302_SIP_A_1_1    =  9.7959645967839E-07                     
            INS-98302_SIP_A_0_2    = -1.5598396806578E-09                     
            INS-98302_SIP_B_ORDER  =                    3                     
            INS-98302_SIP_B_3_0    = -7.7221397202775E-15                     
            INS-98302_SIP_B_2_1    = -7.2808075457509E-08                     
            INS-98302_SIP_B_1_2    =  5.8838386384176E-12                     
            INS-98302_SIP_B_0_3    = -7.3096142266041E-08                     
            INS-98302_SIP_B_2_0    = -1.0305814188049E-09                     
            INS-98302_SIP_B_1_1    =  1.4825209196581E-06                     
            INS-98302_SIP_B_0_2    =  9.8144272268748E-07                     
            INS-98302_SIP_AP_ORDER =                    3                     
            INS-98302_SIP_AP_3_0   =  7.3440595935636E-08                     
            INS-98302_SIP_AP_1_2   =  7.3440595935636E-08                     
            INS-98302_SIP_AP_1_1   = -9.8955970313209E-07                     
            INS-98302_SIP_AP_2_0   = -1.4975995507201E-06                     
            INS-98302_SIP_BP_ORDER =                    3                     
            INS-98302_SIP_BP_2_1   =  7.3440595935636E-08                     
            INS-98302_SIP_BP_0_3   =  7.3440595935636E-08                     
            INS-98302_SIP_BP_0_2   = -9.8955970313209E-07                     
            INS-98302_SIP_BP_1_1   = -1.4975995507201E-06                     
                                                                              
           \begintext                                                         
                                                                              
LORRI CCD Detector Parameters                                                 
----------------------------------------------------------                    
                                                                              
   From [9] and [10], LORRI has the following CCD parameters:                 
                                                                              
      -----------------------------------------------------------------       
      parameter                 1x1 binning mode      4x4 binning mode        
      -----------------------------------------------------------------       
      Detector array size         1024 x 1024            256 x 256            
      Pixel size (microns)      12.997 x 12.997       51.988 x 51.988         
      CCD center                ( 511.5, 511.5)       ( 127.5, 127.5 )        
      -----------------------------------------------------------------       
                                                                              
   These parameters are captured in the following keywords in the same units  
   as in the table:                                                           
                                                                              
           \begindata                                                         
                                                                              
           INS-98301_PIXEL_SAMPLES     = ( 1024 )                             
           INS-98301_PIXEL_LINES       = ( 1024 )                             
           INS-98301_PIXEL_SIZE        = (  12.997  )                         
           INS-98301_CCD_CENTER        = ( 511.5, 511.5 )                     
                                                                              
           INS-98302_PIXEL_SAMPLES     = ( 256 )                              
           INS-98302_PIXEL_LINES       = ( 256 )                              
           INS-98302_PIXEL_SIZE        = ( 51.988 )                           
           INS-98302_CCD_CENTER        = ( 127.5, 127.5 )                     
                                                                              
           \begintext                                                         
                                                                              
   Also defined here is the celestial position angle reference vector. This   
   vector defines the position angle, or angle from celestial north (and      
   passing through celestial east) to the reference vector.                   
                                                                              
           \begindata                                                         
                                                                              
           INS-98300_REFERENCE_VECTOR  = ( 1.0, 0.0, 0.0 )                    
           INS-98301_REFERENCE_VECTOR  = ( 1.0, 0.0, 0.0 )                    
           INS-98302_REFERENCE_VECTOR  = ( 1.0, 0.0, 0.0 )                    
                                                                              
           \begintext                                                         
                                                                              
                                                                              
Platform ID                                                                   
--------------------------------------------------------                      
                                                                              
   This number is the NAIF instrument ID of the platform on which the         
   instrument is mounted.                                                     
                                                                              
           \begindata                                                         
                                                                              
           INS-98300_PLATFORM_ID  = ( -98000 )                                
           INS-98301_PLATFORM_ID  = ( -98000 )                                
           INS-98302_PLATFORM_ID  = ( -98000 )                                
                                                                              
           \begintext                                                         
