PDS_VERSION_ID = PDS3 RECORD_TYPE = STREAM OBJECT = TEXT PUBLICATION_DATE = 2019-10-18 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