PDS_VERSION_ID = PDS3
RECORD_TYPE = STREAM
OBJECT = TEXT
PUBLICATION_DATE = 20161031
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 NHJ/P/SSSPICE6V1.0.
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 (Ikernel) 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 Ikernel might have an entry as follows:
TEXT_KERNEL_ID += 'NEWHORIZONS_LORRI V2.0.1 01MAR2016 IK'
   
   
KERNEL NAME <+   
  V
VERSION <+  KERNEL TYPE

V
ENTRY DATE
LORRI IKernel Version:
\begindata
TEXT_KERNEL_ID += 'NEWHORIZONS_LORRI V2.0.1 01MAR2016 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, fnumber, 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 +Yaxis used
in the published model compared to the LORRI instrument
frame.
 Fixed values for INS9830X_OOC_EM_SIGMA. The exponent
had been omitted unintentionally.
 Added keywords INS9830X_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 3letter 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. LOngRange Reconnaissance Imager (LORRI) Specification
Document, 74009000 Rev A.
2. ``Kernel Pool Required Reading''
3. Spacecraft to LORRI Interface Control Document (ICD),
73999048, 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),
NH73999000v1.6.
7. LOngRange Reconnaissance Imager (LORRI) User's Manual,
74009601, dated Jan. 10, 2006.
8. LORRI_orientation_1906, received on 1/23/2006 by email
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 email
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 343L11002, 06/08/2011
12. Email exchange between Bill Owen and Hal Weaver containing
updated distortion coefficients of [11] using ACO7 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)7785477, Lillian.Nguyen@jhuapl.edu
Howard Taylor, JHU/APL, (443)7785682, 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 Ikernel 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:
INS98300_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 8.2inch (20.8centimeter) 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
footballfield 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), narrowangle camera capable of producing highresolution
imagery. The LORRI will provide imagery of PlutoCharon, 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 RitcheyChretien telescope
made of silicon carbide. The telescope is f/12.75, and feeds an
unfiltered, 1024 x 1024 frame transfer CCD. The effective bandpass 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 fieldofview 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 longrange capability of LORRI will permit the
receipt of highresolution observations of PlutoCharon at least 75 days
before their encounter and of the KuiperBelt Objects (KBOs).
.
.
.
LORRI is a panchromatic visible imager with an angular resolution of 5
microrad/pixel and a fieldofview (FOV) of 0.2912 deg x 0.2912 deg. It
consists of a 20cm 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
INS98300_FOV_FRAME = 'NH_LORRI'
INS98300_FOV_SHAPE = 'RECTANGLE'
INS98300_BORESIGHT = ( 0.0, 0.0, 1.0 )
INS98300_FOV_CLASS_SPEC = 'ANGLES'
INS98300_FOV_REF_VECTOR = ( 1.0, 0.0, 0.0 )
INS98300_FOV_REF_ANGLE = ( 0.14560853 )
INS98300_FOV_CROSS_ANGLE = ( 0.14560853 )
INS98300_FOV_ANGLE_UNITS = 'DEGREES'
\begintext
And are duplicated for the 1x1 and 4x4 binning mode frames:
\begindata
INS98301_FOV_FRAME = 'NH_LORRI_1X1'
INS98301_FOV_SHAPE = 'RECTANGLE'
INS98301_BORESIGHT = ( 0.0, 0.0, 1.0 )
INS98301_FOV_CLASS_SPEC = 'ANGLES'
INS98301_FOV_REF_VECTOR = ( 1.0, 0.0, 0.0 )
INS98301_FOV_REF_ANGLE = ( 0.14560853 )
INS98301_FOV_CROSS_ANGLE = ( 0.14560853 )
INS98301_FOV_ANGLE_UNITS = 'DEGREES'
INS98302_FOV_FRAME = 'NH_LORRI_4X4'
INS98302_FOV_SHAPE = 'RECTANGLE'
INS98302_BORESIGHT = ( 0.0, 0.0, 1.0 )
INS98302_FOV_CLASS_SPEC = 'ANGLES'
INS98302_FOV_REF_VECTOR = ( 1.0, 0.0, 0.0 )
INS98302_FOV_REF_ANGLE = ( 0.14560853 )
INS98302_FOV_CROSS_ANGLE = ( 0.14560853 )
INS98302_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
fnumber 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
INS98301_FOCAL_LENGTH = ( 2618.4775964615382691 )
INS98301_FOCAL_LENGTH_UNITS = 'mm'
INS98301_F/NUMBER = ( 12.59 )
INS98301_IFOV = ( 4.963571 )
INS98301_APERTURE_DIAMETER = ( 208 )
INS98301_APERTURE_DIAM_UNITS = ( 'mm' )
INS98302_FOCAL_LENGTH = ( 2618.4775964615382691 )
INS98302_FOCAL_LENGTH_UNITS = 'mm'
INS98302_F/NUMBER = ( 12.59 )
INS98302_IFOV = ( 19.854284 )
INS98302_APERTURE_DIAMETER = ( 208 )
INS98302_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 nondistorted
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 lefthand 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 2.696E05 0.016E05 mm^{2}
EM5 1.988E05 0.091E05 mm^{1} **
EM6 2.864E05 0.099E05 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 (ACO7), 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 2.716E05 0.016E05 mm^{2}
EM5 1.903E05 0.083E05 mm^{1} **
EM6 2.880E05 0.080E05 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 2.7172539725122498E05
EM5 1.9034392552127415E05 // sign change **
EM6 2.8806647687927984E05
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
INS98301_OOC_FOCAL_LENGTH = 2618.4775964615382691
INS98301_OOC_FOCAL_LENGTH_SIGMA = 0.020
INS98301_OOC_KMAT = (
76.9408555820574094,
0.0,
0.0,
76.9408555820574094
)
INS98301_OOC_EM = (
2.7172539725122498E05,
1.9034392552127415E05,
2.8806647687927984E05
)
INS98301_OOC_EM_SIGMA = (
0.016E05,
0.083E05,
0.080E05
)
INS98301_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
INS98302_OOC_FOCAL_LENGTH = 2618.4775964615382691
INS98302_OOC_FOCAL_LENGTH_SIGMA = 0.020
INS98302_OOC_KMAT = (
19.2352138955143523,
0.0,
0.0,
19.2352138955143523
)
INS98302_OOC_EM = (
2.7172539725122498E05,
1.9034392552127415E05,
2.8806647687927984E05
)
INS98302_OOC_EM_SIGMA = (
0.016E05,
0.083E05,
0.080E05
)
INS98302_OOC_CCD_CENTER = ( 127.5, 127.5 )
\begintext
This small fragment of SPICEbased 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 ( 'INS98301_OOC_FOCAL_LENGTH', 1, 1, N, FL, FND1 )
CALL GDPOOL ( 'INS98301_OOC_KMAT', 1, 4, N, KMAT, FND2 )
CALL GDPOOL ( 'INS98301_OOC_EM', 1, 3, N, EM, FND3 )
CALL GDPOOL ( 'INS98301_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 nonlinear
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 higherorder distortion
polynomials define a unique transformation from pixel
coordinates to the planeofprojection.
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
INS98301_SIP_A_ORDER = 3
INS98301_SIP_A_3_0 = 4.5683524653106E09
INS98301_SIP_A_2_1 = 3.6773993329229E13
INS98301_SIP_A_1_2 = 4.5506608174421E09
INS98301_SIP_A_0_3 = 4.8263827227450E16
INS98301_SIP_A_2_0 = 3.7132883452972E07
INS98301_SIP_A_1_1 = 2.4489911491959E07
INS98301_SIP_A_0_2 = 3.8995992016687E10
INS98301_SIP_B_ORDER = 3
INS98301_SIP_B_3_0 = 4.8263374371619E16
INS98301_SIP_B_2_1 = 4.5505047160943E09
INS98301_SIP_B_1_2 = 3.6773991492864E13
INS98301_SIP_B_0_3 = 4.5685088916275E09
INS98301_SIP_B_2_0 = 2.5764535470748E10
INS98301_SIP_B_1_1 = 3.7063022991452E07
INS98301_SIP_B_0_2 = 2.4536068067188E07
INS98301_SIP_AP_ORDER = 3
INS98301_SIP_AP_3_0 = 4.5900372459772E09
INS98301_SIP_AP_1_2 = 4.5900372459772E09
INS98301_SIP_AP_1_1 = 2.4738992578302E07
INS98301_SIP_AP_2_0 = 3.7439988768003E07
INS98301_SIP_BP_ORDER = 3
INS98301_SIP_BP_2_1 = 4.5900372459772E09
INS98301_SIP_BP_0_3 = 4.5900372459772E09
INS98301_SIP_BP_0_2 = 2.4738992578302E07
INS98301_SIP_BP_1_1 = 3.7439988768003E07
\begintext
The equivalent set of distortion parameters for LORRI in 4x4 mode
were computed from the 1x1 set of parameters listed above:
\begindata
INS98302_SIP_A_ORDER = 3
INS98302_SIP_A_3_0 = 7.3093639444970E08
INS98302_SIP_A_2_1 = 5.8838389330992E12
INS98302_SIP_A_1_2 = 7.2810573079073E08
INS98302_SIP_A_0_3 = 7.7222124763245E15
INS98302_SIP_A_2_0 = 1.4853153381189E06
INS98302_SIP_A_1_1 = 9.7959645967839E07
INS98302_SIP_A_0_2 = 1.5598396806578E09
INS98302_SIP_B_ORDER = 3
INS98302_SIP_B_3_0 = 7.7221397202775E15
INS98302_SIP_B_2_1 = 7.2808075457509E08
INS98302_SIP_B_1_2 = 5.8838386384176E12
INS98302_SIP_B_0_3 = 7.3096142266041E08
INS98302_SIP_B_2_0 = 1.0305814188049E09
INS98302_SIP_B_1_1 = 1.4825209196581E06
INS98302_SIP_B_0_2 = 9.8144272268748E07
INS98302_SIP_AP_ORDER = 3
INS98302_SIP_AP_3_0 = 7.3440595935636E08
INS98302_SIP_AP_1_2 = 7.3440595935636E08
INS98302_SIP_AP_1_1 = 9.8955970313209E07
INS98302_SIP_AP_2_0 = 1.4975995507201E06
INS98302_SIP_BP_ORDER = 3
INS98302_SIP_BP_2_1 = 7.3440595935636E08
INS98302_SIP_BP_0_3 = 7.3440595935636E08
INS98302_SIP_BP_0_2 = 9.8955970313209E07
INS98302_SIP_BP_1_1 = 1.4975995507201E06
\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
INS98301_PIXEL_SAMPLES = ( 1024 )
INS98301_PIXEL_LINES = ( 1024 )
INS98301_PIXEL_SIZE = ( 12.997 )
INS98301_CCD_CENTER = ( 511.5, 511.5 )
INS98302_PIXEL_SAMPLES = ( 256 )
INS98302_PIXEL_LINES = ( 256 )
INS98302_PIXEL_SIZE = ( 51.988 )
INS98302_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
INS98300_REFERENCE_VECTOR = ( 1.0, 0.0, 0.0 )
INS98301_REFERENCE_VECTOR = ( 1.0, 0.0, 0.0 )
INS98302_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
INS98300_PLATFORM_ID = ( 98000 )
INS98301_PLATFORM_ID = ( 98000 )
INS98302_PLATFORM_ID = ( 98000 )
\begintext