#-----------------------------------------------------------------------------
# WCSLIB 8.3 - an implementation of the FITS WCS standard.
# Copyright (C) 1995-2024, Mark Calabretta
#
# This file is part of WCSLIB.
#
# WCSLIB is free software: you can redistribute it and/or modify it under the
# terms of the GNU Lesser General Public License as published by the Free
# Software Foundation, either version 3 of the License, or (at your option)
# any later version.
#
# WCSLIB is distributed in the hope that it will be useful, but WITHOUT ANY
# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
# FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public License for
# more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with WCSLIB.  If not, see http://www.gnu.org/licenses.
#
# Author: Mark Calabretta, Australia Telescope National Facility, CSIRO.
# http://www.atnf.csiro.au/people/Mark.Calabretta
# $Id: SIPTPV.keyrec,v 8.3 2024/05/13 16:33:00 mcalabre Exp $
#-----------------------------------------------------------------------------
#
# FITS header keyrecords used for testing the handling of the "SIP" (Simple
# Imaging Polynomial) and TPV distortions by WCSLIB.
#
# This header was adapted from a pair of FITS files from the Palomar Transient
# Factory (IPAC) provided by David Shupe.  The same distortion was encoded in
# two ways, the primary representation uses the SIP convention, and the 'P'
# alternate the TPV projection.  Translations of both of these into other
# distortion functions were then added as alternates.
#
# Use 'tofits' (supplied) to convert this file to proper FITS format via
#
#     tofits < SIPTPV.keyrec > SIPTPV.fits
#
# Lines in this file beginning with '#' are ignored by tofits.
#
#-----------------------------------------------------------------------------
SIMPLE  =                    T / Conforms to FITS standard
BITPIX  =                  -32 / IEEE single precision floating point
NAXIS   =                    2 / 2 image axes
NAXIS1  =                 2048 / Length of image axis 1
NAXIS2  =                 4096 / Length of image axis 2

COMMENT  -----------------------------------------------------------------------
COMMENT  Simple Imaging Polynomial (SIP) distortion.
COMMENT  SIP does not support alternate representations nor axis mapping.
COMMENT  In the keycomments, x and y refer to axes 1 and 2 respectively.
COMMENT  -----------------------------------------------------------------------

WCSNAME = 'SIPTPV-0: native SIP representation'
CRPIX1  =             -3925.16 / Pixel coordinate of reference point
CRPIX2  =              4360.23 / Pixel coordinate of reference point
CD1_1   =  0.00028610265860158 / [deg] CD matrix element
CD1_2   = -6.2881662833181E-07 / [deg] CD matrix element
CD2_1   = -5.7720701811452E-06 / [deg] CD matrix element
CD2_2   = -0.00028152525617189 / [deg] CD matrix element
CTYPE1  = 'RA---TAN-SIP'       / TAN (gnomonic) projection + SIP distortions
CTYPE2  = 'DEC--TAN-SIP'       / TAN (gnomonic) projection + SIP distortions
CRVAL1  =    274.8069457088980 / [deg] Right ascension at the reference point
CRVAL2  =    -25.9746476963393 / [deg] Declination at the reference point
CUNIT1  = 'deg     '           / Image axis-1 celestial-coordinate units
CUNIT2  = 'deg     '           / Image axis-2 celestial-coordinate units

A_ORDER =                    4 / SIP distortion polynomial order for A
A_2_0   = -4.6101438020313E-06 / SIP coefficient: xx
A_1_1   =  1.4745130969827E-06 / SIP coefficient: xy
A_0_2   = -6.8832077243635E-08 / SIP coefficient: yy
A_3_0   =  5.1080179892854E-10 / SIP coefficient: xxx
A_2_1   = -3.2570122733976E-10 / SIP coefficient: xxy
A_1_2   = -5.4789597808432E-11 / SIP coefficient: xyy
A_0_3   = -3.9165520771852E-11 / SIP coefficient: yyy
A_4_0   = -2.2410038481669E-14 / SIP coefficient: xxxx
A_3_1   =  2.4024589153935E-14 / SIP coefficient: xxxy
A_2_2   =  5.8725301231513E-15 / SIP coefficient: xxyy
A_1_3   =  4.3257176022080E-15 / SIP coefficient: xyyy
A_0_4   = -1.3734790334086E-15 / SIP coefficient: yyyy
A_DMAX  =                96.50 / Maximum absolute value of distortion function

AP_ORDER=                    4 / SIP distortion polynomial order for AP
AP_1_0  =  5.9649623134206E-06 / SIP coefficient: x
AP_0_1  = -8.3563633819506E-06 / SIP coefficient: y
AP_2_0  =  4.6391279824110E-06 / SIP coefficient: xx
AP_1_1  = -1.4755159708559E-06 / SIP coefficient: xy
AP_0_2  =  6.4191937073851E-08 / SIP coefficient: yy
AP_3_0  = -5.0301820040373E-10 / SIP coefficient: xxx
AP_2_1  =  3.2299095062767E-10 / SIP coefficient: xxy
AP_1_2  =  5.9682183111397E-11 / SIP coefficient: xyy
AP_0_3  =  3.8257592980128E-11 / SIP coefficient: yyy
AP_4_0  =  2.1394444946766E-14 / SIP coefficient: xxxx
AP_3_1  = -2.3531528160891E-14 / SIP coefficient: xxxy
AP_2_2  = -6.3049777026371E-15 / SIP coefficient: xxyy
AP_1_3  = -4.0743135634870E-15 / SIP coefficient: xyyy
AP_0_4  =  1.3469594159815E-15 / SIP coefficient: yyyy

B_ORDER =                    4 / SIP distortion polynomial order for B
B_2_0   = -6.2926490499120E-06 / SIP coefficient: xx
B_1_1   =  5.9146560187892E-08 / SIP coefficient: xy
B_0_2   =  2.1061956862630E-07 / SIP coefficient: yy
B_3_0   =  8.6240995389586E-10 / SIP coefficient: xxx
B_2_1   = -6.7715107588365E-11 / SIP coefficient: xxy
B_1_2   = -5.1237410950671E-11 / SIP coefficient: xyy
B_0_3   = -5.0622542139077E-12 / SIP coefficient: yyy
B_4_0   = -4.3853697321471E-14 / SIP coefficient: xxxx
B_3_1   =  4.0077335382236E-15 / SIP coefficient: xxxy
B_2_2   =  3.3307943746343E-15 / SIP coefficient: xxyy
B_1_3   = -1.8559485838936E-15 / SIP coefficient: xyyy
B_0_4   =  5.1753961684558E-16 / SIP coefficient: yyyy
B_DMAX  =                95.54 / Maximum absolute value of distortion function

BP_ORDER=                    4 / SIP distortion polynomial order for BP
BP_1_0  =  2.2440627219345E-05 / SIP coefficient: x
BP_0_1  = -5.3534179990933E-06 / SIP coefficient: y
BP_2_0  =  6.3381348251001E-06 / SIP coefficient: xx
BP_1_1  = -5.7866326487642E-08 / SIP coefficient: xy
BP_0_2  = -2.1754801138237E-07 / SIP coefficient: yy
BP_3_0  = -8.5509468876083E-10 / SIP coefficient: xxx
BP_2_1  =  5.9962354835928E-11 / SIP coefficient: xxy
BP_1_2  =  5.4445150144274E-11 / SIP coefficient: xyy
BP_0_3  =  3.4614188483640E-12 / SIP coefficient: yyy
BP_4_0  =  4.2670473211337E-14 / SIP coefficient: xxxx
BP_3_1  = -2.7332730855666E-15 / SIP coefficient: xxxy
BP_2_2  = -3.3053766170687E-15 / SIP coefficient: xxyy
BP_1_3  =  2.2994237554827E-15 / SIP coefficient: xyyy
BP_0_4  = -5.5022506030438E-16 / SIP coefficient: yyyy

COMMENT  -----------------------------------------------------------------------
COMMENT  The WCSLIB header parser handles a SIP distortion (as above) by
COMMENT  translating its keyrecords internally into a 'SIP' distortion type
COMMENT  for later analysis.  That translation may also be written directly
COMMENT  in a header as done here.
COMMENT
COMMENT  Note the addition of renormalization parameters, explained below:
COMMENT    DP1A.OFFSET.1 = CRPIX1,
COMMENT    DP1A.OFFSET.2 = CRPIX2,
COMMENT    DP2A.OFFSET.1 = CRPIX1,
COMMENT    DP2A.OFFSET.2 = CRPIX2.
COMMENT  These are added to the distortion parameters since the WCSLIB
COMMENT  routines that implement distortions do not have access to CRPIXja.
COMMENT
COMMENT  In the keycomments, x and y refer to axes 1 and 2, which are the RA
COMMENT  and DEC axes.
COMMENT  -----------------------------------------------------------------------

WCSNAMEA= 'SIPTPV-1: SIP translated to a ''SIP'' distortion'
CRPIX1A =             -3925.16 / Pixel coordinate of reference point
CRPIX2A =              4360.23 / Pixel coordinate of reference point
CD1_1A  =  0.00028610265860158 / [deg] CD matrix element
CD1_2A  = -6.2881662833181E-07 / [deg] CD matrix element
CD2_1A  = -5.7720701811452E-06 / [deg] CD matrix element
CD2_2A  = -0.00028152525617189 / [deg] CD matrix element
CTYPE1A = 'RA---TAN'           / TAN (gnomonic) projection
CTYPE2A = 'DEC--TAN'           / TAN (gnomonic) projection
CRVAL1A =    274.8069457088980 / [deg] Right ascension at the reference point
CRVAL2A =    -25.9746476963393 / [deg] Declination at the reference point
CUNIT1A = 'deg     '           / Image axis-1 celestial-coordinate units
CUNIT2A = 'deg     '           / Image axis-2 celestial-coordinate units

CPDIS1A = 'SIP     '           / P = prior distortion, Simple Imaging Polynomial
DP1A    = 'NAXES: 2'           / Two independent variables
DP1A    = 'OFFSET.1: -3925.16'
DP1A    = 'OFFSET.2:  4360.23'
DP1A    = 'SIP.FWD.2_0: -4.6101438020313E-06' / SIP coefficient: xx
DP1A    = 'SIP.FWD.1_1:  1.4745130969827E-06' / SIP coefficient: xy
DP1A    = 'SIP.FWD.0_2: -6.8832077243635E-08' / SIP coefficient: yy
DP1A    = 'SIP.FWD.3_0:  5.1080179892854E-10' / SIP coefficient: xxx
DP1A    = 'SIP.FWD.2_1: -3.2570122733976E-10' / SIP coefficient: xxy
DP1A    = 'SIP.FWD.1_2: -5.4789597808432E-11' / SIP coefficient: xyy
DP1A    = 'SIP.FWD.0_3: -3.9165520771852E-11' / SIP coefficient: yyy
DP1A    = 'SIP.FWD.4_0: -2.2410038481669E-14' / SIP coefficient: xxxx
DP1A    = 'SIP.FWD.3_1:  2.4024589153935E-14' / SIP coefficient: xxxy
DP1A    = 'SIP.FWD.2_2:  5.8725301231513E-15' / SIP coefficient: xxyy
DP1A    = 'SIP.FWD.1_3:  4.3257176022080E-15' / SIP coefficient: xyyy
DP1A    = 'SIP.FWD.0_4: -1.3734790334086E-15' / SIP coefficient: yyyy
CPERR1A =                96.50 / Maximum absolute value of distortion function

DP1A    = 'SIP.REV.1_0:  5.9649623134206E-06' / SIP coefficient: x
DP1A    = 'SIP.REV.0_1: -8.3563633819506E-06' / SIP coefficient: y
DP1A    = 'SIP.REV.2_0:  4.6391279824110E-06' / SIP coefficient: xx
DP1A    = 'SIP.REV.1_1: -1.4755159708559E-06' / SIP coefficient: xy
DP1A    = 'SIP.REV.0_2:  6.4191937073851E-08' / SIP coefficient: yy
DP1A    = 'SIP.REV.3_0: -5.0301820040373E-10' / SIP coefficient: xxx
DP1A    = 'SIP.REV.2_1:  3.2299095062767E-10' / SIP coefficient: xxy
DP1A    = 'SIP.REV.1_2:  5.9682183111397E-11' / SIP coefficient: xyy
DP1A    = 'SIP.REV.0_3:  3.8257592980128E-11' / SIP coefficient: yyy
DP1A    = 'SIP.REV.4_0:  2.1394444946766E-14' / SIP coefficient: xxxx
DP1A    = 'SIP.REV.3_1: -2.3531528160891E-14' / SIP coefficient: xxxy
DP1A    = 'SIP.REV.2_2: -6.3049777026371E-15' / SIP coefficient: xxyy
DP1A    = 'SIP.REV.1_3: -4.0743135634870E-15' / SIP coefficient: xyyy
DP1A    = 'SIP.REV.0_4:  1.3469594159815E-15' / SIP coefficient: yyyy

CPDIS2A = 'SIP     '           / P = prior distortion, Simple Imaging Polynomial
DP2A    = 'NAXES: 2'           / Two independent variables
DP2A    = 'OFFSET.1: -3925.16'
DP2A    = 'OFFSET.2:  4360.23'
DP2A    = 'SIP.FWD.2_0: -6.2926490499120E-06' / SIP coefficient: xx
DP2A    = 'SIP.FWD.1_1:  5.9146560187892E-08' / SIP coefficient: xy
DP2A    = 'SIP.FWD.0_2:  2.1061956862630E-07' / SIP coefficient: yy
DP2A    = 'SIP.FWD.3_0:  8.6240995389586E-10' / SIP coefficient: xxx
DP2A    = 'SIP.FWD.2_1: -6.7715107588365E-11' / SIP coefficient: xxy
DP2A    = 'SIP.FWD.1_2: -5.1237410950671E-11' / SIP coefficient: xyy
DP2A    = 'SIP.FWD.0_3: -5.0622542139077E-12' / SIP coefficient: yyy
DP2A    = 'SIP.FWD.4_0: -4.3853697321471E-14' / SIP coefficient: xxxx
DP2A    = 'SIP.FWD.3_1:  4.0077335382236E-15' / SIP coefficient: xxxy
DP2A    = 'SIP.FWD.2_2:  3.3307943746343E-15' / SIP coefficient: xxyy
DP2A    = 'SIP.FWD.1_3: -1.8559485838936E-15' / SIP coefficient: xyyy
DP2A    = 'SIP.FWD.0_4:  5.1753961684558E-16' / SIP coefficient: yyyy
CPERR2A =                95.54 / Maximum absolute value of distortion function

DP2A    = 'SIP.REV.1_0:  2.2440627219345E-05' / SIP coefficient: x
DP2A    = 'SIP.REV.0_1: -5.3534179990933E-06' / SIP coefficient: y
DP2A    = 'SIP.REV.2_0:  6.3381348251001E-06' / SIP coefficient: xx
DP2A    = 'SIP.REV.1_1: -5.7866326487642E-08' / SIP coefficient: xy
DP2A    = 'SIP.REV.0_2: -2.1754801138237E-07' / SIP coefficient: yy
DP2A    = 'SIP.REV.3_0: -8.5509468876083E-10' / SIP coefficient: xxx
DP2A    = 'SIP.REV.2_1:  5.9962354835928E-11' / SIP coefficient: xxy
DP2A    = 'SIP.REV.1_2:  5.4445150144274E-11' / SIP coefficient: xyy
DP2A    = 'SIP.REV.0_3:  3.4614188483640E-12' / SIP coefficient: yyy
DP2A    = 'SIP.REV.4_0:  4.2670473211337E-14' / SIP coefficient: xxxx
DP2A    = 'SIP.REV.3_1: -2.7332730855666E-15' / SIP coefficient: xxxy
DP2A    = 'SIP.REV.2_2: -3.3053766170687E-15' / SIP coefficient: xxyy
DP2A    = 'SIP.REV.1_3:  2.2994237554827E-15' / SIP coefficient: xyyy
DP2A    = 'SIP.REV.0_4: -5.5022506030438E-16' / SIP coefficient: yyyy

COMMENT  -----------------------------------------------------------------------
COMMENT  WCSLIB implements the 'SIP' distortion (as above), including its
COMMENT  polynomial approximation to the inverse, as a special case of the
COMMENT  more general 'TPD' distortion.
COMMENT
COMMENT  TPD supports all of the constructs defined in WCS Paper IV, and
COMMENT  follows it in computing distortion corrections from pixel coordinates.
COMMENT  However, the independent variables of the SIP polynomial are offsets
COMMENT  from the reference pixel.  This is handled here by setting the
COMMENT  renormalization parameters:
COMMENT    DP1B.OFFSET.1 = CRPIX1,
COMMENT    DP1B.OFFSET.2 = CRPIX2,
COMMENT    DP2B.OFFSET.1 = CRPIX1,
COMMENT    DP2B.OFFSET.2 = CRPIX2.
COMMENT
COMMENT  Keycomments show the mapping between SIP keywords and TPD coefficient
COMMENT  indices.
COMMENT
COMMENT  In the keycomments, x and y refer to axes 1 and 2, which are the RA
COMMENT  and DEC axes.
COMMENT  -----------------------------------------------------------------------

WCSNAMEB= 'SIPTPV-2: SIP translated to a ''TPD'' distortion'
CRPIX1B =             -3925.16 / Pixel coordinate of reference point
CRPIX2B =              4360.23 / Pixel coordinate of reference point
CD1_1B  =  0.00028610265860158 / [deg] CD matrix element
CD1_2B  = -6.2881662833181E-07 / [deg] CD matrix element
CD2_1B  = -5.7720701811452E-06 / [deg] CD matrix element
CD2_2B  = -0.00028152525617189 / [deg] CD matrix element
CTYPE1B = 'RA---TAN'           / TAN (gnomonic) projection
CTYPE2B = 'DEC--TAN'           / TAN (gnomonic) projection
CRVAL1B =    274.8069457088980 / [deg] Right ascension at the reference point
CRVAL2B =    -25.9746476963393 / [deg] Declination at the reference point
CUNIT1B = 'deg     '           / Image axis-1 celestial-coordinate units
CUNIT2B = 'deg     '           / Image axis-2 celestial-coordinate units

CPDIS1B = 'TPD'                / P = prior, Template Polynomial Distortion
DP1B    = 'NAXES: 2'           / Two independent variables
DP1B    = 'OFFSET.1: -3925.16'
DP1B    = 'OFFSET.2:  4360.23'
DP1B    = 'TPD.FWD.0:                   0.0' / TPD coefficient: 1
DP1B    = 'TPD.FWD.1:                   0.0' / TPD coefficient: x     A_1_0
DP1B    = 'TPD.FWD.4:  -4.6101438020313E-06' / TPD coefficient: xx    A_2_0
DP1B    = 'TPD.FWD.5:   1.4745130969827E-06' / TPD coefficient: xy    A_1_1
DP1B    = 'TPD.FWD.6:  -6.8832077243635E-08' / TPD coefficient: yy    A_0_2
DP1B    = 'TPD.FWD.7:   5.1080179892854E-10' / TPD coefficient: xxx   A_3_0
DP1B    = 'TPD.FWD.8:  -3.2570122733976E-10' / TPD coefficient: xxy   A_2_1
DP1B    = 'TPD.FWD.9:  -5.4789597808432E-11' / TPD coefficient: xyy   A_1_2
DP1B    = 'TPD.FWD.10: -3.9165520771852E-11' / TPD coefficient: yyy   A_0_3
DP1B    = 'TPD.FWD.12: -2.2410038481669E-14' / TPD coefficient: xxxx  A_4_0
DP1B    = 'TPD.FWD.13:  2.4024589153935E-14' / TPD coefficient: xxxy  A_3_1
DP1B    = 'TPD.FWD.14:  5.8725301231513E-15' / TPD coefficient: xxyy  A_2_2
DP1B    = 'TPD.FWD.15:  4.3257176022080E-15' / TPD coefficient: xyyy  A_1_3
DP1B    = 'TPD.FWD.16: -1.3734790334086E-15' / TPD coefficient: yyyy  A_0_4
CPERR1B =                96.50 / Maximum absolute value of distortion function

DP1B    = 'TPD.REV.0:                   0.0' / TPD coefficient: 1
DP1B    = 'TPD.REV.1:   5.9649623134206E-06' / TPD coefficient: x     AP_1_0
DP1B    = 'TPD.REV.2:  -8.3563633819506E-06' / TPD coefficient: y     AP_0_1
DP1B    = 'TPD.REV.4:   4.6391279824110E-06' / TPD coefficient: xx    AP_2_0
DP1B    = 'TPD.REV.5:  -1.4755159708559E-06' / TPD coefficient: xy    AP_1_1
DP1B    = 'TPD.REV.6:   6.4191937073851E-08' / TPD coefficient: yy    AP_0_2
DP1B    = 'TPD.REV.7:  -5.0301820040373E-10' / TPD coefficient: xxx   AP_3_0
DP1B    = 'TPD.REV.8:   3.2299095062767E-10' / TPD coefficient: xxy   AP_2_1
DP1B    = 'TPD.REV.9:   5.9682183111397E-11' / TPD coefficient: xyy   AP_1_2
DP1B    = 'TPD.REV.10:  3.8257592980128E-11' / TPD coefficient: yyy   AP_0_3
DP1B    = 'TPD.REV.12:  2.1394444946766E-14' / TPD coefficient: xxxx  AP_4_0
DP1B    = 'TPD.REV.13: -2.3531528160891E-14' / TPD coefficient: xxxy  AP_3_1
DP1B    = 'TPD.REV.14: -6.3049777026371E-15' / TPD coefficient: xxyy  AP_2_2
DP1B    = 'TPD.REV.15: -4.0743135634870E-15' / TPD coefficient: xyyy  AP_1_3
DP1B    = 'TPD.REV.16:  1.3469594159815E-15' / TPD coefficient: yyyy  AP_0_4

CPDIS2B = 'TPD'                / P = prior, Template Polynomial Distortion
DP2B    = 'NAXES: 2'           / Two independent variables
DP2B    = 'OFFSET.1: -3925.16'
DP2B    = 'OFFSET.2:  4360.23'
DP2B    = 'TPD.FWD.0:                   0.0' / TPD coefficient: 1
DP2B    = 'TPD.FWD.2:                   0.0' / TPD coefficient: y     B_0_1
DP2B    = 'TPD.FWD.4:  -6.2926490499120E-06' / TPD coefficient: xx    B_2_0
DP2B    = 'TPD.FWD.5:   5.9146560187892E-08' / TPD coefficient: xy    B_1_1
DP2B    = 'TPD.FWD.6:   2.1061956862630E-07' / TPD coefficient: yy    B_0_2
DP2B    = 'TPD.FWD.7:   8.6240995389586E-10' / TPD coefficient: xxx   B_3_0
DP2B    = 'TPD.FWD.8:  -6.7715107588365E-11' / TPD coefficient: xxy   B_2_1
DP2B    = 'TPD.FWD.9:  -5.1237410950671E-11' / TPD coefficient: xyy   B_1_2
DP2B    = 'TPD.FWD.10: -5.0622542139077E-12' / TPD coefficient: yyy   B_0_3
DP2B    = 'TPD.FWD.12: -4.3853697321471E-14' / TPD coefficient: xxxx  B_4_0
DP2B    = 'TPD.FWD.13:  4.0077335382236E-15' / TPD coefficient: xxxy  B_3_1
DP2B    = 'TPD.FWD.14:  3.3307943746343E-15' / TPD coefficient: xxyy  B_2_2
DP2B    = 'TPD.FWD.15: -1.8559485838936E-15' / TPD coefficient: xyyy  B_1_3
DP2B    = 'TPD.FWD.16:  5.1753961684558E-16' / TPD coefficient: yyyy  B_0_4
CPERR2B =                95.54 / Maximum absolute value of distortion function

DP2B    = 'TPD.REV.0:                   0.0' / TPD coefficient: 1
DP2B    = 'TPD.REV.1:   2.2440627219345E-05' / TPD coefficient: x     BP_1_0
DP2B    = 'TPD.REV.2:  -5.3534179990933E-06' / TPD coefficient: y     BP_0_1
DP2B    = 'TPD.REV.4:   6.3381348251001E-06' / TPD coefficient: xx    BP_2_0
DP2B    = 'TPD.REV.5:  -5.7866326487642E-08' / TPD coefficient: xy    BP_1_1
DP2B    = 'TPD.REV.6:  -2.1754801138237E-07' / TPD coefficient: yy    BP_0_2
DP2B    = 'TPD.REV.7:  -8.5509468876083E-10' / TPD coefficient: xxx   BP_3_0
DP2B    = 'TPD.REV.8:   5.9962354835928E-11' / TPD coefficient: xxy   BP_2_1
DP2B    = 'TPD.REV.9:   5.4445150144274E-11' / TPD coefficient: xyy   BP_1_2
DP2B    = 'TPD.REV.10:  3.4614188483640E-12' / TPD coefficient: yyy   BP_0_3
DP2B    = 'TPD.REV.12:  4.2670473211337E-14' / TPD coefficient: xxxx  BP_4_0
DP2B    = 'TPD.REV.13: -2.7332730855666E-15' / TPD coefficient: xxxy  BP_3_1
DP2B    = 'TPD.REV.14: -3.3053766170687E-15' / TPD coefficient: xxyy  BP_2_2
DP2B    = 'TPD.REV.15:  2.2994237554827E-15' / TPD coefficient: xyyy  BP_1_3
DP2B    = 'TPD.REV.16: -5.5022506030438E-16' / TPD coefficient: yyyy  BP_0_4

COMMENT  -----------------------------------------------------------------------
COMMENT  The SIP representation above translated to Polynomial as a prior
COMMENT  distortion, including SIP's polynomial approximation to the inverse.
COMMENT
COMMENT  The comments above for the translation to TPD apply here as well.
COMMENT
COMMENT  In the keycomments, x and y refer to axes 1 and 2, which are the RA
COMMENT  and DEC axes.
COMMENT  -----------------------------------------------------------------------

WCSNAMEC= 'SIPTPV-3: SIP translated to a ''Polynomial'' distortion'
CRPIX1C =             -3925.16 / Pixel coordinate of reference point
CRPIX2C =              4360.23 / Pixel coordinate of reference point
CD1_1C  =  0.00028610265860158 / [deg] CD matrix element
CD1_2C  = -6.2881662833181E-07 / [deg] CD matrix element
CD2_1C  = -5.7720701811452E-06 / [deg] CD matrix element
CD2_2C  = -0.00028152525617189 / [deg] CD matrix element
CTYPE1C = 'RA---TAN'           / TAN (gnomonic) projection
CTYPE2C = 'DEC--TAN'           / TAN (gnomonic) projection
CRVAL1C =    274.8069457088980 / [deg] Right ascension at the reference point
CRVAL2C =    -25.9746476963393 / [deg] Declination at the reference point
CUNIT1C = 'deg     '           / Image axis-1 celestial-coordinate units
CUNIT2C = 'deg     '           / Image axis-2 celestial-coordinate units

CPDIS1C = 'Polynomial'         / P = prior, Polynomial distortion
DP1C    = 'NAXES:  2'          / Two independent variables
DP1C    = 'OFFSET.1: -3925.16'
DP1C    = 'OFFSET.2:  4360.23'
DP1C    = 'NTERMS: 14'         / Number of terms in the polynomial
DP1C    = 'TERM.1.COEFF:                   0.0' / Poly coefficient: 1
DP1C    = 'TERM.2.COEFF:                     0' / Poly coefficient: x     A_1_0
DP1C    = 'TERM.2.VAR.1:                     1' / Poly power 1 (x): x
DP1C    = 'TERM.3.COEFF:  -4.6101438020313E-06' / Poly coefficient: xx    A_2_0
DP1C    = 'TERM.3.VAR.1:                     2' / Poly power 1 (x): xx
DP1C    = 'TERM.4.COEFF:   1.4745130969827E-06' / Poly coefficient: xy    A_1_1
DP1C    = 'TERM.4.VAR.1:                     1' / Poly power 1 (x): xy
DP1C    = 'TERM.4.VAR.2:                     1' / Poly power 2 (y): xy
DP1C    = 'TERM.5.COEFF:  -6.8832077243635E-08' / Poly coefficient: yy    A_0_2
DP1C    = 'TERM.5.VAR.2:                     2' / Poly power 2 (y): yy
DP1C    = 'TERM.6.COEFF:   5.1080179892854E-10' / Poly coefficient: xxx   A_3_0
DP1C    = 'TERM.6.VAR.1:                     3' / Poly power 1 (x): xxx
DP1C    = 'TERM.7.COEFF:  -3.2570122733976E-10' / Poly coefficient: xxy   A_2_1
DP1C    = 'TERM.7.VAR.1:                     2' / Poly power 1 (x): xxy
DP1C    = 'TERM.7.VAR.2:                     1' / Poly power 2 (y): xxy
DP1C    = 'TERM.8.COEFF:  -5.4789597808432E-11' / Poly coefficient: xyy   A_1_2
DP1C    = 'TERM.8.VAR.1:                     1' / Poly power 1 (x): xyy
DP1C    = 'TERM.8.VAR.2:                     2' / Poly power 2 (y): xyy
DP1C    = 'TERM.9.COEFF:  -3.9165520771852E-11' / Poly coefficient: yyy   A_0_3
DP1C    = 'TERM.9.VAR.2:                     3' / Poly power 2 (y): yyy
DP1C    = 'TERM.10.COEFF: -2.2410038481669E-14' / Poly coefficient: xxxx  A_4_0
DP1C    = 'TERM.10.VAR.1:                    4' / Poly power 1 (x): xxxx
DP1C    = 'TERM.11.COEFF:  2.4024589153935E-14' / Poly coefficient: xxxy  A_3_1
DP1C    = 'TERM.11.VAR.1:                    3' / Poly power 1 (x): xxxy
DP1C    = 'TERM.11.VAR.2:                    1' / Poly power 2 (y): xxxy
DP1C    = 'TERM.12.COEFF:  5.8725301231513E-15' / Poly coefficient: xxyy  A_2_2
DP1C    = 'TERM.12.VAR.1:                    2' / Poly power 1 (x): xxyy
DP1C    = 'TERM.12.VAR.2:                    2' / Poly power 2 (y): xxyy
DP1C    = 'TERM.13.COEFF:  4.3257176022080E-15' / Poly coefficient: xyyy  A_1_3
DP1C    = 'TERM.13.VAR.1:                    1' / Poly power 1 (x): xyyy
DP1C    = 'TERM.13.VAR.2:                    3' / Poly power 2 (y): xyyy
DP1C    = 'TERM.14.COEFF: -1.3734790334086E-15' / Poly coefficient: yyyy  A_0_4
DP1C    = 'TERM.14.VAR.2:                    4' / Poly power 2 (y): yyyy
CPERR1C =                96.50 / Maximum absolute value of distortion function

CPDIS2C = 'Polynomial'         / P = prior, Polynomial distortion
DP2C    = 'NAXES:  2'          / Two independent variables
DP2C    = 'OFFSET.1: -3925.16'
DP2C    = 'OFFSET.2:  4360.23'
DP2C    = 'NTERMS: 14'         / Number of terms in the polynomial
DP2C    = 'TERM.1.COEFF:                   0.0' / Poly coefficient: 1
DP2C    = 'TERM.2.COEFF:                     0' / Poly coefficient: y     B_0_1
DP2C    = 'TERM.2.VAR.2:                     1' / Poly power 2 (y): y
DP2C    = 'TERM.3.COEFF:  -6.2926490499120E-06' / Poly coefficient: xx    B_2_0
DP2C    = 'TERM.3.VAR.1:                     2' / Poly power 1 (x): xx
DP2C    = 'TERM.4.COEFF:   5.9146560187892E-08' / Poly coefficient: xy    B_1_1
DP2C    = 'TERM.4.VAR.1:                     1' / Poly power 1 (x): xy
DP2C    = 'TERM.4.VAR.2:                     1' / Poly power 2 (y): xy
DP2C    = 'TERM.5.COEFF:   2.1061956862630E-07' / Poly coefficient: yy    B_0_2
DP2C    = 'TERM.5.VAR.2:                     2' / Poly power 2 (y): yy
DP2C    = 'TERM.6.COEFF:   8.6240995389586E-10' / Poly coefficient: xxx   B_3_0
DP2C    = 'TERM.6.VAR.1:                     3' / Poly power 1 (x): xxx
DP2C    = 'TERM.7.COEFF:  -6.7715107588365E-11' / Poly coefficient: xxy   B_2_1
DP2C    = 'TERM.7.VAR.1:                     2' / Poly power 1 (x): xxy
DP2C    = 'TERM.7.VAR.2:                     1' / Poly power 2 (y): xxy
DP2C    = 'TERM.8.COEFF:  -5.1237410950671E-11' / Poly coefficient: xyy   B_1_2
DP2C    = 'TERM.8.VAR.1:                     1' / Poly power 1 (x): xyy
DP2C    = 'TERM.8.VAR.2:                     2' / Poly power 2 (y): xyy
DP2C    = 'TERM.9.COEFF:  -5.0622542139077E-12' / Poly coefficient: yyy   B_0_3
DP2C    = 'TERM.9.VAR.2:                     3' / Poly power 2 (y): yyy
DP2C    = 'TERM.10.COEFF: -4.3853697321471E-14' / Poly coefficient: xxxx  B_4_0
DP2C    = 'TERM.10.VAR.1:                    4' / Poly power 1 (x): xxxx
DP2C    = 'TERM.11.COEFF:  4.0077335382236E-15' / Poly coefficient: xxxy  B_3_1
DP2C    = 'TERM.11.VAR.1:                    3' / Poly power 1 (x): xxxy
DP2C    = 'TERM.11.VAR.2:                    1' / Poly power 2 (y): xxxy
DP2C    = 'TERM.12.COEFF:  3.3307943746343E-15' / Poly coefficient: xxyy  B_2_2
DP2C    = 'TERM.12.VAR.1:                    2' / Poly power 1 (x): xxyy
DP2C    = 'TERM.12.VAR.2:                    2' / Poly power 2 (y): xxyy
DP2C    = 'TERM.13.COEFF: -1.8559485838936E-15' / Poly coefficient: xyyy  B_1_3
DP2C    = 'TERM.13.VAR.1:                    1' / Poly power 1 (x): xyyy
DP2C    = 'TERM.13.VAR.2:                    3' / Poly power 2 (y): xyyy
DP2C    = 'TERM.14.COEFF:  5.1753961684558E-16' / Poly coefficient: yyyy  B_0_4
DP2C    = 'TERM.14.VAR.2:                    4' / Poly power 2 (y): yyyy
CPERR2C =                95.54 / Maximum absolute value of distortion function

COMMENT  =======================================================================
COMMENT  The above SIP distortion translated to TPV differs only in CTYPEia and
COMMENT  the keyrecords relating to the distortion polynomial.  The polynomial
COMMENT  coefficients differ from SIP because the TPV distortion follows the
COMMENT  linear transformation (sequent), rather than preceding it (prior).
COMMENT
COMMENT  TPV supports alternate representations, with axis mapping tied to the
COMMENT  celestial axes.  In the keycomments, x and y for TPV refer to the RA
COMMENT  and DEC axes respectively, which are axes 1 and 2 here.
COMMENT  -----------------------------------------------------------------------

WCSNAMEP= 'SIPTPV-4: native TPV representation'
CRPIX1P =             -3925.16 / Pixel coordinate of reference point
CRPIX2P =              4360.23 / Pixel coordinate of reference point
CD1_1P  =  0.00028610265860158 / [deg] CD matrix element
CD1_2P  = -6.2881662833181E-07 / [deg] CD matrix element
CD2_1P  = -5.7720701811452E-06 / [deg] CD matrix element
CD2_2P  = -0.00028152525617189 / [deg] CD matrix element
CTYPE1P = 'RA---TPV'           / TAN (gnomonic) projection + distortions
CTYPE2P = 'DEC--TPV'           / TAN (gnomonic) projection + distortions
CRVAL1P =    274.8069457088980 / [deg] Right ascension at the reference point
CRVAL2P =    -25.9746476963393 / [deg] Declination at the reference point
CUNIT1P = 'deg     '           / Image axis-1 celestial-coordinate units
CUNIT2P = 'deg     '           / Image axis-2 celestial-coordinate units

PV1_1P  =                  1.0 / TPV coefficient: x
PV1_4P  = -0.01616956178892100 / TPV coefficient: xx
PV1_5P  = -0.00517474938746320 / TPV coefficient: xy
PV1_6P  = -0.00023850435805678 / TPV coefficient: yy
PV1_7P  =  0.00629760478963159 / TPV coefficient: xxx
PV1_8P  =  0.00397207946734115 / TPV coefficient: xxy
PV1_9P  = -0.00067729620645185 / TPV coefficient: xyy
PV1_10P =  0.00050354679706662 / TPV coefficient: yyy
PV1_12P = -0.00097355342974408 / TPV coefficient: xxxx
PV1_13P = -0.00102312736844768 / TPV coefficient: xxxy
PV1_14P =  0.00025362356834782 / TPV coefficient: xxyy
PV1_15P = -0.00020021192475813 / TPV coefficient: xyyy
PV1_16P = -6.2162660705097E-05 / TPV coefficient: yyyy

PV2_1P  =                  1.0 / TPV coefficient: y
PV2_4P  = -0.00074364565692291 / TPV coefficient: yy
PV2_5P  =  0.00018425002539649 / TPV coefficient: yx
PV2_6P  =  0.02197159197666640 / TPV coefficient: xx
PV2_7P  = -7.5449775263740E-05 / TPV coefficient: yyy
PV2_8P  =  0.00064935718511019 / TPV coefficient: yyx
PV2_9P  = -0.00081219646536117 / TPV coefficient: yxx
PV2_10P = -0.01050984336151780 / TPV coefficient: xxx
PV2_12P = -2.1755521894303E-05 / TPV coefficient: yyyy
PV2_13P = -7.9010371768005E-05 / TPV coefficient: yyyx
PV2_14P = -0.00015571170306733 / TPV coefficient: yyxx
PV2_15P =  0.00016933561718011 / TPV coefficient: yxxx
PV2_16P =  0.00186540574051853 / TPV coefficient: xxxx

COMMENT  -----------------------------------------------------------------------
COMMENT  WCSLIB handles a TPV "projection" (as above) by translating its PVi_ma
COMMENT  keyrecords internally into a 'TPV' distortion type for later analysis.
COMMENT  That translation may also be written directly in a header as done
COMMENT  here.
COMMENT
COMMENT  In the keycomments, x and y refer to axes 1 and 2, which are the RA
COMMENT  and DEC axes.  Here, identification of the variables associated with
COMMENT  the TPV coefficients swaps between DQ1 and DQ2 due to the axis maps:
COMMENT    DQ1Q.AXIS.1 = 1,
COMMENT    DQ1Q.AXIS.2 = 2,
COMMENT  versus
COMMENT    DQ2Q.AXIS.1 = 2,
COMMENT    DQ2Q.AXIS.2 = 1.
COMMENT  -----------------------------------------------------------------------

WCSNAMEQ= 'SIPTPV-5: TPV translated to a ''TPV'' distortion'
CRPIX1Q =             -3925.16 / Pixel coordinate of reference point
CRPIX2Q =              4360.23 / Pixel coordinate of reference point
CD1_1Q  =  0.00028610265860158 / [deg] CD matrix element
CD1_2Q  = -6.2881662833181E-07 / [deg] CD matrix element
CD2_1Q  = -5.7720701811452E-06 / [deg] CD matrix element
CD2_2Q  = -0.00028152525617189 / [deg] CD matrix element
CTYPE1Q = 'RA---TAN'           / TAN (gnomonic) projection
CTYPE2Q = 'DEC--TAN'           / TAN (gnomonic) projection
CRVAL1Q =    274.8069457088980 / [deg] Right ascension at the reference point
CRVAL2Q =    -25.9746476963393 / [deg] Declination at the reference point
CUNIT1Q = 'deg     '           / Image axis-1 celestial-coordinate units
CUNIT2Q = 'deg     '           / Image axis-2 celestial-coordinate units

CQDIS1Q = 'TPV'                / Q = sequent distortion
DQ1Q    = 'NAXES:  2'          / Two independent variables
DQ1Q    = 'AXIS.1: 1'          / 1st independent variable: axis 1 = x
DQ1Q    = 'AXIS.2: 2'          / 2nd independent variable: axis 2 = y
DQ1Q    = 'TPV.1:                   1.0' / TPV coefficient: x
DQ1Q    = 'TPV.4:  -0.01616956178892100' / TPV coefficient: xx
DQ1Q    = 'TPV.5:  -0.00517474938746320' / TPV coefficient: xy
DQ1Q    = 'TPV.6:  -0.00023850435805678' / TPV coefficient: yy
DQ1Q    = 'TPV.7:   0.00629760478963159' / TPV coefficient: xxx
DQ1Q    = 'TPV.8:   0.00397207946734115' / TPV coefficient: xxy
DQ1Q    = 'TPV.9:  -0.00067729620645185' / TPV coefficient: xyy
DQ1Q    = 'TPV.10:  0.00050354679706662' / TPV coefficient: yyy
DQ1Q    = 'TPV.12: -0.00097355342974408' / TPV coefficient: xxxx
DQ1Q    = 'TPV.13: -0.00102312736844768' / TPV coefficient: xxxy
DQ1Q    = 'TPV.14:  0.00025362356834782' / TPV coefficient: xxyy
DQ1Q    = 'TPV.15: -0.00020021192475813' / TPV coefficient: xyyy
DQ1Q    = 'TPV.16: -6.2162660705097E-05' / TPV coefficient: yyyy
CQERR1Q =                96.50 / Maximum absolute value of distortion function

CQDIS2Q = 'TPV'                / Q = sequent distortion
DQ2Q    = 'NAXES:  2'          / Two independent variables
DQ2Q    = 'AXIS.1: 2'          / 1st independent variable: axis 2 = y
DQ2Q    = 'AXIS.2: 1'          / 2nd independent variable: axis 1 = x
DQ2Q    = 'TPV.1:                   1.0' / TPV coefficient: y
DQ2Q    = 'TPV.4:  -0.00074364565692291' / TPV coefficient: yy
DQ2Q    = 'TPV.5:   0.00018425002539649' / TPV coefficient: yx
DQ2Q    = 'TPV.6:   0.02197159197666640' / TPV coefficient: xx
DQ2Q    = 'TPV.7:  -7.5449775263740E-05' / TPV coefficient: yyy
DQ2Q    = 'TPV.8:   0.00064935718511019' / TPV coefficient: yyx
DQ2Q    = 'TPV.9:  -0.00081219646536117' / TPV coefficient: yxx
DQ2Q    = 'TPV.10: -0.01050984336151780' / TPV coefficient: xxx
DQ2Q    = 'TPV.12: -2.1755521894303E-05' / TPV coefficient: yyyy
DQ2Q    = 'TPV.13: -7.9010371768005E-05' / TPV coefficient: yyyx
DQ2Q    = 'TPV.14: -0.00015571170306733' / TPV coefficient: yyxx
DQ2Q    = 'TPV.15:  0.00016933561718011' / TPV coefficient: yxxx
DQ2Q    = 'TPV.16:  0.00186540574051853' / TPV coefficient: xxxx
CQERR2Q =                95.54 / Maximum absolute value of distortion function

COMMENT  -----------------------------------------------------------------------
COMMENT  WCSLIB implements the 'TPV' distortion as a special case of the more
COMMENT  general 'TPD' distortion.
COMMENT
COMMENT  Using the same axis mapping as above, the 'TPV' distortion translates
COMMENT  straightforwardly to 'TPD' which is a super-set.
COMMENT
COMMENT  This transformation is done internally by WCSLIB (by tpvset()) in
COMMENT  implementing TPV as TPD.
COMMENT  -----------------------------------------------------------------------

WCSNAMER= 'SIPTPV-6: TPV translated to a ''TPD'' distortion'
CRPIX1R =             -3925.16 / Pixel coordinate of reference point
CRPIX2R =              4360.23 / Pixel coordinate of reference point
CD1_1R  =  0.00028610265860158 / [deg] CD matrix element
CD1_2R  = -6.2881662833181E-07 / [deg] CD matrix element
CD2_1R  = -5.7720701811452E-06 / [deg] CD matrix element
CD2_2R  = -0.00028152525617189 / [deg] CD matrix element
CTYPE1R = 'RA---TAN'           / TAN (gnomonic) projection
CTYPE2R = 'DEC--TAN'           / TAN (gnomonic) projection
CRVAL1R =    274.8069457088980 / [deg] Right ascension at the reference point
CRVAL2R =    -25.9746476963393 / [deg] Declination at the reference point
CUNIT1R = 'deg     '           / Image axis-1 celestial-coordinate units
CUNIT2R = 'deg     '           / Image axis-2 celestial-coordinate units

CQDIS1R = 'TPD'                / Q = sequent, Template Polynomial Distortion
DQ1R    = 'DOCORR: 0'          / Polynomial gives corrected coordinate
DQ1R    = 'NAXES:  2'          / Two independent variables
DQ1R    = 'AXIS.1: 1'          / 1st independent variable: axis 1 = x
DQ1R    = 'AXIS.2: 2'          / 2nd independent variable: axis 2 = y
DQ1R    = 'TPD.FWD.1:                   1.0' / TPD coefficient: x
DQ1R    = 'TPD.FWD.4:  -0.01616956178892100' / TPD coefficient: xx
DQ1R    = 'TPD.FWD.5:  -0.00517474938746320' / TPD coefficient: xy
DQ1R    = 'TPD.FWD.6:  -0.00023850435805678' / TPD coefficient: yy
DQ1R    = 'TPD.FWD.7:   0.00629760478963159' / TPD coefficient: xxx
DQ1R    = 'TPD.FWD.8:   0.00397207946734115' / TPD coefficient: xxy
DQ1R    = 'TPD.FWD.9:  -0.00067729620645185' / TPD coefficient: xyy
DQ1R    = 'TPD.FWD.10:  0.00050354679706662' / TPD coefficient: yyy
DQ1R    = 'TPD.FWD.12: -0.00097355342974408' / TPD coefficient: xxxx
DQ1R    = 'TPD.FWD.13: -0.00102312736844768' / TPD coefficient: xxxy
DQ1R    = 'TPD.FWD.14:  0.00025362356834782' / TPD coefficient: xxyy
DQ1R    = 'TPD.FWD.15: -0.00020021192475813' / TPD coefficient: xyyy
DQ1R    = 'TPD.FWD.16: -6.2162660705097E-05' / TPD coefficient: yyyy
CQERR1R =                96.50 / Maximum absolute value of distortion function

CQDIS2R = 'TPD'                / Q = sequent, Template Polynomial Distortion
DQ2R    = 'DOCORR: 0'          / Polynomial gives corrected coordinate
DQ2R    = 'NAXES:  2'          / Two independent variables
DQ2R    = 'AXIS.1: 2'          / 1st independent variable: axis 2 = y
DQ2R    = 'AXIS.2: 1'          / 2nd independent variable: axis 1 = x
DQ2R    = 'TPD.FWD.1:                   1.0' / TPD coefficient: y
DQ2R    = 'TPD.FWD.4:  -0.00074364565692291' / TPD coefficient: yy
DQ2R    = 'TPD.FWD.5:   0.00018425002539649' / TPD coefficient: yx
DQ2R    = 'TPD.FWD.6:   0.02197159197666640' / TPD coefficient: xx
DQ2R    = 'TPD.FWD.7:  -7.5449775263740E-05' / TPD coefficient: yyy
DQ2R    = 'TPD.FWD.8:   0.00064935718511019' / TPD coefficient: yyx
DQ2R    = 'TPD.FWD.9:  -0.00081219646536117' / TPD coefficient: yxx
DQ2R    = 'TPD.FWD.10: -0.01050984336151780' / TPD coefficient: xxx
DQ2R    = 'TPD.FWD.12: -2.1755521894303E-05' / TPD coefficient: yyyy
DQ2R    = 'TPD.FWD.13: -7.9010371768005E-05' / TPD coefficient: yyyx
DQ2R    = 'TPD.FWD.14: -0.00015571170306733' / TPD coefficient: yyxx
DQ2R    = 'TPD.FWD.15:  0.00016933561718011' / TPD coefficient: yxxx
DQ2R    = 'TPD.FWD.16:  0.00186540574051853' / TPD coefficient: xxxx
CQERR2R =                95.54 / Maximum absolute value of distortion function

COMMENT  -----------------------------------------------------------------------
COMMENT  The TPV representation above translated to TPD as a sequent
COMMENT  distortion, but this time without using an axis mapping.  Note how
COMMENT  the indices of the TPD coefficients for axis 2 now differ from TPV.
COMMENT
COMMENT  In the keycomments, as before, x and y refer to axes 1 and 2, which
COMMENT  are the RA and DEC axes.
COMMENT  -----------------------------------------------------------------------

WCSNAMES= 'SIPTPV-7: TPV translated to a ''TPD'' distortion without axis map'
CRPIX1S =             -3925.16 / Pixel coordinate of reference point
CRPIX2S =              4360.23 / Pixel coordinate of reference point
CD1_1S  =  0.00028610265860158 / [deg] CD matrix element
CD1_2S  = -6.2881662833181E-07 / [deg] CD matrix element
CD2_1S  = -5.7720701811452E-06 / [deg] CD matrix element
CD2_2S  = -0.00028152525617189 / [deg] CD matrix element
CTYPE1S = 'RA---TAN'           / TAN (gnomonic) projection
CTYPE2S = 'DEC--TAN'           / TAN (gnomonic) projection
CRVAL1S =    274.8069457088980 / [deg] Right ascension at the reference point
CRVAL2S =    -25.9746476963393 / [deg] Declination at the reference point
CUNIT1S = 'deg     '           / Image axis-1 celestial-coordinate units
CUNIT2S = 'deg     '           / Image axis-2 celestial-coordinate units

CQDIS1S = 'TPD'                / Q = sequent, Template Polynomial Distortion
DQ1S    = 'DOCORR: 0'          / Polynomial gives corrected coordinate
DQ1S    = 'NAXES:  2'          / Two independent variables
DQ1S    = 'TPD.FWD.1:                   1.0' / TPD coefficient: x
DQ1S    = 'TPD.FWD.4:  -0.01616956178892100' / TPD coefficient: xx
DQ1S    = 'TPD.FWD.5:  -0.00517474938746320' / TPD coefficient: xy
DQ1S    = 'TPD.FWD.6:  -0.00023850435805678' / TPD coefficient: yy
DQ1S    = 'TPD.FWD.7:   0.00629760478963159' / TPD coefficient: xxx
DQ1S    = 'TPD.FWD.8:   0.00397207946734115' / TPD coefficient: xxy
DQ1S    = 'TPD.FWD.9:  -0.00067729620645185' / TPD coefficient: xyy
DQ1S    = 'TPD.FWD.10:  0.00050354679706662' / TPD coefficient: yyy
DQ1S    = 'TPD.FWD.12: -0.00097355342974408' / TPD coefficient: xxxx
DQ1S    = 'TPD.FWD.13: -0.00102312736844768' / TPD coefficient: xxxy
DQ1S    = 'TPD.FWD.14:  0.00025362356834782' / TPD coefficient: xxyy
DQ1S    = 'TPD.FWD.15: -0.00020021192475813' / TPD coefficient: xyyy
DQ1S    = 'TPD.FWD.16: -6.2162660705097E-05' / TPD coefficient: yyyy
CQERR1S =                96.50 / Maximum absolute value of distortion function

CQDIS2S = 'TPD'                / Q = sequent, Template Polynomial Distortion
DQ2S    = 'DOCORR: 0'          / Polynomial gives corrected coordinate
DQ2S    = 'NAXES:  2'          / Two independent variables
DQ2S    = 'TPD.FWD.2:                   1.0' / TPD coefficient: y
DQ2S    = 'TPD.FWD.6:  -0.00074364565692291' / TPD coefficient: yy
DQ2S    = 'TPD.FWD.5:   0.00018425002539649' / TPD coefficient: yx
DQ2S    = 'TPD.FWD.4:   0.02197159197666640' / TPD coefficient: xx
DQ2S    = 'TPD.FWD.10: -7.5449775263740E-05' / TPD coefficient: yyy
DQ2S    = 'TPD.FWD.9:   0.00064935718511019' / TPD coefficient: yyx
DQ2S    = 'TPD.FWD.8:  -0.00081219646536117' / TPD coefficient: yxx
DQ2S    = 'TPD.FWD.7:  -0.01050984336151780' / TPD coefficient: xxx
DQ2S    = 'TPD.FWD.16: -2.1755521894303E-05' / TPD coefficient: yyyy
DQ2S    = 'TPD.FWD.15: -7.9010371768005E-05' / TPD coefficient: yyyx
DQ2S    = 'TPD.FWD.14: -0.00015571170306733' / TPD coefficient: yyxx
DQ2S    = 'TPD.FWD.13:  0.00016933561718011' / TPD coefficient: yxxx
DQ2S    = 'TPD.FWD.12:  0.00186540574051853' / TPD coefficient: xxxx
CQERR2S =                95.54 / Maximum absolute value of distortion function

COMMENT  -----------------------------------------------------------------------
COMMENT  The TPV representation above translated to Polynomial as a sequent
COMMENT  distortion using an axis mapping.
COMMENT
COMMENT  The comments above for the translation to TPD apply here as well.
COMMENT
COMMENT  In the keycomments, x and y refer to axes 1 and 2, which are the RA
COMMENT  and DEC axes.
COMMENT  -----------------------------------------------------------------------

WCSNAMET= 'SIPTPV-8: TPV translated to a ''Polynomial'' distortion'
CRPIX1T =             -3925.16 / Pixel coordinate of reference point
CRPIX2T =              4360.23 / Pixel coordinate of reference point
CD1_1T  =  0.00028610265860158 / [deg] CD matrix element
CD1_2T  = -6.2881662833181E-07 / [deg] CD matrix element
CD2_1T  = -5.7720701811452E-06 / [deg] CD matrix element
CD2_2T  = -0.00028152525617189 / [deg] CD matrix element
CTYPE1T = 'RA---TAN'           / TAN (gnomonic) projection
CTYPE2T = 'DEC--TAN'           / TAN (gnomonic) projection
CRVAL1T =    274.8069457088980 / [deg] Right ascension at the reference point
CRVAL2T =    -25.9746476963393 / [deg] Declination at the reference point
CUNIT1T = 'deg     '           / Image axis-1 celestial-coordinate units
CUNIT2T = 'deg     '           / Image axis-2 celestial-coordinate units

CQDIS1T = 'Polynomial'         / Q = sequent, Polynomial distortion
DQ1T    = 'DOCORR: 0'          / Polynomial gives corrected coordinate
DQ1T    = 'NAXES:  2'          / Two independent variables
DQ1T    = 'AXIS.1: 1'          / 1st independent variable: axis 1 = x
DQ1T    = 'AXIS.2: 2'          / 2nd independent variable: axis 2 = y
DQ1T    = 'NTERMS: 13'         / Number of terms in the polynomial
DQ1T    = 'TERM.1.COEFF:                     1' / Poly coefficient: x
DQ1T    = 'TERM.1.VAR.1:                     1' / Poly power 1 (x): x
DQ1T    = 'TERM.2.COEFF:  -0.01616956178892100' / Poly coefficient: xx
DQ1T    = 'TERM.2.VAR.1:                     2' / Poly power 1 (x): xx
DQ1T    = 'TERM.3.COEFF:  -0.00517474938746320' / Poly coefficient: xy
DQ1T    = 'TERM.3.VAR.1:                     1' / Poly power 1 (x): xy
DQ1T    = 'TERM.3.VAR.2:                     1' / Poly power 2 (y): xy
DQ1T    = 'TERM.4.COEFF:  -0.00023850435805678' / Poly coefficient: yy
DQ1T    = 'TERM.4.VAR.2:                     2' / Poly power 2 (y): yy
DQ1T    = 'TERM.5.COEFF:   0.00629760478963159' / Poly coefficient: xxx
DQ1T    = 'TERM.5.VAR.1:                     3' / Poly power 1 (x): xxx
DQ1T    = 'TERM.6.COEFF:   0.00397207946734115' / Poly coefficient: xxy
DQ1T    = 'TERM.6.VAR.1:                     2' / Poly power 1 (x): xxy
DQ1T    = 'TERM.6.VAR.2:                     1' / Poly power 2 (y): xxy
DQ1T    = 'TERM.7.COEFF:  -0.00067729620645185' / Poly coefficient: xyy
DQ1T    = 'TERM.7.VAR.1:                     1' / Poly power 1 (x): xyy
DQ1T    = 'TERM.7.VAR.2:                     2' / Poly power 2 (y): xyy
DQ1T    = 'TERM.8.COEFF:   0.00050354679706662' / Poly coefficient: yyy
DQ1T    = 'TERM.8.VAR.2:                     3' / Poly power 2 (y): yyy
DQ1T    = 'TERM.9.COEFF:  -0.00097355342974408' / Poly coefficient: xxxx
DQ1T    = 'TERM.9.VAR.1:                     4' / Poly power 1 (x): xxxx
DQ1T    = 'TERM.10.COEFF: -0.00102312736844768' / Poly coefficient: xxxy
DQ1T    = 'TERM.10.VAR.1:                    3' / Poly power 1 (x): xxxy
DQ1T    = 'TERM.10.VAR.2:                    1' / Poly power 2 (y): xxxy
DQ1T    = 'TERM.11.COEFF:  0.00025362356834782' / Poly coefficient: xxyy
DQ1T    = 'TERM.11.VAR.1:                    2' / Poly power 1 (x): xxyy
DQ1T    = 'TERM.11.VAR.2:                    2' / Poly power 2 (y): xxyy
DQ1T    = 'TERM.12.COEFF: -0.00020021192475813' / Poly coefficient: xyyy
DQ1T    = 'TERM.12.VAR.1:                    1' / Poly power 1 (x): xyyy
DQ1T    = 'TERM.12.VAR.2:                    3' / Poly power 2 (y): xyyy
DQ1T    = 'TERM.13.COEFF: -6.2162660705097E-05' / Poly coefficient: yyyy
DQ1T    = 'TERM.13.VAR.2:                    4' / Poly power 2 (y): yyyy
CQERR1T =                96.50 / Maximum absolute value of distortion function

CQDIS2T = 'Polynomial'         / Q = sequent, Polynomial distortion
DQ2T    = 'DOCORR: 0'          / Polynomial gives corrected coordinate
DQ2T    = 'NAXES:  2'          / Two independent variables
DQ2T    = 'AXIS.1: 2'          / 1st independent variable: axis 2 = y
DQ2T    = 'AXIS.2: 1'          / 2nd independent variable: axis 1 = x
DQ2T    = 'NTERMS: 13'         / Number of terms in the polynomial
DQ2T    = 'TERM.1.COEFF:                     1' / Poly coefficient: y
DQ2T    = 'TERM.1.VAR.1:                     1' / Poly power 1 (x): y
DQ2T    = 'TERM.2.COEFF:  -0.00074364565692291' / Poly coefficient: yy
DQ2T    = 'TERM.2.VAR.1:                     2' / Poly power 1 (x): yy
DQ2T    = 'TERM.3.COEFF:   0.00018425002539649' / Poly coefficient: yx
DQ2T    = 'TERM.3.VAR.1:                     1' / Poly power 1 (x): yx
DQ2T    = 'TERM.3.VAR.2:                     1' / Poly power 2 (y): yx
DQ2T    = 'TERM.4.COEFF:   0.02197159197666640' / Poly coefficient: xx
DQ2T    = 'TERM.4.VAR.2:                     2' / Poly power 2 (y): xx
DQ2T    = 'TERM.5.COEFF:  -7.5449775263740E-05' / Poly coefficient: yyy
DQ2T    = 'TERM.5.VAR.1:                     3' / Poly power 1 (x): yyy
DQ2T    = 'TERM.6.COEFF:   0.00064935718511019' / Poly coefficient: yyx
DQ2T    = 'TERM.6.VAR.1:                     2' / Poly power 1 (x): yyx
DQ2T    = 'TERM.6.VAR.2:                     1' / Poly power 2 (y): yyx
DQ2T    = 'TERM.7.COEFF:  -0.00081219646536117' / Poly coefficient: yxx
DQ2T    = 'TERM.7.VAR.1:                     1' / Poly power 1 (x): yxx
DQ2T    = 'TERM.7.VAR.2:                     2' / Poly power 2 (y): yxx
DQ2T    = 'TERM.8.COEFF:  -0.01050984336151780' / Poly coefficient: xxx
DQ2T    = 'TERM.8.VAR.2:                     3' / Poly power 2 (y): xxx
DQ2T    = 'TERM.9.COEFF:  -2.1755521894303E-05' / Poly coefficient: yyyy
DQ2T    = 'TERM.9.VAR.1:                     4' / Poly power 1 (x): yyyy
DQ2T    = 'TERM.10.COEFF: -7.9010371768005E-05' / Poly coefficient: yyyx
DQ2T    = 'TERM.10.VAR.1:                    3' / Poly power 1 (x): yyyx
DQ2T    = 'TERM.10.VAR.2:                    1' / Poly power 2 (y): yyyx
DQ2T    = 'TERM.11.COEFF: -0.00015571170306733' / Poly coefficient: yyxx
DQ2T    = 'TERM.11.VAR.1:                    2' / Poly power 1 (x): yyxx
DQ2T    = 'TERM.11.VAR.2:                    2' / Poly power 2 (y): yyxx
DQ2T    = 'TERM.12.COEFF:  0.00016933561718011' / Poly coefficient: yxxx
DQ2T    = 'TERM.12.VAR.1:                    1' / Poly power 1 (x): yxxx
DQ2T    = 'TERM.12.VAR.2:                    3' / Poly power 2 (y): yxxx
DQ2T    = 'TERM.13.COEFF:  0.00186540574051853' / Poly coefficient: xxxx
DQ2T    = 'TERM.13.VAR.2:                    4' / Poly power 2 (y): xxxx
CQERR2T =                95.54 / Maximum absolute value of distortion function

COMMENT  -----------------------------------------------------------------------
COMMENT  The TPV representation above translated to Polynomial as a sequent
COMMENT  distortion, this time without using an axis mapping.
COMMENT
COMMENT  The auxiliary (radial) variable is not used and was added solely for
COMMENT  testing wcshdo().
COMMENT
COMMENT  In the keycomments, x and y refer to axes 1 and 2, which are the RA
COMMENT  and DEC axes.
COMMENT  -----------------------------------------------------------------------

WCSNAMEU= 'SIPTPV-9: TPV translated to ''Polynomial'' without axis mapping'
CRPIX1U =             -3925.16 / Pixel coordinate of reference point
CRPIX2U =              4360.23 / Pixel coordinate of reference point
CD1_1U  =  0.00028610265860158 / [deg] CD matrix element
CD1_2U  = -6.2881662833181E-07 / [deg] CD matrix element
CD2_1U  = -5.7720701811452E-06 / [deg] CD matrix element
CD2_2U  = -0.00028152525617189 / [deg] CD matrix element
CTYPE1U = 'RA---TAN'           / TAN (gnomonic) projection
CTYPE2U = 'DEC--TAN'           / TAN (gnomonic) projection
CRVAL1U =    274.8069457088980 / [deg] Right ascension at the reference point
CRVAL2U =    -25.9746476963393 / [deg] Declination at the reference point
CUNIT1U = 'deg     '           / Image axis-1 celestial-coordinate units
CUNIT2U = 'deg     '           / Image axis-2 celestial-coordinate units

CQDIS1U = 'Polynomial'         / Q = sequent, Polynomial distortion
DQ1U    = 'DOCORR: 0'          / Polynomial gives corrected coordinate
DQ1U    = 'NAXES:  2'          / Two independent variables
DQ1U    = 'NTERMS: 13'         / Number of terms in the polynomial
DQ1U    = 'NAUX: 1'            / One auxiliary variable (not used)
DQ1U    = 'AUX.1.COEFF.1: 1'   / Coefficient of first variable
DQ1U    = 'AUX.1.POWER.1: 2'   / Power of first variable
DQ1U    = 'AUX.1.COEFF.2: 1'   / Coefficient of second variable
DQ1U    = 'AUX.1.POWER.2: 2'   / Power of second variable
DQ1U    = 'AUX.1.POWER.0: 0.5' / Power of the sum of the terms
DQ1U    = 'TERM.1.COEFF:                     1' / Poly coefficient: x
DQ1U    = 'TERM.1.VAR.1:                     1' / Poly power 1 (x): x
DQ1U    = 'TERM.2.COEFF:  -0.01616956178892100' / Poly coefficient: xx
DQ1U    = 'TERM.2.VAR.1:                     2' / Poly power 1 (x): xx
DQ1U    = 'TERM.3.COEFF:  -0.00517474938746320' / Poly coefficient: xy
DQ1U    = 'TERM.3.VAR.1:                     1' / Poly power 1 (x): xy
DQ1U    = 'TERM.3.VAR.2:                     1' / Poly power 2 (y): xy
DQ1U    = 'TERM.4.COEFF:  -0.00023850435805678' / Poly coefficient: yy
DQ1U    = 'TERM.4.VAR.2:                     2' / Poly power 2 (y): yy
DQ1U    = 'TERM.5.COEFF:   0.00629760478963159' / Poly coefficient: xxx
DQ1U    = 'TERM.5.VAR.1:                     3' / Poly power 1 (x): xxx
DQ1U    = 'TERM.6.COEFF:   0.00397207946734115' / Poly coefficient: xxy
DQ1U    = 'TERM.6.VAR.1:                     2' / Poly power 1 (x): xxy
DQ1U    = 'TERM.6.VAR.2:                     1' / Poly power 2 (y): xxy
DQ1U    = 'TERM.7.COEFF:  -0.00067729620645185' / Poly coefficient: xyy
DQ1U    = 'TERM.7.VAR.1:                     1' / Poly power 1 (x): xyy
DQ1U    = 'TERM.7.VAR.2:                     2' / Poly power 2 (y): xyy
DQ1U    = 'TERM.8.COEFF:   0.00050354679706662' / Poly coefficient: yyy
DQ1U    = 'TERM.8.VAR.2:                     3' / Poly power 2 (y): yyy
DQ1U    = 'TERM.9.COEFF:  -0.00097355342974408' / Poly coefficient: xxxx
DQ1U    = 'TERM.9.VAR.1:                     4' / Poly power 1 (x): xxxx
DQ1U    = 'TERM.10.COEFF: -0.00102312736844768' / Poly coefficient: xxxy
DQ1U    = 'TERM.10.VAR.1:                    3' / Poly power 1 (x): xxxy
DQ1U    = 'TERM.10.VAR.2:                    1' / Poly power 2 (y): xxxy
DQ1U    = 'TERM.11.COEFF:  0.00025362356834782' / Poly coefficient: xxyy
DQ1U    = 'TERM.11.VAR.1:                    2' / Poly power 1 (x): xxyy
DQ1U    = 'TERM.11.VAR.2:                    2' / Poly power 2 (y): xxyy
DQ1U    = 'TERM.12.COEFF: -0.00020021192475813' / Poly coefficient: xyyy
DQ1U    = 'TERM.12.VAR.1:                    1' / Poly power 1 (x): xyyy
DQ1U    = 'TERM.12.VAR.2:                    3' / Poly power 2 (y): xyyy
DQ1U    = 'TERM.13.COEFF: -6.2162660705097E-05' / Poly coefficient: yyyy
DQ1U    = 'TERM.13.VAR.2:                    4' / Poly power 2 (y): yyyy
CQERR1U =                96.50 / Maximum absolute value of distortion function

CQDIS2U = 'Polynomial'         / Q = sequent, Polynomial distortion
DQ2U    = 'DOCORR: 0'          / Polynomial gives corrected coordinate
DQ2U    = 'NAXES:  2'          / Two independent variables
DQ2U    = 'NAUX: 1'            / One auxiliary variable (not used)
DQ2U    = 'AUX.1.COEFF.1: 1'   / Coefficient of first variable
DQ2U    = 'AUX.1.POWER.1: 2'   / Power of first variable
DQ2U    = 'AUX.1.COEFF.2: 1'   / Coefficient of second variable
DQ2U    = 'AUX.1.POWER.2: 2'   / Power of second variable
DQ2U    = 'AUX.1.POWER.0: 0.5' / Power of the sum of the terms
DQ2U    = 'NTERMS: 13'         / Number of terms in the polynomial
DQ2U    = 'TERM.1.COEFF:                     1' / Poly coefficient: y
DQ2U    = 'TERM.1.VAR.2:                     1' / Poly power 1 (y): y
DQ2U    = 'TERM.2.COEFF:  -0.00074364565692291' / Poly coefficient: yy
DQ2U    = 'TERM.2.VAR.2:                     2' / Poly power 1 (y): yy
DQ2U    = 'TERM.3.COEFF:   0.00018425002539649' / Poly coefficient: xy
DQ2U    = 'TERM.3.VAR.1:                     1' / Poly power 1 (y): xy
DQ2U    = 'TERM.3.VAR.2:                     1' / Poly power 2 (x): xy
DQ2U    = 'TERM.4.COEFF:   0.02197159197666640' / Poly coefficient: xx
DQ2U    = 'TERM.4.VAR.1:                     2' / Poly power 2 (x): xx
DQ2U    = 'TERM.5.COEFF:  -7.5449775263740E-05' / Poly coefficient: yyy
DQ2U    = 'TERM.5.VAR.2:                     3' / Poly power 1 (y): yyy
DQ2U    = 'TERM.6.COEFF:   0.00064935718511019' / Poly coefficient: xyy
DQ2U    = 'TERM.6.VAR.1:                     1' / Poly power 2 (x): xyy
DQ2U    = 'TERM.6.VAR.2:                     2' / Poly power 1 (y): xyy
DQ2U    = 'TERM.7.COEFF:  -0.00081219646536117' / Poly coefficient: xxy
DQ2U    = 'TERM.7.VAR.1:                     2' / Poly power 2 (x): xxy
DQ2U    = 'TERM.7.VAR.2:                     1' / Poly power 1 (y): xxy
DQ2U    = 'TERM.8.COEFF:  -0.01050984336151780' / Poly coefficient: xxx
DQ2U    = 'TERM.8.VAR.1:                     3' / Poly power 2 (x): xxx
DQ2U    = 'TERM.9.COEFF:  -2.1755521894303E-05' / Poly coefficient: yyyy
DQ2U    = 'TERM.9.VAR.2:                     4' / Poly power 1 (y): yyyy
DQ2U    = 'TERM.10.COEFF: -7.9010371768005E-05' / Poly coefficient: xyyy
DQ2U    = 'TERM.10.VAR.1:                    1' / Poly power 2 (x): xyyy
DQ2U    = 'TERM.10.VAR.2:                    3' / Poly power 1 (y): xyyy
DQ2U    = 'TERM.11.COEFF: -0.00015571170306733' / Poly coefficient: xxyy
DQ2U    = 'TERM.11.VAR.1:                    2' / Poly power 2 (x): xxyy
DQ2U    = 'TERM.11.VAR.2:                    2' / Poly power 1 (y): xxyy
DQ2U    = 'TERM.12.COEFF:  0.00016933561718011' / Poly coefficient: xxxy
DQ2U    = 'TERM.12.VAR.1:                    3' / Poly power 2 (x): xxxy
DQ2U    = 'TERM.12.VAR.2:                    1' / Poly power 1 (y): xxxy
DQ2U    = 'TERM.13.COEFF:  0.00186540574051853' / Poly coefficient: xxxx
DQ2U    = 'TERM.13.VAR.1:                    4' / Poly power 2 (x): xxxx
CQERR2U =                95.54 / Maximum absolute value of distortion function

END
