Version 1.0 FITS header document

 

 

Document Title

WFCAM HDS container and FITS headers

Document Number

 

Issue

1.0

Date

2003-Oct-21

 

Document Prepared By:

Alan Pickup

Signature and Date

 

Document Approved By:

 

Signature and Date

 

Document Released By:

 

Signature and Date

 

 

 

CHANGE RECORD

Issue

Date

Section affected

Change Description

0.1

2002-Oct-16

all

1st version for time of Software CDR

0.2

2003-Feb-10

all

Tables include comment records; new headers including "TSCAN"s

0.3

2003-Feb-13

all

Correction of typos (thanks to Jim Lewis); some additional comments; addition of sections listing example headers.

0.4

2003-Feb-14

all

"TSCAN" becomes "JITTER"; added READOUT; expanded environment headers (from JAC); updated examples.

0.5

2003-Feb-24

all

Document title changed form WFCAM FITS headers to WFCAM HDS container and FITS headers

New section on contents of HDS container

New astrometric (WCS) headers: CDi_j and PV1_n

New examples

0.6

2003-Mar-05

all

Removed NOFFSETS header

Added SURVEY, SURVEY_I, DETECTID, PCSYSID, SDSUID, CAMROLE and GAIN headers

New HDSTRACE and examples

1.0

2003-Oct-21

all

Added TILENUM, MJD-OBS

Revised WCS items following discussions

Added section on WFCAM WCS usage

Added types for FITS values

New HDSTRACE and examples

       
       

 

 

APPLICABLE DOCUMENTS

Reference

Document Title

Document Number

Issue & Date

       
       
       
       
       

 

 

Table of contents

 

1. Introduction *

2. WFCAM HDS container *

2.1 Example HDSTRACE of WFCAM container file *

3. WFCAM FITS headers *

3.1 Definition of top level FITS headers *

3.1.1 Example of top level FITS headers *

3.2 Definition of frame level FITS headers *

3.2.1 Example of frame level FITS headers *

4. WFCAM WCS usage *

4.1 CTYPEn FITS items *

4.2 CRVAL and CRPIX FITS items *

4.3 CD FITS items *

4.4 PV FITS items *

 

 

  1. Introduction
  2. This document illustrates the contents of a typical HDS container file into which WFCAM data is written and provides a list of FITS headers for that instrument. The FITS headers were based initially on those used for imaging with UIST but have been modified in the light of discussions, primarily in the area of the World Coordinate System headers.

     

  3. WFCAM HDS container

Data from each of the four WFCAM cameras is to be written as NDF structures into separate HDS container files, usually as one file for each camera for each frame in a microstep pattern.

For a microstep frame, each container holds two NDF structures:

The reason for having separate HEADER and I1 structures is to make it possible to add additional I2, I3 etc structures in the same container, with the contents of HEADER being common to all the frames. At present, this facility will be exploited for focus tests, with frames at multiple focus positions being written as separate NDF structures into the one container, each with its own focus setting encoded in its own frame level MORE.FITS.

See the following section for a listing of the typical structure of a WFCAM HDS container file.

 

    1. Example HDSTRACE of WFCAM container file

The following listing illustrates the structure of a typical WFCAM container file, generated using the HDSTRACE command.

X20031020_00008 <UKIRT_HDS>

I1 <NDF> {structure}

DATA_ARRAY <ARRAY> {structure}

DATA(2048,2048) <_INTEGER> 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,

... 21,21,21,21,21,21,21,21,21,21,21

ORIGIN(2) <_INTEGER> 1,1

HISTORY <HISTORY> {structure}

CREATED <_CHAR*24> '2003-OCT-20 22:04:46.000'

CURRENT_RECORD <_INTEGER> 1

RECORDS(10) <HIST_REC> {array of structures}

Contents of RECORDS(1)

DATE <_CHAR*24> '2003-OCT-20 22:04:46.000'

COMMAND <_CHAR*9> '<unknown>'

USER <_CHAR*5> 'wfcam'

HOST <_CHAR*15> 'wfdr2.roe.ac.uk'

DATASET <_CHAR*48> '/home/wfcam/data/raw/20031020/...'

TEXT(2) <_CHAR*72> 'Arguments: <unknown>','Softwar...'

AXIS(2) <AXIS> {array of structures}

Contents of AXIS(1)

DATA_ARRAY <ARRAY> {structure}

DATA(2048) <_REAL> 0.5,1.5,2.5,3.5,4.5,5.5,6.5,

... 2044.5,2045.5,2046.5,2047.5

ORIGIN(1) <_INTEGER> 1

MORE <EXT> {structure}

FITS(4) <_CHAR*80> 'UTSTART = 14.409722 /...'

... 'FOC_OFF = 0.00...'

HEADER <NDF> {structure}

DATA_ARRAY <ARRAY> {structure}

DATA(1,1) <_REAL> 0

ORIGIN(2) <_INTEGER> 1,1

HISTORY <HISTORY> {structure}

CREATED <_CHAR*24> '2003-OCT-20 22:04:47.000'

CURRENT_RECORD <_INTEGER> 1

RECORDS(10) <HIST_REC> {array of structures}

Contents of RECORDS(1)

DATE <_CHAR*24> '2003-OCT-20 22:04:47.000'

COMMAND <_CHAR*9> '<unknown>'

USER <_CHAR*5> 'wfcam'

HOST <_CHAR*15> 'wfdr2.roe.ac.uk'

DATASET <_CHAR*52> '/home/wfcam/data/raw/20031020/...'

TEXT(2) <_CHAR*72> 'Arguments: <unknown>','Softwar...'

MORE <EXT> {structure}

FITS(129) <_CHAR*80> ' ',' ...'

... 'DET_TEMP= 25....'

End of Trace.

 

  1. WFCAM FITS headers

Two tables are provided:

Each table lists the:

 

The possible sources of the FITS value are:

fix - the value is fixed in the header definition table;

om - set from the sequencer level of observation control via the OM Translator and the OOS task. This is likely to be blank (see below) when WFCAM is run from its non-OM engineering interface;

inst - set from the instrument control level (the WFIS);

TCS - read from the telescope control system;

EPICS - obtained from an EPICS database. When this is not available during engineering tests, this may be a fixed value;

data - obtained as attribute alongside data received from camera controller;

DHS - set within the DHS system;

CSO - obtained from CSO monitor task;

blank - the FITS value field will be blank

Note that these sources are as seen from the point of view of the DHS. The ones in the "om" may, in turn, originate in some aspect of a survey definition, be specified by the Observer, or be specified or derived in some other way, for example from an entry in a lookup table read by the OT.

 

 

    1. Definition of top level FITS headers
    2. FITS name

      FITS comment

      UKIRT source

      Eng source

      Type

       

      Identification:

           

      TELESCOP

      Telescope name

      fix

      fix

      string

      INSTRUME

      Instrument

      fix

      fix

      string

      CAMNUM

      Number of this camera

      data

      data

      integer

      DHSVER

      Data handling version

      fix

      fix

      string

      HDTFILE

      Name of global hdt file

      fix

      fix

      string

      HDTFILE2

      Name of camera-specific hdt file

      fix

      fix

      string

      OBSERVER

      Observers names

      om

      om

      string

      USERID

      Userid logged in as

      om

      om

      string

      OBSREF

      PATT or other reference

      om

      om

      string

      PROJECT

      Time-allocation code

      om

      om

      string

      SURVEY

      Survey name

      om

      om

      string

      SURVEY_I

      Pointing ID within survey

      om

      om

      string

      MSBID

      Id min.schedulable block

      om

      om

      string

      OBJECT

      Object name from telescope

      TCS

      blank

      string

               
       

      Data reduction:

           

      RECIPE

      Data reduction recipe to be used

      om

      om

      string

      OBSTYPE

      Type (BIAS|DARK|FLAT|OBJECT|SKY|FOCUS)

      inst

      inst

      string

      OBSNUM

      Observation number

      DHS

      DHS

      integer

      GRPNUM

      Group number applied to all members

      DHS

      DHS

      integer

      GRPMEM

      Group membership

      om

      om

      logical

      TILENUM

      Tile number applied to all members

      DHS

      DHS

      integer

      STANDARD

      Is the target a standard star

      om

      om

      logical

      NJITTER

      Number of positions in telescope jitter pattern

      om

      om

      integer

      JITTER_I

      Serial number in this telescope jitter pattern

      om

      om

      integer

      JITTER_X

      [arcsec] X (RA) offset in telescope jitter pattern

      om

      om

      float

      JITTER_Y

      [arcsec] Y (Dec) offset in telescope jitter pattern

      om

      om

      float

      NUSTEP

      Number of positions in microstep pattern

      om

      om

      integer

      USTEP_I

      Serial number in this microstep pattern

      om

      om

      integer

      USTEP_X

      [arcsec] X (RA) offset in microstep pattern

      om

      om

      float

      USTEP_Y

      [arcsec] Y (Dec) offset in microstep pattern

      om

      om

      float

      NFOC

      Number of positions in focus scan

      inst

      inst

      integer

      NFOCSCAN

      Number of focus scans in focus test

      inst

      inst

      integer

               
       

      Astrometric and time information:

           

      UTDATE

      UT date as integer in yyyymmdd format

      inst

      inst

      string

      DATE-OBS

      Date and time (UTC) of start of observation

      data

      data

      string

      DATE-END

      Date and time (UTC) of end of observation

      data

      data

      string

      MJD-OBS

      DATE-OBS as Modified Julian Date

      data

      data

      float

      WCSAXES

      Number of axes in world co-ordinate system

      fix

      fix

      integer

      RADESYS

      Mean IAU 1984 equatorial co-ordinates

      fix

      fix

      string

      EQUINOX

      [yr] Equinox of object position

      TCS

      fix

      float

      CTYPE1

      Algorithm type for axis 1

      fix

      fix

      string

      CTYPE2

      Algorithm type for axis 2

      fix

      fix

      string

               

      CRPIX1

      [pixel] Reference pixel along axis 1 (RA)

      inst

      inst

      float

      CRPIX2

      [pixel] Reference pixel along axis 2 (Dec)

      inst

      inst

      float

      CRVAL1

      [deg] Right ascension at the reference pixel

      TCS

      fix

      float

      CRVAL2

      [deg] Declination at the reference pixel

      TCS

      fix

      float

      CRUNIT1

      Unit of right ascension co-ordinates

      fix

      fix

      string

      CRUNIT2

      Unit of declination co-ordinates

      fix

      fix

      string

               

      CD1_1

      Transformation matrix element

      inst

      inst

      float

      CD1_2

      Transformation matrix element

      inst

      inst

      float

      CD2_1

      Transformation matrix element

      inst

      inst

      float

      CD2_2

      Transformation matrix element

      inst

      inst

      float

               

      PV2_1

      Pol. coeff. for pixel -> celestial coord.

      inst

      inst

      float

      PV2_2

      Pol. coeff. for pixel -> celestial coord.

      inst

      inst

      float

      PV3_3

      Pol. coeff. for pixel -> celestial coord.

      inst

      inst

      float

               

      RABASE

      [h] Right ascension of base position

      TCS

      fix

      float

      DECBASE

      [deg] Declination of base position

      TCS

      fix

      float

      TRAOFF

      [arcsec] Right ascension telescope offset

      TCS

      fix

      float

      TDECOFF

      [arcsec] Declination telescope offset

      TCS

      fix

      float

      AMSTART

      Airmass at start of observation

      TCS

      fix

      float

      AMEND

      Airmass at end of observation

      TCS

      fix

      float

      TELRA

      [h] Current telescope right ascension

      TCS

      fix

      float

      TELDEC

      [deg] Current telescope declination

      TCS

      fix

      float

      GSRA

      [h] Right ascension of guide star

      TCS

      fix

      float

      GSDEC

      [deg] Declination of guide star

      TCS

      fix

      float

               
       

      Instrument detector configuration:

           

      DETECTOR

      Type of detector array used

      fix

      fix

      string

      DETECTID

      Serial number of detector array

      data

      data

      string

      NINT

      Number of integrations in observation

      data

      data

      integer

      DROWS

      [pixel] Number of detector rows

      data

      data

      integer

      DCOLUMNS

      [pixel] Number of detector columns

      data

      data

      integer

      RDOUT_X1

      Start column of array readout

      data

      data

      integer

      RDOUT_X2

      End column of array readout

      data

      data

      integer

      RDOUT_Y1

      Start row of array readout

      data

      data

      integer

      RDOUT_Y2

      End row of array readout

      data

      data

      integer

      PIXLSIZE

      [arcsec] Pixel size

      inst

      inst

      float

               
       

      Detector controller:

           

      PCSYSID

      PC system identifier

      inst

      inst

      string

      SDSUID

      Serial number of SDSU controller

      inst

      inst

      string

      READMODE

      Name of camera readmode

      inst

      inst

      string

      CAPPLICN

      Name of camera readout application

      data

      data

      string

      CAMROLE

      Camera role (master|slave|unsync)

      inst

      inst

      string

      READOUT

      Camera readout (CDS|NDR|SAR|RRR)

      data

      data

      string

      EXP_TIME

      [s] Integration time per exposure

      inst

      inst

      float

      NEXP

      Number of exposures in integration

      inst

      inst

      integer

      READINT

      [s] Interval between reads

      data

      data

      float

      NREADS

      Number of reads per exposure

      data

      data

      Integer

      GAIN

      [electrons/ADU] Detector gain

      data

      data

      float

               
       

      Instrument optical configuration:

           

      FILTER

      Filter name

      EPICS

      EPICS

      string

      FOC_MM

      [mm] Base focus position

      EPICS

      EPICS

      string

               
       

      Environment:

           

      AIRTEMP

      [degC] Air temperature

      EPICS

      fix

      float

      BARPRESS

      Ambient pressure

      EPICS

      fix

      float

      DEWPOINT

      [degC] Dewpoint

      EPICS

      fix

      float

      DOMETEMP

      [degC] Dome temperature

      EPICS

      fix

      float

      HUMIDITY

      Relative humidity

      EPICS

      fix

      float

      MIRRBSW

      [degC] Temperature mirror B SW

      EPICS

      fix

      float

      MIRR_NE

      [degC] Mirror temperature NE

      EPICS

      fix

      float

      MIRR_NW

      [degC] Mirror temperature NW

      EPICS

      fix

      float

      MIRR_SE

      [degC] Mirror temperature SE

      EPICS

      fix

      float

      MIRR_SW

      [degC] Mirror temperature SW

      EPICS

      fix

      float

      MIRRBTNW

      [degC] Mirror bottom temp. NW

      EPICS

      fix

      float

      MIRRTPNW

      [degC] Mirror top temp. NW

      EPICS

      fix

      float

      SECONDAR

      [degC] Temperature of secondary

      EPICS

      fix

      float

      TOPAIRNW

      [degC] Top air NW

      EPICS

      fix

      float

      TRUSSENE

      [degC] Truss leg ENE

      EPICS

      fix

      float

      TRUSSWSW

      [degC] Truss leg WSW

      EPICS

      fix

      float

      WIND_DIR

      [deg] Wind direction, azimuth

      EPICS

      fix

      float

      WIND_SPD

      [km/h] Wind speed

      EPICS

      fix

      float

      CSOTAU

      Tau at 225 GHz from CSO

      CSO

      fix

      float

      TAUDATE

      Time and date of Tau reading

      CSO

      fix

      string

      TAUSRC

      Source of opacity data

      CSO

      fix

      string

               
       

      Engineering:

           

      CNFINDEX

      Configuration index

      EPICS

      EPICS

      integer

      DET_TEMP

      [K] Array temperature

      EPICS

      EPICS

      float

       

      < More camera engineering data will go here >

           
               

       

       

        1. Example of top level FITS headers

      Identification:

      TELESCOP= 'UKIRT ' / Telescope name

      INSTRUME= 'WFCAM ' / Instrument

      CAMNUM = 2 / Number of WFCAM camera (1, 2, 3 or 4)

      DHSVER = 'UKDHS 2002 Oct 31 ' / Data handling version

      HDTFILE = 'wfcam.hdt ' / Name of global hdt file

      HDTFILE2= 'wfcam2.hdt ' / Name of camera-specific hdt file

      OBSERVER= 'Mrs Observer' / Observers names

      USERID = 'abc ' / Userid logged in as

      OBSREF = 'notPATT99' / PATT or other reference

      PROJECT = 'Example WFCAM data' / Time-allocation code

      SURVEY = 'Demo survey 123' / Survey name

      SURVEY_I= 'B1.99.4 ' / Pointing ID within survey

      MSBID = '42 ' / Id min.-schedulable block

      OBJECT = 'Laboratory wall' / Object name from telescope

      Data Reduction:

      RECIPE = 'QUICK_LOOK' / Data reduction recipe to be used

      OBSTYPE = 'OBJECT ' / BIAS|DARK|SKYFLAT|DOMEFLAT|OBJECT|SKY|FOCUS

      OBSNUM = 8 / Observation number

      GRPNUM = 8 / Group number applied to all members

      GRPMEM = T / Group membership

      TILENUM = 0 / Tile number applied to all members

      STANDARD= F / Is the target a standard star observation?

      NJITTER = 4 / Number of positions in tel jitter pattern

      JITTER_I= 1 / Serial number in this tel jitter pattern

      JITTER_X= 0.00 / [arcsec] X (RA) offset in tel jitter pattern

      JITTER_Y= 0.00 / [arcsec] Y (Dec) offset in tel jitter pattern

      NUSTEP = 4 / Number of positions in microstep pattern

      USTEP_I = 1 / Serial number in this microstep pattern

      USTEP_X = 0.00 / [arcsec] X (RA) offset in microstep pattern

      USTEP_Y = 0.00 / [arcsec] Y (Dec) offset in microstep pattern

      NFOC = 0 / Number of positions in focus scan

      NFOCSCAN= 0 / Number of focus scans in focus test

      Astrometric and time information:

      UTDATE = '20031020' / UT date as integer in yyyymmdd format

      DATE-OBS= '2003-10-20T14:24:35Z' / Date and time (UTC) of start of observation

      DATE-END= '2003-10-20T14:24:39Z' / Date and time (UTC) of end of observation

      MJD-OBS = 52932.60040 / DATE-OBS as Modified Julian Date

      WCSAXES = 2 / Number of axes in world co-ordinate system

      RADESYS = 'FK5 ' / Mean IAU 1984 equatorial co-ordinates

      EQUINOX = 2000.000 / [yr] Equinox of object position

      CTYPE1 = 'RA---ZPN' / Algorithm type for axis 1

      CTYPE2 = 'DEC--ZPN' / Algorithm type for axis 2

      CRPIX1 = -1000.0 / [pixel] Reference pixel along axis 1 (RA)

      CRPIX2 = -1000.0 / [pixel] Reference pixel along axis 2 (Rec)

      CRVAL1 = 300.16419 / [deg] Right ascension at the reference pixel

      CRVAL2 = 29.9749447 / [deg] Declination at the reference pixel

      CRUNIT1 = 'deg ' / Unit of right ascension co-ordinates

      CRUNIT2 = 'deg ' / Unit of declination co-ordinates

      CD1_1 = 0.000000E+00 / Transformation matrix element

      CD1_2 = -1.000000E+00 / Transformation matrix element

      CD2_1 = 5.000000E-01 / Transformation matrix element

      CD2_2 = -5.000000E-01 / Transformation matrix element

      PV2_1 = 1.000000E+00 / Pol.coeff. for pixel -> celestial coord

      PV2_2 = 0.000000E+00 / Pol.coeff. for pixel -> celestial coord

      PV2_3 = 7.500000E+01 / Pol.coeff. for pixel -> celestial coord

      RABASE = 20.0109458 / [h] Right ascension of base position

      DECBASE = 29.9749447 / [deg] Declination of base position

      TRAOFF = 0.000 / [arcsec] Right ascension telescope offset

      TDECOFF = 0.000 / [arcsec] Declination telescope offset

      AMSTART = 1.771 / Airmass at start of observation

      AMEND = 1.769 / Airmass at end of observation

      TELRA = 20.0123456 / [h] Current telescope right ascension

      TELDEC = 29.9876543 / [deg] Current telescope declination

      GSRA = 20.0103456 / [h] Right ascension of guide star

      GSDEC = 29.9806543 / [deg] Declination of guide star

      Instrument detector configuration:

      DETECTOR= 'RSC Hawaii 2' / Type of detector array used

      DETECTID= 'a.bc.234' / Serial number of detector array

      NINT = 1 / Number of integrations in observation

      DROWS = 2048 / [pixel] Number of detector rows

      DCOLUMNS= 2048 / [pixel] Number of detector columns

      RDOUT_X1= 1 / Start column of array readout

      RDOUT_X2= 2048 / Start column of array readout

      RDOUT_Y1= 1 / Start row of array readout

      RDOUT_Y2= 2048 / Start row of array readout

      PIXLSIZE= 0.4000 / [arcsec] Pixel size

      Detector controller:

      PCSYSID = 'wfacq2 ' / PC system identifier

      SDSUID = '00223 ' / Serial number of SDSU controller

      READMODE= 'CDS_v1 ' / Name of camera readmode

      CAPPLICN= 'applic01' / Name of camera readout application

      CAMROLE = 'master ' / Camera role (master|slave|unsync)

      READOUT = 'CDS ' / Camera readout (CDS|NDR|SAR|RRR)

      EXP_TIME= 1.000000 / [s] Integration time per exposure

      NEXP = 1 / Number of exposures in integration

      READINT = 1.000000 / [s] Interval between reads

      NREADS = 0 / Number of reads per exposure

      GAIN = 1.0 / [electrons/ADU] Detector gain

      Instrument optical configuration:

      FILTER = 'whatever' / Filter name

      FOC_MM = 12.34 / [mm] Base focus position

      Environment:

      AIRTEMP = 5.785 / [degC] Air temperature

      BARPRESS= 650.000 / Ambient pressure

      DEWPOINT= 2.000 / [degC] Dewpoint

      DOMETEMP= 7.095 / [degC] Dome temperature

      HUMIDITY= 35.450 / Relative humidity

      MIRRBSW = 7.123 / [degC] Temperature mirror B SW

      MIRRNE = 7.124 / [degC] Mirror temperature NE

      MIRRNW = 7.125 / [degC] Mirror temperature NW

      MIRRSE = 7.126 / [degC] Mirror temperature SE

      MIRRSW = 7.127 / [degC] Mirror temperature SW

      MIRRBTNW= 7.128 / [degC] Mirror bottom temp. NW

      MIRRTPNW= 7.129 / [degC] Mirror top temp. NW

      SECONDAR= 7.130 / [degC] Temperature of secondary

      TOPAIRNW= 7.131 / [degC] Top air NW

      TRUSSENE= 7.132 / [degC] Truss leg ENE

      TRUSSWSW= 7.133 / [degC] Truss leg WSW

      WIND_DIR= 106.987 / [deg] Wind direction, azimuth

      WIND_SPD= 16.089 / [km/h] Wind speed

      CSOTAU = 0.047 / Tau at 225 GHz from CSO

      TAUDATE = '2001-11-30T04:07' / Time and date of Tau reading

      TAUSRC = 'CSO ' / Source of opacity data

      Engineering:

      CNFINDEX= 1 / Configuration index

      DET_TEMP= 25.0 / [K] Detector array temperature

       

    3. Definition of frame level FITS headers
    4. FITS name

      FITS comment

      UKIRT source

      Eng source

      Type

      UTSTART

      [h] Start time of integration

      data

      data

      float

      UTEND

      [h] End time of integration

      data

      data

      float

      FOC_I

      Serial number in focus scan

      data

      data

      integer

      FOC_OFF

      [mm] Offset from base focus position

      data

      data

      float

       

        1. Example of frame level FITS headers

 

UTSTART = 14.409722 / [h] Start time of integration

UTEND = 14.410833 / [h] End time of integration

FOC_I = 0 / Serial number in focus scan

FOC_OFF = 0.000 / [mm] Offset from base focus position

 

 

  1. WFCAM WCS usage
  2. Several items in the top-level FITS headers are concerned with World Coordinate System (WCS) information. Thanks to Andy Vick for the explanations.

    Note that all but the CTYPEn values are candidates for being updated with new values during commissioning.

     

    1. CTYPEn FITS items
    2. CTYPE1 and CTYPE2 give the output format. That is to say, they give the format for the coordinates after you have applied all the transformations. In our case CTYPE1 is "RA---ZN" and CTYPE2 is "DEC--ZPN". This implies that the transformation is a Zenithal radial polynomial one.

       

    3. CRVAL and CRPIX FITS items
    4. These define the position of the reference pixel, which will initially be set to as near the optical axis of the instrument as possible.

       

    5. CD FITS items
    6. The CD FITS items (CD1_1, etc) specify a matrix to convert pixel coordinates into (φ, θ),

      and allow scaling and rotation.

       

    7. PV FITS items

A comment in the FITS WCS document states in order to do a radial expansion, as in ZPN, then the coefficients go in the PV matrix keywords appropriate for the 'latitude' axis, which in our case is the second (declination) axis. The information is carried, therefore by the FITS keywords of the form PV2_n, and the PV1_n keywords are not used.

The initial values are:

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