A standard set of keywords is needed to describe the celestial coordinate system for each of the 3 FITS image representations discussed above. The RCCF paper has already defined the keywords to be used with images stored in a FITS primary array or image extension, and we repeat them here without any modification. Since it is not possible to use the exact same keywords in the other 2 cases (for one reason, the keyword names must all have an index number pointing to the column to which they apply), we have defined an analogous set of keywords to be used in these cases, as shown in the following table.

Keyword | Primary | BINTABLE | Table |

Description | Array | Vector | Pixel List |

Axis Type | CTYPEi |
iCTYPn |
TCTYPn |

Axis Units | CUNITi |
iCUNIn |
TCUNIn |

Reference Pixel | CRPIXi |
iCRPXn |
TCRPXn |

Reference Value | CRVALi |
iCRVLn |
TCRVLn |

Pixel Increment | CDELTi |
iCDLTn |
TCDLTn |

Axis Rotation | CROTAi |
iCROTn |
TCROTn |

Rotation Matrix | PCiiijjj |
ijPCn |
TPCnnmm |

Coord. Rotation | LONGPOLE |
LONGPOLE or |
LONGPOLE or |

LONGPn |
LONGPn |
||

Coord. Rotation | LATPOLE |
LATPOLE or |
LATPOLE or |

LATPn |
LATPn |
||

Proj. Param. 1 | PROJP1 |
PROJP1 or |
PROJP1 or |

P1PROn |
P1PROn |
||

Proj. Param. 2 | PROJP2 |
PROJP2 or |
PROJP2 or |

P2PROn |
P2PROn |
||

Coord. Epoch | EQUINOX |
EQUINOX or |
EQUINOX or |

EQUINn |
EQUINn |
||

MJD of Obs. | MJD-OBS |
MJD-OBS or |
MJD-OBS or |

MJDOBn |
MJDOBn |
||

Reference Frame | RADECSYS |
RADECSYS or |
RADECSYS or |

RADECn |
RADECn |

Notes:

- *i, j* are integer axis numbers referring to an axis of the array.

- When used as a keyword prefix these are limited to 1 digit.

- *iii, jjj* are 3-digit integer axis numbers, including leading zeros (001-999).

- *n* is an integer table column number (1-999) without any leading zeros.

- *mm, nn* are 2-digit integer table column numbers (01-99).

The following paragraphs briefly describe each type of keyword.

- 1.
- Axis Type: a character string label which defines the type of axis. In the case of the celestial coordinate system projections discussed in RCCF, this keyword also specifies the type of map projection and implicitly defines the units of the physical coordinates (see also the Axis Units keyword below).
- 2.
- Axis Units: specifies the physical units of each axis. For celestial coordinates, angles must always be given in units of degrees (i.e., 'deg').
- 3.
- Reference Pixel: the pixel coordinate of the reference point. When dealing with arrays, the first pixel runs from coordinate number 0.5 to 1.5 on each axis and the coordinate (1.0, 1.0) refers to the center of the lower left pixel in a 2-D image.
- 4.
- Reference Value: the physical coordinate value at the position of the reference pixel. For celestial coordinates this is always given in units of degrees.
- 5.
- Pixel Increment: the increment per pixel of the physical coordinate value at the position of the reference pixel. For celestial coordinates this is always given in units of degrees.
- 6.
- Axis Rotation: the rotation angle between the pixel axis and the
physical coordinate axis in degrees. This keyword is superseded by the
Rotation Matrix keywords, but the
`CROTA`*i*keyword should still be written to assist older FITS-reading programs. This keyword is only appropriate for 2-dimensional arrays and should only be given for the 2nd axis (i.e.,`CROTA2`). - 7.
- Rotation Matrix: the rotation (and skew) terms needed to convert
from the pixel coordinate system to the physical coordinate system.
After this transformation has been applied the coordinates are aligned
with the physical axes but are still in pixel units. The Pixel
Increment value is then used to scale the pixel values to the physical
values. Note that in the table pixel list image format the
`TPC`*nnmm*keyword is limited to 2-digit column numbers, thus one is restricted to using columns 1 - 99 for storing the X and Y pixel coordinates. - 8.
- Coordinate Rotation: the longitude and latitude in the native
coordinate system of the standard system's north pole. These keywords
are only applicable to certain celestial coordinate system
projections (see RCCF). If different columns of the table contain images with
different rotations, then the
`LONGP`*n*and`LATP`*n*form of the keyword must be used to give the rotation for each column individually. - 9.
- Projection Parameters: some projections require additional
parameters. The interpretation of these keywords depends on the value
of the Axis Type keyword. If different columns of the table contain
images with different projection parameters, then the
`P1PRO`*n*and`P2PRO`*n*form of the keywords must be used to give the parameter for each column individually. - 10.
- Coordinate Epoch: epoch of the mean equator and equinox in
years. It is recommended that the value of this keyword be either
1950.0 or 2000.0. If different columns of the table contain images
with different epochs, then the
`EQUIN`*n*form of the keyword must be used to give the epoch value for each column individually. - 11.
- MJD of Observation: the modified Julian date of the observation
in decimal days. If different columns of the table contain images with
different dates, then the
`MJDOB`*n*form of the keyword must be used to give the date for each column individually. - 12.
- Reference Frame: the frame of reference of the equatorial
coordinates (e.g., `FK4' for EQUINOX 1950.0 and `FK5' for EQUINOX
2000.0). If different columns of the table contain images with different
reference frames, then the
`RADEC`*n*form of the keyword must be used to give the frame for each column individually.

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