World Coordinate Systems in multi-HDU FITS files produced by UCO/Lick mosaic detectors

FITS WCS Paper I defines the fundamental properties of world coordinate systems. It allows for one primary WCS and 26 alternate WCSs in each FITS HDU. The alternate WCSs are denoted by suffixes on the keywords consisting of the letters A through Z.

The data acquisition systems (whose components are lickserv, watch_ccd, and write_image) for mosaic detectors built at UCO/Lick Observatory employ the primary WCS and several of the alternate WCS. The letters denoting the alternate WCS are used in a mnemonic fashion.

The following list does not contain all of the keywords for each of the WCS versions. Only those keywords which indicate the distinctive characteristics of each are given. The others take their meanings directly from FITS WCS Paper I.

One aspect of the coordinate systems docuemented by the keywords from the UCO/Lick mosaic detectors deserves note. Most of the coordinate systems used below are purely linear transformations. Since the inception of FITS in the first paper by Wells et al. (1981), the FITS WCS keywords have contained more expressive power than is needed for a purely linear transformation. The UCO/Lick mosaic data aquisition system uses the CRPIXna keywords to indicate the outside corner of the initial light-sensitive pixel on each CCD. The CRVALna keywords indicate the coordinate values at the outside edge of that pixel expressed in the particular WCS. Although the same WCS information could be transmitted by other values in these keywords, this usage highlights the special nature of the particular location on the silicon of each CCD.

The primary Coordinate System
WCSNAME = 'pane'
CUNITn = 'pixel'
CTYPE1 = 'PANE_X'
CTYPE2 = 'PANE_Y'

The primary coordinate system is identical to the Pane coordinate system which is described below.

The Amplifier Coordinate System
WCSNAMEA = 'amplifier'
CUNITnA = 'pixel' / unbinned pixels on the CCD
CTYPE1A = 'AMPLIFIER_X'
CTYPE2A = 'AMPLIFIER_Y'

A world coordinate system whose integer coordinate values correspond directly to an array of pixels on detector with a raster geometry (e.g., a CCD).

A CCD may have more than one amplifier. In such a case there is one amplifier WCS for each amplifier on the CCD. Each WCS will typically have integral offsets from the others, and their relative orientations may be flipped or even transposed.

The pixel coordinate values are numbered starting with 1 for the initial pixel which is part of the normal imaging array, and the coordinate values increase by 1 for each successive pixel that is read from the detector.

The world coordinate system values on the detector correspond to un-binned pixels.

In keeping with longstanding FITS practice, the centers of the pixels have integral coordinate values. The edges of the pixels have half-integral coordinate values.

The geometry of the amplifiers on the silicon of many CCDs creates non-image, pre-scan pixels which must be read prior to the actual image pixels. These pixels should have non-positive coordinate values.

The amplifier coordinate system only makes sense if a single FITS HDU consists of data from a single amplifier. If the pixel data from more than one amplifier are combined into one image, then the amplifier WCSNAME should not be used.

This definition is adapted directly from the work of Frank Valdes at NOAO .

The CCD Coordinate System
WCSNAMEC = 'CCD'
CUNITnC = 'pixel' / unbinned pixels on the CCD
CTYPE1C = 'CCD_X'
CTYPE2C = 'CCD_Y'

The CCD WCS is chosen as one of the amplifier WCS that apply to a particular detector. Aside from the choice of one canonical amplifier, this WCS is in all other respects identical to the amplifier WCS. One CCD WCS can be applied to any regularly spaced rectangular grid of pixels.

In this case ``detector'' typically means a single CCD, but the actual definition is more precise. It is conceivable that a single CCD could have multiple amplifiers each of which reads out a rectangular array of pixels which is disjoint or non-contiguously oriented from the others. In that case the CCD would be classified as multiple CCDs for the purposes of WCSNAME.

This definition is intended to match the definition used by Frank Valdes at NOAO .

The Image Coordinate System
WCSNAMEI = 'image'
CUNITnI = 'pixel' / pixels in the FITS array
CTYPE1I = 'IMAGE_X'
CTYPE2I = 'IMAGE_Y'

The image WCS is a redundant reiteration of the default FITS pixel coordinate system. I.e., it is the coordinate system which would be attributed to the FITS array in the absence of any WCS keywords. The initial pixel along each axis has coordinate value 1, and the coordinate value increments by one for each pixel. The centers of the pixels have integral coordinate values, and the edges have half-integral values. This is equivalent to IRAF logical coordinates .

The Detector Coordinate System
WCSNAMED = 'detector'
CUNITnD = 'pixel'
CTYPE1D = 'DETECTOR_X'
CTYPE2D = 'DETECTOR_Y'


This coordinate system is intended to follow the definition created by Frank Valdes for the NOAO mosaic detector . It is effectively an extension of the notion of CCD coordinates. It presumes that a mosaic detector is comprised of a rectangular array of identical CCDs. It permits these CCDs to be flipped, but not rotated, with respect to each other. (Therefore a pinwheeled configuration of CCDs, or CCDs with differing pixel sizes, cannot be described.)

It is not clear whether a detector coordinate system which includes gaps would be a legal use. Neither is it clear whether such a scheme would be understood by various different software implementations of FITS readers.

In the practice of the NOAO mosaic detector the enumeration of the pixel values in detector coordinates is continuous across CCD boundaries as if they were contiguously abutted. Within the range of legal detector coordinate values there are no values that correspond to locations between the CCDs. The usage for DEIMOS makes the same presumption.

The Pane Coordinate System
WCSNAMEP = 'pane'
CUNITnP = 'pixel'
CTYPE1P = 'PANE_X'
CTYPE2P = 'PANE_Y'


This coordinate system is used by the PANEn keywords of the DEIMOS mosaic CCD readout system. Its purpose is to define a single, intuitively natural, coordinate system which can refer unambiguously to any pixel in the DEIMOS mosaic. Pane coordinates presume that the overall array of pixels is rectangular. Pane coordinates permit CCDs to be rotated in 90 degree increments.

Pane coordinates will typically have no gaps between CCDs. Nevertheless, if the most natural description of a mosaic detector layout includes gaps, they are legal.

The pane coordinate system adopts the more common, but non-FITS, notion that the centers of pixels are half-integral. Therefore the initial corner has coordinate value 0.0, and its center is at 0.5. However, when referred to in the integer-valued PANEn control keywords, the entire initial pixel is referred to as pixel 0.

In practice for DEIMOS this means that its coordinate values differ by one-half pixel (as real-valued coordinates) or one pixel (as integer-valued coordinates) from that of the ``detector'' coordinate system.

The Gap Coordinate System
WCSNAMEG = 'gap' (aka 'ccd2gap')
CUNITnG = 'pixel'
CTYPE1G = 'GAP_X'
CTYPE2G = 'GAP_Y'


This coordinate system is an interim test scheme which is like pane coordinates except that it incorporates the gaps between each of the CCDs. It is intended to be used as a means of instructing an image display how to layout a mosaic image such that it approximately matches the actual mosaic geometry.



The SlitMask Coordinate System
WCSNAMEM = 'slitmask'
CUNITnM = 'mm'
CTYPE1M = 'SLITMASK_X'
CTYPE2M = 'SLITMASK_Y'


This coordinate system has not yet been implemented for DEIMOS, but could be implemented at any time. Its coordinate values give the location on the slitmask as measured in the coordinate system which is used for milling the masks. Because of nonlinearities in the optical system of the spectrograph this WCS will not be strictly linear. But the deviations from linearity should be small, and they will be handled well by the techniques to be documented in FITS WCS Paper IV.