Description of 2D Spectroscopic Image Data

1. Introduction

This document defines a description for two-dimensional spectroscopic image data produced when light from a telescope is passed through zero or more apertures in the focal plane, spectrally dispersed in one direction, and detected by a 2D digital array detector. This type of data includes long-slit (LS), multi-object (MOS), integral field unit (IFU), and slitless spectroscopy.

The description is intended for use by data reduction software to locate the spectra in the recorded 2D image format and propagate relevant information through extraction, calibration, and analysis. For IFU data the information is used to build data cubes or display the spectra in two spatial as well as spatial/wavelength planes. It also serves as an archival description of the observational data.

This document is intended to be independent of any particular data reduction system. However, the keyword represenation described here will be used by the IRAF APEXTRACT package to automatically interpret 2D spectroscopic image data.

While it is always desirable to be accurate it will be the case that some of the information is known only approximately. This information is still valuable for data reduction software since the approximate values can be refined as the processing proceeds. In some cases the absolute values may be offset by some amount but the relative values are accurate. This is common in multi-object spectroscopy where the positioning of the apertures, and the resulting projection on to a detector are well known but the absolute position on the detector will be less certain due to instrument flexure or alignment.

Section 2 identifies the logical elements or pieces of information which describe the spectra in 2D spectral images. Section 3 discusses how this information is represented and stored. The keyword mapping from the logical elements is defined in section 4 . Section 5 , presents examples for each of the major classes of 2D spectral data.

2. Classes Describing 2D Spectroscopic Data

This section identifies the information about a 2D spectral observation that is relevant to documenting the image data and allowing software to locate and extract the spectra. The document Classes Describing Astronomical Observations presents an methodology for identifying elements or pieces of information about an astronomical observation. The approach is to separate the observation and image information into a logical class hierarchy. That document also defines a particular class hierarchy which is used here.

The classes which are relevant for describing 2D spectral data are shown in Table 1. This does not mean that the full description of the image and observational data will not include other classes. The table shows each class expanded to the individual elements or pieces of information. The syntax is that classes begin with a capital letter and elements begin with a lower case letter. The notation "[n]" indicates that there may be multiple instances of each. In this case there may be many objects and apertures.

Table 1: Classes and Class Elements for 2D Spectral Data

OBJECT Class:
    Object[n].name
    Object[n].type
    COORDINATE.EQUATORIAL Class:
	Object[n].Coordinate.Equatorial.ra
	Object[n].Coordinate.Equatorial.dec
	Object[n].Coordinate.Equatorial.raunit
	Object[n].Coordinate.Equatorial.decunit
	Object[n].Coordinate.Equatorial.epoch
	Object[n].Coordinate.Equatorial.system
	Object[n].Coordinate.Equatorial.equinox

APERTURE Class:
    Aperture[n].apertureid
    Aperture[n].aperturetype
    Aperture[n].diameter
    Aperture[n].length
    Aperture[n].width
    Aperture[n].apunit
    Aperture[n].posangle
    Aperture[n].paunit
    COORDINATE.EQUATORIAL Class:
	Aperture[n].Coordinate.Equatorial.ra
	Aperture[n].Coordinate.Equatorial.dec
	Aperture[n].Coordinate.Equatorial.raunit
	Aperture[n].Coordinate.Equatorial.decunit
	Aperture[n].Coordinate.Equatorial.epoch
	Aperture[n].Coordinate.Equatorial.system
	Aperture[n].Coordinate.Equatorial.equinox
    SPECTRUM Class:
	WCS Class:
	    Aperture[n].Spectrum.Wcs.ctype1
	    Aperture[n].Spectrum.Wcs.ctype2
	    Aperture[n].Spectrum.Wcs.ctype3
	    Aperture[n].Spectrum.Wcs.crpix1
	    Aperture[n].Spectrum.Wcs.crpix2
	    Aperture[n].Spectrum.Wcs.crpix3
	    Aperture[n].Spectrum.Wcs.cd[1,1]
	    Aperture[n].Spectrum.Wcs.cd[1,2]
	    Aperture[n].Spectrum.Wcs.cd[1,3]
	    Aperture[n].Spectrum.Wcs.cd[2,1]
	    Aperture[n].Spectrum.Wcs.cd[2,2]
	    Aperture[n].Spectrum.Wcs.cd[2,3]
	    Aperture[n].Spectrum.Wcs.cd[3,1]
	    Aperture[n].Spectrum.Wcs.cd[3,2]
	    Aperture[n].Spectrum.Wcs.cd[3,3]
	    COORDINATE.DISPERSION Class:
		Aperture[n].Spectrum.Wcs.Coordinate.dispersion.dispval
		Aperture[n].Spectrum.Wcs.Coordinate.dispersion.dispunit
		Aperture[n].Spectrum.Wcs.Coordinate.dispersion.dispframe
		Aperture[n].Spectrum.Wcs.Coordinate.dispersion.velzero
		Aperture[n].Spectrum.Wcs.Coordinate.dispersion.velzerounit
	    COORDINATE.EQUITORIAL Class:
		Aperture[n].Spectrum.Wcs.Coordinate.Equatorial.ra
		Aperture[n].Spectrum.Wcs.Coordinate.Equatorial.dec
		Aperture[n].Spectrum.Wcs.Coordinate.Equatorial.raunit
		Aperture[n].Spectrum.Wcs.Coordinate.Equatorial.decunit
		Aperture[n].Spectrum.Wcs.Coordinate.Equatorial.epoch
		Aperture[n].Spectrum.Wcs.Coordinate.Equatorial.system
		Aperture[n].Spectrum.Wcs.Coordinate.Equatorial.equinox
	WCSREGION Class:
	    Aperture[n].Spectrum.Wcsregion.pmin[1]
	    Aperture[n].Spectrum.Wcsregion.pmax[1]
	    Aperture[n].Spectrum.Wcsregion.pmin[2]
	    Aperture[n].Spectrum.Wcsregion.pmax[2]
	    Aperture[n].Spectrum.Wcsregion.pmin[3]
	    Aperture[n].Spectrum.Wcsregion.pmax[3]
	    Aperture[n].Spectrum.Wcsregion.cmin[1]
	    Aperture[n].Spectrum.Wcsregion.cmax[1]
	    Aperture[n].Spectrum.Wcsregion.cmin[2]
	    Aperture[n].Spectrum.Wcsregion.cmax[2]
	    Aperture[n].Spectrum.Wcsregion.cmin[3]
	    Aperture[n].Spectrum.Wcsregion.cmax[3]
	Aperture[n].Spectrum.fwhm

The WCS or world coordinate system is generally not known precisely and will be given in a lower order representation than is actually the case for a particular type of disperser. However, it is useful for defining the orientation of extraction apertures, allowing information to be specified in physical units such as wavelength, and giving archival researchers information about the dispersion coverage. A rough dispersion WCS also allows reduction software to more easily and automatically perform the dispersion calibration by giving guidance as to where arc calibration lines are likely to be found and about the dispersion per pixel. However it would be valid to use a pixel WCS if the information about the location and orientation of the spectra is only available as pixels on the detector.

2.1 Restricting the Elements

There is redundancy in the description provided by the elements in Table 1. In this section we restrict some of the elements to provide a specific description.

The main simplification is to merge the aperture position information and the spatial part of the WCS reference coordinate. In other words, the position of each aperture on the sky is defined by the spatial world reference coordinate for the WCS describing that aperture.

The WCS describes the dispersion value and spatial coordinate of each pixel in the image. Defining the region of the image containing the spectrum may be done using the WCSREGION class. We eliminate the limits in pixel space (the pmin/pmax elements) and use just the world coordinate limits. The limits along the dispersion are set by these elements. For many observations the limits in the dispersion will be the same for all apertures and so a common value can be used.

The limits in celestial coordinates could also be provided. But each aperture would then require four values for each aperture and the appropriate points corresponding to the projection of the aperture to the one spatial axis of the image would need to be given. So instead the aperture type and dimensions are used to define the spatial extent on the image. The cmin/cmax elements for the spatial world coordinate dimensions are therefore eliminated.

3. The Data Representation

There are two obvious representations for the information shown in Table 1. These are as a table and as a set of keywords. They can be stored in a text file or as a FITS file. For keywords the information can be included in the image header of the data image. Both tables and keywords can also be associated with the data as extensions in the same FITS file with the observational image data.

A keyword representation consists of a set of FITS format keyword cards. When stored as a separate text file the syntax is the same except for replacing the 80 character card format with newline separators and eliminating superfluous trailing spaces needed to make up the card length. When the keywords are stored in a FITS header they can be included with the header of the spectral image data, as the header in a dataless image extension, or as a separate dataless image file. The data extraction software, such as the IRAF APEXTRACT tasks, would then just use a filename specifying the text file or image file, where an image extension is just a special kind of image name.

4. The Keywords

This sections takes the logical description given in Table 1 and reduces it to a set of FITS keywords. This includes both removing redundant information and defining keywords.

Each remaining element in Table 1 is mapped to a FITS keyword. In addition, keywords are defined that replace a set of keywords for the common case that all values are the same. The elements are mapped to FITS keywords through a FITS keyword data dictionary. The keywords given here are described in the NOAO FITS Keyword Dictionary. A subset of this dictionary which includes only those keywords used here is given in FITS Keyword Dictionary: Spectroscopic Aperture Subset.

The FITS dictionary defines keywords for each logical element and a chain of default keywords if the keyword is missing. The default keyword chain allows use of one keyword to cover many related class elements. If the last keyword in the chain is missing then the data dictionary defines an implicit value. In this document all elements have an explicit value including the units.

Table 2 shows all the class elements and their keyword chains from the specific keyword on the left to the global defaults to the right. Since spectral data may include more than one spectrum per image the elements are shown with the "[n]" array notation and the keywords are shown with the notation "%4d" representing a 4 digit index with leading zeros as needed. Due to the FITS keyword limit of 8 characters and the need to discriminate keywords, this naming scheme only supports up to 9999 spectra.

Table 2: Class Element to Keyword Mapping

Class Element Name         Keywords (from individual to global)

Object[n].name:            OBJ%4d   OBJNAME   OBJECT
Object[n].type:            OBJT%4d  OBJTYPE
Object[n].*.ra:            ORA%4d   OBJRA     RA
Object[n].*.dec:           ODEC%4d  OBJDEC    DEC
Object[n].*.raunit:        ORAU%4d  OBJRAU    RAUNIT
Object[n].*.decunit:       ODEU%4d  OBJDECU   DECUNIT
Object[n].*.epoch:         OEPO%4d  OBJEPOCH  EPOCH
Object[n].*.system:        ORDS%4d  OBJRADEC  RADECSYS
Object[n].*.equinox:       OEQU%4d  OBJEQUIN  EQUINOX

Aperture[n].apertureid:    APER%4d            APERTURE
Aperture[n].aperturetype:  APTY%4d            APTYPE
Aperture[n].diameter:      APDI%4d            APERDIA
Aperture[n].length:        APLE%4d            APERLEN
Aperture[n].width:         APWI%4d            APERWID
Aperture[n].apunit:        APUN%4d            APUNIT
Aperture[n].posangle:      APPA%4d            APERPA
Aperture[n].paunit:        APAU%4d            APPAUNIT

Aperture[n].*.ctype1:      CTY1%4d            CTYPE1
Aperture[n].*.ctype2:      CTY2%4d            CTYPE2
Aperture[n].*.ctype3:      CTY3%4d            CTYPE3
Aperture[n].*.crpix1:      CRP1%4d            CRPIX1
Aperture[n].*.crpix2:      CRP2%4d            CRPIX2
Aperture[n].*.crpix3:      CRP3%4d            CRPIX3
Aperture[n].*.cd[1,1]:     CD11%4d            CD1_1
Aperture[n].*.cd[1,2]:     CD12%4d            CD1_2
Aperture[n].*.cd[1,3]:     CD13%4d            CD1_3
Aperture[n].*.cd[2,1]:     CD21%4d            CD2_1
Aperture[n].*.cd[2,2]:     CD22%4d            CD2_2
Aperture[n].*.cd[2,3]:     CD23%4d            CD2_3
Aperture[n].*.cd[3,1]:     CD31%4d            CD3_1
Aperture[n].*.cd[3,2]:     CD32%4d            CD3_2
Aperture[n].*.cd[3,3]:     CD33%4d            CD3_3
Aperture[n].*.dispval:     CRV1%4d            CRVAL1
Aperture[n].*.dispunit:    CUN1%4d            CUNIT1
Aperture[n].*.dispframe:   SSYS%4d            SPECSYS
Aperture[n].*.velzero:     RSTF%4d            RESTFRQ
Aperture[n].*.velzero:     RSTW%4d            RESTWAV
Aperture[n].*.ra:          CRV2%4d            CRVAL2
Aperture[n].*.raunit:      CUN2%4d            CUNIT2
Aperture[n].*.dec:         CRV3%4d            CRVAL3
Aperture[n].*.decunit:     CUN3%4d            CUNIT3
Aperture[n].*.system:      CRDS%4d            RADECSYS
Aperture[n].*.equinox:     CEQU%4d            EQUINOX

Aperture[n].*.cmin1:       CMN1%4d            CMIN1
Aperture[n].*.cmax1:       CMX1%4d            CMAX1
Aperture[n].*.fwhm:        SWID%4d            SPECFWHM

The data provider is free to choose how much defaulting is done. At one extreme every spectrum can have every piece of information shown in Table 2. The application software, such as APEXTRACT, will start with the most specific keyword and then follow the default chain until a value is found. It does not really care how compact the description is. But use of the defaults for different types of spectral data makes the description more compact and human readable. Also it is highly unlikely that things such as units and equatorial systems will differ between different spectra.

The minimal complete set of keywords needed to describe the different types of spectral data is obtained by using the most global keywords whenever possible. In other words, if some piece of information is different for each spectrum the indexed keywords are used but if the information is the same the global value is used. If some element does not apply to a type of spectral data then it is left out. Another way to look at this is that the global values are overridden by more specific keywords.

Ideally the keyword information described here will be part of the data provided to the data reduction software and the user, either with the image data or as a separate text file. However, this may not be the case for particular instruments. For example the information may be some mask definition file or a list of coordinates. In these cases specialized translation programs will be developed. These might be fairly specific, such as for GMOS, or fairly generic such as for objective prism data.

5. Examples

This section provides examples of the various types of 2D spectral data formats. The examples try to be realistic though there may be some inconsistencies. Following each example, comments are made about the various keywords and groups of keywords.

5.1 Fiber and Lenslet/Fiber IFUs

A fiber-based IFU uses optical fibers placed in some closely spaced pattern to sample a particular object or region of the sky. The output of the fibers are arranged in a linear or zig-zag geometry at the entrance of the spectrograph to make maximum use of the 2D detector. Because fibers by themselves can not completely sample a contiguous region due to cladding and packing constraints, one type of IFU uses a lenslet array to collect the light from contiguous hexagonal regions to feed the fibers. The example below is for a lenslet/fiber IFU represented by the CIRPASS instrument. An example of a purely fiber system, DENSPAK, would require only minor modifications.

OBJECT  = 'CIRPASS: m51 V 600s' / Observation title

OBJNAME = 'M 51    '           / Target object
OBJRA   = '13:29:24.00'        / Right ascension of object (hr)
OBJDEC  = '47:15:34.00'        / Declination of object (deg)
OBJEPOCH=               2000.1 / Epoch of object coordinates (yr)
EQUINOX =               2000.0 / Default coordinate equinox (yr)
RADECSYS= 'FK5     '           / Default coordinate system
RAUNIT  = 'hr      '           / Right ascension unit
DECUNIT = 'deg     '           / Declination unit

APERTURE= 'CIRPASS IFU'        / Aperture identification
APTYPE  = 'hexlens+fiber'      / Aperture type
APERDIA =                 0.36 / Aperture diameter (arcsec)
APERPA  =                 90.0 / Hexagon angle (deg)
APUNIT  = 'arcsec  '           / Aperture dimension unit
APPAUNIT= 'deg     '           / Aperture position angle unit
APEPOCH =               2000.1 / Aperture coordinate epoch (yr)

CRVAL1  =                  1.1 / Spectrum dispersion center (um)
CRPIX1  =               1024.0 / Spectrum center (pixel)
CMIN1   =                  0.9 / Spectrum dispersion limit (um)
CMAX1   =                  1.3 / Spectrum dispersion limit (um)
CTYPE1  = 'WAVE-WAV'           / Spectrum coordinate type
CTYPE2  = 'RA---TAN'           / RA coordinate type
CTYPE3  = 'DEC--TAN'           / DEC coordinate type
CUNIT1  = 'um'                 / Spectrum coordinate unit
CD1_1   =              0.00022 / Coord matrix (um/pixel)
CD2_2   =          2.777778E-4 / Coord matrix (deg/pixel)
CD3_3   =          2.777778E-4 / Coord matrix (deg/pixel)
SPECFWHM=                  2.0 / Fiber FWHM (pixel)

CRV20001= '13:29:24.00'        / Aperture right ascension (hr)
CRV30001= '47:15:34.00'        / Aperture declination (deg)
CRP20001=                500.0 / Spectrum center (pixel)

CRV20002= '13:29:24.00'        / Aperture right ascension (hr)
CRV30002= '47:15:34.36'        / Aperture declination (deg)
CRP20002=                504.0 / Spectrum center (pixel)

There is only one IFU targeting one object or region of the sky. So there is only one object name, ra, and dec. Also all equatorial coordinates are given in the same units, equinox, and coordinate system. If OBJNAME is not given, though it is recommended, then the OBJECT keyword would serve as the identification.
The aperture identification specifies the IFU. The aperture type, aperture diameter, and aperture position angle are the same for each spectrum. This information is used to construct a data cube or spatial/dispersion displays in conjunction with the aperture centers. The position angle is for one of the hexagonal edges and would orient the hexagons when reconstructing a spatial display or data cube. For a purely fiber IFU (such as DENSPAK) much the same description would be used except the position angle would be eliminated.
The world coordinate system for each spectrum is similar for the case where the fibers are linearly aligned to form the spectrograph slit entrance. If the fibers are zig-zaged the WCS may still be treated as approximately the same. Note that the WCS is defined such that the mapping for the first coordinate axis is always dispersion and the CD matrix elements are used to define the direction of the dispersion relative to the detector.
The center of each spectrum in world coordinates is given by the CRVAL keywords. In this example each spectrum is centered at about 1.1 micron in the dispersion direction and 0 pixels in the cross-dispersion direction. The cross-dispersion coordinates are defined as pixels from the center of the fiber profile since there is no real spatial information.
The region the spectra cover in world coordinates are given by the CMIN/CMAX keywords. In this example the spectra cover the range 0.9 to 1.3 microns along the dispersion and -1.5 to 1.5 pixels relative to the fiber profile center. Note that if the spectra cover the full range of the detector then the dispersion limits simply need to be large enough to extend beyond the actual detector boundaries. These keywords are important for defining the region to be extracted.
The CD keywords define the conversion between world coordinates and pixels on the detector. They also define any possible tilt of the dispersion path relative to the detector pixels. In this example the dispersion is 0.22 nm per pixel along the first image axis (along the detector rows) and there is no tilt.
The fiber full width at half maximum (SPECFWHM) gives the fiber profile FWHM at the detector in the units of the spatial WCS, in this case pixels. This is used to guide the tracing and extraction of blended fiber profiles.
The ARA/ADEC keywords give the center positions of each lenslet element or fiber. While it is desirable for the absolute coordinates to be accurate it is more important that the relative positions be fairly precise. The absolute center of the array could be refined later. It is these keywords that determine the reconstructed field and gives the IFU sampling pattern and orientation. The relative positions of the lenslets or fibers on the sky is something that should be well-known for each IFU instrument.
The CRP keywords override the CRPIX keyword and provide the positions of the fiber spectra on the detector. In this case they define the CRPIX2 or line position for each fiber. CRPIX1 is refers to the middle of this 2048 line detector. In this example the spectra cover the entire length of the detector.
The pixel position values may be offset from the expected positions due to flexure or alignment errors. It is the relative separations that are important and can be used by the extraction software to tweak up the positions of the spectra based on the pattern. Broken fibers should be removed from the description, particularly those at the ends, to both avoid misidentifications and to aid in the pattern matching. If the fiber array at the spectrograph entrance is constructed to include characteristic gaps this will also aid in the automatic identification of the fibers by the extraction software.

5.2 Fiber MOS

In a fiber multi-object spectrograph the entrance of each fiber is placed on a different target. The targets are either astronomical objects or blank sky. An example of this type of spectrograph are the NOAO Hydra instruments. However this example is quite generic for any fiber positioning spectrograph.

OBJECT  = 'HYDRA: Field 2125'  / Observation title

OBJEPOCH=               2000.1 / Epoch of object coordinates (yr)
EQUINOX =               2000.0 / Default coordinate equinox (yr)
RADECSYS= 'FK5     '           / Default coordinate system
RAUNIT  = 'hr      '           / Right ascension unit
DECUNIT = 'deg     '           / Declination unit

APERTURE= 'f2125red.hydra'     / Aperture identification
APTYPE  = 'fiber   '           / Aperture type
APERDIA =                   2. / Aperture diameter (arcsec)
APUNIT  = 'arcsec  '           / Aperture dimension unit

CRVAL1  =               5000.0 / Spectrum dispersion center (Angstrom)
CRVAL2  =                    0 / Spectrum cross-dispersion center (pixel)
CRPIX1  =               1024.0 / Spectrum center (pixel)
CRPIX2  =               1024.0 / Spectrum center (pixel)
CMIN1   =               3000.0 / Spectrum dispersion limit (Angstrom)
CMAX1   =               7000.0 / Spectrum dispersion limit (Angstrom)
PMIN2   =                 -2.0 / Spectrum cross-dispersion limit (pixel)
PMAX2   =                  2.0 / Spectrum cross-dispersion limit (pixel)
CTYPE1  = 'WAVE-WAV'           / Spectrum coordinate type
CTYPE2  = 'RA---TAN'           / Spectrum coordinate type
CTYPE3  = 'DEC--TAN'           / Spectrum coordinate type
CUNIT1  = 'Angstrom'           / Spectrum coordinate unit
OUNIT2  = 'arcsec'             / Spatial offset unit
CD1_1   =                  0.0 / Spec coord matrix (Angstrom/pixel)
CD1_2   =                -1.56 / Spec coord matrix (Angstrom/pixel)
CD2_1   =                  1.0 / Spec coord matrix (pixel/pixel)
CD2_2   =                  0.0 / Spec coord matrix (pixel/pixel)

OBJ0001 = 'Target 123'         / Target object
OBJT0001= 'galaxy  '           / Type of object
ORA0001 = '13:29:24.00'        / Right ascension of object (hr)
ODEC0001= '47:15:34.00'        / Declination of object (deg)
APER0001= '2 f2125red.hydra'   / Aperture identification
CRP10001=               500.00 / Spectrum center (pixel)

OBJ0002 = 'Sky       '         / Target object
OBJT0002= 'sky     '           / Type of object
ORA0002 = '13:29:44.71'        / Right ascension of object (hr)
ODEC0002= '47:15:24.82'        / Declination of object (deg)
APER0002= '3 f2125red.hydra'   / Aperture identification
CRP10002=               505.00 / Spectrum center (pixel)

Since each fiber targets a different point in the sky there is no global coordinate but all coordinates are specified in the J2000 coordinate system with units of hours and degrees.
The aperture identification specifies the fiber configuration. The aperture type and aperture diameter are the same for each spectrum. In this case the aperture type is fiber and the only dimension is the fiber diameter specified in units of arc seconds on the sky.
Typically the fibers are arranged in a straight line at the spectrograph entrance. Therefore the WCS for each fiber spectrum will be the same except for the spectrum center in the cross-dispersion direction on the detector. The WCS keywords indicate a dispersion center of 5000A with a range between 3000A and 7000A. When the spectra extend across the entire detector the limits can be set to any value outside the detector coverage. The cross-dispersion part of the WCS is given in pixels from the profile center with a range of -2 to 2 pixels.
By definition the dispersion is specified by the first world coordinate axis and the cross-dispersion by the second. The mapping to the image axis is made with the CD coordinate matrix elements. In this case the CD terms indicate the dispersion runs along the second detector dimension, that is vertically, with no tilt. It also indicates that the dispersion decreases with increasing line coordinates. The cross-dispersion coordinates are simply pixels with direction increasing with column coordinate.
Since the fibers target different objects the information that must be specified for each fiber separately are the object name, object type, object coordinates, aperture identification, and detector position across the dispersion. The object type is used to identify fibers measuring the background sky. The object coordinates double as the aperture coordinates for the case of fibers. The aperture identifications identify the fiber used. The cross-dispersion positions override the CRPIX1 keyword and specify the column position of the spectrum at the line given by the CRPIX2 keyword, the middle of the detector in this case.
The positions on the detector should correctly give the relative spacing between the spectra though the absolute positions may be off due to flexure or alignment. The pattern of the positions will be matched to the data to refine the positions. All visible spectra should be defined and any broken fibers, which don't produce a spectrum, should be removed to avoid misidentifications. If the positions have characteristic gaps this will also aid in the automatic identification of the fibers.

5.3 Slit Mask MOS

A slit mask multi-object spectrograph places a mask with a number of slits in the focal plane. The slits are placed on individual targets. Generally the slits will be oriented in the same way and the number and positions of the slits are optimized to maximize the detector coverage. Part of the optimization is to not exactly center each slit on the target object. Also the slits may be optimized to have more than one slit image along the dispersion direction on the detector. In other words the slit images may be stacked along both dimensions on the detector.

A related type of mask where sky subtraction is done using separate apertures (as with a fiber MOS), or not at all, uses circular apertures. This increases the density of objects. The description would be very similar to slits except the aperture type would be circular and the dimension would be a diameter. Also, like the fiber MOS, only the object coordinates would be used.

The example below is for a slit mask such as is planned for GMOS.

OBJECT  = 'GMOS: m51 V 600s'   / Observation title

OBJEPOCH=               2000.1 / Epoch of object coordinates (yr)
EQUINOX =               2000.0 / Default coordinate equinox (yr)
RADECSYS= 'FK5     '           / Default coordinate system
RAUNIT  = 'hr      '           / Right ascension unit
DECUNIT = 'deg     '           / Declination unit

APERTURE= 'Mask 12345'         / Aperture identification
APTYPE  = 'slit mask'          / Aperture type
APERWID =                  0.5 / Slit width (arcsec)
APERLEN =                   2. / Slit length (arcsec)
APERPA  =                  0.0 / Slit angle (deg)
APUNIT  = 'arcsec  '           / Aperture dimension unit
APPAUNIT= 'deg     '           / Aperture position angle unit
APEPOCH =               2000.1 / Aperture coordinate epoch (yr)

CRVAL1  =               5015.0 / Spectrum dispersion center (Angstrom)
CRVAL2  =                   0. / Spectrum cross-dispersion center (arcsec)
CMIN1   =               4015.0 / Spectrum dispersion limit (Angstrom)
CMAX1   =               6015.0 / Spectrum dispersion limit (Angstrom)
CTYPE1  = 'WAVE-WAV'           / Spectrum coordinate type
CTYPE2  = 'RA---TAN'           / Spectrum coordinate type
CTYPE3  = 'DEC--TAN'           / Spectrum coordinate type
CUNIT1  = 'Angstrom'           / Spectrum coordinate unit
OUNIT2  = 'arcsec'             / Spatial offset unit
CD1_1   =                  0.0 / Spec coord matrix (Angstrom/pixel)
CD1_2   =                 -6.2 / Spec coord matrix (Angstrom/pixel)
CD2_1   =                 0.08 / Spec coord matrix (arcsec/pixel)
CD2_2   =                  0.0 / Spec coord matrix (arcsec/pixel)

OBJ0001 = 'Target 12'          / Target object
OBJT0001= 'galaxy  '           / Type of object
ORA0001 = '13:29:24.12'        / Right ascension of object (hr)
ODEC0001= '47:15:34.34'        / Declination of object (deg)
ARA0001 = '13:29:24.12'        / Aperture right ascension (hr)
ADEC0001= '47:15:32.78'        / Aperture declination (deg)
CRP10001=               500.00 / Spectrum center (pixel)
CRP20001=               500.00 / Spectrum center (pixel)
CMN20001=                -1.44 / Spectrum cross-dispersion limit (arcsec)
CMX20001=                 0.56 / Spectrum cross-dispersion limit (arcsec)

OBJ0002 = 'Target 32'          / Target object
OBJT0002= 'galaxy  '           / Type of object
ORA0002 = '13:29:23.23'        / Right ascension of object (hr)
ODEC0002= '47:15:44.45'        / Declination of object (deg)
ARA0002 = '13:29:23.23'        / Aperture right ascension (hr)
ADEC0002= '47:15:44.30'        / Aperture declination (deg)
CRP10002=               900.00 / Spectrum center (pixel)
CRP20002=              1200.00 / Spectrum center (pixel)
CMN20002=                -0.85 / Spectrum cross-dispersion limit (arcsec)
CMX20002=                 1.15 / Spectrum cross-dispersion limit (arcsec)

Since each fiber targets a different point in the sky there is no global coordinate but all coordinates are specified in the J2000 coordinate system with units of hours and degrees.
The aperture identification specifies the mask and the aperture type is 'slit'. The slits are all the same width (0.5 arcsec) and length (2 arcsec) and in the same position angle on the sky (0 degrees). Slit sizes are specified in arc seconds on the sky and slit position angles are specified as degrees from north through east for the long dimension of the slit. If the slits have different dimensions and orientations then the APWI, APLE, and APPA indexed keywords would be used to override the default values.
The WCS for each slit spectrum define a coordinate system in Angstroms for the dispersion and in arc seconds for the the cross-dispersion. The reference position for each spectrum is at 5015A and 0 arcsec from the object coordinate. The dispersion coverage is 4015A to 6015A. This is used to define the extent of the slit spectrum image that is extracted.
It is important to notice that the cross-dispersion coordinate system is centered on the object and not the center of the aperture. This is useful to automate identification of sky regions for each slit. The cross-dispersion limits defining the extent of the slit image to be extracted will, therefore, vary for each slit and are given by the CMN and CMX keywords.
By definition the dispersion is specified by the first coordinate axis and the cross-dispersion by the second. The mapping to the image axis is made with the CD coordinate matrix elements. In this case the CD terms indicate the dispersion runs along the second detector dimension, that is vertically, with no tilt. It also indicates that the dispersion decreases at 6.2 Angstroms per pixel with increasing line coordinates. The cross-dispersion coordinates increase with the column coordinate and the scale is 0.78 arc second per pixel.
The remaining keywords describe each slit. Each slit is placed on a different object so each has an object name, object type, and object coordinate. The slit apertures have slightly different coordinates since they are where the slit is centered and the object need not be placed at the center of the slit. Finally the coordinate reference pixels give the position on the detector for the reference dispersion coordinate, which is the object center corresponding to the object coordinate.

5.4 Image Slicer IFU

This section considers the case of image slicers that break a rectangular region of the sky into a set of "slits" and arrange the slit images next to each other on the detector.

OBJECT  = 'SLICER: m51 V 600s' / Observation title

OBJNAME = 'M 51    '           / Target object
OBJRA   = '13:29:24.00'        / Right ascension of object (hr)
OBJDEC  = '47:15:34.00'        / Declination of object (deg)
OBJEPOCH=               2000.1 / Epoch of object coordinates (yr)
EQUINOX =               2000.0 / Default coordinate equinox (yr)
RADECSYS= 'FK5     '           / Default coordinate system
RAUNIT  = 'hr      '           / Right ascension unit
DECUNIT = 'deg     '           / Declination unit

APERTURE= 'Image slicer IFU'   / Aperture identification
APTYPE  = 'slit    '           / Aperture type
APERWID =                  0.5 / Slit width (arcsec)
APERLEN =                  10. / Slit length (arcsec)
APERPA  =                 90.0 / Slit angle (deg)
APUNIT  = 'arcsec  '           / Aperture dimension unit
APPAUNIT= 'deg     '           / Aperture position angle unit
APEPOCH =               2000.1 / Aperture coordinate epoch (yr)

CRVAL1  =               5015.0 / Spectrum dispersion center (Angstrom)
CRVAL2  =                   0. / Spectrum cross-dispersion center (arcsec)
CRPIX1  =               1024.0 / Spectrum center (pixel)
CRPIX2  =               1024.0 / Spectrum center (pixel)
CMIN1   =               3015.0 / Spectrum dispersion limit (Angstrom)
CMAX1   =               7015.0 / Spectrum dispersion limit (Angstrom)
CMIN2   =                 -4.9 / Spectrum cross-dispersion limit (arcsec)
CMAX2   =                  4.9 / Spectrum cross-dispersion limit (arcsec)
CTYPE1  = 'WAVE-WAV'           / Spectrum coordinate type
CTYPE2  = 'RA---TAN'           / Spectrum coordinate type
CTYPE3  = 'DEC--TAN'           / Spectrum coordinate type
CUNIT1  = 'Angstrom'           / Spectrum coordinate unit
OUNIT2  = 'arcsec'             / Spatial offset unit
CD1_1   =                  0.0 / Spec coord matrix (Angstrom/pixel)
CD1_2   =                 -2.2 / Spec coord matrix (Angstrom/pixel)
CD2_1   =                  0.1 / Spec coord matrix (arcsec/pixel)
CD2_2   =                  0.0 / Spec coord matrix (arcsec/pixel)

ARA0001 = '13:29:24.56'        / Aperture right ascension (hr)
ADEC0001= '47:15:32.78'        / Aperture declination (deg)
CRP20001=                500.0 / Spectrum center (pixel)

ARA0002 = '13:29:24.56'        / Aperture right ascension (hr)
ADEC0002= '47:15:33.28'        / Aperture declination (deg)
CRP20002=                610.0 / Spectrum center (pixel)

This example is for a single IFU which targets one object as given by the object name and object coordinates. All coordinates are specified as right ascension in hours and declination in degrees in the J2000 coordinate system.
The aperture identification identifies the IFU unit. The aperture type, since the slicer produces a set of slit spectra, is 'slit'. The slit images are all the same width (0.5 arcsec) and length (10 arcsec) and in the same position angle on the sky (90 degrees). Slit sizes are specified in arc seconds on the sky and slit position angles are specified as degrees from north through east for the long dimension of the slit.
The WCS for each slit spectrum defines a coordinate system in Angstroms for the dispersion and in arc seconds for the the cross-dispersion. The reference position for each spectrum is at 5015A and 0 arcsec from the aperture coordinate. The dispersion coverage is 4015A to 6015A. This is used to define the extent of the slit spectrum image that is extracted.
It is important to notice that the cross-dispersion coordinate system is centered on the aperture and not the center of the object. This is the opposite of the slit mask case. The cross-dispersion limits defining the extent of the slit image to be extracted will, therefore, all be the same and are given as -4.9 to 4.9 arc seconds for each slit (0.1 arc second is excluded from the full slit length at each end to avoid problems with the edges of the slit).
By definition the dispersion is specified by the first coordinate axis and the cross-dispersion by the second. The mapping to the image axis is made with the CD coordinate matrix elements. In this case the CD terms indicate the dispersion runs along the second detector dimension, that is vertically, with no tilt. It also indicates that the dispersion decreases at 2.2 Angstroms per pixel with increasing line coordinates. The cross-dispersion coordinates increase with the column coordinate and the scale is 0.10 arc second per pixel.
The remaining keywords describe each slice. This consists of the position of each slice on the sky and the corresponding position of the slit image on the detector along the cross dispersion dimension.

5.5 Slitless Spectroscopy

This section considers the case of slitless spectroscopy. Here the spectra fall randomly on the detector and are generally at low dispersion to produce short spectra.

OBJECT  = 'Field 75 - 3deg prism' / Observation title

OBJEPOCH=               2000.1 / Epoch of object coordinates (yr)
EQUINOX =               2000.0 / Default coordinate equinox (yr)
RADECSYS= 'FK5     '           / Default coordinate system
RAUNIT  = 'hr      '           / Right ascension unit
DECUNIT = 'deg     '           / Declination unit


APTYPE  = 'none    '           / Aperture type

CRVAL1  =               6000.0 / Spectrum dispersion center (Angstrom)
CRVAL2  =                   0. / Spectrum cross-dispersion center (arcsec)
CMIN1   =               3000.0 / Spectrum dispersion limit (Angstrom)
CMAX1   =               9000.0 / Spectrum dispersion limit (Angstrom)
CMIN2   =                 -3.0 / Spectrum cross-dispersion limit (arcsec)
CMAX2   =                  3.0 / Spectrum cross-dispersion limit (arcsec)
CTYPE1  = 'WAVE-WAV'           / Spectrum coordinate type
CTYPE2  = 'RA---TAN'           / Spectrum coordinate type
CTYPE3  = 'DEC--TAN'           / Spectrum coordinate type
CUNIT1  = 'Angstrom'           / Spectrum coordinate unit
OUNIT2  = 'arcsec'             / Spatial offset unit
CD1_1   =                  1.0 / Spec coord matrix (Angstrom/pixel)
CD1_2   =                -49.0 / Spec coord matrix (Angstrom/pixel)
CD2_1   =                 2.64 / Spec coord matrix (arcsec/pixel)
CD2_2   =               0.0425 / Spec coord matrix (arcsec/pixel)

OBJ0001 = 'Target 12'          / Target object
OBJT0001= 'star    '           / Type of object
ORA0001 = '13:29:24.12'        / Right ascension of object (hr)
ODEC0001= '47:15:34.34'        / Declination of object (deg)
CRP10001=               500.00 / Spectrum center (pixel)
CRP20001=               500.00 / Spectrum center (pixel)

OBJ0002 = 'Target 32'          / Target object
OBJT0002= 'galaxy  '           / Type of object
ORA0002 = '13:28:23.23'        / Right ascension of object (hr)
ODEC0002= '47:14:44.45'        / Declination of object (deg)
CRP10002=               900.00 / Spectrum center (pixel)
CRP20002=              1200.00 / Spectrum center (pixel)

All coordinates are specified as right ascension in hours and declination in degrees in the J2000 coordinate system.
Slitless spectra differ from aperture spectra in that they actually have two coordinate systems. One is a celestial coordinate system. This example shows using a second coordinate system to describe this although it is not necessary for describing the spectra.
The aperture is obviously "none" since there is no aperture.
The WCS for each spectrum in this example is shown as Angstroms along some dispersion direction and arc seconds across the dispersion. All spectra will have the same WCS apart from being placed at different points in the detector. The central wavelength and wavelength limits in this example are 6000A and 3000A to 9000A. For the cross-dispersion coordinate the center of the object is set to a reference value of zero and the extent is -3 to 3 arc seconds. The WCS limits define the extraction aperture (in world coordinates) to be used.
By definition the dispersion is specified by the first coordinate axis and the cross-dispersion by the second. The mapping to the image axes is made with the CD coordinate matrix elements. In this case the CD terms indicate the dispersion runs mostly along the second detector dimension, that is vertically. The tilt is approximately
```
    tilt = arctan (1./-49) or arctan (0.0425/2.64) ~ 1 degree
```
The dispersion decreases at 50 Angstroms / pixel and the plate scale across the dispersion is 2.64 arc seconds / pixel.
The remaining keywords identify each object, the object type, the object coordinates, and the position of the spectrum corresponding to the WCS reference coordinates (6000A and 0 arc seconds from the spectrum center).