Montage Header Templates

Introduction

The header templates used by several of the Montage modules are just like a normal FITS image header, with two exceptions: they don't need to be padded to 80 characters on each line, and each line ends in a newline.

Some of the ways to create a template header are:

Carriage Returns: If a header template contains carriage returns (i.e., created/modified on a Windows machine), Montage modules will create and use a temporary copy of the header template from which the carriage returns have been removed. This is in order to avoid problems with the WCS library when trying to process headers. The original header template is not modified, and the process should be completely invisible to the user.

Image Coverage: It is best for the background correction algorithms if the area described in the header template completely encloses all of the input images in their entirety. If parts of input images are "chopped off" by the header template, the background correction will be affected. We recommend you use an expanded header for the reprojection and background modeling steps, returning to the originally desired header size for the final coaddition.

The ZPN, COE, CEA, and DSS projections all require additional parameters beyond the standard FITS keywords. For more information on these projections, see Calabretta & Greisen's Representations of world coordinates in FITS.

See the caveats section for more information on Montage and the WCS library.

 

Header Keywords:

The keywords used in FITS to characterize coordinates have evolved over the years, culminating an official standard (Greisen and Calabretta, A&A 395, 1061-1075 and 1077-1122).

Three areas tend to cause some confusion and we would like to comment on them (see the above papers for full details): rotation, celestial coordinate system, and projection parameters.

1) Rotation

Coordinates in FITS are relative to some reference pixel location. This doesn't need to be at the center or corner of the pixel or on the image; it's just a place where we tie a coordinate on the sky to a coordinate in pixel space.

In pixel space, this location is given by CRPIX1 and CRPIX2 (in horizontal "i" and vertical "j" directions). On the sky this location is at CRVAL1 and CRVAL2 coordinates in the native image coordinate system (e.g. RA, Dec).

This reference pixel also has size (i.e. the extent of the pixel on the sky) given by CDELT1 and CDELT2.

The first step in projecting a pixel location onto the sky is to convert the pixel (i,j) coordinate to an angular scale (i.e. psuedo-degrees still on the image plane surface).

If there were no rotation, this would be simply

x' = CDELT1 * (i - CRPIX1)
y' = CDELT2 * (j - CRPIX2)

The oldest approach to dealing with rotation used a simple rotation angle, CROTA2, to indicate how much the y' axis was rotated relative to North. Therefore the true (x,y) needed for input into projection formulae was

x = x' * cos(CROTA2) - y' * sin(CROTA2)
y = x' * sin(CROTA2) + y' * cos(CROTA2)

or

x = CDELT1*(i-CRPIX1)*cos(CROTA2) - CDELT2*(j-CRPIX2)*sin(CROTA2)
y = CDELT1*(i-CRPIX1)*sin(CROTA2) + CDELT2*(j-CRPIX2)*cos(CROTA2)

This approach doesn't allow for skewed pixels, etc. and no version of it based on, for instance, CROTA1 was ever widely used (if at all).

Instead, there are two alternative approaches which recognize that the above is essentially a matrix transform. One approach replaces the above with

x = (i-CRPIX1)*CD1_1 + (j-CRPIX2)*CD1_2
y = (i-CRPIX1)*CD2_1 + (j-CRPIX2)*CD2_2

The CD matrix elements here absorb both the CDELT values and the sin()/cos() of the rotation angle.

The second approach (which is the preferred one in the standard) keeps the CDELT values distinct:

x = CDELT1*(i-CRPIX1)*PC1_1 + CDELT2*(j-CRPIX2)*PC1_2
y = CDELT1*(i-CRPIX1)*PC2_1 + CDELT2*(j-CRPIX2)*PC2_2

In the case where the CDELT values are equal, the PC matrix is a pure rotation.

Any of these three approaches are valid (two CDELTs and CROTA2, a CD matrix, or two CDELTs and a PC matrix) though the first relies on a parameter (CROTA2) which has been deprecated in the standard (and which cannot handle skewed pixels).

Montage relies on the WCS library from SAO (Doug Mink, incorporating the work of Calabretta) and this library carefully checks for all the possible historical variations above. However, this library (and therefore Montage) does not enforce any standards but instead does its best to interpret the intent of the data supplier. However, not all software is this conscientious and some confusion may arise if certain combinations of keywords are used. Therefore care should be taken in constructing headers for Montage use.

 

2) Celestial Coordinate System

The basic coordinate system information is given in the first few characters of the CTYPE1 and CTYPE2 keywords and can be (RA,Dec), (Glon, Glat), etc. For equatorial and ecliptic coordinates it is also necessary to specify both the equinox of the coordinate system and the detailed "system" to which the coordinates refer (FK4, FK5, ICRS):

EQUINOX = 2000.0
RADESYS = 'IRCS'

Different software packages deal with defaulting these values (or one if the other is given) in different ways. In the WCS library (and as documented in the standard):

RADESYS defaults to IRCS unless EQUINOX is given alone, in which case it defaults to FK4 prior to 1984 and FK5 after 1984.

EQUINOX defaults to 2000 unless RADESYS is FK4, in which case it defaults to 1950.

 

3) Projection Parameters

About half the projections available through the WCS library require additional parameters. These can be quantities like reference latitudes and spacing information. These are all documented the reference above.

Usually, there are only one or two such values, though Zenithal Polynomial (ZPN), as the name implies, requires a set of polynomial coefficients (up to 20).

Some existing data uses an early proposed syntax for these parameters: PROJP1, PROJP2, etc. This has been superceded in the standard by PV2_1, PV2_2, etc. (While the formalism allows for associating parameters with any axis, the current ones are invariably linked to latitude, hence always PV2_n). While the WCS library can handle both, it is not guaranteed that other software will.

 

References: