Celestial And Image Coordinate Projections Using FITS WCS

Provides and illustrates functions to transform between RA and DEC and image XY using FITS WCS information.

Astrometry.net [1] plate solves images by matching 4-star (quad) asterisms of a select number of stars that it finds in the image to those in a quad database. It fits the pixel coordinates of matched stars allowing for distortion and determines the viewing angle in celestial coordinates of each pixel. It provides in a FITS-format files the right ascension (RA) and declination (DEC) and pixel coordinates (x,y) of reference stars and of the center of the image, and the RA and DEC of each pixel in parametric form.

In order to search for additional stars within the field of view and to project these to image coordinates, or to project stars one can find oneself in the image (in addition to matched stars) and to match these to known stars using their RA and DEC, one requires functions transforming between RA DEC and xy in both directions, based on the World Coordinate System (WCS) parameters found in the FITS files. Such functions may be found in various astrometry toolkits including the freely available astrometry.net package and astropy package that require installation and often compilation. This script provides and illustrates the use of simple MATLAB functions ra_dec_to_pix and pix_to_ra_dec for this purpose.

The FITS headers include a number of fit parameters in standard form: CD_ij parameters describing a linear transformation (rotation and shear) and matrices A_ij and B_ij of coefficients in a conventionally defined Simple Imaging Polynomial (SIP) used to correct the image for distortion and transform to intermediate scaled coordinates in degree units before projecting onto the sky with a tangent plane to celestial sphere nonlinear transformation. [2]. (Different angular projections would be applied for different sky coordinates, e.g. galactic coordinates or other projections described in Ref [2].) The reverse transformation requires the inverse of the projection, the inverse of the distortion defined by with coefficients AP_ij and BP_ij, and the inverse of the CD matrix. Astrometry.net defaults to a 2nd order SIP but if requested will fit to order 9th order. The illustrations provided here are a 2nd order fit and an 8th order fit to a handheld 0.5 s exposure mobile phone image with about 200 matched stars.

This script may interest students and instructors of physics and astronomy who wish to identify the stars in their own mobile phone images using nova.astronomy.net or in other astronomy FITS image files. It is a companion to the astrometry tutorial Mobile Phone Astrometry Explorer. 'Try this' suggestions are included for further exploration.