Shared Python interface for World Coordinate Systems

Background

The WCS class implements what is considered the most common ‘standard’ for representing world coordinate systems in FITS files, but it cannot represent arbitrarily complex transformations and there is no agreement on how to use the standard beyond FITS files. Therefore, other world coordinate system transformation approaches exist, such as the gwcs package being developed for the James Webb Space Telescope (which is also applicable to other data).

Since one of the goals of the Astropy Project is to improve interoperability between packages, we have collaboratively defined a standardized application programming interface (API) for world coordinate system objects to be used in Python. This API is described in the Astropy Proposal for Enhancements (APE) 14: A shared Python interface for World Coordinate Systems.

The core astropy package provides base classes that define the low- and high- level APIs described in APE 14 in the astropy.wcs.wcsapi module, and these are listed in the Reference/API section below.

Overview

While the full details and motivation for the API are detailed in APE 14, this documentation summarizes the elements that are implemented directly in the astropy core package. The high-level interface is likely of most interest to the average user. In particular, the most important methods are the pixel_to_world() and world_to_pixel() methods. These provide the essential elements of WCS: mapping to and from world coordinates. The remainder generally provide information about the kind of world coordinates or similar information about the structure of the WCS.

In a bit more detail, the key classes implemented here are a high-level that provides the main user interface (BaseHighLevelWCS and subclasses), and a lower-level interface (BaseLowLevelWCS and subclasses). These can be distinct objects or the same one. For FITS-WCS, the WCS object meant for FITS-WCS follows both interfaces, allowing immediate use of this API with files that already contain FITS-WCS. More concrete examples are outlined below.

Pixel conventions and definitions

This API assumes that integer pixel values fall at the center of pixels (as assumed in the FITS-WCS standard, see Section 2.1.4 of Greisen et al., 2002, A&A 446, 747), while at the same time matching the Python 0-index philosophy. That is, the first pixel is considered pixel 0, but pixel coordinates (0, 0) are the center of that pixel. Hence the first pixel spans pixel values -0.5 to 0.5.

There are two main conventions for ordering pixel coordinates. In the context of 2-dimensional imaging data/arrays, one can either think of the pixel coordinates as traditional Cartesian coordinates (which we call x and y here), which are usually given with the horizontal coordinate (x) first, and the vertical coordinate (y) second, meaning that pixel coordinates would be given as (x, y). Alternatively, one can give the coordinates by first giving the row in the data, then the column, i.e. (row, column). While the former is a more common convention when e.g. plotting (think for example of the Matplotlib scatter(x, y) method), the latter is the convention used when accessing values from e.g. Numpy arrays that represent images (image[row, column]).

The order of the pixel coordinates ((x, y) vs (row, column)) in the API discussed here depends on the method or property used, and this can normally be determined from the property or method name. Properties and methods containing pixel assume (x, y) ordering, while properties and methods containing array assume (row, column) ordering.

Basic usage

Let’s start off by looking at the shared Python interface for WCS by using a simple image with two celestial axes (Right Ascension and Declination):

>>> from astropy.wcs import WCS
>>> from astropy.utils.data import get_pkg_data_filename
>>> from astropy.io import fits
>>> filename = get_pkg_data_filename('galactic_center/gc_2mass_k.fits')  
>>> hdu = fits.open(filename)[0]  
>>> wcs = WCS(hdu.header)  
>>> wcs  
WCS Keywords
Number of WCS axes: 2
CTYPE : 'RA---TAN'  'DEC--TAN'
CRVAL : 266.4  -28.93333
CRPIX : 361.0  360.5
NAXIS : 721  720

We can check how many pixel and world axes are in the transformation as well as the shape of the data the WCS applies to:

>>> wcs.pixel_n_dim  
2
>>> wcs.world_n_dim  
2
>>> wcs.array_shape  
(720, 721)

Note that the array shape should match that of the data:

>>> hdu.data.shape  
(720, 721)

As mentioned in Pixel conventions and definitions, what would normally be considered the ‘y-axis’ of the image (when looking at it visually) is the first dimension, while the ‘x-axis’ of the image is the second dimension. Thus array_shape returns the shape in the opposite order to the NAXIS keywords in the FITS header (in the case of FITS-WCS). If you are interested in the data shape in the reverse order (which would match the NAXIS order in the case of FITS-WCS), then you can use pixel_shape:

>>> wcs.pixel_shape  
(721, 720)

Let’s now check what the physical type of each axis is:

>>> wcs.world_axis_physical_types  
['pos.eq.ra', 'pos.eq.dec']

This is indeed an image with two celestial axes.

The main part of the new interface defines standard methods for transforming coordinates. The most convenient way is to use the high-level methods pixel_to_world() and world_to_pixel(), which can transform directly to astropy objects:

>>> coord = wcs.pixel_to_world([1, 2], [4, 3])  
>>> coord  
<SkyCoord (FK5: equinox=2000.0): (ra, dec) in deg
    [(266.97242993, -29.42584415), (266.97084321, -29.42723968)]>

Similarly, we can transform astropy objects back - we can test this by creating Galactic coordinates and these will automatically be converted:

>>> from astropy.coordinates import SkyCoord
>>> coord = SkyCoord('00h00m00s +00d00m00s', frame='galactic')
>>> pixels = wcs.world_to_pixel(coord)  
>>> pixels  
[array(356.85179997), array(357.45340331)]

If you are looking to index the original data using these pixel coordinates, be sure to instead use world_to_array_index() which returns the coordinates in the correct order to index Numpy arrays, and also rounds to the nearest integer values:

>>> index = wcs.world_to_array_index(coord)  
>>> index  
(357, 357)
>>> hdu.data[index]  
563.7532

Advanced usage

Let’s now take a look at a WCS for a spectral cube (two celestial axes and one spectral axis):

>>> filename = get_pkg_data_filename('l1448/l1448_13co.fits')  
>>> hdu = fits.open(filename)[0]  
>>> wcs = WCS(hdu.header)  
>>> wcs  
WCS Keywords
Number of WCS axes: 3
CTYPE : 'RA---SFL'  'DEC--SFL'  'VOPT'
CRVAL : 57.6599999999  0.0  -9959.44378305
CRPIX : -799.0  -4741.913  -187.0
PC1_1 PC1_2 PC1_3  : 1.0  0.0  0.0
PC2_1 PC2_2 PC2_3  : 0.0  1.0  0.0
PC3_1 PC3_2 PC3_3  : 0.0  0.0  1.0
CDELT : -0.006388889  0.006388889  66.42361
NAXIS : 105  105  53

As before we can check how many pixel and world axes are in the transformation as well as the shape of the data the WCS applies to, as well as the physical types of each axis:

>>> wcs.pixel_n_dim  
3
>>> wcs.world_n_dim  
3
>>> wcs.array_shape  
(53, 105, 105)
>>> wcs.world_axis_physical_types  
['pos.eq.ra', 'pos.eq.dec', 'spect.dopplerVeloc.opt']

This is indeed a spectral cube, with RA/Dec and a velocity axis.

As before, we can convert between pixels and high-level Astropy objects:

>>> celestial, spectral = wcs.pixel_to_world([1, 2], [4, 3], [2, 3])  
>>> celestial  
<SkyCoord (ICRS): (ra, dec) in deg
    [(51.73115731, 30.32750025), (51.72414268, 30.32111136)]>
>>> spectral  
<Quantity [2661.04211695, 2727.46572695] m / s>

and back:

>>> from astropy import units as u
>>> coord = SkyCoord('03h26m36.4901s +30d45m22.2012s')
>>> pixels = wcs.world_to_pixel(coord, 3000 * u.m / u.s)  
>>> pixels  
[array(8.11341207), array(71.0956641), array(7.10297292)]

And as before we can index array values using:

>>> index = wcs.world_to_array_index(coord, 3000 * u.m / u.s)  
>>> index  
(7, 71, 8)
>>> hdu.data[index]  
0.22262384

If you are interested in converting to/from world values as simple Python scalars or Numpy arrays without using high-level astropy objects, there are methods such as pixel_to_world_values() to do this - see Reference/API for more details.

Extending the physical types in FITS-WCS

As shown above, the world_axis_physical_types property returns the list of physical types for each axis. For FITS-WCS, this is determined from the CTYPE values in the header. In cases where the physical type is not known, None is returned. However, it is possible to override the physical types returned by using the custom_ctype_to_ucd_mapping context manager. Consider a WCS with the following CTYPE:

>>> from astropy.wcs import WCS
>>> wcs = WCS(naxis=1)
>>> wcs.wcs.ctype = ['SPAM']
>>> wcs.world_axis_physical_types
[None]

We can specify that for this CTYPE, the physical type should be 'food.spam':

>>> from astropy.wcs.wcsapi.fitswcs import custom_ctype_to_ucd_mapping
>>> with custom_ctype_to_ucd_mapping({'SPAM': 'food.spam'}):
...     wcs.world_axis_physical_types
['food.spam']

Reference/API

astropy.wcs.wcsapi Package

Functions

validate_physical_types(physical_types)

Validate a list of physical types against the UCD1+ standard

Classes

BaseHighLevelWCS	Abstract base class for the high-level WCS interface.
BaseLowLevelWCS	Abstract base class for the low-level WCS interface.
HighLevelWCSMixin	Mix-in class that automatically provides the high-level WCS API for the low-level WCS object given by the low_level_wcs property.
HighLevelWCSWrapper(low_level_wcs)	Wrapper class that can take any BaseLowLevelWCS object and expose the high-level WCS API.

Class Inheritance Diagram

astropy.wcs.wcsapi.fitswcs Module

Classes

custom_ctype_to_ucd_mapping(mapping)	A context manager that makes it possible to temporarily add new CTYPE to UCD1+ mapping used by FITSWCSAPIMixin.world_axis_physical_types.
FITSWCSAPIMixin	A mix-in class that is intended to be inherited by the WCS class and provides the low- and high-level WCS API

Class Inheritance Diagram