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# World Coordinate System (`astropy.wcs`)

## Introduction

World Coordinate Systems (WCSs) describe the geometric transformations between one set of coordinates and another. A common application is to map the pixels in an image onto the celestial sphere. Another common application is to map pixels to wavelength in a spectrum.

`astropy.wcs` contains utilities for managing World Coordinate System (WCS) transformations defined in several elaborate FITS WCS standard conventions. These transformations work both forward (from pixel to world) and backward (from world to pixel).

For historical reasons and to support legacy software, `astropy.wcs` maintains two separate application interfaces. The `High-Level API` should be used by most applications. It abstracts out the underlying object and works transparently with other packages which support the Common Python Interface for WCS, allowing for a more flexible approach to the problem and avoiding the limitations of the FITS WCS standard.

The `Low Level API` is the original `astropy.wcs` API and originally developed as `pywcs`. It ties applications to the `astropy.wcs` package and limits the transformations to the three distinct types supported by it:

- Core WCS, as defined in the FITS WCS standard, based on Mark Calabretta’s wcslib. (Also includes `TPV` and `TPD` distortion, but not `SIP`).

- Simple Imaging Polynomial (SIP) convention. (See note about SIP in headers.)

- Table lookup distortions as defined in the FITS WCS distortion paper.

### Pixel Conventions and Definitions

Both APIs assume 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).

However, there’s a difference in what is considered to be the first pixel. The `High Level API` follows the Python and C convention that the first pixel is the 0-th one, i.e. the first pixel spans pixel values -0.5 to + 0.5. The `Low Level API` takes an additional `origin` argument with values of 0 or 1 indicating whether the input arrays are 0- or 1-based. The Low-level interface assumes Cartesian order (x, y) of the input coordinates, however the Common Interface for World Coordinate System accepts both conventions. The order of the pixel coordinates ((x, y) vs (row, column)) in the Common API 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.

## A Simple Example

One example of the use of the high-level WCS API is to use the `pixel_to_world` to yield the simplest WCS with default values, converting from pixel to world coordinates:

    >>> from astropy.io import fits
    >>> from astropy.wcs import WCS
    >>> from astropy.utils.data import get_pkg_data_filename
    >>> fn = get_pkg_data_filename('data/j94f05bgq_flt.fits', package='astropy.wcs.tests')
    >>> f = fits.open(fn)
    >>> w = WCS(f[1].header)
    >>> sky = w.pixel_to_world(30, 40)
    >>> print(sky)
    <SkyCoord (ICRS): (ra, dec) in deg
        (5.52844243, -72.05207809)>
    >>> f.close()

Similarly, another use of the high-level API is to use the `world_to_pixel` to yield another simple WCS, while converting from world to pixel coordinates:

    >>> from astropy.io import fits
    >>> from astropy.wcs import WCS
    >>> from astropy.utils.data import get_pkg_data_filename
    >>> fn = get_pkg_data_filename('data/j94f05bgq_flt.fits', package='astropy.wcs.tests')
    >>> f = fits.open(fn)
    >>> w = WCS(f[1].header)
    >>> x, y = w.world_to_pixel(sky)
    >>> print(x, y)
    30.00000214673885 39.999999958235094
    >>> f.close()

## Using `astropy.wcs`

- Shared Python Interface for World Coordinate Systems
  - Background
  - Overview
  - Basic usage
  - Advanced usage
  - Extending the physical types in FITS-WCS
  - Preserving units in FITS-WCS
  - Slicing of WCS objects
- Legacy Interface
  - astropy.wcs API
  - Core wcslib API
- Supported Projections

## Examples creating a WCS programmatically

- Example of Imaging WCS
- Example of Cube WCS
- Example of a Planetary WCS
- Loading From a FITS File

## WCS Tools

- Subsetting and Pixel Scales
- Matplotlib plots with correct WCS projection

## Relax Constants

- Header-reading relaxation constants
- Header-writing relaxation constants

## Other Information

- astropy.wcs History
- Validation and Bounds checking

## Reference/API

- Reference/API
  - astropy.wcs Package
  - astropy.wcs.utils Module
  - astropy.wcs.wcsapi Package

## See Also

- wcslib

## Acknowledgments and Licenses

wcslib is licenced under the GNU Lesser General Public License.