Switch between coordinates of pixel and physical coordinates in n-dimensional FITS image using Astropy

Question

I have a FITS image with a header containing information about the coordinates along each axis

NAXIS   =                    3
NAXIS1  =                  259
NAXIS2  =                  272
NAXIS3  =                  100
CDELT1  = -0.08333333330000001
CDELT2  =  0.08333333330000001
CDELT3  =                  0.1
CRPIX1  =                130.5
CRPIX2  =    132.1906015909634
CRPIX3  =                    0
CRVAL1  =                255.0
CRVAL2  =                 60.0
CRVAL3  =                15.45

Is there an easy way (eg and Astropy function) to get the actual (physical) coordinates from the pixel coordinates?

Conversely, is there a built-in function in Astropy to get the coordinates of the closest pixel from actual coordinates?

Edit: I found the WCS.all_pix2world function, but I don't understand how to use it and I didn't find any examples of use.

From the documentation:

There are two accepted forms for the positional arguments:

        - 2 arguments: An N x naxis array of coordinates, and an origin.
        - more than 2 arguments: An array for each axis, followed by an origin. These arrays must be broadcastable to one another.

In the first case, what is N ? Wouldn't origin always be [0,0,0] ?

Answer 1

• N is the number of points for which you want to do the conversion, ie you can compute the pixel or world coordinates for an array of N points.

• origin is just of matter of convention, about the coordinate of the upper left corner. With Python arrays use 0 based indexing, so it is 0. See example below:

In [1]: from astropy.wcs import WCS                                                            

In [2]: from astropy.io import fits                                                            

In [3]: hdr = fits.Header.fromstring("""\ 
   ...: NAXIS   =                    3 
   ...: NAXIS1  =                  259 
   ...: NAXIS2  =                  272 
   ...: NAXIS3  =                  100 
   ...: CDELT1  = -0.08333333330000001 
   ...: CDELT2  =  0.08333333330000001 
   ...: CDELT3  =                  0.1 
   ...: CRPIX1  =                130.5 
   ...: CRPIX2  =    132.1906015909634 
   ...: CRPIX3  =                    0 
   ...: CRVAL1  =                255.0 
   ...: CRVAL2  =                 60.0 
   ...: CRVAL3  =                15.45 
   ...: """, sep='\n')                                                                         

In [4]: wcs = WCS(hdr)                                                                         

In [5]: wcs                                                                                    
Out[5]: 
WCS Keywords

Number of WCS axes: 3
CTYPE : ''  ''  ''  
CRVAL : 255.0  60.0  15.45  
CRPIX : 130.5  132.1906015909634  0.0  
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 : -0.0833333333  0.0833333333  0.1  
NAXIS : 259  272  100

Now you can compute the world coordinate of the upper left corner:

In [6]: wcs.all_pix2world([[0, 0, 0]], 0)                                                      
Out[6]: array([[265.79166666,  49.06744987,  15.55      ]])

Here you could use an array of Nx3 indices.

So if you have pixel indices and want to convert them to sky coordinates, you need to use origin=0, and the same for the opposite, to convert sky coordinates to pixel indices with wcs.all_world2pix .

Using origin=1 may sometimes be useful if you have pixel indices stored in a catalog using the FITS/Fortran convention.