[AstroPy] Determining when world and pixel axes are independent

[Phil Hodge]

Consider the case of celestial coordinates with the center of the image 
close to either the north or south pole, but with the declination axis 
aligned with the image Y axis.  You will need both right ascension and 
declination to calculate an X coordinate in the image, or both X and Y 
to calculate either right ascension or declination.  So you can't just 
look at the off-diagonal elements of the PC matrix.

You could take pixel coordinates [1, 0, ...], [0, 1, ...], etc., and 
transform each of them to world coordinates.  If the world coordinates 
have non-zero elements in more than one world coordinate vector, the 
axes are not independent.

Phil

On 01/13/2014 02:11 PM, Thomas Robitaille wrote:
> I have the same question. Just brainstorming here since I don't know
> the final answer, but I guess there are (as you said) two things going
> on here - one being the fact that certain projections can couple
> coordinates (such as RA/Dec) in some projections (e.g. TAN), and the
> other being rotations of coordinate systems relative to the pixel
> axes. For the latter, I *guess* one could look at the non-diagonal
> elements of the PC matrix:
>
>      >>> w = WCS(...)
>      >>> w.wcs.get_pc()
>      array([[ 1.,  0.,  0.],
>             [ 0.,  1.,  0.],
>             [ 0.,  0.,  1.]])
>
> in the above case, there is no rotation. But for axes 1 and 2 the
> projection is not -CAR:
>
>      In [9]: w.wcs.ctype
>      Out[9]: ['RA---SFL', 'DEC--SFL', 'VOPT']
>
> so axes 1 and 2 are linked (but axis 3 is independent). Maybe the
> solution to find if an axes is independent of the others is:
>
> - check that the non-diagonal elements for that axis are zero
> - check that the projection for that axis is not a spherical
> projection, unless it's -CAR in which case it's also fine
>
> What do others think? Is this robust? Or are there projections that
> are not the usual spherical projections that might link axes? Does one
> need to also check that there are no distortion coefficients in
> addition to the above criteria?
>
> Cheers,
> Tom
>
>
> On 13 January 2014 19:58, Chris Beaumont <beaumont at hawaii.edu> wrote:
>> Hi,
>>
>> Given a WCS object, I'd like to know which pixel and world axes are
>> independent of each other. For example:
>>
>>   * X/Y are generally NOT orthogonal to RA or DEC in the tan projection (to
>> compute RA or DEC, you need both X and Y)
>>   * X is independent to DEC in cartesian projection, UNLESS something like
>> cd2_1 or crota are nonzero
>> * the velocity axis in a spectral data cube is usually orthogonal to the
>> spatial axes (you can translate between Z and V without knowledge of X and
>> Y).
>>
>> I'm sure there are lots of corner cases here. Is there any way I can
>> introspect a WCS object to generally determine if a given world and pixel
>> axis are independent of each other?
>>
>> Thanks,
>> Chris
>>
>> _______________________________________________
>> AstroPy mailing list
>> AstroPy at scipy.org
>> http://mail.scipy.org/mailman/listinfo/astropy
>>
> _______________________________________________
> AstroPy mailing list
> AstroPy at scipy.org
> http://mail.scipy.org/mailman/listinfo/astropy