[AstroPy] Determining when world and pixel axes are independent

[Thomas Robitaille]

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
>
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