[fitswcs] Long-slit spectroscopy WCS

[Mark Calabretta]

On Tue 2002/02/05 08:40:23 PDT, Frank Valdes wrote
in a message to: fitswcs at NRAO.EDU

>I'm a little concerned that the examples are again misleading because
>of the assumption that there is no tilt in the path of the spectrum
>through the image.  For a coarse WCS provided at the telescope where
>the setup gets as close as possible this may be true but at higher
>accuracy it will not be.  Of course there will be a curvature also which
>will require use of the DCF transformation.  But if we just consider
>a tilt of the spectrum then the simplest examples using just two
>CD terms is not quite so simple.  In this case there is a rotation
>between the spatial and spectral axes.

Frank et al.,

Here are several reasonable ways to account for non-alignment of the
slit with a pixel axis (including that arising from skewness of the
spectral and spatial axes),

   1) Use the matrix (CDj_i or PCj_i) just to align the spectral and
      spatial axes, and use LONPOLE to do the position angle rotation
      (Frank's suggestion).

      This keeps the two geometric operations separate which has some
      benefits, including easier human interpretation.

   2) Form the matrix (CDj_i or PCj_i) from the product of two rotation
      matrices, the first aligns the spectral and spatial axes, the
      second does the position angle.  The CDELTj can either be kept
      separate or folded into the PCj_i matrix as in methods (a) and
      (c) of my previous email.

      This method is probably closer to the original intent of the
      linear transformation matrix.  It combines the two geometric
      operations but it's not such a big deal - a comment could be
      added.

   3) Use PCj_i to align the spectral and spatial axes and CDELTj to
      do the position angle rotation as in method (c) of my previous
      email.

      This again keeps the two geometric operations separate and may
      be prefered by those who feel uncomfortable with LONPOLE.

In fact, there are infinitely many ways to encode the long-slit
geometry.  Most would be considered perverse for human interpretation
but fine for software.

>people think?  The only change I might advocate is some keyword like
>CPA that would work in addition to LONGPOL to define the mapping from
>some arbitrary instrument/detector orientation to a standard celestial
>system.

Sounds like CROTAn by another name to me!

Cheers, Mark