[fitswcs] Re: State of the discussion

[Doug Mink]

Don Wells wrote:

> The geometry of most optical cameras can be represented by the
> distortion notation used by the DSS [Digital Sky Survey]. It appears
> to me that there is, effectively, a consensus existing among the
> [fitswcs] readership that a solution of that general form would be
> acceptable and sufficient. I see several remaining questions:
> 
> 1) What keyword notation for the distortion coefficients? In
>    particular, should we adapt the DSS numbering convention or should
>    we 'clean up' the notation. Somebody needs to make a choice.
>    Probably that somebody is me.

I agree about adopting the DSS numbering convention, cleaned up or
not.  In my WCSTools trial implementation, I cleaned it up.

> 2) Which axis-association convention for celestial projection
>    distortion keywords? Should all of the distortion keywords be
>    associated with the latitude-like axis, as we have done in the
>    existing WCS conventions (e.g. CROTA2 for the usual case of RA on
>    axis 1 and DEC on axis 2)? My personal opinion is 'yes', but some
>    other [fitswcs] participants have argued against this. Somebody
>    needs to make a choice. Again, probably that somebody is me.

The analogy should be to the proposed standard CD matrix, which
associates
coefficients with resulting coordinates, i.e. CD1_1 and CD1_2 are
associated
with the first output axis coordinate and CD2_1 and CD2_2 with the
second,
rather than using an analogy to the old CROTA2.

> 3) Do we need more than one axis point? Prior FITS WCS conventions
>    have defined the terms relative to the tangent point specified by
>    the CRPIXi. I.e., the FITS reference point (reference pixel) is
>    assumed to be at the tangent point. This is the correct description
>    of the geometry of optical cameras which have only one optical
>    axis. However! Some optical cameras, e.g. the HST's WF-PC cameras,
>    have reimaging optical elements with their own axes which are not
>    collinear with the axis of their main telescope optics. This means
>    that, in principle at least, some of the geometric terms should be
>    expanded about the telescope axis and other terms should be
>    expanded about one or more other axes. WF/PC-1 and -2 have four
>    separate reimaging cameras working in quadrants of the HST's field.
>    ESO is building an analogous camera for the VLT (are you working on
>    it, Eric?). For the WFPC2 this situation is discussed in section 7
>    (p.174) of Holtzman etal, PASP 107, 156 (1995): '..the dominant
>    distortion is expected to be cubic arising from the field
>    flattener..'. The polynomical terms used in STSDAS software for
>    each of the four cameras of WFPC2 are 2-D cubics expanded about the
>    center pixels of the cameras. The wording of the Holtzman
>    discussion leaves me slightly uncertain whether CRPIXi is set to
>    the center pixels of each CCD or is set to the pixel position of
>    the pyramid apex in the pixel system of each CCD. I.e., does the
>    WFPC2 implementation have only one axis point, or does it have two?
>    If WFPC2 uses two axis points (which I suspect), then our
>    distortion keywords will need a convention to express the second
>    point relative to the tangent point defined by CRPIXi. The
>    [fitswcs] subscribers who are associated with re-imaging cameras
>    should declare their requirements.

The BTC camera also reimages each element of its chip array, but I
found I could fit the WCS pretty well with a 2nd-order polynomial.
I tried a second rotation (but not distortion) center first, but that
did not improve matters much over a single rotation center.  My feeling
is that we should try the polnomial distortion first on images from the
instruments which may present problems and proced to a more complicated
model only if the data requires it.

-Doug Mink
 Telescope Data Center
 Harvard-Smithsonian Center for Astrophysics
 Cambridge, Massachusetts USA