[fitswcs] Detector distortion correction representations in FITS

[Doug Mink]

Mark Calabretta wrote:

> However, my answer is basically unchanged for the reasons previously given.
> Building a transformation matrix into TAN+poly itself seems the way to go,
> possibly even adding one ahead of the polynomial as well as after it so
> that the CD matrix could be used for scaling, etc. in the way you expect
> and provide a good first-order approximation.  It would look like
> 
>    (i,j) -> (x,y)               ...CD matrix
> 
>    (x,y) -> (i,j)               ...pre-poly matrix   }
>    (i,j) -> (I,J)               ...polynomial        }  Augmented TAN+poly
>    (I,J) -> (xi,eta)            ...post-poly matrix  }
> 
> The pre-poly matrix would effectively undo the CD matrix; the post-poly
> matrix would apply it again.  The combined effect is that of applying the
> polynomial before the CD matrix.  Admittedly it's a little clumsy but it's
> conceptually straightforward and should work and, most importantly, the
> added complexity is confined to one projection.
> ...
> Does anyone else on this list have anything to say?

I did something like this with the TAN + polynomial I implemented in WCSTools.
If the polynomial keywords are present, I simply ignore the CD matrix, which
is present for software which doesn't include my subroutines.  I build the
CD matrix into the polynomial so I don't have a post-poly matrix, though
I think the post-poly matrix would have been a better way to go.  The
CD/pre-poly combination Mark is proposing is a bit more computation than
I would like.  Couldn't the software which knows about this standard simply
ignore the CD matrix and pre-poly reversal thereof if a pre-poly matrix
and/or post-poly matrix is present, start by applying the polynomial directly
on the pixels, and then apply the post-poly matrix?

-Doug Mink