[fitswcs] Polynomial projection

[William Pence]

I'm not clear about what is planned for Paper IV.  To cite a particular 
example of the type of spectral analysis that I used to do, suppose you 
record an optical spectrum on a 1024-pixel 1-D detector.  The wavelength 
dispersion equation is nearly linear on this detector, but higher order 
terms are typically fit using a polynomial of the form:

   wavelength(angstroms) = A_0 + A_1 * (i/1000) + A_2 * (i/1000)**2 +
         A_3 * (i/1000)**3

where 'i' is the detector pixel number in the range 1 to 1024.  The division 
by 1000 is done to approximately normalize the range of the independent 
variable, to help increase the numerical precision in the least squares 
determination of the coefficients.

Will Paper VI provide a mechanism for using this sort of polynomial fit (or 
something similar to it) as a spectral WCS projection?

Bill


Mark Calabretta wrote:
> On Fri 2005/04/29 11:54:35 -0400, William Thompson wrote
> in a message to: fitswcs at nrao.edu
> 
> 
>>The new projection would be -PLY, and would be defined such that
>>
>>	S = S_r + w + A_2*w^2 + A_3*w^3 + ... + A_20*w^20
> 
> 
> Historically, early drafts of Paper III contained a Sect. 2.2, "Higher
> Order Corrections", which described such a mechanism for all spectral
> coordinate types.  After 2001/07/04, when it was decided that
> distortions should be handled separately, the text of this section
> was replaced with a forward reference to Paper IV, and likewise the
> polynomial extension to the TAN projection in Paper II was removed.
> After 2001/10/29 the whole of Sect. 2.2 was removed from Paper III lest
> it preempt the methods of Paper IV; only a reference to Paper IV was
> left in the introduction.  The rationale was that the distortion
> correction is supposed to be "small" and optional and that it would be
> better to do it properly and just in one place.

-- 
____________________________________________________________________
Dr. William Pence                          William.D.Pence at nasa.gov
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