[fitsbits] comment on SIP, optical distortion

[Norbert Zacharias]

080917

Dear Bill Pence and FITS community,

reading about the proposed SIP conventions I would like
to draw your attention to the most commonly seen, pure
optical distortion (3rd order) term.  This could be
expressed with the SIP mechanism, however typically
a single coefficient is applicable for many telescopes
to control "distortion" (besides the knowledge of the
"center" i.e. the location of the optical axis on the
detector, which I see is already handled).

Let D3 be the coefficient of (3rd order) optical distortion,
and dx, dy the corrections to be applied to the x, y
coordinates (e.g. in pixel unit), then

dx = D3 * x * r**2
dy = D3 * y * r**2

with  r**2 = x**2 + y**2

The SIP mechanism is more general but has the disadvantage
that users (or people working on the calibrations of a
detector) often try to solve for a full 3rd order polynomial,
while the data might be better represented with just that
single D parameter in order to keep the error propagation
low.

The D3 parameter is used since at least a century in the
astrometric community, and having a FITS keywork mechanism
for it as alternative option to the SIP for many applications
would be good to have.

Norbert


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Norbert Zacharias, Ph.D.
Chief of Cataloging Division
Astrometry Department
US Naval Observatory     voice: 202 762 1423
3450 Mass. Ave. NW         fax: 202 762 1516
Washington, DC 20392    e-mail: nz at usno.navy.mil
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