Subject: Distortion Formula

From: sutin (Sarcast Van Zot)
Date: Fri, 3 Nov 1995 13:59:02 -0800

Steve,

Here is the distortion formula.

Brian
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The distortion of the telescope and camera are below.  They are polynomial
fits.  The argument is the radius from the center of the telescope or
camera center, in arcmin of sky.  The result is the radial movement of the
resulting point on the detector, in pixels.

telescope:

dT = 8.056121663e-02 * R					[pixels]
   - 9.854431080e-01 * R^2
   + 4.585744900e-02 * R^3

camera:

dC =
   - 2.981488078e-02 * R					[pixels]
   + 3.837548331e-02 * R^2
   + 5.818240867e-02 * R^3
   + 3.123005326e-03 * R^4
   - 2.396621712e-04 * R^5

So is the initial position of a star is (X,Y) in arcmin, and the camera
is centered at (4.5,0.0) arcmin, then the offest of a star in pixels at
the detector is

    Rt = sqrt(  X     ^2 + Y^2 )				[arcmin]
    Rc = sqrt( (X-4.5)^2 + Y^2 )				[arcmin]

    dXpix = X * dT(Rt) / Rt +  (X - 4.5) * dC(Rc) / Rc		[pixels]
    dYpix = Y * dT(Rt) / Rt +   Y        * dC(Rc) / Rc		[pixels]

The accuracy here is on the order of 0.01 pixel for each fit.  The
algorithm here of adding the distortions rather than multiplying adds
an error of about 1 pixel at the worst.

The scale used here came out to be 0.1186474 arcsec/pixel at 0.5500 microns.