Distortion at the Prime Focus of the Shane Telescope with the Epps Atmospheric Dispersion Compensator

In 1994 June the Shane prime focus Atmospheric Dispersion Corrector (ADC) was used to expose several plates. The plates were held in a test rig intended to match the future position of the MOS plate. Burt Jones produced a plate solution that included a radial polynomial distortion. The text of his writeup is given below.

Minor rewriting has been done to replace subscripts and Greek letters with TeX-like representations suitable for HTML2 WWW browsers.

P.F. Corrector Plate Distortions from Burt Jones

Set up standard coordinates x_t, y_t using

plate center as tangent point
refracted coordinates for field center and star positions
scale of 12.3230 "/mm

Then positions of stars in mm in Focal Plate will be

x = x_t + alpha * (x_t - x_0) * r^2 + beta * (x_t - x_0) * r^4
y = y_t + alpha * (y_t - y_0) * r^2 + beta * (y_t - y_0) * r^4

where
r^2 = (x_t - x_0)^2 + (y_t - y_0)^2
alpha = 4.489E-7 mm^-2
beta = 1.731E-12 mm^-4
x_0 = 6.399 mm
y_0 = -0.215 mm

Further discussion with Burt Jones suggests that some of this transformation may not be suitable for use with the MOS. Some good references are
Murray, MNRAS 154, 429 (1971)
Herbig & Jones, AJ 86(8), 1232 (1981)

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Steve Allen <sla@ucolick.org>