Published on *CTIO* (http://www.ctio.noao.edu/noao)

In an astrograph, the spherical sky is presumed to be projected onto a flat plate perpendicular to the beam of the astrograph. In this ideal case, the distance r_{0} from the optical axis to a point on a plate is given by *r _{0}=f tan(A)*, where

Correctors such as the PFADC deviate from this model via radial pincushion distortion, called optical field angle distortion (OFAD), which varies as a function of the distance from the optical axis. We will represent distortion using the model in Chiu's 1976 paper

*r = f tan(A)[1+d _{3} tan^{2}(A) +d_{5} tan^{4}(A)]*

Here, *r* is the measured distance from the center of the field to the image in the detector plane. Distortion is modeled via the third and fifth order dimensionless distortion coefficients d_{3} and d_{5.}

The inverted model

*r _{0} = r b_{3} r^{3} +b_{5} r^{5}*

is usually preferred for analyzing plates, along with the image scale *S*, usually expressed in arcsec/mm. The two models are equivalent for our purpose and easily interchangeable via the simple relations

*f = 206265/S, d _{3 }= -b_{3}f^{2} *and