SLA_UNPCD - Remove Radial Distortion   

ACTION:

Remove pincushion/barrel distortion from a distorted $[\,x,y\,]$ to give tangent-plane $[\,x,y\,]$.

CALL:

CALL sla_UNPCD (DISCO,X,Y)

GIVEN:

DISCO pincushion/barrel distortion coefficient

$$[\,x,y\,]$$ X,Y D

RETURNED:

$$[\,x,y\,]$$ X,Y

NOTES:

1.

The distortion is of the form $\rho = r (1 + c r^{2})$, where r is the radial distance from the tangent point, c is the DISCO argument, and $\rho$ is the radial distance in the presence of the distortion.

2.

For pincushion distortion, C is +ve; for barrel distortion, C is -ve.

3.

For X,Y in units of one projection radius (in the case of a photographic plate, the focal length), the following DISCO values apply:

Geometry DISCO

astrograph 0.0

Schmidt -0.3333

AAT PF doublet +147.069

AAT PF triplet +178.585

AAT f/8 +21.20

JKT f/8 +14.6

4.

The present routine is an approximate inverse to the companion routine sla_PCD, obtained from two iterations of Newton's method. The mismatch between the sla_PCD and sla_UNPCD is negligible for astrometric applications; to reach 1 milliarcsec at the edge of the AAT triplet or Schmidt field would require field diameters of $2^{\circ} \hspace{-0.37em}.\hspace{0.02em}4$ and $42^{\circ}$ respectively.