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	D	pincushion/barrel distortion coefficient
X,Y	D	distorted $[\,x,y\,]$

RETURNED:

X,Y

D

tangent-plane $[\,x,y\,]$

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 a rigorous inverse of the companion routine sla_PCD. The expression for $\rho$ in Note 1 is rewritten in the form $x^3 + ax + b = 0$ and solved by standard techniques.

5. Cases where the cubic has multiple real roots can sometimes occur, corresponding to extreme instances of barrel distortion where up to three different undistorted $[\,x,y\,]$s all produce the same distorted $[\,x,y\,]$. However, only one solution is returned, the one that produces the smallest change in $[\,x,y\,]$.