SLA_UNPCD

Remove Radial Distortion

ACTION:

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

CALL:

CALL sla_UNPCD (DISCO,X,Y)

GIVEN:

RETURNED:

NOTES:

(1)

The distortion is of the form $\rho =r\left(1+c{r}^2\right)$, 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 $\left[x,y\right]$s all produce the same distorted $\left[x,y\right]$. However, only one solution is returned, the one that produces the smallest change in $\left[x,y\right]$.