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      SUBROUTINE slUPCD (DISCO,X,Y)

     - - - - - -
      U P C D
     - - - - - -

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

  Given:
     DISCO    d      pincushion/barrel distortion coefficient
     X,Y      d      distorted coordinates

  Returned:
     X,Y      d      tangent-plane coordinates

  Notes:

  1)  The distortion is of the form RP = R*(1 + C*R**2), where R is
      the radial distance from the tangent point, C is the DISCO
      argument, and RP 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 "radians" - units of one projection radius,
      which in the case of a photograph is the focal length of
      the camera - 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          +13.32

  4)  The present routine is an approximate inverse to the
      companion routine slPCD, obtained from two iterations
      of Newton's method.  The mismatch between the slPCD and
      slUPCD routines is negligible for astrometric applications;
      to reach 1 milliarcsec at the edge of the AAT triplet or
      Schmidt field would require field diameters of 2.4 degrees
      and 42 degrees respectively.

  P.T.Wallace   Starlink   1 August 1994

  Copyright (C) 1995 Rutherford Appleton Laboratory
  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.

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