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<H2><A NAME="SECTION0004176000000000000000">SLA_UNPCD - Remove Radial Distortion</A>
<A NAME="xref_SLA_UNPCD"> </A><A NAME="SLA_UNPCD"> </A>
</H2>
<DL>
<DT><STRONG>ACTION:</STRONG>
<DD>Remove pincushion/barrel distortion from a distorted
<IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img20.gif"
ALT="$[\,x,y\,]$"> to give tangent-plane <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img20.gif"
ALT="$[\,x,y\,]$">.<P> <DT><STRONG>CALL:</STRONG>
<DD><TT>CALL sla_UNPCD (DISCO,X,Y)</TT>
<P> </DL>
<P> <DL>
<DT><STRONG>GIVEN:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>DISCO</EM></TD>
<TH ALIGN="LEFT"><B>D</B></TH>
<TD ALIGN="LEFT" NOWRAP>pincushion/barrel distortion coefficient</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>X,Y</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>distorted <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img20.gif"
ALT="$[\,x,y\,]$"></TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>RETURNED:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>X,Y</EM></TD>
<TH ALIGN="LEFT"><B>D</B></TH>
<TD ALIGN="LEFT" NOWRAP>tangent-plane <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img20.gif"
ALT="$[\,x,y\,]$"></TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>NOTES:</STRONG>
<DD><DL COMPACT>
<DT>1.
<DD>The distortion is of the form <IMG WIDTH="103" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img128.gif"
ALT="$\rho = r (1 + c r^{2})$">, where <I>r</I> is
the radial distance from the tangent point, <I>c</I> is the DISCO
argument, and <IMG WIDTH="11" HEIGHT="25" ALIGN="MIDDLE" BORDER="0"
SRC="img129.gif"
ALT="$\rho$"> is the radial distance in the presence of
the distortion.
<DT>2.
<DD>For <I>pincushion</I> distortion, C is +ve; for
<I>barrel</I> distortion, C is -ve.
<DT>3.
<DD>For X,Y in units of one projection radius (in the case of
a photographic plate, the focal length), the following
DISCO values apply:
<P> <BR>
<BR>
<BR>
<P> <TABLE CELLPADDING=3 BORDER="1">
<TR VALIGN="TOP"><TD ALIGN="LEFT" NOWRAP>Geometry</TD>
<TD ALIGN="CENTER" NOWRAP>DISCO</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT" NOWRAP>astrograph</TD>
<TD ALIGN="CENTER" NOWRAP>0.0</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT" NOWRAP>Schmidt</TD>
<TD ALIGN="CENTER" NOWRAP>-0.3333</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT" NOWRAP>AAT PF doublet</TD>
<TD ALIGN="CENTER" NOWRAP>+147.069</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT" NOWRAP>AAT PF triplet</TD>
<TD ALIGN="CENTER" NOWRAP>+178.585</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT" NOWRAP>AAT f/8</TD>
<TD ALIGN="CENTER" NOWRAP>+21.20</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT" NOWRAP>JKT f/8</TD>
<TD ALIGN="CENTER" NOWRAP>+14.6</TD>
</TR>
</TABLE>
<P> <BR>
<BR>
<BR>
<P> <DT>4.
<DD>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 <IMG WIDTH="25" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img232.gif"
ALT="$2^{\circ}
\hspace{-0.37em}.\hspace{0.02em}4$"> and <IMG WIDTH="26" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img233.gif"
ALT="$42^{\circ}$"> respectively.
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<ADDRESS>
<I>SLALIB --- Positional Astronomy Library<BR>Starlink User Note 67<BR>P. T. Wallace<BR>12 October 1999<BR>E-mail:ptw@star.rl.ac.uk</I>
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