#This file was created by <jones> Thu Apr 11 15:48:56 2002
#LyX 1.0 (C) 1995-1999 Matthias Ettrich and the LyX Team
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\begin_inset Formula 
\[
\left( \begin{array}{c}
x\\
\theta \\
y\\
\phi \\
\delta 
\end{array}\right) _{fp}=\left( \begin{array}{ccccc}
<x|x>=-2.17 & <x|\theta >=-0.203 & 0 & 0 & <x|\delta >=11.89\\
<\theta |x>=-0.101 & <\theta |\theta >=-0.469 & 0 & 0 & <\theta |\delta >=1.963\\
0 & 0 & <y|y> & <y|\phi > & 0\\
0 & 0 & <\phi |y> & <\phi |\phi > & 0\\
0 & 0 & 0 & 0 & 1
\end{array}\right) \left( \begin{array}{c}
x\\
\theta \\
y\\
\phi \\
\delta 
\end{array}\right) _{tg}\]

\end_inset 

Now the inverse of the matrix to go from focal plane to target.
\begin_inset Formula 
\[
\left( \begin{array}{c}
x\\
\theta \\
y\\
\phi \\
\delta 
\end{array}\right) _{tg}=\left( \begin{array}{ccccc}
<x|x>^{i}=-0.469 & <x|\theta >^{i}=0.203 & 0 & 0 & <x|\delta >^{i}=5.18\\
<\theta |x>^{i}=0.101 & <\theta |\theta >^{i}=-2.17 & 0 & 0 & <\theta |\delta >^{i}=3.06\\
0 & 0 & <y|y>^{i} & <y|\phi >^{i} & 0\\
0 & 0 & <\phi |y>^{i} & <\phi |\phi >^{i} & 0\\
0 & 0 & 0 & 0 & 1
\end{array}\right) \left( \begin{array}{c}
x\\
\theta \\
y\\
\phi \\
\delta 
\end{array}\right) _{fp}\]

\end_inset 

so delta correction is the second term in the equation:
\begin_inset Formula 
\[
\delta _{fp}=\frac{-<x|x>^{i}*x_{fp}-<x|\theta >^{i}*\theta _{tg}}{<x|\delta >^{i}}+\frac{x_{tg}}{<x|\delta >^{i}}\]

\end_inset 

To calculate the theta correction first write:
\begin_inset Formula 
\[
\theta _{tg}=<\theta |x>^{i}*x_{fp}+<\theta |\theta >^{i}*\theta _{fp}+\delta _{fp}*<\theta |\delta >^{i}\]

\end_inset 

 substitue 
\begin_inset Formula \( \delta _{fp} \)
\end_inset 

 from 3rd equation and one gets
\begin_inset Formula 
\[
\theta _{tg}=x_{tg}\frac{<\theta |\delta >^{i}}{<x|\delta >^{i}}+standard\]

\end_inset 

so the correction is 0.59 which is slightly different than what is in ext_tar_cor.
f .
 I think that I got the values from Michael Kuss and maybe he had slightly
 different first order optics coefficients.
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