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| ''M'' is the total beam magnification given by <math>M = k_1 k_2 k_3 \cdots k_r</math>, where ''k'' is defined in the previous entry and ''B'' is the total optical propagation distance{{clarify|date=July 2019}} of the multiple prism expander.<ref name=TLO />
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== Common Decomposition of Ray Transfer Matrix ==
There exist infinite ways to decompose a ray transfer matrix <math> \mathbf{T} = \begin{bmatrix} A & B \\ C & D \end{bmatrix} </math> into a concatenation of multiple transfer matrix. For example:
# <math> \begin{bmatrix} A & B \\ C & D \end{bmatrix}
=
\left[\begin{array}{ll}
1 & 0 \\
D / B & 1
\end{array}\right]\left[\begin{array}{rr}
B & 0 \\
0 & 1 / B
\end{array}\right]\left[\begin{array}{ll}
0 & 1 \\
-1 & 0
\end{array}\right]\left[\begin{array}{ll}
1 & 0 \\
A / B & 1
\end{array}\right] </math>.
# <math> \begin{bmatrix} A & B \\ C & D \end{bmatrix}
=
\left[\begin{array}{ll}
1 & 0 \\
C / A & 1
\end{array}\right]\left[\begin{array}{rr}
A & 0 \\
0 & A^{-1}
\end{array}\right]\left[\begin{array}{ll}
1 & B / A \\
0 & 1
\end{array}\right] </math>
# <math> \begin{bmatrix} A & B \\ C & D \end{bmatrix}
=
\left[\begin{array}{ll}
1 & A / C \\
0 & 1
\end{array}\right]\left[\begin{array}{lr}
-C^{-1} & 0 \\
0 & -C
\end{array}\right]\left[\begin{array}{ll}
0 & 1 \\
-1 & 0
\end{array}\right]\left[\begin{array}{ll}
1 & D / C \\
0 & 1
\end{array}\right] </math>
# <math> \begin{bmatrix} A & B \\ C & D \end{bmatrix}
=
\left[\begin{array}{ll}
1 & B / D \\
0 & 1
\end{array}\right]\left[\begin{array}{ll}
D^{-1} & 0 \\
0 & D
\end{array}\right]\left[\begin{array}{ll}
1 & 0 \\
C / D & 1
\end{array}\right] </math>
== Resonator stability ==
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