Ray transfer matrix analysis: Difference between revisions

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== Some examples ==
=== Free space example ===
As one example, if there is free space between the two planes, the ray transfer matrix is given by: <math display="block"> \mathbf{S} = \begin{bmatrix} 1 & d \\ 0 & 1 \end{bmatrix} , </math> where {{mvar|d}} is the separation distance (measured along the optical axis) between the two reference planes. The ray transfer equation thus becomes: <math display="block"> \begin{bmatrix} x_2 \\ \theta_2 \end{bmatrix} = \mathbf{S} \begin{bmatrix} x_1 \\ \theta_1\end{bmatrix} , </math> and this relates the parameters of the two rays as: <math display="block"> \begin{matrixaligned}
x_2 & = & x_1 + d\theta_1 \\
\theta_2 & = &\hphantom{x_1 + d}\theta_1
\end{matrixaligned} </math>
 
=== Thin lens example ===