Ray transfer matrix analysis: Difference between revisions

Revision as of 04:30, 2 November 2023

Revision as of 04:33, 2 November 2023

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|Quadratic phase factor

|<math>\begin{pmatrix} 1 & 0\\ c & 1 \end{pmatrix} </math>

|<math>Q[c]=\exp ji \frac{k_{0}}{2} c x^{2}</math>

|<math>k_0</math>: wave number

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|Fresnel free-space-propagation operator

|<math>\begin{pmatrix} 1 & d\\ 0 & 1 \end{pmatrix} </math>

|<math>\mathcal{R}[d]\left\{U\left(x_{1}\right)\right\}=\frac{1}{\sqrt{ji \lambda d}} \int_{-\infty}^{\infty} U\left(x_{1}\right) e^{ji \frac{k}{2 d}\left(x_{2}-x_{1}\right)^{2}} d x_1 </math>

|<math>x_1 </math>: coordinate of the source

<math>x_2 </math>: coordinate of the goal

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|Normalized Fourier-transform operator

|<math>\begin{pmatrix} 0 & 1\\ -1 & 0 \end{pmatrix} </math>

|<math>\mathcal{F}=\left(ji \lambda_{0}\right)^{-1 / 2} \int_{-\infty}^{\infty} d x\left[\exp \left(ji k_{0} p x\right)\right] \ldots </math>

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