Example: Constant astigmatism equation: Difference between revisions

Revision as of 07:15, 6 December 2013

$z_{y y} + (1 / z)_{x x} + 2 = 0 .$

$A = (\begin{array}{cc} \frac{1}{8} \frac{(a^{2} + 1) z_{x}}{a z} + \frac{1}{8} \frac{(- a^{2} + 1) z_{y}}{a} & \frac{1}{4} \frac{(a + 1)^{2} \sqrt{z}}{a} \\ \frac{1}{4} \frac{(a - 1)^{2} \sqrt{z}}{a} & - \frac{1}{8} \frac{(a^{2} + 1) z_{x}}{a z} - \frac{1}{8} \frac{(- a^{2} + 1) z_{y}}{a} \end{array}),$

$B = (\begin{array}{cc} \frac{1}{8} \frac{(- a^{2} + 1) z_{x}}{a z^{2}} + \frac{1}{8} \frac{(a^{2} + 1) z_{y}}{a z} & \frac{1}{4} \frac{- a^{2} + 1}{a \sqrt{z}} \\ \frac{1}{4} \frac{- a^{2} + 1}{a \sqrt{z}} & - \frac{1}{8} \frac{(- a^{2} + 1) z_{x}}{a z^{2}} - \frac{1}{8} \frac{(a^{2} + 1) z_{y}}{a z} \end{array})$

@@ Line 1: / Line 1: @@
 <math>\displaystyle z_{yy} + \bigl(1/z\bigr)_{xx} + 2 = 0.</math>
+<math>
+A = \left(\begin{array}{cc}
+\displaystyle \frac{1}{8} \frac{(a^2 + 1) z_x}{a z} + \frac{1}{8} \frac{(-a^2 + 1) z_y}{a} &
+\displaystyle \frac{1}{4} \frac{(a + 1)^2 \sqrt{z}}{a} \\ \\
+\displaystyle \frac{1}{4} \frac{(a - 1)^2 \sqrt{z}}{a} &
+\displaystyle -\frac{1}{8} \frac{(a^2 + 1) z_x}{a z} - \frac{1}{8} \frac{(-a^2 + 1) z_y}{a}
+ \end{array}\right),
+</math>
+<math>
+B = \left(\begin{array}{cc}
+\displaystyle \frac{1}{8} \frac{(-a^2 + 1) z_x}{a z^2} + \frac{1}{8} \frac{(a^2 + 1) z_y}{a z} &
+\displaystyle \frac{1}{4} \frac{-a^2 + 1}{a \sqrt{z}} \\ \\
+\displaystyle \frac{1}{4} \frac{-a^2 + 1}{a \sqrt{z}} &
+\displaystyle -\frac{1}{8} \frac{(-a^2 + 1) z_x}{a z^2} - \frac{1}{8} \frac{(a^2 + 1) z_y}{a z}
+ \end{array}\right)
+</math>
 [[Category:Examples]]

Example: Constant astigmatism equation: Difference between revisions

Revision as of 07:15, 6 December 2013

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