Example: Constant astigmatism equation

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

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

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

Example: Constant astigmatism equation

Navigation menu

Search