Zernikes

General equations

$Zx_{even} = Z^m_n(\rho,\phi) = R^m_n(\rho)cos(m\phi)$
$Zx_{odd} = Z^{-m}_n(\rho,\phi) = R^m_n(\rho)sin(m\phi)$
$R^m_n(\rho) = \sum_{k=0}^{\frac{n-m}{2}} \frac{(-1)^k(n-k)!}{ k!(\frac{n+m}{2}-k)!(\frac{n-m}{2}-k)! }\rho^{n-2k}$

Equation-images courtesy of $codecogs.com$

Zernikes

General equations

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