ZernikeCoefficientΒΆ

Type:section
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This section is used to define an expansion coefficient either for the phase aberration function w(\pvec{p}), the apodization damping exponent d(\pvec{p}) or for the Jones pupil function \TField{J}(\pvec{p}). See parent section OpticalSystem for their definitions. For example

ZernikeCoefficient {
  IndexAngle = 3
  IndexRadial = 2
  Side = Image
  Phase = 0.1
}

contributes to the image-sided phase aberration as

\begin{eqnarray*}
w(\pvec{p}) & = & \dots\, +\, 0.1 \cdot Z_2^3(\pvec{p})\, \dots ,
\end{eqnarray*}

whereas

ZernikeCoefficient {
  IndexAngle = 3
  IndexRadial = 2
  Side = Image
  JonesMatrix = [0.1   0.001
                 0001  0.11]
}

contributes to the image-sided Jones pupil function \TField{J}(\pvec{p}) in a similar way. Z_n^m(\pvec{p})=Z_j(\pvec{p}) are the Zernike polynomials as defined in the appendix Zernike Polynomials. Multiple definitions are summed up and are added to the definitions in PhaseExpansion or JonesExpansion.