ZernikeCoefficient¶

Type:	section
Appearance:	multiple

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.