PhaseExpansion¶

Type:	Vector<float>
Range:	[v_1, …]
Default:	-/-
Appearance:	optional

This vector parameter is used to define the phase aberration function $w(\pvec{p})$ as introduced in the parent section OpticalSystem. This is done by means of an expansion into Zernike polynomials.

As the amplitude of normalized coordinate vector $\pvec{p}$ ranges from $0$ to $1$ , the phase aberration function $w(\pvec{p})$ is defined on the unit disk and one may switch to polar coordinates $(\rho, \varphi)$ ,

$\begin{eqnarray*} \pvec{p} = r (\cos(\varphi), \sin(\varphi)). \end{eqnarray*}$

The phase aberration function $w(\pvec{p})$ is expanded into Zernike polynomials,

$\begin{eqnarray*} w(\rho, \varphi) = \sum_{j=1}^{\infty} c_j Z_j(\rho, \varphi), \end{eqnarray*}$

where $Z_j$ are the Zernike polynomials and $c_j \in \rnum$ are the expansion coefficients as passed by the discussed vector parameter.

Warning

Different orderings and different scalings of the Zernike polynomials are in use. The section Zernike Polynomials in the appendix gives a detailed definition of the Zernike polynomials as used in JCMsuite.

Section ZernikeCoefficient allows for an alternative definition of a phase aberration coefficient. There, the index pair $(m, n)$ can be used.