ObjectSidedApodizationExpansion¶

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

This vector parameter is used to define the object-sided apodization exponent function $d_{\mathrm{obj}}(\pvec{p})$ 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 apodization aberration function $d_{\mathrm{obj}}(\pvec{p})$ 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 function $d_{\mathrm{obj}}(\pvec{p})$ is expanded into Zernike polynomials,

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

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 apodiziation exponent coefficient. There, the index pair $(m, n)$ can be used.