ObjectSidedJonesExpansion

Type:Matrix<float>
Range:[v_11, …, v_1j; …; v_i1, …; v_ij], j<=4
Default:-/-
Appearance:optional

This vector parameter is used to define the object-sided Jones aberration function \TField{J}_\mathrm{obj}(\pvec{p}) as introduced in the parent section OpticalSystem. This is done by means of an expansion into Zernike polynomials.

Note

The 2-by-2 Jones matrix acts on the x, y components of the electric field in the pupil plane.

As the amplitude of the normalized coordinate vector \pvec{p} ranges from 0 to 1, components of the Jones matrix J_{ij}(\pvec{p}) are 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 Jones aberration matrix \TField{J}(\pvec{p}) is expanded into Zernike polynomials,

\begin{eqnarray*}
\TField{J}(\rho, \varphi) = \sum_{j=1}^{\infty} \TField{J}_j Z_j(\rho, \varphi),
\end{eqnarray*}

where Z_j are the Zernike polynomials and \TField{J}_j are the 2-by-2 matrix expansion coefficients as passed by the discussed vector parameter. Hereby, four subsequent entries of the parameter vector form a matrix \TField{J}_{j, kl}. E.g. the input may look like this:

JonesExpansion = [ J1_11 J1_12
                   J1_21 J2_22

                   J2_11 J2_12
                   J2_21 J2_22

                   ...
                 ]

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 Jones pupil coefficient. There, the index pair (m, n) can be used.