InnerNumericalApertureΒΆ

Type:float
Range:[0, inf]
Default:0.0
Appearance:simple

Setting the inner numerical aperture \mathrm{NA_\mathrm{inner}} will block Fourier modes propagating close to the optical axis. With the notation of the parent section OpticalSystem, a ray passing the optical system must satisfies

\begin{eqnarray*}
n_\mathrm{img} \sin(\alpha_\mathrm{img}) \geq \mathrm{NA}_{\mathrm{inner}, \mathrm{img}},
\end{eqnarray*}

or, equivalently

\begin{eqnarray*}
n_\mathrm{obj} \sin(\alpha_\mathrm{obj}) \geq \mathrm{NA}_{\mathrm{inner}, \mathrm{obj}}.
\end{eqnarray*}

The discussed parameter \mathrm{NA}_\mathrm{inner} refers to the image side inner numerical aperture \mathrm{NA}_{\mathrm{inner}, \mathrm{img}} for diminishing systems with magnification |m|\leq 1, and to the object side inner numerical aperture \mathrm{NA}_{\mathrm{inner}, \mathrm{obj}} for magnifying systems, in order to match the standard conventions used in photolithography and microscopy respectively. In terms of the pupil function P(\pvec{p}) with normalized coordinates \pvec{p} this means that

\begin{eqnarray*}
P(\pvec{p}) & = & 0,\; \mbox{for}\; |\pvec{p}| < \varepsilon,
\end{eqnarray*}

with the obscuration ratio \varepsilon = \mathrm{NA}_{\mathrm{inner}, \mathrm{img}}/n_{\mathrm{img}}=\mathrm{NA}_{\mathrm{inner}, \mathrm{obj}}/n_{\mathrm{obj}}.

Compare also the parameter NumericalAperture which blocks all Fourier modes with larger NA than the specified value.