InnerNumericalAperture¶

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.