The angular aperture of a lens is the angular size of the lens aperture as seen from the focal point:
a=2\arctan\left(
| D/2 | |
| f |
\right)=2\arctan\left(
| D | |
| 2f |
\right)
where
f
D
In a medium with an index of refraction close to 1, such as air, the angular aperture is approximately equal to twice the numerical aperture of the lens.[1]
Formally, the numerical aperture in air is:
NA=\sina/2=\sin\arctan\left(
| D | |
| 2f |
\right)
In the paraxial approximation, with a small aperture,
D<f
NA ≈ a/2