Angular aperture

Image:Angular aperture.svg with focal point at F and an aperture of diameter $D$ .|thumb|250px]]

The angular aperture of a lens is the angular size of the lens aperture as seen from the focal point:

: $a = 2 \arctan \left( \frac {D/2} {f} \right) = 2 \arctan \left( \frac {D} {2f} \right)$

where

Relation to numerical aperture

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.{{cite book|title=Studies in Optics |author=Albert Abraham Michelson|year= 1995|publisher=Courier Dover|pages=32|isbn=0-486-68700-7|url= https://books.google.com/books?id=m2tUZ4_8WGMC&q=%22Angular+aperture%22&pg=PA32}}

Formally, the numerical aperture in air is:

: $\mathrm{NA} = \sin a/2 = \sin \arctan \left( \frac {D} {2 f} \right)$

In the paraxial approximation, with a small aperture, $D :$

: $\mathrm{NA} \approx a/2$

Angular aperture

Relation to numerical aperture

References

See also