Angular aperture

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The angular aperture of a thin lens with focal point at F and an aperture of diameter d.
The angular aperture of a thin lens with focal point at F and an aperture of diameter d.

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

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

where

f is the focal length
d is the diameter of the aperture.

[edit] 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.[1]

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 < f:

\mathrm{NA} \approx a/2

[edit] References

  1. ^ Albert Abraham Michelson (1995). Studies in Optics. Courier Dover, 32. ISBN 0486687007. 

[edit] See also

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