Angle opening

Focal opening of a thin lens with focal point F and diameter opening D.

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

a=2arctan D2f{displaystyle a=2arctan {frac {D}{2f}}}}

where f{displaystyle f} is the focal distance and D{displaystyle D} the diameter of the opening.

Relation to numerical aperture

In a medium with a refractive index close to 1, such as air, the angular aperture is approximately twice the numerical aperture of the lens.

Formally, the numerical aperture in air is:

AN=without a/2=without arctan (D2f){displaystyle mathrm {AN} =sin a/2=sin arctan left({frac {D{2f}}}right)}

In the paraxial approach, with a small opening, <math alttext="{displaystyle DD.f{displaystyle D habitf}<img alt="{displaystyle D:

AN≈ ≈ a/2{displaystyle mathrm {AN} approx a/2}