Editing Numerical aperture (section)

==Laser physics==
In [[laser physics]], numerical aperture is defined slightly differently. Laser beams spread out as they propagate, but slowly. Far away from the narrowest part of the beam, the spread is roughly linear with distance—the laser beam forms a cone of light in the "far field". The relation used to define the {{abbr|NA|numerical aperture}} of the laser beam is the same as that used for an optical system,

<math display="block">\text{NA} = n \sin \theta,</math>

but {{math|''θ''}} is defined differently. Laser beams typically do not have sharp edges like the cone of light that passes through the [[aperture]] of a lens does. Instead, the [[irradiance]] falls off gradually away from the center of the beam. It is very common for the beam to have a [[Gaussian beam|Gaussian]] profile. Laser physicists typically choose to make {{math|''θ''}} the ''divergence'' of the beam: the [[far-field]] angle between the beam axis and the distance from the axis at which the irradiance drops to {{math|''e''<sup>−2</sup>}} times the on-axis irradiance. The {{abbr|NA|numerical aperture}} of a Gaussian laser beam is then related to its minimum spot size ("beam waist") by

<math display="block">\text{NA} \simeq \frac{\lambda_0}{\pi w_0},</math>

where {{math|''λ''<sub>0</sub>}} is the [[vacuum wavelength]] of the light, and {{math|2''w''<sub>0</sub>}} is the diameter of the beam at its narrowest spot, measured between the {{math|''e''<sup>−2</sup>}} irradiance points ("Full width at {{math|''e''<sup>−2</sup>}} maximum of the intensity"). This means that a laser beam that is focused to a small spot will spread out quickly as it moves away from the focus, while a large-diameter laser beam can stay roughly the same size over a very long distance. See also: [[Gaussian beam#Beam waist|Gaussian beam width]].