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Radiant Intensity

Definition: radiant flux per unit solid angle

German: Strahlstärke

Categories: general optics, light detection and characterization, optical metrology

Units: W/sr

Formula symbol: <$I_{\textrm{e},\Omega }$> or <$I$>

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Cite the article using its DOI: https://doi.org/10.61835/l7c

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radiant intensity
Figure 1: Radiant intensity is radiant flux per unit solid angle.

The radiant intensity <$I_{\rm{e},\Omega }$> (or just <$I$>) of a light source is defined as the emitted radiant flux per unit solid angle. It can also be applied to transmitted, reflected or received radiation. The term is mostly applied with the approximation of a point source, i.e., in distances which are large to the extent of the source.

In the SI system, radiant intensities are specified in units of W/sr (watts per steradian). The corresponding photometric quantity is the luminous intensity in units of candela (cd) = lm/sr.

At a distance <$d$> from a source with radiant intensity <$I$>, an area element with its normal direction at an angle <$\theta$> against the direction to the source receives an irradiance <$E = I \cos \theta / d^2$>. The total radiant flux of a source with uniform omnidirectional emission (i.e., and intensity not depending on the direction) is <$\Phi = 4 \pi I$>.

A related radiometric quantity is the spectral intensity, which is defined as the radiant intensity per unit optical frequency or wavelength interval.

Generally, the radiant intensity depends on the observation direction, and the total radiant flux is obtained by integration over all directions. In the case of isotropic radiation (i.e., with constant radiant intensity), the total radiant flux is simply <$4\pi$> sr times the radiant intensity.

The radiant intensity is relevant, for example, for calculating how much optical intensity impinges a photodetector placed in some distance from the light source.

In contrast to the radiance, the emitting area does not matter for the radiant intensity. The radiance can be considered as radiant intensity per unit emitting area.

The radiant intensity should not be confused with the optical intensity as used in optical physics.

See also: radiometry, radiant flux, radiance, irradiance

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