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In optics, Lambert's cosine law says that the observed radiant intensity or luminous intensity from an ideal diffusely reflecting surface or ideal diffuse radiator is directly proportional to the cosine of the angle θ between the observer's line of sight and the surface normal; I = I 0 cos θ.
Radiant intensity is used to characterize the emission of radiation by an antenna: [2], = (), where E e is the irradiance of the antenna;; r is the distance from the antenna.; Unlike power density, radiant intensity does not depend on distance: because radiant intensity is defined as the power through a solid angle, the decreasing power density over distance due to the inverse-square law is ...
Diagram of Lambertian diffuse reflection. The black arrow shows incident radiance, and the red arrows show the reflected radiant intensity in each direction. When viewed from various angles, the reflected radiant intensity and the apparent area of the surface both vary with the cosine of the viewing angle, so the reflected radiance (intensity per unit area) is the same from all viewing angles.
Mathematically, for the spectral power distribution of a radiant exitance or irradiance one may write: =where M(λ) is the spectral irradiance (or exitance) of the light (SI units: W/m 2 = kg·m −1 ·s −3); Φ is the radiant flux of the source (SI unit: watt, W); A is the area over which the radiant flux is integrated (SI unit: square meter, m 2); and λ is the wavelength (SI unit: meter, m).
Radiant intensity: I e,Ω [nb 5] watt per steradian: W/sr: M⋅L 2 ⋅T −3: Radiant flux emitted, reflected, transmitted or received, per unit solid angle. This is a directional quantity. Spectral intensity: I e,Ω,ν [nb 3] watt per steradian per hertz W⋅sr −1 ⋅Hz −1: M⋅L 2 ⋅T −2: Radiant intensity per unit frequency or wavelength.
Radiant intensity: I e,Ω [nb 5] watt per steradian: W/sr: M⋅L 2 ⋅T −3: Radiant flux emitted, reflected, transmitted or received, per unit solid angle. This is a directional quantity. Spectral intensity: I e,Ω,ν [nb 3] watt per steradian per hertz W⋅sr −1 ⋅Hz −1: M⋅L 2 ⋅T −2: Radiant intensity per unit frequency or wavelength.
I v is the luminous intensity in candelas (cd), I e is the radiant intensity in watts per steradian (W/sr), ¯ is the standard luminosity function. If more than one wavelength is present (as is usually the case), one must sum or integrate over the spectrum of wavelengths present to get the luminous intensity:
Radiant intensity: I e,Ω [nb 5] watt per steradian: W/sr: M⋅L 2 ⋅T −3: Radiant flux emitted, reflected, transmitted or received, per unit solid angle. This is a directional quantity. Spectral intensity: I e,Ω,ν [nb 3] watt per steradian per hertz W⋅sr −1 ⋅Hz −1: M⋅L 2 ⋅T −2: Radiant intensity per unit frequency or wavelength.