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A steradian can be defined as the solid angle subtended at the centre of a unit sphere by a unit area (of any shape) on its surface. For a general sphere of radius r, any portion of its surface with area A = r 2 subtends one steradian at its centre. [3] A solid angle in the form of a circular cone is related to the area it cuts out of a sphere:
The external surface area A of the cap equals r2 only if solid angle of the cone is exactly 1 steradian. Hence, in this figure θ = A /2 and r = 1 . The solid angle of a cone with its apex at the apex of the solid angle, and with apex angle 2 θ , is the area of a spherical cap on a unit sphere
English: A solid angle is a three-dimensional analog of a circular angle that relates a portion of the volume of a sphere to the surface area it subtends. If that area equals the sphere’s radius squared, the solid angle is one steradian.
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 ...
The lumen is defined as amount of light given into one steradian by a point source of one candela strength; while the candela, a base SI unit, is defined as the luminous intensity of a source of monochromatic radiation, of frequency 540 terahertz, and a radiant intensity of 1/683 watts per steradian.
The measure for the amount of light traveling along a ray is radiance, denoted by L and measured in W·sr −1 ·m −2; i.e., watts (W) per steradian (sr) per square meter (m 2). The steradian is a measure of solid angle, and meters squared are used as a measure of cross-sectional area, as shown at right.
The latter is commonly measured in W⋅sr −1 ⋅m −2 ⋅nm −1. This is a directional quantity. This is sometimes also confusingly called "spectral intensity". L e,Ω,λ [nb 4] watt per steradian per square metre, per metre W⋅sr −1 ⋅m −3: M⋅L −1 ⋅T −3: Irradiance Flux density: E e [nb 2] watt per square metre W/m 2: M⋅T −3
Diagram showing a section through the centre of a cone (1) subtending a solid angle of 1 steradian in a sphere of radius r, along with the spherical "cap" (2). The fact that the external surface of the cap has an area of r 2 is shown. Note that this applies only if the solid angle of the cone is exactly 1 steradian. Date: 30 September 2007: Source