Solid angle
 

In order to apply fully the quantitative aspects associated with radiation flow, the concept of solid angle first needs to be appreciated.
When an assembly of atoms emits energy, the radiation flows in a range of directions and the dispersed power may not be isotropic. In order to describe such situations, the radiated power is described in terms of a flow into a cone with some specific angle. If at some distance d from the source, power is received in an area A , the associated solid angle is simply defined as
Ω = A/d².
A solid angle is expressed in units of steradians (abbreviated to sterads [sr]). One steradian corresponds to a unit area placed at unit distance. Since the area of a sphere is given by 4π R², where R is its radius, it is easy to see that the solid angle subtended by the sphere at its centre is equal to 4π steradians.
So far we have considered the measurement of angles along arcs of the celestial sphere. When objects of angular extent such as a nebula are seen on the celestial sphere, they subtend angles which are essentially two-dimensional. In terms of the measured power received from such an extended source, this obviously depends on the extent of the solid angle over which the radiation is collected. It is, therefore, important to know the strength of the source per steradian or in terms of some other two-dimensional measure such as ‘arc seconds squared’ . Figure 1 provides an illustration of an extended source but with only part of it with a small solid angle being examined by a telescope’s field of view.

Figure 1. When directed to an extended source, the radiation received in the field of view of a telescope is limited to some solid angle, Ω.