# What is the solid angle $d\Omega$ in radiative transfer?

The Wikipedia article for radiative transfer gives the following definition:

In terms of the spectral radiance, $$I_{\nu }$$, the energy flowing across an area element of area $$da$$, located at $$\mathbf{r}$$ in time $$dt$$, in the solid angle $$d\Omega$$ about the direction $${\hat {\mathbf {n} }}$$ in the frequency interval $$\nu +d\nu$$, is $$dE_{\nu }=I_{\nu }(\mathbf {r} ,{\hat {\mathbf {n} }},t)\cos \theta \ d\nu \,da\,d\Omega \,dt,$$ where $$\theta$$ is the angle that the unit direction vector $${\hat {\mathbf {n} }}$$ makes with a normal to the area element.

It isn't clear to me what the solid angle $$d\Omega$$ is supposed to be. I would greatly appreciate it if people would please take the time to explain this.

The solid angle $$\Omega$$ is simply defined as the ratio of a surface area element $$A$$ of a sphere and its squared radius $$R^2$$: $$\Omega=\frac{A}{R^2}$$
The same goes when you have a small infinitesimal solid angle $$d\Omega$$ and surface area element $$dA$$: $$d\Omega=\frac{dA}{R^2}$$