Radiometric nomenclature survival guide

Electromagnetic waves are complicated. They have a lot of related quantities with similar names that are often useful, but also equally often misnamed in as many ways as there are branches of physics. This article is a survival guide on radiometric nomenclature to try to convey a common standard to make sense of all of this. It does not attempt to be a complete or exhaustive explanation of these quantities: the point is to dispel confusion, clarify the connections between them and provide a common terminology.

Some conventions:

1. by "wave" I always mean "electromagnetic wave".
2. by "radiation" I always mean "electromagnetic radiation".
3. square brackets contain the SI units for the quantity in question.
4. I generally do not provide a conventional letter or symbol for the quantity. This may change in the future.

Radiant energy $[\text{J}]$ is the energy carried by a wave. Radiant energy density $[\text{J/m}^{3}]$ is the volume density of radiant energy. "Radiant" is often dropped for brevity if it's obvious that we're talking about waves.

Radiant power $[\text{W}]$ is the power of radiant energy (energy per unit time). It is also called radiant flux. This is a ludicrous name since it is not an energy flux (power per unit area) and will therefore not be used anywhere in these notes. Radiant power is a key quantity since it describes a movement of energy, which is generally what you are interested in when talking about radiation. In practice, however, it's not often the quantity you are looking for. Rather, you are looking the power spread over a certain region of space. There are a several quantities to express this depending on the context:

1. Irradiance $[\text{W/m}^{2}]$ is radiant power received by a surface. Also confusingly called "intensity". Generally speaking the most useful quantity in physics.
2. Radiant exitance $[\text{W/m}^{2}]$ is radiant power emitted by a surface. Also confusingly called "intensity".
3. Radiosity $[\text{W/m}^{2}]$ is radiant power leaving a surface. This includes emission, reflection and transmission. Radiant exitance is a part of radiosity. Also confusingly called "intensity".
4. Radiant intensity $[\text{W/sr}]$ is radiant power per solid angle ($\text{sr}$ is steradian). It includes all energy: emitted, reflected, transmitted and received. It is the amount of power going through a specific direction (the solid angle).
5. Radiance $[\text{W/sr/m}^{2}]$ is radiant intensity per unit area. It is the amount of power going through a direction over a surface.

One last note. I could not find specific terms for the "intensity" of reflected and transmitted radiation specifically, since radiant exitance is technically only for emitted waves, which are distinct from reflected and transmitted ones. Since these come up all the time when dealing with material interfaces, I'll call them reflected exitance and transmitted exitance, with hopefully clear meaning.