Terminology for this article 

Reading various Wikipedia articles, it's apparent that Wikipedia is as about as muddled in terminology as the literature is. I am clear on a concept, which Chandrasekhar calls "specific intensity", which fully characterizes the radiation field in a medium, without physical surfaces.  is the energy passing thru an area element dA into a small solid angle  about the normal to the area element in a small frequency band  in a small time interval dt. It has SI units of watts/meter^2/sr/hz. Apparently many people refer to this as "radiance". Can we please settle on a term for this concept, and use it consistently? 

Next is the question of a physical surface. What is the term that fully characterizes the radiation coming out of a physical surface element that corresponds to "specific intensity", but is only specified for radiation out of the surface, and is undefined into the surface? It cannot have the same name, because its only like, half of the specific intensity. How do we describe the fact that this radiation is independent of direction, as long as that direction is out of the physical surface?

These are questions that need to be settled on before we can write a decent article. In my mind, I use the terms "specific intensity" or "spectral intensity" for the first paragraph above, and "radiance" for the second, but I don't care what names are used, as long as they are precisely defined and a case can be made that it is a common definition.