Confusion over concept of 'radiance'.

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I have some confusion about what 'radiance' means as used in radiometry; specifically, I don't understand what it is a function of. For example: radiant energy is specified over some region, radiant energy density is specified at a point, radiant flux is specified across some surface, Irradiance -- often called intensity -- is specified either across some finite surface or at a point in a given direction (by taking an infinitesimal area normal to the given direction), and intensity -- adopting the SI definition -- is specified along a line from a point-like source. But radiance? I don't understand. I became especially confused when my book tries to prove that 'radiance' is uniform along a ray or beam. All I really know is it is measured in flux per unit area per unit steradian.
 
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