Light theory - radiance vs material exitance?

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I'm currently going through chapter 5 of Real Time Rendering and on page 110 (5.5. Shading) there is a distinction made between "exitance" of light from a material, or in other words, the counterpart of "irradiance" that is reflected from the material's surface, where irradiance is the measure of the amount of light hitting the surface, and "radiance", which is the brightness and colour of a single ray of light. It seems to me that the exitance value Mdiffuse, that equation 5.3 shows, represents a ray of light leaving the surface in a given direction is the same thing conceptually as the radiance value perceived at the receiving end of that ray of light. Why then does equation 5.4 then calculate the radiance Ldiffuse as a function of the exitance value? How are they not the same thing?

Edited by axefrog

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Why then does equation 5.4 then calculate the radiance Ldiffuse as a function of the exitance value? How are they not the same thing?

The medium in which the light travels might change the light (fog, atmosphere).

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"Exitance" refers to the amount of light being reflected off the surface in all directions about the hemisphere. "Outgoing radiance" refers to the amount of light being reflected in a single direction (basically, the amount you would see from a given viewpoint). To get the exitance for a surface, you would integrate all outgoing radiance values about the hemisphere. This makes it an exact counterpart of irradiance, which you calculate by integrating incoming radiance about the hemisphere. The reason why the equations for exitance and outgoing radiance are so similar for the diffuse term is because lambertian diffuse assumes that light scatters equally in all directions. Your typical specular terms is more complex than this, and will scatter different amounts of lights in different directions (which is why it's view-dependent).

If you haven't yet, I would strongly suggest reading through chapter 7. It goes into detail about radiometry and the related integrals, and it should provide the understanding that you need for section 5.5 to really make sense.

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Ok cool, thanks. I'll do that.

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