The ##I_i## are the intensity of the rays, in other words energy per surface units per radians by seconds.
The d##\Omega## are the solid angles
The equation p75 isis what I don't understand. I suppose that each side represent the energy going and out of the surface dS but I don't understand why it has this form. It looks like the projection of the intensities along the x-axis, as if energy was a a vector quantity (like the momentum, for which the three components are conserved separately). But only the total energy going through dS should matter and I don't understand why it has this form.
If we say that ##I_1## is independant of the spacetime coordinates and is large enough to wrap around dS, the energy going in should be ##I_1 d\Omega dS## since the surface is totally exposed to the ray. I am probably wrong but I don't know why.