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In-Scattering

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I am trying to understand in-scattering along a ray. Ignoring emission, the book Physically Based Rendering gives the following formula for the amount of light added to a point due to in-scattering as: S(p,w) = o_s(p,w) * SphericalIntegral( phaseFunc(p,-w'-->w)*L_i(p,w')dw' ) where o_s is the scattering coefficient (probability density of light scattering per unit length), L_i is the incoming radiance at p from direction w'. My understanding is that the SphericalIntegral is basically summing the incoming light from all directions around p that scatter in the direction w. So now we have all the light that has scattered into the viewing ray. How come we multiply this by o_s(p,w)? Is it because some of the in-scattered light is out-scattered again? From the notation, it sounds like o_s(p,w) is the same function they use for out-scattering, but I am not sure if it is just overloading the notation. Thanks.

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