# [Subsurface Scattering]What's the meaning of diffuse coefficient Rd in bssrdf

Recently, i am reading the papaer A Practical Model for Subsurface Light Transport . I have understand the radiative transport equation :

and the approximation of the diffusion equation:

.

In BRDF lighting model, we define BRDF coefficient as below :

and in the bssrdf lighting model we have :

However i saw the diffuse BSSRDF Rd definition:

, i can't understand the meaning of Rd. Why we need that definition which describes "the radiant exitance divided by the incident flux" .

$$R_d$$ is the diffusion profile. It's a falloff function that describes how light spreads through the material, as a function of the distance between the entering and exiting point.
If you imagine a tiny, bright beam of light (like a laser) illuminating the surface at an incident point $$x_i$$, it would produce a glow on the surface surrounding it, as light scatters around in the material and then exits at nearby points. The diffusion profile gives the brightness of this glow (the radiant exitance), as a function of distance ($$r$$) from the incident point, and proportional to the brightness of the incoming light (the incident flux).