<p><span class="math-container">$R_d$</span> 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.</p>
<p>If you imagine a tiny, bright beam of light (like a laser) illuminating the surface at an incident point <span class="math-container">$x_i$</span>, 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 (<span class="math-container">$r$</span>) from the incident point, and proportional to the brightness of the incoming light (the incident flux).</p>

CC BY-SA 4.0
2021-12-27T04:36:25.110Z
perfect answer, it enlight me!
danding
CC BY-SA 4.0
2021-12-26T19:00:12.587Z
2021-12-26T19:00:12.587Z
Nathan Reed
<p>Recently, i am reading the papaer <a href="https://graphics.stanford.edu/papers/bssrdf/bssrdf.pdf" rel="nofollow noreferrer">A Practical Model for Subsurface Light Transport</a> . I have understand the radiative transport equation :</p>
<p><a href="https://i.sstatic.net/3FSkN.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/3FSkN.png" alt="enter image description here" /></a></p>
<p>and the approximation of the diffusion equation:</p>
<p><a href="https://i.sstatic.net/i6C1Z.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/i6C1Z.jpg" alt="enter image description here" /></a>
.</p>
<p>In BRDF lighting model, we define BRDF coefficient as below :
<a href="https://i.sstatic.net/xGkyo.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/xGkyo.jpg" alt="enter image description here" /></a></p>
<p>and in the bssrdf lighting model we have :
<a href="https://i.sstatic.net/cOyhN.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/cOyhN.jpg" alt="enter image description here" /></a>
<a href="https://i.sstatic.net/dEbjI.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/dEbjI.png" alt="enter image description here" /></a></p>
<p>However i saw the diffuse BSSRDF <code>Rd</code> definition:<a href="https://i.sstatic.net/qW0fk.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/qW0fk.jpg" alt="definition" /></a></p>
<p>, i can't understand the meaning of <code>Rd</code>. Why we need that definition which describes
&quot;the radiant exitance divided by the incident flux&quot; .</p>

<lighting><subsurface-scattering>
[Subsurface Scattering]What's the meaning of diffuse coefficient `Rd` in bssrdf
danding
# [Subsurface Scattering]What's the meaning of diffuse coefficient `Rd` in bssrdf

(Asked by: username_0 on 2021-12-26)

Recently, i am reading the papaer [A Practical Model for Subsurface Light Transport](https://graphics.stanford.edu/papers/bssrdf/bssrdf.pdf) . I have understand the radiative transport equation :

[![enter image description here](https://i.sstatic.net/3FSkN.png)](https://i.sstatic.net/3FSkN.png)

and the approximation of the diffusion equation:

[![enter image description here](https://i.sstatic.net/i6C1Z.jpg)](https://i.sstatic.net/i6C1Z.jpg)
.

In BRDF lighting model, we define BRDF coefficient as below :
[![enter image description here](https://i.sstatic.net/xGkyo.jpg)](https://i.sstatic.net/xGkyo.jpg)

and in the bssrdf lighting model we have :
[![enter image description here](https://i.sstatic.net/cOyhN.jpg)](https://i.sstatic.net/cOyhN.jpg)
[![enter image description here](https://i.sstatic.net/dEbjI.png)](https://i.sstatic.net/dEbjI.png)

However i saw the diffuse BSSRDF `Rd` definition:[![definition](https://i.sstatic.net/qW0fk.jpg)](https://i.sstatic.net/qW0fk.jpg)

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

**Tags:** lighting, subsurface-scattering


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## 1 answers

### Answer by username_1 on 2021-12-26. Score: 1 | Accepted answer

$R\_d$ 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).

> **Comments:**
> **username_0**: perfect answer, it enlight me!  

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