<p>We have two different terms, for example, let's talk about scattering only.</p>
<ul>
<li>Scattering coefficient</li>
<li>Scattering cross-section</li>
</ul>
<p>These two terms are supposed to have different physical meaning. I read it from the <a href="https://www.pbr-book.org/3ed-2018/Volume_Scattering/Volume_Scattering_Processes#Absorption" rel="nofollow noreferrer">PBR-book - Chapter 11</a> :</p>
<blockquote>
<p>Absorption is described by the medium’s absorption cross section, , which is the probability density that light is absorbed per unit distance traveled in the medium.</p>
</blockquote>
<p>But the wikipedia told me:</p>
<blockquote>
<p>The SI unit of attenuation coefficient is the reciprocal metre (m−1). <a href="https://en.wikipedia.org/wiki/Attenuation_coefficient" rel="nofollow noreferrer">Reference</a></p>
</blockquote>
<p>And this:</p>
<blockquote>
<p>This is also commonly expressed as: <span class="math-container">$\sigma = \alpha /n$</span>, where <span class="math-container">$\alpha$</span> is the absorption coefficient, <span class="math-container">$n$</span> is the atomic number density <a href="https://en.wikipedia.org/wiki/Absorption_cross_section" rel="nofollow noreferrer">Reference</a></p>
</blockquote>
<p>So I suppose <strong>xxx cross-section</strong> and <strong>xxx coefficient</strong> should be different, therefore should have different unit. But it seems that, in rendering, these two terms are interchangeable? Like in mitsuba and PBRT we will set <strong><span class="math-container">$\sigma$</span></strong> instead of <span class="math-container">$\mu$</span>, although they are just names. In rendering, the so-called <strong>cross-section</strong> (in PBR-book) has the same unit as <strong>xxx coefficient</strong> (<span class="math-container">$m^{-1}$</span>), but they should be distinguished by <span class="math-container">$N$</span>, which should have the unit of <span class="math-container">$m^{-3}$</span>.</p>
<p>My confusion is what exactly are we setting in those renderers, and in theory, which term is the correct term to use? And, whether there is anything more work I should do, to convert the <em>unitless</em> distance in those renderers to be a physical value (Like multiply <span class="math-container">$\sigma_x$</span> by N)?</p>

CC BY-SA 4.0
2023-03-28T22:41:52.287Z
Normally publications refer to the "scattering coefficient" is the "out scattering coefficient" which is the probability of a photon, being out scattered. Where as the "scattering cross-section" is usually computed as part of the "absorption cross-section". Which is a measure of how likely a photon is going to absorbed as it travels through a medium. They are related but separate concepts. Most models use a unitless combination of the two called the scattering coefficient. But alone they do have units. If the two are not separated out internally then combining them seems like a good approach.
pmw1234
CC BY-SA 4.0
2023-03-29T10:10:15.043Z
@pmw1234 Thanks for the comment. I just found that they might be separated in other related fields lile optics, but not in CG. Since I wish my rendering to correspond well with realistic data, I don't want any misunderstanding in the parameter settings in the renderer.
Enigmatisms
<physically-based><volume-rendering><theory><volumetric-scattering><scattering>
Term confusion about volume scattering
Enigmatisms
# Term confusion about volume scattering

(Asked by: username_0 on 2023-03-27)

We have two different terms, for example, let's talk about scattering only.

* Scattering coefficient
* Scattering cross-section

These two terms are supposed to have different physical meaning. I read it from the [PBR-book - Chapter 11](https://www.pbr-book.org/3ed-2018/Volume_Scattering/Volume_Scattering_Processes#Absorption) :

> Absorption is described by the medium’s absorption cross section, , which is the probability density that light is absorbed per unit distance traveled in the medium.

But the wikipedia told me:

> The SI unit of attenuation coefficient is the reciprocal metre (m−1). [Reference](https://en.wikipedia.org/wiki/Attenuation_coefficient)

And this:

> This is also commonly expressed as: $\sigma = \alpha /n$, where $\alpha$ is the absorption coefficient, $n$ is the atomic number density [Reference](https://en.wikipedia.org/wiki/Absorption_cross_section)

So I suppose **xxx cross-section** and **xxx coefficient** should be different, therefore should have different unit. But it seems that, in rendering, these two terms are interchangeable? Like in mitsuba and PBRT we will set **$\sigma$** instead of $\mu$, although they are just names. In rendering, the so-called **cross-section** (in PBR-book) has the same unit as **xxx coefficient** ($m^{-1}$), but they should be distinguished by $N$, which should have the unit of $m^{-3}$.

My confusion is what exactly are we setting in those renderers, and in theory, which term is the correct term to use? And, whether there is anything more work I should do, to convert the *unitless* distance in those renderers to be a physical value (Like multiply $\sigma\_x$ by N)?

**Tags:** physically-based, volume-rendering, theory, volumetric-scattering, scattering

> **Comments:**
> **username_1**: Normally publications refer to the "scattering coefficient" is the "out scattering coefficient" which is the probability of a photon, being out scattered. Where as the "scattering cross-section" is usually computed as part of the "absorption cross-section". Which is a measure of how likely a photon is going to absorbed as it travels through a medium. They are related but separate concepts. Most models use a unitless combination of the two called the scattering coefficient. But alone they do have units. If the two are not separated out internally then combining them seems like a good approach.  
> **username_0**: @username_1 Thanks for the comment. I just found that they might be separated in other related fields lile optics, but not in CG. Since I wish my rendering to correspond well with realistic data, I don't want any misunderstanding in the parameter settings in the renderer.  

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## 0 answers

