# Surface Scattering

Surface Scattering in KostaCLOUD

## Lambertian Scattering Model

Used for extremely diffusive surfaces. Perfect hemispherical scatter distribution.

#### Validity

• Isotropic Surface Roughness
• Ideal Diffuser.
• Only valid for perfectly diffusing materials.

#### BSDF

$\text{BSDF}(\beta-\beta_0) = \frac{R}{\pi}$
Where
$\beta = \sin(\theta_\text{scatter})$
,
$\beta_0=\sin(\theta_\text{scatter})$
where R is the reflectivity of the sample.

#### Example Values

These values below were provided by the reference below, and re-presented here. These values are built into the "Simplistic Presets", where the idea of this table for this model in Rich Pfisterer's words: "Approximated Scatter Model"
Surface
R
Ideal diffuser
1
Typical matte paper at normal incidence
0.85
Typical diffuse black paint at normal incidence
0.5
Perfect absorber
0
1. 1.
J. E. Harvey, Understanding surface scatter phenomena: A linear systems formulation, SPIE Press, Bellingham (2019).

## ABg Scattering Model

Used for approximating smooth surface finishes.

#### Validity

• Isotropic Surface Roughness
• RMS Surface Roughness
$\ll \lambda$
(Smooth Surfaces)
• Surface Roughness is Bandwidth Limited. I.e. The roughness is not just a single sinusoidal frequency, but a spread of frequencies about some dominant frequency.
• Simplistic Model, Ideal for quick turn-around. Wavelength dependence, and model parameters may differ from reality.

#### BSDF

$\text{BSDF}(\beta-\beta_0) = \frac{A}{B+(\beta-\beta_0)^g}$
Where
$\beta = \sin(\theta_\text{scatter})$
,
$\beta_0=\sin(\theta_\text{scatter})$
with some fitting parameters: A,B, and g.

#### Example Values

These values below were provided by the reference below, and re-presented here. These values are built into the "Simplistic Presets", where the idea of this table for this model in Rich Pfisterer's words: "Approximated Scatter Model"
Mirrors
Lenses
Polish
g
B
A
Super
2.5
0.00001
$1.4\:(\frac{\sigma}{\lambda})^2$
Slightly better than Standard
2.0
0.0001
$5.46\:(\frac{\sigma}{\lambda})^2$
Standard
1.5
0.001
$13.92\: (\frac{\sigma}{\lambda})^2$
Slightly worse than Standard
1.0
0.01
$25.51\: (\frac{\sigma}{\lambda})^2$
Polish
g
B
A
Super
2.5
0.00001
$0.35\:(\frac{\sigma\Delta n}{\lambda})^2$
Slightly better than Standard
2.0
0.0001
$1.37\:(\frac{\sigma\Delta n}{\lambda})^2$
Standard
1.5
0.001
$3.50\:(\frac{\sigma\Delta n}{\lambda})^2$
Slightly worse than Standard
1.0
0.01
$6.35\: (\frac{\sigma\Delta n}{\lambda})^2$

## Rayleigh-Rice Scattering Model

#### References

J. E. Harvey, Understanding surface scatter phenomena: A linear systems formulation, SPIE Press, Bellingham (2019).

## Beckmann-Kirchoff Scattering Model

#### References

J. E. Harvey, Understanding surface scatter phenomena: A linear systems formulation, SPIE Press, Bellingham (2019).

## Harvey-Shack Scattering Model

#### References

J. E. Harvey, Understanding surface scatter phenomena: A linear systems formulation, SPIE Press, Bellingham (2019).

## K-Correlation Scattering Model

#### References

J. E. Harvey, Understanding surface scatter phenomena: A linear systems formulation, SPIE Press, Bellingham (2019).