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
BSDF(β−β0)=Rπ\text{BSDF}(\beta-\beta_0) = \frac{R}{\pi}BSDF(β−β0​)=πR​
Where β=sin⁡(θscatter)\beta = \sin(\theta_\text{scatter})β=sin(θscatter​)
, β0=sin⁡(θscatter)\beta_0=\sin(\theta_\text{scatter})β0​=sin(θscatter​)
 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
References
1.J. E. Harvey, Understanding surface scatter phenomena: A linear systems formulation, SPIE Press, Bellingham (2019).
2.​Approximated Scatter Models for Stray Light Analysis, Richard N. Pfisterer​
ABg Scattering Model
Used for approximating smooth surface finishes.
Validity
Isotropic Surface Roughness
RMS Surface Roughness ≪λ\ll \lambda≪λ
 (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
BSDF(β−β0)=AB+(β−β0)g\text{BSDF}(\beta-\beta_0) = \frac{A}{B+(\beta-\beta_0)^g}BSDF(β−β0​)=B+(β−β0​)gA​
Where β=sin⁡(θscatter)\beta = \sin(\theta_\text{scatter})β=sin(θscatter​)
, β0=sin⁡(θscatter)\beta_0=\sin(\theta_\text{scatter})β0​=sin(θscatter​)
 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 (σλ)21.4\:(\frac{\sigma}{\lambda})^21.4(λσ​)2
​
Slightly better than Standard
2.0
0.0001
​5.46 (σλ)25.46\:(\frac{\sigma}{\lambda})^25.46(λσ​)2
​
Standard
1.5
0.001
​13.92 (σλ)213.92\: (\frac{\sigma}{\lambda})^213.92(λσ​)2
​
Slightly worse than Standard
1.0
0.01
​25.51 (σλ)225.51\: (\frac{\sigma}{\lambda})^225.51(λσ​)2
​
Polish
g
B
A
Super
2.5
0.00001
​0.35 (σΔnλ)20.35\:(\frac{\sigma\Delta n}{\lambda})^20.35(λσΔn​)2
​
Slightly better than Standard
2.0
0.0001
​1.37 (σΔnλ)21.37\:(\frac{\sigma\Delta n}{\lambda})^21.37(λσΔn​)2
​
Standard
1.5
0.001
​3.50 (σΔnλ)23.50\:(\frac{\sigma\Delta n}{\lambda})^23.50(λσΔn​)2
​
Slightly worse than Standard
1.0
0.01
​6.35 (σΔnλ)26.35\: (\frac{\sigma\Delta n}{\lambda})^26.35(λσΔn​)2
​
References
 Approximated Scatter Models for Stray Light Analysis, Richard N. Pfisterer​
Bidirectional Scattering Distribution Function (BSDF)
Sum of ABg Parameters. See ABg for more information.
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).

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

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	$6.35\: (\frac{\sigma\Delta n}{\lambda})^2$

Wave Tracing

Volumetric Scattering

Last modified 3mo ago