Links

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(ββ0)=Rπ\text{BSDF}(\beta-\beta_0) = \frac{R}{\pi}
Where
β=sin(θscatter)\beta = \sin(\theta_\text{scatter})
,
β0=sin(θscatter)\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

References

  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
    λ\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

BSDF(ββ0)=AB+(ββ0)g\text{BSDF}(\beta-\beta_0) = \frac{A}{B+(\beta-\beta_0)^g}
Where
β=sin(θscatter)\beta = \sin(\theta_\text{scatter})
,
β0=sin(θscatter)\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(σλ)21.4\:(\frac{\sigma}{\lambda})^2
Slightly better than Standard
2.0
0.0001
5.46(σλ)25.46\:(\frac{\sigma}{\lambda})^2
Standard
1.5
0.001
13.92(σλ)213.92\: (\frac{\sigma}{\lambda})^2
Slightly worse than Standard
1.0
0.01
25.51(σλ)225.51\: (\frac{\sigma}{\lambda})^2
Polish
g
B
A
Super
2.5
0.00001
0.35(σΔnλ)20.35\:(\frac{\sigma\Delta n}{\lambda})^2
Slightly better than Standard
2.0
0.0001
1.37(σΔnλ)21.37\:(\frac{\sigma\Delta n}{\lambda})^2
Standard
1.5
0.001
3.50(σΔnλ)23.50\:(\frac{\sigma\Delta n}{\lambda})^2
Slightly worse than Standard
1.0
0.01
6.35(σΔnλ)26.35\: (\frac{\sigma\Delta n}{\lambda})^2

References

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).