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

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 $\ll \lambda$ (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

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	$25.51\: (\frac{\sigma}{\lambda})^2$

Lenses

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

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).