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On this page
  • Lambertian Scattering Model
  • ABg Scattering Model
  • Bidirectional Scattering Distribution Function (BSDF)
  • Rayleigh-Rice Scattering Model
  • Beckmann-Kirchoff Scattering Model
  • Harvey-Shack Scattering Model
  • K-Correlation Scattering Model

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  1. KostaCLOUD
  2. Optical Design
  3. Optical Design Modes
  4. Imaging

Surface Scattering

Surface Scattering in KostaCLOUD

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Last updated 1 year ago

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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).

ABg Scattering Model

Used for approximating smooth surface finishes.

Validity

  • Isotropic Surface Roughness

  • 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

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"

Polish
g
B
A

Super

2.5

0.00001

Slightly better than Standard

2.0

0.0001

Standard

1.5

0.001

Slightly worse than Standard

1.0

0.01

Polish
g
B
A

Super

2.5

0.00001

Slightly better than Standard

2.0

0.0001

Standard

1.5

0.001

Slightly worse than Standard

1.0

0.01

References

Bidirectional Scattering Distribution Function (BSDF)

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).

RMS Surface Roughness ≪λ\ll \lambda≪λ (Smooth Surfaces)

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.

Sum of ABg Parameters. See for more information.

1.4 (σλ)21.4\:(\frac{\sigma}{\lambda})^21.4(λσ​)2
5.46 (σλ)25.46\:(\frac{\sigma}{\lambda})^25.46(λσ​)2
13.92 (σλ)213.92\: (\frac{\sigma}{\lambda})^213.92(λσ​)2
25.51 (σλ)225.51\: (\frac{\sigma}{\lambda})^225.51(λσ​)2
0.35 (σΔnλ)20.35\:(\frac{\sigma\Delta n}{\lambda})^20.35(λσΔn​)2
1.37 (σΔnλ)21.37\:(\frac{\sigma\Delta n}{\lambda})^21.37(λσΔn​)2
3.50 (σΔnλ)23.50\:(\frac{\sigma\Delta n}{\lambda})^23.50(λσΔn​)2
6.35 (σΔnλ)26.35\: (\frac{\sigma\Delta n}{\lambda})^26.35(λσΔn​)2
Approximated Scatter Models for Stray Light Analysis, Richard N. Pfisterer
Approximated Scatter Models for Stray Light Analysis, Richard N. Pfisterer
ABg