Scattering Properties

You can define the volume scattering (material like fog).

In General group box, you must select scattering variation model.

Unscattering Material

If you select Unscattering material, the material does not include scattering variation.

Give Particles Specifications: Optical Properties of the Medium will be Evaluated using MIE Theory

If you select Give particles specifications: Optical properties of the medium will be evaluated using MIE theory, the scattering variation is described by a table of diffusion coefficients (mm-1) for each wavelength (nm) corresponding to the list of particles.

The MIE theory describes the volume scattering material with small particles. With the MIE theory, the User Material Editor allows you to define the Particles properties. Scattering variation, Scattering phase function and Particles absorption variation tabs are automatically computed and updated according to the particles properties defined in the Particles tab.

Note: You can modify the wavelengths of the Scattering variation and Particles absorption variation tab.

You cannot modify the information of the Scattering phase function tab.

The Diffusion coefficient is the inverse of the mean free path : σd=1/ｌ with ｌ being the mean free path.

The Mean free path corresponds to the average distance that a ray travels before being scattered by a particle in a medium. It gives you an idea of the scattering capabilities of a medium. The higher the Mean free path, the smaller the Diffusion coefficient, meaning that the medium is little scattering.

The transmission corresponds to the quantity of energy going through a medium without being scattered.

The scattering material transmission formula is
  • Ͳ = transmission percentage
  • ｌ = thickness (mm)

  • σe=σa+σd = attenuation coefficient (mm-1)

    The attenuation coefficient informs on, in average, how many light-matter interaction occur on a given distance.
    • σa = particles' absorption coefficient
    • σd = Diffusion coefficient

Give Scattering Coefficient and Phase Function of the Medium

If you select Give scattering coefficient and phase function of the medium, the scattering variation is described by a table of diffusion coefficients (mm-1) for each wavelength (nm) and by a phase function.

Unlike the MIE theory, here you select a model and define the phase function. Particles properties are then calculated according to the phase function.

You can define the phase function:
  • by giving the scattering efficiency according to the scattering angle
  • according to the Henyey-Greenstein model
  • according to the double Henyey-Greenstein model
  • according to the Gegenbauer model

Henyey-Greenstein

Henyey-Greenstein model simplifies the phase function's definition for the intensity distribution. With this model, you have to give the anisotropic factor to describe the intensity distribution. This data can be found in data sheet.

All the difficulty in diffusing material coding is in the appropriate choice of phase function to be as closer as possible to physical laws.

Note: Jacques and Prahl [S. L. Jacques, C. A. Alter, and S. A. Prahl. Angular dependence of HeNe laser light scattering by human dermis. Lasers Life Sci., 1:309{333, 1987.] have shown that the following phase function is appropriate to simulate human skin.

Theta is the angle between and .

g = 0

g = 0.8

Double Henyey-Greenstein

Double Henyey-Greenstein model is for diffuse material in volume.

The Double Henyey-Greenstein model formula is the following:

F(Theta)= Ratio*f(Theta, Anisotropy factor1)+ (1-Ratio)*f(theta, Anisotropy factor 2)

Note: For details about Scattering phase function tab, refer to Scattering Phase Function.

Gegenbauer

Gegenbauer model allows you to define the phase function for volume scattering.

Gegenbauer is a more general model than Henyey-Greenstein model. In addition to the anisotropic coefficient "g", the Gegenbauer model integrates an alpha coefficient α that can vary according to wavelengths and allows you to be more accurate.

The Gegenbauer formula is

The Henyey-Greenstein model is a specific Gegenbauer model where α = 0,5

Note: For more information on the Anisotropy coefficient and Alpha coefficient, refer to Scattering Phase Function.
Note: For more information, refer to the publication "Approximate two-parameter phase function for light scattering", L. O. Reynolds and N. J. McCormick.

Phase Function Changes According to the Wavelength

In case of MIE theory, if you select the Phase function changes according to the wavelength check box, you first need to add one particle. For more details, you can view Particles.

In case of Give scattering coefficient and phase function of the medium, if you select the Phase function changes according to the wavelength check box, you can Add or Delete a wavelength and/or an angle.

The wavelength list is the same than the one displayed in the Scattering variation tab. If you want to add a wavelength to the phase table, you can do it from Scattering variation tab.

With Wavelength to display, you can select the wavelength of the table for which the phase function's display has been made.