Light Scattering for Material Appearence

Graduate course, Institut d'Optique Graduate School, 2023

The objective of this master course is to present and explain the physical mechanisms of light scattering, as well as modeling methods to predict the propagation of light in scattering media in the radiative transfer approximation.


The course begins with an introduction describing the various fields of application of light scattering: astronomy, medical imaging, computer graphics, appearance of materials.
The formalism of the radiative transfer equation (RTE) is then described in a first part: notion of collision coefficient, phase function, establishment of the RTE, diffuse or specular illumination and method of resolution by the discrete coordinate method. Some exercises illustrate this part of the course.
The formalism of the diffusion equation is then described in a second part, establishment of the diffusion equation in the isotropic case, method of resolution (in the framework of exercises) in the 1D (layer) and 2D cases (dipole method, Fourier transform method).

The course is structured as follows:

  • 7 Lectures of three hours each
  • 1 Practical Session of three hours

The files are in their current version, thank you to report by mail any typo or error.


  1. Lecture Handout
  2. Lecture Slides on Internal Reflections
  3. Lecture Slides on Main Concepts of Monte Carlo
  4. Practical Session on Monte Carlo

Lecture Handout

Current Version from Raphaƫl Clerc -


  1. Introduction
  2. Definition of important physical quantities in transport theory
    2.1. Plane-Parallel geometry
    2.2. Specific intensity, flux, energy density
  3. Equation of transfer in radiative transport theory
    3.1 Derivation of the radiative transfer equation
    3.2 Flux conservation
    3.3 Reduced incident intensity and diffuse intensity
  4. Solution of the transfer radiative equation in the first order approximation
  5. Solution of the radiative transfer equation by the discrete ordinates method
    5.1 Discretization of the radiative transfer equation by the discrete ordinates method
    5.2 Boundary conditions
  6. The diffusion approximation of the transfer equation
    6.1 Derivation of the diffusion equations
    6.2 Boundary conditions for diffusion equations

Lecture Slides on study of internal reflections at flat interfaces

Lecture Slides on the Main concepts of Monte Carlo simulations

Practical Session on Monte-Carlo using MCX

Pratical Session Subject: