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Monte-Carlo Radiative Transfer for a Suspension of Homogeneous Spherical Particles.


Radiative transfer calculations are a versatile and efficient tool for the calculation of the optical properties of inhomogeneous media. The play an important role particularly in astrophysics (interstellar dust clouds) and atmospheric physics (clouds) where the basic assumptions underlying the formalism are excellently fulfilled. Applications to other media such as biological tissue, powders, paints etc. also have a long history (namely, the Kubelka-Munk theory). With the increasing popularity of laser applications, radiative transfer calculations plays a more and more important role in applied sciences. The applet presented on this Web-page demonstates raditive transfer for the very simple (yet frequently encountered) case of a not too thick layer consisting of a suspension of homogeneous spherical particles. More than one particle species may be included in the calculations. Reflection of radiation from the surface of the layer is not considered.

Basic assumptions of radiative transfer theory are:

Neglection of interferences requires that the typical inter-particle separation is much larger than the wavelength and that the volumetric concentration of the particles is small. These conditions can be relaxed in practical applications: radiative transfer theory even works in powders, where the particles are touching. With appropriate corrections, it produces good results even for densely packed materials with volume concentrations of the particles up to 50% (A. Kokhanovsky, Optics of Light Scattering Media, Wiley-Praxis Series, Chichester, 1999). The particles should be substantially larger than the wavelength in the latter case. If the particles' sizes and inter-particle separations are comparable to or smaller than the wavelength, radiatiative transfer theory is not applicable. Random medium formalisms such as the Strong Property Fluctuation Theory (L. Tsang, J. A. Kong, T. Shin, Theory of Microwave Remote Sensing, Wiley, New York, 1986; B. Michel, A. Lakhtakia, J. Phys. D: Appl. Phys 32, 404-406, 1999) should be used instead. For even smaller particles/separation distances, effective medium formalisms are recommended (A. Lakhtakia et., Selected Papers on Linear Optical Composite Materials, SPIE Milestone Series, Vol. 120, SPIE Press, Washington, 1996).

In Monte-Carlo radiative transfer calculations, a large number of "model photons" (also called "weighted photons") propagate through the layer in a random process which consists of a sequence of two steps:

Note that the "model photons" do not represent real photons. They are just a numerical trick to solve the radiative transfer equation by means of a random process.

About the applet

With the applet you can trace the path of single model photons propagating through an inhomogeneous layer. It is assumed that the layer consists of of monodisperse spherical particles surrounded by vacuum (or air). This means that no refraction and specular reflection occurs at the surface of the layer.

The applet uses a vector radiative transfer model based on Mie scattering, i.e., the full Stokes vector of the model photons is propagated through the layer. The layer is parallel to the xy-plane and the light is assumed to be initially unpolarized and perpendicularly incident on the layer. The code is kept quite general for sake of upward-compatibility. With not too much extra effort one can do full radiative transfer calculations.

How to use the applet

Interested in radiative transfer? Don't hesitate to contact me.