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

**General**

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:

- The particles in the suspension are well-separated
- interference of light radiated from neighboring particles can be neglected

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:

- the photon is scattered by a single particle. Additionally the intensity (energy carried by the photon) is reduced by the amount absorbed by the particle. The direction of the scattered photon is determined from a random process, taking the phase function of the particle as probability distribution.
- Straight propagation of the photon through the medium. The pathlength is determined randomly, based on the extinction coefficient of the inhomogeneous medium.

**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**

- Enter the following parameters into the text fields:
- radius of the particles
- filling factor (volume portion) of the particles in the layer
- real part n' of the refractive index of the particles
- imaginary part n'' of the refractive index of the particles
- thickness of the layer
- wavelength of the incident radiation

- Use the Run-button to display the path of a single photon in the x-z plane. Press this button several times to display the paths of more than one photon. The displayed traces of the photons' paths contain quite a bit of physical information:
- how often the photons are scattered,
- whether mainly forward scattering takes place,
- how much the incident beam is broadened
- You may delete the plot window without harm. The next click on Run will then cause a new plot window to be opened.