The radiative transfer equation (RTE) is a mathematical description of radiative gains and losses experienced by a propagating electromagnetic wave in a participating medium. Except for an isotropic lossless vacuum, all other volumes have the potential to scatter, absorb and emit radiant energy. Of these possible events, the global scattering term is the greatest obstacle between a radiative transfer problem and its solution. Historically, the RTE has been solved using a host of analytical approximations and numerical methods. Typical solution models exploit plane-parallel assumptions where it is assumed that optical properties may vary vertically with depth, but have an infinite horizontal extent. For more complicated scenarios that include pronounced 3D variability, a photon mapping Monte Carlo statistical approach to the radiative transfer solution is often utilized. The synthetic image shown here depicts the photon mapped solution of a step function submerged in a scattering volume at three different depths (increasing from top to bottom) and with variable photon mapping parameters that impact the resolution and SNR associated with the step function.
Ref. This research was carried out in partial fulfilment of a Doctorate of Philosopy in Imaging Science at the Rochester Institute of Technology (Rochester, New York), in collaboration with Dr. John Schott, Dr. Adam Goodenough and Dr. Scott Brown.