Using the method of images, we examine the three boundary conditions commonly applied to the surface of a semi-infinite turbid medium. We find that the image-charge configurations of the partial-current and extrapolated-boundary conditions have the same dipole and quadrupole moments and that the two corresponding solutions to the diffusion equation are approximately equal. In the application of...

We estimate the optical signal for an oceanographic lidar from the one-dimensional transient (time-dependent) radiative transfer equation using the discrete ordinates method. An oceanographic lidar directs a pulsed blue or green laser into the ocean and measures the time-dependent backscattered light. A large number of parameters affect the performance of such a system. Here the optical signal ...

A linear form of the radiative transfer equation for the simultaneous retrieval of atmospheric temperature and absorbing gas profiles and surface temperature from radiance spectra was derived in the classic paper by Smith et al. (1991). The derivation started with the RTE difference between the true and initial radiance spectra. It is shown that there exists a dual representation of this RTE di...

The fundamental phenomenological equations of radiative transfer, e.g., Lambert's cosine rule and the radiant transport equation, are derived from an analysis based on the Cauchy flux theory of continuum mechanics. For the classical case, where the radiance is distributed regularly over the unit sphere, it is shown that Lambert's rule follows from a balance law for the transfer of radiative pow...

Modeling the atmospheres of SNe Ia requires the solution of the NLTE radiative transfer equation. We discuss the formulation of the radiative transfer equation in the co-moving frame. For characteristic velocities larger than ∼ 2000 km s, the effects of advection on the synthetic spectra are non-negligible, and hence should be included in model calculations. We show that the time-independent or...

A method for the fast and accurate solution of the radiative transfer equation in plane-parallel media with coherent isotropic scattering is presented. This largely analytical approach uses the formalism of meromorphic functions in order to obtain the total solution, i.e. the angle and depth variation of the radiation field. A discretization of space and angle coordinates is not required. For t...

The discretization of the multi{dimensional radiative transfer equation results in a very large linear system of equations. The standard solution method used by astrophysicists is a simpliied xed point iteration (called approximate {iteration) which becomes slow for problems most interesting in astrophysics. As an alternative, a class of (block) conjugate gradient{like methods is proposed, toge...

To my parents, Laiping Sheng and Chengai Shi, who offered me unconditional love and support all the way since the beginning of my studies. This brief dedication is not enough room to express my gratitude that they are my parents. ii ACKNOWLEDGEMENTS I would like to thank several people for their help making this thesis possible. First and foremost, my greatest thankfulness goes to my advisor, P...

We report on the derivation and implementation of the first three-dimensional optical tomographic image reconstruction scheme that is based on the time-independent equation of radiative transfer (ERT) and allows for arbitrarily shaped medium boundaries and arbitrary spatial material distributions. The scheme builds on the concept of model-based iterative image reconstruction, in which a forward...

We are interested in the homogenization of heat transfer in periodic porous media where the fluid part is made of long thin parallel cylinders, the diameter of which is of the same order than the period. The heat is transported by conduction in the solid part of the domain and by conduction, convection and radiative transfer in the fluid part (the cylinders). A non-local boundary condition mode...