Photon density wave is the modulated optical intensity wave which propagates through the diffuse medium and exhibits the amplitude and phase variations. It satisfies the time-dependent radiative transfer equation and is similar to temperature wave field, and has been used in medical imaging. This paper discusses the basic characteristics of the photon density wave and gives exact numerical solu...

Interaction of photons with a host medium is described by a linear transport equation. This equation has a very simple physical interpretation; it is a mathematical statement of the energy conservation law. In spite of the different physics behind radiation transfer in clouds and vegetation, these media have certain macro and micro-scale features in common. First, both are characterized by stro...

We present a generalized delta-Eddington phase function to simplify the radiative transfer equation to an integral equation with respect to the photon flux vector. The solution of the integral equation is highly accurate to model the photon propagation in the biological tissue over a broad range of optical parameters, especially in the visible light spectrum where the diffusion approximation br...

Abstract. The present paper discusses the diffusion approximation of the linear Boltzmann equation in cases where the collision frequency is not uniformly large in the spatial domain. Our results apply for instance to the case of radiative transfer in a composite medium with optically thin inclusions in an optically thick background medium. The equation governing the evolution of the approximat...

A three-dimensional Monte Carlo simulation of transient radiative transfer is performed for short pulse laser transport in scattering and absorbing medium. Experimental results of a 60 ps pulse laser transmission in scattering medium are presented and compared with simulation. Good agreement between the Monte Carlo simulation and experimental measurement is found. The refractive index of the sc...

The stationary monochromatic radiative transfer equation is a partial differential transport equation stated on a five-dimensional phase space. To obtain a well-posed problem, inflow boundary conditions have to be prescribed. The sparse tensor product discretization has been successfully applied to finite element methods in radiative transfer with wavelet discretization of the angular domain (W...

We present the first tomographic reconstruction algorithm for optical molecular imaging that is based on the equation of radiative transfer. The reconstruction code recovers the spatial distribution of fluorescent sources in highly scattering biological tissue. An objective function, which describes the discrepancy of measured near-infrared light with predicted numerical data on the tissue surf...

We solve the radiative transfer problem analytically in the anisotropic, plane-parallel atmosphere. Chandrasekhar formalized the radiative transfer process as a simultaneous, two-variable, non-linear, integral equation and obtained the analytical solution of the second approximation for the isotropic plane-parallel atmosphere. We obtain the second approximation for the anisotropic atmosphere, b...

The rays propagate along curved path determined by the Fermat principle in the graded index medium. The radiative transfer equation in graded index medium (GRTE) contains two specific redistribution terms (with partial derivatives to the angular coordinates) accounting for the effect of the curved ray path. In this paper, the hybrid finite volume with finite element method (hybrid FVM/FEM) (P.J...