Related papers: Numerical algorithms of the radiative transport eq…
In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective…
A new approach for solving the optical inverse problem of quantitative photoacoustic tomography is introduced, which interpolates between the well-known diffusion approximation and a radiative transfer equation based model. The proposed…
We describe a new algorithm to solve the time dependent, frequency integrated radiation transport (RT) equation implicitly, which is coupled to an explicit solver for equations of magnetohydrodynamics (MHD) using {\sf Athena++}. The…
A unified method for three-dimensional reconstruction of objects from transmission images collected at multiple illumination directions is described. The method may be applicable to experimental conditions relevant to absorption-based,…
We present an accurate quadrature formula on the sphere with less localized quadrature points for efficient numerical computation of the radiative transport equation (RTE) in the three dimensions. High accuracy of the present method…
An iterative method is derived for image reconstruction. Among other attributes, this method allows constraints unrelated to the radiation measurements to be incorporated into the reconstructed image. A comparison is made with the widely…
The Rytov approximation has been commonly used to obtain reconstructed images for optical tomography. However, the method requires linearization of the nonlinear inverse problem. Here, we demonstrate nonlinear Rytov approximations by…
We consider the imaging problem of the reconstruction of a three-dimensional object via optical diffraction tomography under the assumptions of the Born approximation. Our focus lies in the situation that a rigid object performs an…
Many questions in physical cosmology regarding the thermal and ionization history of the intergalactic medium are now successfully studied with the help of cosmological hydrodynamical simulations. Here we present a numerical method that…
The stochastic differential and integral equations describing the system of particles weakly interacting among themselves which are absorbed and scattered by particles of a medium are considered. The time-dependent transport equation with…
Achieving efficient and accurate simulation of the radiative transfer has long been a research challenge. Here we introduce the general synthetic iterative scheme as an easy-to-implement approach to address this issue. First, a macroscopic…
Structured illumination enables the tailoring of an imaging device's optical transfer function to enhance resolution. We propose the incorporation of a temporal periodic modulation, specifically a rotating mask, to encode multiple transfer…
In this work we present a solution of the one-dimensional spherical symmetric time-dependent neutron transport equation (written for a moving system in lagrangian coordinates) by using the characteristic method. One of the objectives is to…
An explicit numerical scheme is proposed for solving the initial-boundary value problem for the radiative transport equation in a rectangular domain with completely absorbing boundary condition. An upwind finite difference approximation is…
We consider the problem of optical tomographic imaging in the mesoscopic regime where the photon mean free path is of order of the system size. Within the accuracy of the single-scattering approximation to the radiative transport equation,…
We present a new numerical approach that is able to solve the multi-dimensional radiative transfer equations in all opacity regimes on a Lagrangian, unstructured network of characteristics based on a stochastic point process. Our method…
We present a new approach to numerically model continuum radiative transfer based on the Optically Thin Variable Eddington Tensor (OTVET) approximation. Our method insures the exact conservation of the photon number and flux (in the…
Optical diffraction tomography (ODT) is a three-dimensional (3D) quantitative phase imaging technique, which enables the reconstruction of the 3D refractive index (RI) distribution of a transparent sample. Due to its fast, non-invasive, and…
In recent years, the first author has developed three successful numerical methods to solve the 1D radiative transport equation yielding highly precise benchmarks. The second author has shown a keen interest in novel solution methodologies…
In this paper, we describe the numerical reconstruction method for quantitative photoacoustic tomography (QPAT) based on the radiative transfer equation (RTE), which models light propagation more accurately than diffusion approximation…