Related papers: The radiative transport equation with heterogeneou…
The transport of intensity equation (TIE) has revolutionized phase retrieval in optical microscopy, yet its application to complex media with absorption/scattering remains challenging. Here, we present a coupled TIE-TPE (transport of phase…
We consider optical tomography with structured illumination in spatial-frequency domain using the three-dimensional radiative transport equation. Without the diffusion approximation, the radiative transport equation is solved by the…
We investigate the accuracy of the recently proposed nonclassical transport equation. This equation contains an extra independent variable compared to the classical transport equation (the path-length $s$), and models particle transport…
We consider the radiation transfer problem in the discrete-ordinate, plane-parallel approach. We introduce two benchmark problems with exact known solutions and show that for strongly non-homogeneous media the homogeneous layers…
This is a companion report for the paper "Transverse electric scattering on inhomogeneous objects: Spectrum of integral operator and preconditioning" by the present authors. In this report we formulate the two-dimensional transverse…
When solving the time-dependent radiative transport equation (RTE), implicit time discretization is often employed for its robustness and stability. This results in a sequence of steady-state RTEs with identical cross-sections but varying…
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…
We discuss the implementation of physically meaningful branching ratios between the CRD and PRD contributions to the emissivity of a polarized multi-term atom in the presence of both inelastic and elastic collisions. Our derivation is based…
The radiative transfer equation (RTE) models the transport of light inside photonic scattering samples such as paint, foam and tissue. Analytic approximations to solve the RTE fail for samples with strong absorption and dominant anisotropic…
The nucleon spectral function in infinite nuclear matter is calculated in a quantum transport theoretical approach. Exploiting the known relation between collision rates and correlation functions the spectral function is derived…
We derive a reciprocity relation for vector radiative transport equation (vRTE) that describes propagation of polarized light in multiple-scattering media. We then show how this result, together with translational invariance of a…
The paper considers a linear system of Boltzmann transport equations modelling the evolution of three species of particles, photons, electrons and positrons. The system is coupled because of the collision term (an integral operator). The…
The computation of the radiative transfer equation is expensive mainly due to two stiff terms: the transport term and the collision operator. The stiffness in the former comes from the fact that particles (such as photons) travels at the…
When lifting the assumption of spatially-independent scattering centers in classical linear transport theory, collision rate is no longer proportional to angular flux / radiance because the macroscopic cross-section $\Sigma_t(s)$ depends on…
We develop a hybrid classical-quantum algorithm to solve a type of linear reaction-diffusion equation, the neutron diffusion (generalized) k-eigenvalue problem that establishes nuclear criticality. The algorithm handles an equation with…
We show that the inverse problems for a class of kinetic equations can be solved by classical tools in PDE analysis including energy estimates and the celebrated averaging lemma. Using these tools, we give a unified framework for the…
The photoacoustic tomography (PAT) is a hybrid modality that combines the optics and acoustics to obtain high resolution and high contrast imaging of heterogeneous media. In this work, our objective is to study the inverse problem in the…
A new formalism is introduced for the transfer of polarized radiation. Stokes parameters are shown to be four-vectors in a Minkowski-like space and, most strikingly, the radiative transfer equation (RTE) turns out to be an infinitesimal…
The radiative transfer equation for spectral lines from an extended gas is derived from first principles, treating the gas as a system of many atoms/molecules rather than isolated ones. Line broadening effects are assumed to be dominated by…
The construction of exact solutions for radiative transfer in a plane-parallel medium has been addressed by Hemsch and Ferziger in 1972 for a partial frequency redistribution model of the formation of spectral lines consisting in a linear…