Radiative transfer in a turbid medium with a varying refractive index: comment

Singular radiation fields in scattering media with refraction

Radiative transfer in scattering media with spatially varying refractive indices, such as plasma with density fluctuations, is considered. It has been shown that singularities of diffuse radiation intensity can appear in the scattered field if the gradient of the refractive index is strong enough. To do that, we solve the scalar radiative transfer equation approximately and then analyze the solution qualitatively. Examples of the analytic singular solutions of the scalar radiative transfer equation in flat layered and spherically symmetric media, typically occurring in remote sensing applications, are provided. Conditions of formation of these singularities are discussed. Monte Carlo simulation results exhibiting singularities are compared with the derived analytical solutions.

Polarized light transport in refractive weak scattering media

This paper is devoted to modeling of the light transport in refractive and weak scattering media by means of the vector radiative transfer equation. In refractive media polarization of light depends not only on the law of scattering but also on the refractive index distribution and can change along curved light trajectories according to the Rytov law of the polarization ellipse rotation. Results of numerical simulations are presented in the form of CCD camera images, which is how data are acquired in tomographic imaging experiments.

Light transport in refractive turbid media

Light scattering in refractive media can be used for visualization of caustics and singularities of wavefronts of the incident radiation. Its modeling requires solving the radiative transfer equation. Numerical solution of the radiative transfer equation in turbid media with a spatially varying refractive index is presented and discussed in this paper. The approach is based on the self-consistent approximation of the radiative transfer equation and results in a relatively inexpensive and robust numerical algorithm. Simulations are presented for several cases including a weakly scattering medium with varying refractive index and a refractive weakly scattering medium with embedded highly scattering objects.

Analytical reconstruction of the bioluminescent source with priors

Bioluminescence imaging has been a popular tool in small animal imaging. During the last decade, the efforts have focused on the development of tomographic systems. However, due to the difficulties in the nature of inverse source problem, multi-modal systems have been the center of attention for the last couple of years. These systems provide complementary information such that the difficulties of the inverse source problem could be overcome using the a priori information obtained. Motivated by these advances in multi-modal systems, this work presents a novel analytical reconstruction of the bioluminescent source. It is shown that if source strength is known a priori then source position could be calculated or vice versa, if source location is known a priori, source strength could be calculated as well as the photon fluence rate. The determination of the source location can be achieved by another imaging system such as X-ray computed tomography. Therefore, in bioluminescence tomography together with an imaging system can be utilized as a multi-modal system. In this work, conventional finite element based simulations are also performed and the numerical results are compared with the analytical ones. It turns out to be that the analytical results are in a good accordance with the numerical results.

Coherent backscattering enhancement in refracting media: diffusion approximation

The weak localization (coherent backscattering enhancement) phenomenon in media with graded refraction index is investigated within the diffusion approximation. The obtained analytic results are compared with numerical solutions by finite-difference and Monte Carlo calculations.

Analytic evaluation of diffuse fluence error in multilayer scattering media with discontinuous refractive index

A simple analytic method of estimating the error involved in using an approximate boundary condition for diffuse radiation in two adjoining scattering media with differing refractive indices is presented. The method is based on asymptotic planar fluences and enables the relative error to be readily evaluated without recourse to Monte Carlo simulation. Three examples of its application are considered: (1) evaluating the error in calculating the diffuse fluences at a boundary between two media with differing refractive index and dissimilar scattering properties, (2) the dependence of the relative error in a multilayer medium with discontinuous refractive index on the ratio of the reduced scattering coefficient to the absorption coefficient μ(s)'/μ(a), and (3) the parametric dependence of the error in the radiant flux J(s) at the surface of a three-layer medium. The error is significant for strongly forward-biased scattering media with non-negligible absorption and is cumulative in multilayered media with refractive index increments between layers.

On the eigenfunctions of acousto-optic modulation in a homogeneously absorbing optical medium

A closed form solution for time-averaged modulated fluence rate is presented for acoustically modulated diffusive light propagation in a medium. The solution assumes that the component of modulated light flux in the direction of acoustic pressure variation is zero.

Radiative energy transfer in disordered photonic crystals

The difficulty of description of the radiative transfer in disordered photonic crystals arises from the necessity to consider on an equal footing the wave scattering by periodic modulations of the dielectric function and by its random inhomogeneities. We resolve this difficulty by approaching this problem from the standpoint of the general multiple scattering theory in media with an arbitrary regular profile of the dielectric function. We use the general asymptotic solution of the Bethe-Salpeter equation in order to show that for a sufficiently weak disorder the diffusion limit in disordered photonic crystals is presented by incoherent superpositions of the modes of the ideal structure with weights inversely proportional to the respective group velocities. The radiative transfer and the diffusion equations are derived as a relaxation of long scale deviations from this limiting distribution. In particular, it is shown that in general the diffusion is anisotropic unless the crystal has sufficiently rich symmetry, say, the square lattice in 2D or the cubic lattice in 3D. In this case, the diffusion is isotropic and only in this case can the effect of the disorder be characterized by a single mean free path depending on frequency.

Diffuse light propagation in a turbid medium with varying refractive index: Monte Carlo modeling in a spherically symmetrical geometry

We report on the development of Monte Carlo software that can model media with spatially varying scattering coefficient, absorption, and refractive index. The varying refractive index is implemented by calculating curved photon paths in the medium. The results of the numerical simulations are compared with analytical solutions obtained using the diffusion approximation. The model under investigation is a scattering medium that contains a spherically symmetrical inclusion (inhomogeneity) created by variation in optical properties and having no sharp boundaries. The following steady-state cases are considered: (a) a nonabsorbing medium with a spherically symmetrical varying refractive index, (b) an inclusion with varying absorption and scattering coefficients and constant refractive index, and (c) an inclusion with varying absorption, scattering, and refractive index. In the latter case it is shown that the interplay between the absorption coefficient and the refractive index may create the effect of a hidden inclusion.

Radiative transfer equations with varying refractive index: a mathematical perspective

Established mathematical techniques to model the energy density of high-frequency waves in random media by radiative transfer equations and to model the small mean-free-path limit of radiative transfer solutions by diffusion equations are reviewed. These techniques are then applied to the derivation of radiative transfer and diffusion equations for the radiance, also known as specific intensity, of electromagnetic waves in situations where the refractive index of the underlying structure varies smoothly in space.