Exact analytical solutions and corresponding Monte Carlo models for the problem of light transport in turbid media with continuous absorption and discrete scattering at the single scattering approximation (original) (raw)

Fast semianalytical Monte Carlo simulation for time-resolved light propagation in turbid media

Journal of The Optical Society of America A-optics Image Science and Vision, 1996

The statistical estimator concept, created in the nuclear engineering field, has been adapted to the elaboration of a new and fast semianalytical Monte Carlo numerical simulation for time-resolved light-scattering problems. This concept has also been generalized to the case of unmatched boundaries. The model, discussed in detail in this paper, contains two stages. The first stage is the information generator in which, for each scattering event, the contribution to the total reflectance and transmittance is evaluated and subtracted from the photon current energy. This procedure reduces the number of photons required to produce a given accuracy, which makes it possible to store all event positions and energies. In the second stage, called the information processor, the results of the first stage are used to calculate analytically any desired result. Examples are given for scattering slabs of isotropic or anisotropic scatterers when collimated-beam incidence is used. Reflections at the boundaries are taken into account. The results obtained either with this new method or with classical Monte Carlo methods are very similar. However, the convergence of our new model is much better and, because of the separation into two stages, any quantity related to the problem can be easily calculated afterward without recomputing the simulation.

Equivalence of four Monte Carlo methods for photon migration in turbid media

Journal of the Optical Society of America A, 2012

In the field of photon migration in turbid media, different Monte Carlo methods are usually employed to solve the radiative transfer equation. We consider four different Monte Carlo methods, widely used in the field of tissue optics, that are based on four different ways to build photons' trajectories. We provide both theoretical arguments and numerical results showing the statistical equivalence of the four methods. In the numerical results we compare the temporal point spread functions calculated by the four methods for a wide range of the optical properties in the slab and semi-infinite medium geometry. The convergence of the methods is also briefly discussed.

Comparative analysis of discrete and continuous absorption weighting estimators used in Monte Carlo simulations of radiative transport in turbid media

Journal of the Optical Society of America A, 2014

We examine the relative error of Monte Carlo simulations of radiative transport that employ two commonly used estimators that account for absorption differently, either discretely, at interaction points, or continuously, between interaction points. We provide a rigorous derivation of these discrete and continuous absorption weighting estimators within a stochastic model that we show to be equivalent to an analytic model, based on the radiative transport equation (RTE). We establish that both absorption weighting estimators are unbiased and, therefore, converge to the solution of the RTE. An analysis of spatially resolved reflectance predictions provided by these two estimators reveals no advantage to either in cases of highly scattering and highly anisotropic media. However, for moderate to highly absorbing media or isotropically scattering media, the discrete estimator provides smaller errors at proximal source locations while the continuous estimator provides smaller errors at distal locations. The origin of these differing variance characteristics can be understood through examination of the distribution of exiting photon weights.

Multipurpose Monte Carlo simulator for photon transport in turbid media

2009 Ieee Nuclear Science Symposium Conference Record, Vols 1-5, 2009

Monte Carlo methods provide a flexible and rigorous solution to the problem of light transport in turbid media, which enable approaching complex geometries for a closed analytical solution is not feasible. The simulator implements local rules of propagation in the form of probability density functions that depend on the local optical properties of the tissue.

Monte Carlo modeling of light propagation in highly scattering tissues. I. Model predictions and comparison with diffusion theory

1989

Abstruct-Using optical interaction coefficients typical of mammalian soft tissues in the red and near infrared regions of the spectrum, calculations of fluence-depth distributions, effective penetration depths and diffuse reflectance from two models of radiative transfer, diffusion theory, and Monte Carlo simulation are compared for a semi-infinite medium. The predictions from diffusion theory are shown to be increasingly inaccurate as the albedo tends to zero andlor the average cosine of scatter tends to unity.

Monte Carlo methods for light propagation in biological tissues

Mathematical biosciences, 2015

Light propagation in turbid media is driven by the equation of radiative transfer. We give a formal probabilistic representation of its solution in the framework of biological tissues and we implement algorithms based on Monte Carlo methods in order to estimate the quantity of light that is received by a homogeneous tissue when emitted by an optic fiber. A variance reduction method is studied and implemented, as well as a Markov chain Monte Carlo method based on the Metropolis-Hastings algorithm. The resulting estimating methods are then compared to the so-called Wang-Prahl (or Wang) method. Finally, the formal representation allows to derive a non-linear optimization algorithm close to Levenberg-Marquardt that is used for the estimation of the scattering and absorption coefficients of the tissue from measurements.

Monte Carlo Procedure for Investigating Light Propagation and Imaging of Highly Scattering Media

Applied Optics, 1998

A Monte Carlo procedure has been developed to study photon migration through highly scattering nonhomogeneous media. When two scaling relationships are used, the temporal response when scattering or absorbing inhomogeneities are introduced can be evaluated in a short time from the results of only one simulation carried out for the homogeneous medium. Examples of applications to the imaging of defects embedded into a diffusing slab, a model usually used for optical mammography, are given. Comparisons with experimental results show the correctness of the results obtained.