Preliminary experiments at the NIST Spectral Tri-function Automated Reference Reflectometer (STARR) facility have been conducted with the goal of providing the diffuse optical properties of a solid reference standard with optical properties similar to human skin. Here, we describe an algorithm for determining the best-fit parameters and the statistical uncertainty associated with the measurement. The objective function is determined from the profile log likelihood, including both experimental and Monte Carlo uncertainties. Initially, the log likelihood is determined over a large parameter search box using a relatively small number of Monte Carlo samples such as 2·104. The search area is iteratively reduced to include the 99.9999% confidence region, while doubling the number of samples at each iteration until the experimental uncertainty dominates over the Monte Carlo uncertainty. Typically this occurs by 1.28·106 samples. The log likelihood is then fit to determine a 95% confidence ellipse. The inverse problem requires the values of the log likelihood on many points. Our implementation uses importance sampling to calculate these points on a grid in an efficient manner. Ultimately, the time-to-solution is approximately six times the cost of a Monte Carlo simulation of the radiation transport problem for a single set of parameters with the largest number of photons required. The results are found to be 64 times faster than our implementation of Particle Swarm Optimization.
SummaryOur recent research on Monte Carlo simulation of light propagation in biomedical phantoms has involved the implementation of an algorithm to solve for the optical attenuation and scattering coefficients of a single-layer material, or µa and µs [1]. It also involved the development of a parallel version of MCML [2], a popular light propagation model with over 2100 citations, according to ScienceDirect. The algorithm for the inverse problem involves three components: a profile log-likelihood evaluation, importance sampling, and an optimization procedure. In this article, we present two C++/OpenMP codes: MCMLpar, the parallel version of MCML, and MCSLinv, a program to solve the inverse problem for a single layer.In MCMLpar, [3] a particle class is introduced to represent photons. The particles all enter an optical medium at the same point, travelling parallel to the vector normal to the surface. The particle weights are initially set to the probability of transmitting into the material, calculated by the Fresnel equation using the air and first layer indices of refraction. Each particle's path length to an interaction is calculated by sampling the exponential distribution with mean µt = µa + µs. If the interaction is within the layer, the particle's direction is updated by sampling the Henyey-Greenstein distribution for the polar angle θ relative to the direction of travel. The relative azimuthal angle φ is sampled uniformly on [0, 2π). The particle's
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