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# Algorithm for rapid determination of optical scattering parameters

Published

### Author(s)

Zachary H. Levine, Adam L. Pintar, Richelle H. Streater, Anne-Michelle R. Lieberson, Catherine C. Cooksey, Paul Lemaillet

### Abstract

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$\cdot10^4$. The search area is iteratively reduced to include the {99.9999\percent} 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 2.56$\cdot10^6$ samples. The log-likelihood is then fit to determine a {95\percent} confidence ellipse. The inverse problem requires the values of the log likelihood on a large number of points. Our implementation uses importance sampling to calculate these points on a grid in an efficient manner. Ultimately, the time-to-solution is approximately three 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 about 100 times faster than our implementation of particle swarm optimization.
Citation
Optics Express
Volume
25
Issue
22

### Keywords

MCML , angle-resolved scattering , Monte Carlo , inverse problems
Created October 18, 2017, Updated January 27, 2020