# Algorithm for rapid determination of optical scattering parameters

Published: October 18, 2017

### 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
Pub Type: Journals