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An MLE approach for measuring laser propagation axes, with uncertainty estimated through Monte-Carlo simulation

Program in Applied Mathematics Brown Bag Seminar

An MLE approach for measuring laser propagation axes, with uncertainty estimated through Monte-Carlo simulation
Series: Program in Applied Mathematics Brown Bag Seminar
Location: ONLINE
Presenter: Sheldon Deeny, Program in Applied Mathematics, University of Arizona

I will present an overview of the project I worked on this past summer for the Nevada National Security Site (NNSS). My mentors were Daniel J. Champion (UArizona Math PhD, 2011) and Marylesa Howard, senior scientists in the Signal Processing and Applied Mathematics group.  We applied the maximum likelihood estimator (MLE) approach to recover spatial parameters of individual laser beams emitted from an optical diagnostics probe. Determining which direction each of the 96 beams is pointing, as well as the location in space of the beam origin, is critical in collecting accurate measurements of multiple, high velocity target objects.  Under a specific geometric arrangement, in which the probe is shifted with respect to a reflective surface, an optical reflectometer is used to collect probe-to-surface distance data for each individual probe laser and each shift. We factor in the measurement uncertainty from this device and calculate the MLE for beam axis orientation and location for each probe. On our sample data set, this method resulted in an estimated beam axis with angular separation from ground truth of less than 1.7 degrees on average.  In order to determine the variance of the estimators, we used Monte-Carlo simulation to populate a sample distribution of recovered parameters. This resulted in a 0.07 degree standard deviation of angular separation from ground truth, averaged over the 96 beams.  I will conclude with my comments on the computational tools I used and the overall experience I had working for NNSS.