Samuel J. Grauer

Bayesian approach to the design of chemical species tomography experiments.

Reconstruction accuracy in chemical species tomography depends strongly on the arrangement of optical paths transecting the imaging domain. Optimizing the path arrangement requires a scheme that can predict the quality of a proposed arrangement prior to measurement. This paper presents a new Bayesian method for scoring path arrangements based on the estimated a posteriori covariance matrix. This technique focuses on defining an objective function that incorporates the same a priori information about the flow needed to carry out limited data tomography. Constrained and unconstrained path optimization studies verify the predictive capabilities of the objective function, and that superior reconstruction quality is obtained with optimized path arrangements.

General error model for analysis of laser-induced incandescence signals.

This paper presents a novel error model for TiRe-LII signals and illustrates how the model can be used to diagnose a detection system, quantify uncertainties in TiRe-LII, and characterize fluctuations in the measured process. Noise in a single TiRe-LII measurement shot obeys a Poisson-Gaussian noise model. Variation in the aerosol results in shot-to-shot fluctuations in the measured signals. These fluctuations induce a quadratic relationship between the mean and variance of a set of signals. We show how this model can elucidate aspects of the measurement system and fundamental properties of the aerosol, by comparing the noise model to four sets of experimental data.

Measurement-based meshing, basis selection, and prior assignment in chemical species tomography

Gas distributions imaged by chemical species tomography (CST) vary in quality due to the discretization scheme, arrangement of optical paths, errors in the measurement model, and prior information included in reconstruction. There is currently no mathematically-rigorous framework for comparing the finite bases available to discretize a CST domain. Following from the Bayesian formulation of tomographic inversion, we show that Bayesian model selection can identify the mesh density, mode of interpolation, and prior information best-suited to reconstruct a set of measurement data. We validate this procedure with a simulated CST experiment, and generate accurate reconstructions despite limited measurement information. The flow field is represented using the finite element method, and Bayesian model selection is used to choose between three forms of polynomial support for a range of mesh resolutions, as well as four priors. We show that the model likelihood of Bayesian model selection is a good predictor of reconstruction accuracy.

Predicting the heat of vaporization of iron at high temperatures using time-resolved laser-induced incandescence and Bayesian model selection

Competing theories have been proposed to account for how the latent heat of vaporization of liquid iron varies with temperature, but experimental confirmation remains elusive, particularly at high temperatures. We propose time-resolved laser-induced incandescence measurements on iron nanoparticles combined with Bayesian model plausibility, as a novel method for evaluating these relationships. Our approach scores the explanatory power of candidate models, accounting for parameter uncertainty, model complexity, measurement noise, and goodness-of-fit. The approach is first validated with simulated data and then applied to experimental data for iron nanoparticles in argon. Our results justify the use of Romans equation to account for the temperature dependence of the latent heat of vaporization of liquid iron.