Date of Graduation

2017

Document Type

Thesis

Degree Type

MS

College

Statler College of Engineering and Mineral Resources

Department

Mechanical and Aerospace Engineering

Committee Chair

John A Christian

Committee Co-Chair

Jason Gross

Committee Member

Yu Gu

Abstract

Optical data from point sources of light plays a key role in systems from many different industries. In real optical systems, the photons from point sources are distributed in a pattern on the focal plane. This pattern is described by the Point Spread Function (PSF). Centroiding, defined here as calculating the center of a PSF, provides data that can subsequently be used in various state estimation problems. Thus, it is crucial to determine expected centroid accuracy so that uncertainty can be accounted for. Manufacturing defects and real-world effects affect the structure of a PSF. Much of this structure is often well-captured by the five classic optical aberrations. This thesis prevents a novel framework for simulating PSFs affected by optical aberrations, then uses this simulation to quantify the accuracy of various centroiding algorithms in the presence of optical aberrations. The method of PSF simulation leverages Johnson distributions, which is a method of simulating distributions as a function of the desired mean, variance, skewness, and kurtosis. This method is chosen because of the flexibility and ease-of-visualization it provides the analyst. In addition, the analytic true centers of the Johnson distributions have been derived for use in analysis as the true centroid. The three centroiding algorithms analyzed are the Center of Intensity (COI) algorithm, the Cross-Correlation (CC) algorithm, and the Model Matching (MM) algorithm. It is found that in the case of symmetric, Gaussian PSFs, all three algorithms find the true centroid exactly. However, performance deteriorates for an asymmetric PSF, especially for the CC and MM algorithm. This is because both of these algorithms assume a 2D Gaussian structure. When that assumption no longer holds, the algorithms do not perform as well. This work concludes that PSFs highly affected by asymmetric optical aberrations should expect lower centroiding accuracy when using the CC and MM algorithms.

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