Date of Award

Spring 5-5-2017

Level of Access

Campus-Only Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics

Advisor

Andre Khalil

Second Committee Member

David Bradley

Third Committee Member

Robert Niemeyer

Abstract

Standard numerical focusing and reconstruction of hologram time series for detailed 3D particle tracking is slow and computationally expensive. Motion detection and particle tracking is an unsolved problem in unreconstructed, off-axis holograms. This thesis proposes an automated wavelet-based method of tracking particles in unreconstructed, off-axis holograms, with the purpose of providing rough estimates of the presence of motion and particle trajectories in hologram time series.

The wavelet transform modulus maxima (WTMM) multifractal method is used to estimate background noise as a Hurst exponent 𝐻~ βˆ’ 0.04 in a real hologram time series. This is used to create hologram time series simulations for calibration purposes. A WTMM segmentation method is developed to extract Airy disks, which represent particles, from hologram time series. This method is run on simulations and extended to a real hologram time series. The method accurately tracks particle positions in the π‘₯𝑦-plane. Depth estimation works on some simulations, but breaks down in noisy real data.

Depth estimation may be improved by coupling the method in this thesis with phase demodulation methods. Particle density is limiting in this method as the desired closed chains are not found when the central lobes of Airy patterns overlap. Particle centroids can be stitched together using algorithms more robust to missed detections. The method proposed in this thesis shows potential for motion detection, and estimating particle tracks in low-particle- density time series or in time series where all tracks behave roughly the same.

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