Novel Applications Using Maximum-Likelihood Estimation in Optical Metrology and Nuclear Medical Imaging: Point-Diffraction Interferometry and BazookaPET

Abstract

This dissertation aims to investigate two different applications in optics using maximum-likelihood (ML) estimation. The first application of ML estimation is used in optical metrology. For this application, an innovative iterative search method called the synthetic phase-shifting (SPS) algorithm is proposed. This search algorithm is used for estimation of a wavefront that is described by a finite set of Zernike Fringe (ZF) polynomials. In this work, we estimate the ZF coefficient, or parameter values of the wavefront using a single interferogram obtained from a point-diffraction interferometer (PDI). In order to find the estimates, we first calculate the squared-difference between the measured and simulated interferograms. Under certain assumptions, this squared-difference image can be treated as an interferogram showing the phase difference between the true wavefront deviation and simulated wavefront deviation. The wavefront deviation is defined as the difference between the reference and the test wavefronts. We calculate the phase difference using a traditional phase-shifting technique without physical phase-shifters. We present a detailed forward model for the PDI interferogram, including the effect of the nite size of a detector pixel. The algorithm was validated with computational studies and its performance and constraints are discussed. A prototype PDI was built and the algorithm was also experimentally validated. A large wavefront deviation was successfully estimated without using null optics or physical phase-shifters. The experimental result shows that the proposed algorithm has great potential to provide an accurate tool for non-null testing. The second application of ML estimation is used in nuclear medical imaging. A high-resolution positron tomography scanner called BazookaPET is proposed. We have designed and developed a novel proof-of-concept detector element for a PET system called BazookaPET. In order to complete the PET configuration, at least two detector elements are required to detect positron-electron annihilation events. Each detector element of the BazookaPET has two independent data-acquisition channels. One of the detector channels is a 4 x 4 silicon photomultiplier (SiPM) array referred to as the SiPM-side. The SiPM-side is directly coupled to an optical window of the scintillator with optical grease. The other channel is a CCD-based gamma camera with an imaging intensifier called the Bazooka-side. Instead of coupling by direct contact like the SiPM-side, an F/1.4 lens pair is used for optical coupling. The scintillation light from the opposite optical window to the SiPM-side is imaged by the F/1.4 lens to the Bazooka-side. Using these two separate channels, we can potentially obtain high energy, temporal and spatial resolution data by associating the data outputs via several ML estimation steps. We present the concept of the system and the prototype detector element. In this work, we focus on characterizing individual detector channels, and initial experimental calibration results are shown along with preliminary performance-evaluation results. We also address the limitations and the challenges of associating the outputs of the two detector channels.