Precision bounds in localization microscopy

Abstract

This thesis presents two independent studies in theoretical and experimental optical imaging. The first part investigates the theoretical limits and simulation of Single-Pixel Localization Microscopy (SPLM), a computational imaging technique that employs spatio-temporally modulated (STM) illumination to enable sub-diffraction localization with a single-pixel detector. To quantitatively assess the performance of SPLM, we analyze the localization precision limit using the Cramér-Rao Lower Bound (CRLB) under shot-noise-limited conditions. To account for discrepancies between the assumed and actual imaging models —-- such as those caused by optical aberrations —-- we further introduce the Misspecified Cramér-Rao Bound (MCRB), which quantifies changes in estimation precision limit under model mismatch. These theoretical tools establish performance limits and characterize the robustness of SPLM to experimental imperfections. Following these analyses, we simulate photon detection from fluorescent emitters via Binomial point processes and perform localization on a discrete grid using Fast Iterative Shrinkage-Thresholding Algorithm (FISTA), with further refinement via a BFGS-based line search method, assuming an accurate forward model. The second part of the thesis reports the experimental development of Quantitative Scattering Microscopy (QSCAT), a label-free phase imaging technique designed for in situ materials characterization. The system employs a digital light processing (DLP) device and LED illumination to project half pupil patterns onto the back aperture of an objective, enabling differential phase contrast imaging. The recorded intensity measurements are inverted to recover the quantitative phase of the sample, providing optical susceptibility information. We demonstrate the utility of QSCAT by measuring the height of chromium features on a USAF resolution target. Additionally, we incorporate a convolutional neural network (CNN) for phase retrieval, representing a novel integration of learning-based reconstruction into scattering-based microscopy.