Quantum Limits and Optimal Receivers for Passive Sub-Diffraction Imaging

Abstract

Superresolution imaging provides insight into physical systems that are smaller or more distant than conventional imaging techniques can possibly allow. For more than 100 years, the canonical theory of diffraction in image science has upheld strict limits below which unavoidable quantitative error will make high-precision, far-field, passive imaging impossible. Surprisingly, recent work has emphatically shown that these diffraction limits are \emph{not} in fact fundamental and can be \emph{directly} broken in many cases. This was theoretically proven by modeling the classical light available to an optical receiver as a quantum state, enabling powerful theoretical analyses of the optimal sensing precision among all measurements that obey the laws of physics. Such analyses revealed that conventional measurements fail to efficiently extract all of the information that is available in the collected light. Breakthrough theoretical and experimental work has subsequently shown that alternative ``quantum-inspired" measurements can provide greatly improved sensitivity to sub-diffraction spatial scene features. In this dissertation, I present new evidence that this quantum-inspired sensing approach could yield large benefits for new passive, sub-diffraction optical imaging technologies. I have expanded the study of quantum-inspired superrresolution imaging along three directions. First, my work broadened the scope of quantitative imaging tasks that can be addressed by quantum-inspired methods. My theoretical calculations show notable performance improvements over conventional methods, approaching or obtaining the ultimate performance limits set by quantum mechanics, for localizing the centroid of an object, estimating the separation between sources that emit broadband radiation, and, most generally, identifying an object from \emph{any} known library of candidates. Second, I developed two of the first adaptive measurement schemes for quantum-inspired superresolution imaging that are robust against nonidealities such as receiver misalignment, excess detector noise, and optical background, demonstrating via simulations that updating the measurements being made during an acquisition can enhance precision, reduce integration times, and augment imaging range. Third, I designed and built the first fully reconfigurable spatial-mode-sorting system that will execute proof-of-principle demonstrations to provide key experimental validation of the quantitative benefits of adaptive superresolution imaging protocols. In addition, I highlight fundamental theoretical results I discovered in the course of my study of the quantum limits of superresolution imaging that have already proven useful both for imaging research and to the broader quantum information science community.