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Title:
Abstract:
Quantum information theory has opened a new paradigm in the field of optical imaging, establishing the narrative that pre-processing the information bearing light following a quantum optimal detection strategy can achieve the fundamental performance limit. In this dissertation, we apply this narrative to study two important imaging areas : (1) passive optical superresolution imaging and (2) beam-displacement active optical sensing.
Over the past decade, passive optical superresolution imaging has been extensively studied using the canonical problem of resolving two incoherent point sources. Direct detection suffers from Rayleigh’s curse when the separation goes below the Rayleigh criterion, whereas performing Spatial Mode Demultiplexing (SPADE), a quantum optimal detection strategy, gets rid of this curse, refuting Rayleigh’s minimum resolution formula. SPADE is built with multiple stratified phase masks in a multi-plane light-conversion (MPLC) setup. In the first part of this dissertation, we study how placing a single-phase mask at the pupil plane of an imaging system can affect its resolution under direct detection. We use the Classical Fisher Information (CFI) as the information metric to quantify the performance of separation estimation. Also known as PSF Engineering, we find that while this method improves the small-separation Fisher Information scaling for Gaussian PSFs (a zero-less PSF), it is not able to do the same for PSFs with zeros (Sinc PSF/hard aperture). We also study this behavior from the perspective of hypothesis testing between one versus two-point sources and derive the Bhattacharyya exponent. After this, we explore sparse aperture configurations for the hypothesis test between one versus two-point source discrimination problem. We also analyze the separation estimation problem under atmospheric turbulence and low-order wavefront correction to study the robustness of direct detection and BSPADE (Binary SPADE) performance. The atmospheric turbulence is realized using phase masks. We find that under low to moderate turbulence, BSPADE offers an advantage over direct detection measurement. We also present a Photomagnetically actuated deformable mirror (PMADM) design which can be useful for low-order wavefront correction.
In the second part of the thesis, we study coherent beam displacement sensing, an active optical sensing problem. We study a free-space propagation channel with soft Gaussian apertures that supports Hermite–Gaussian (HG) modes, with the relative displacement between the apertures representing the change to be detected. Classical relative entropy (CRE) between the pre-change and post-change measurement distributions is used as the performance metric as a larger relative entropy corresponds to a shorter asymptotic change detection delay. We show that coherent probe and mode engineering strategies can increase this relative entropy and thereby reduce detection latency. In particular, we compare an optimized classical coherent probe with a spray-painted probe in which a small quantum resource (squeezing) is distributed across an optimized coherent spatial mode. We evaluate the performance using the CRE between the probability distributions of the pre-change and post-change states produced by phase matched homodyne detection.
Together, these results support a unified view of pre-processing the information bearing light and using it for optical superresolution and optical sensing purposes. The dissertation explores methods such as PSF, aperture, and modal engineering, which can find applications ranging from astronomy and microscopy to optomechanical sensing.
Committee:
Dr. Dal Wilson (Co-Chair)