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.
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.
For more than a century, the diffraction limit has defined the resolution achievable by passive optical imaging systems. Although some resolution improvement can be gained through classical data processing of the image, it is limited by the noise arising from quantum nature of light. Minimizing the effect of this noise requires quantum treatment of optical imaging. By reformulating imaging as a problem of quantum measurement and estimation, it becomes possible to identify optimal detection strategies that recover spatial information previously thought inaccessible. This review summarizes the theoretical framework that underpins this development, from the formulation of quantum Cramer-Rao bounds and Chernoff bounds to the construction of receivers that attain them, such as those based on spatial-mode demultiplexing. We show how these methods can beat conventional imaging in the classification, localization, and imaging of sub-Rayleigh incoherent sources. We then discuss extensions to multiparameter and partially coherent scenarios, and highlight the unifying connections between estimation and discrimination tasks. Finally, we survey recent experimental demonstrations that approach quantum-limited resolution and outline emerging applications in microscopy, astronomy, and optical sensing.
Optical precision measurement is evolving from conventional intensity and phase readout toward a paradigm centered on mode selection, statistical estimation, and information extraction. Conventional intensity- and phase-based schemes can achieve high sensitivity, but their performance is often constrained by finite-aperture diffraction, reference stability, optical path control, and environmental perturbations in systems. Quantum estimation theory provides a physical framework for optical resolution and measurement precision by optimizing the measurement basis. Inspired by spatial mode demultiplexing, this paper extends quantum parameter estimation from incoherent point-source resolution to small-displacement measurement. Metasurface enabled mode control converts displacement induced optical-field variations into measurable changes in orthogonal modal coefficients, providing a route for extracting sub-diffraction-scale displacement information. This paper introduces Rayleigh’s curse, Fisher information, and spatial mode projection, discusses their applications in one-dimensional displacement measurement and two-dimensional super-resolution imaging, and outlines future directions in digital optics, Engineering Optics 2.0, mode-basis optimization, two-dimensional information reconstruction, and intelligent optical measurement systems for engineering applications.
Far-field optical imaging inevitably involves low-pass spatial filtering, limiting the resolution. Moreover, conventional imaging suppresses high spatial frequency components close to the cutoff, making them invisible under noise, particularly the shot noise arising from discrete and random nature of quantum light. Here we propose and implement a method for reducing the effect of this noise by optically pre-processing the incoming light prior to detection, thereby optimizing the quantum measurement performed on it. Our scheme, termed Fourier Domain Division (FDD), partitions the Fourier plane into multiple regions for independent detection and subsequent post-processing for image reconstruction. By analyzing the quantum and classical Fisher information, we show that our method is advantageous with respect to direct imaging for high spatial-frequency components. As a result, the number of photons required to achieve a certain signal-to-noise-ratio in the Fourier domain is reduced, thus enhancing the overall resolution in the photon-starved regime. We demonstrate our method in microscopy, achieving 5-fold improvement of Fisher information on high spatial-frequency components. Unlike active super-resolution methods, FDD is passive, making it broadly applicable in microscopy and other imaging scenarios where active illumination is impractical, including astronomy and remote sensing. Our work establishes a general strategy for designing quantum optimized superresolution imaging systems, bridging fundamental quantum limits, practical image analysis and computer vision applications.
Imaging systems measuring intensity in the far field succumb to Rayleigh's curse, a resolution limitation dictated by the finite aperture of the optical system. Many proof-of-principle and some two-dimensional imaging experiments have shown that, by using spatial mode demultiplexing (SPADE), the field information collected is maximal, and, thus, the resolution increases beyond the Rayleigh criterion. Hitherto, the SPADE approaches are based on resolving the lateral splitting of a Gaussian wave function. Here, we consider the case in which the light field originates from a biphoton source, i.e., spontaneous parametric down-conversion, and a horizontal separation is introduced in one of the two photons. We show that a separation induced in the signal photon arm can be superresolved using coincidence measurements after projecting both photons on Hermite-Gauss modes. Remarkably, the Fisher information associated with the measurement is enhanced compared to the ordinary SPADE techniques by K, where K is the Schmidt number of the two-photon state that quantifies the amount of spatial entanglement between the two photons.
Optical measurements that can achieve the fundamental quantum limits have the potential to improve the imaging of subdiffraction objects in important applications, including optical astronomy and fluorescence microscopy. Working towards the goal of implementing such quantum-inspired measurements for real applications, we experimentally demonstrate the localization of two incoherent optical point sources and the semiparametric estimation of object moments in the subdiffraction regime via spatial-mode demultiplexing (SPADE). In the case of two sources, we are able to estimate both of their locations accurately, not just their separation, by exploiting the asymmetric response of our SPADE device. In the case of semiparametric estimation, we demonstrate that, even if the source number is unknown, the moments of the source distribution can still be estimated accurately. Our demonstration paves the way towards the use of SPADE for optical superresolution in practical scenarios, where adaptive measurements are difficult and many parameters are unknown.
Abstract We analyze the fundamental quantum limit of the resolution of an optical imaging system from the perspective of the detection problem of deciding whether the optical field in the image plane is generated by one incoherent on-axis source with brightness ϵ ϵ or by two ϵ/2 ϵ ∕ 2 -brightness incoherent sources that are symmetrically disposed about the optical axis. Using the exact thermal-state model of the field, we derive the quantum Chernoff bound for the detection problem, which specifies the optimum rate of decay of the error probability with increasing number of collected photons that is allowed by quantum mechanics. We then show that recently proposed linear-optic schemes approach the quantum Chernoff bound—the method of binary spatial-mode demultiplexing (B-SPADE) is quantum-optimal for all values of separation, while a method using image inversion interferometry (SLIVER) is near-optimal for sub-Rayleigh separations. We then simplify our model using a low-brightness approximation that is very accurate for optical microscopy and astronomy, derive quantum Chernoff bounds conditional on the number of photons detected, and show the optimality of our schemes in this conditional detection paradigm. For comparison, we analytically demonstrate the superior scaling of the Chernoff bound for our schemes with source separation relative to that of spatially resolved direct imaging. Our schemes have the advantages over the quantum-optimal (Helstrom) measurement in that they do not involve joint measurements over multiple modes, and that they do not require the angular separation for the two-source hypothesis to be given a priori and can offer that information as a bonus in the event of a successful detection.