Conventional superresolution of closely spaced point sources using image intensity data acquired by noiseless single-photon detectors suffers from Rayleigh’s diffraction curse that can only be overcome at photon numbers that scale quartically with the degree of required superresolution. By contrast, acquiring and processing suitably chosen mode projections of the wavefront, which contain dual information of its intensity and phase, can reduce the photon budget to one that is quadratic in the degree of superresolution and achieve quantum-limited performance. Such dramatic improvements enabled by the wavefront projection (WFP) approach have been realized both in computer simulation and laboratory experiments over the last five years. The invited talk will explore the fundamental, theoretically insuperable limits on superresolution imaging by presenting computations of quantum Fisher information and practical realizations of the novel WFP approach that can reach these limits for a variety of point and extended source geometries and operating conditions.
Conventional superresolution of closely spaced point sources using image intensity data acquired by noiseless single-photon detectors suffers from Rayleigh’s diffraction curse that can only be overcome at photon numbers that scale quartically with the degree of required superresolution. By contrast, acquiring and processing suitably chosen mode projections of the wavefront, which contain dual information of its intensity and phase, can reduce the photon budget to one that is quadratic in the degree of superresolution and achieve quantum-limited performance. Such dramatic improvements enabled by the wavefront projection (WFP) approach have been realized both in computer simulation and laboratory experiments over the last five years. The invited talk will explore the fundamental, theoretically insuperable limits on superresolution imaging by presenting computations of quantum Fisher information and practical realizations of the novel WFP approach that can reach these limits for a variety of point and extended source geometries and operating conditions.
Superresolution has been demonstrated to overcome the limitation of Rayleigh's criterion and achieve significant precision improvement in resolving the separation of two incoherent optical point sources. However, in recent years, it was found that, if the photon numbers of two incoherent optical sources are unknown, the precision of superresolution vanishes when the photon numbers are actually different. In this work, we first analyze in detail the estimation precision of the separation for two incoherent optical sources with the same point-spread functions and show that, when the two photon numbers are different but sufficiently close, the superresolution can still be realized but with different precisions. We find the condition on how close the photon numbers need to be to realize the superresolution and derive the precision of superresolution in different regimes of the photon number difference. We further consider the superresolution for two incoherent optical sources with different point-spread functions and show that the competition between the difference of photon numbers, the difference of point-spread functions, and the separation of source locations determines the precision of superresolution. The results exhibit precision limits distinct from that of two identical point-spread functions with equal photon numbers and extend the realizable regimes of quantum superresolution. Finally, the results are illustrated by Gaussian point-spread functions. Published by the American Physical Society 2024
Super-resolution imaging holds a solid place in biological and chemical sciences, but many new developments allow the beating of diffraction (Rayleigh) limit in better and more subtle ways. The modern understanding of the Rayleigh limit comes from information theory where it is identified as vanishing information about the separation of two sources for small separations - the Rayleigh curse. The surprising observation [1] that the quantum Cramer-Rao bound (CRB), which identifies maximum information available in the optical field, does not vanish even for zero separation, led to so-called quantum-inspired superresolution methods that suggest to fully exploit information already present in the field by performing tailored measurements [1]. Such an approach is starkly different approach compared with methods relying on nonlinear processes such as STED or specific emission statistics.
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.
Historically, the resolution of optical imaging systems was dictated by diffraction, and the Rayleigh criterion was long considered an unsurpassable limit. In superresolution microscopy, this limit is overcome by manipulating the emission properties of the object. However, in passive imaging, when sources are uncontrolled, reaching sub-Rayleigh resolution remains a challenge. Here, we implement a quantum-metrolgy-inspired approach for estimating the separation between two incoherent sources, achieving a sensitivity five orders of magnitude beyond the Rayleigh limit. Using a spatial mode demultiplexer, we examine scenes with bright and faint sources, through intensity measurements in the Hermite-Gauss basis. Analysing sensitivity and accuracy over an extensive range of separations, we demonstrate the remarkable effectiveness of demultiplexing for sub-Rayleigh separation estimation. These results effectively render the Rayleigh limit obsolete for passive imaging.
The optical diffraction limit, formulated by Abbe 140 years ago, imposes a bound on imaging resolution in classical optics. Over the last twenty years, many theoretical schemes have been presented for overcoming the diffraction barrier in optical imaging using quantum properties of light. An experimental realization of sub-diffraction limited quantum imaging has, however, remained elusive. Here, we demonstrate a quantum imaging method taking advantage of non-classical light naturally produced in fluorescence microscopy due to photon antibunching, a fundamentally quantum phenomenon prohibiting simultaneous emission of multiple photons. Using a photon counting digital camera, we detect antibunching-induced second and third order intensity correlations and perform sub-diffraction limited quantum imaging in a standard wide-field fluorescence microscope.
The "Rayleigh limit" is not an intrinsic property of light, but a consequence of sub-optimal measurement of collected photons by the imaging instrument. To overcome this limitation, we present Adaptive Information Mining, a framework that achieves super-resolution by using sequentially refined measurements for incoming photons. Our approach employs a reconfigurable imaging system that dynamically reshapes the instrument measurement responses to maximize the Fisher information and guide scene estimation toward the fundamental quantum limit, even in deep sub-Rayleigh regimes. We demonstrate that this approach achieves an estimation error 2-5 times closer to the fundamental quantum limit than traditional direct imaging when imaging point sources, without requiring any prior knowledge of their positions and brightnesses. Importantly, we demonstrate that AIM can be extended to fully blind multi-parameter estimation in scenarios involving an unknown number of sources or turbulence-induced wavefront distortions. Our approach addresses the limitations of conventional fixed imaging, offering a practical path toward quantum-limited super-resolution imaging.