This monograph explores advanced methodologies in quantum parameter estimation, with a particular focus on sub-Rayleigh imaging for incoherent point sources, building on the foundational work of Tsang, Nair, and Lu in "Quantum Theory of Superresolution for Two Incoherent Optical Point Sources" \cite{Tsang2016Quantum}. We thoroughly review and verify existing research, exploring the limitations of classical imaging techniques and highlighting strategies that rely on quantum optics principles to improve resolution and accuracy. Employing the Estimation Theory as a framework, we examine the efficiency of different measurements. Finally, the research results indicate that the use of spatial mode demultiplexing in the Hermite-Gauss basis functions substantially enhances the precision of estimating the separations in two point sources imaging systems. This work aims to contribute to the theoretical understanding of quantum parameter estimation.
This monograph explores advanced methodologies in quantum parameter estimation, with a particular focus on sub-Rayleigh imaging for incoherent point sources, building on the foundational work of Tsang, Nair, and Lu in "Quantum Theory of Superresolution for Two Incoherent Optical Point Sources" \cite{Tsang2016Quantum}. We thoroughly review and verify existing research, exploring the limitations of classical imaging techniques and highlighting strategies that rely on quantum optics principles to improve resolution and accuracy. Employing the Estimation Theory as a framework, we examine the efficiency of different measurements. Finally, the research results indicate that the use of spatial mode demultiplexing in the Hermite-Gauss basis functions substantially enhances the precision of estimating the separations in two point sources imaging systems. This work aims to contribute to the theoretical understanding of quantum parameter estimation.
Due to the wave nature of light, optical imaging is inherently subject to diffraction, which typically dictates the resolution limit for two-point sources. A practical way to describe this phenomenon is through Rayleigh’s criterion, which states that two sources are barely resolvable when the minimum of one source's diffraction pattern coincides with the maximum of the other. However, recent advances in optical quantum metrology have shown that this classical limit can be surpassed by leveraging the spatial correlations within the light field. Specifically, decomposing the light into a Hermite-Gauss mode basis provides substantially more information than traditional direct imaging, which measures local intensity [1,2,3]. In this work, we implement a spatial demultiplexing technique to estimate the separation between light sources of unequal brightness. This unknown imbalance adds complexity to the estimation task, making it inherently a multiparameter problem and thus requiring a multimode approach [4]. By optimizing the measurement strategy and introducing a shift between two demultiplexers, we achieve sub-Rayleigh resolution in distance measurements without assuming prior knowledge of the intensity imbalance or alignment. [1] Tsang, M., Nair, R., & Lu, X. M. (2016). Quantum theory of superresolution for two incoherent optical point sources. Physical Review X, 6(3), 031033. [2] Sorelli, G., Gessner, M., Walschaers, M., & Treps, N. (2021). Optimal observables and estimators for practical superresolution imaging. Physical Review Letters, 127(12), 123604. [3] Rouvière, C., Barral, D., Grateau, A., Karuseichyk, I., Sorelli, G., Walschaers, M., & Treps, N. (2024). Ultra-sensitive separation estimation of optical sources. Optica, 11(2), 166-170. [4] Řeháček, J., Hradil, Z., Koutný, D., Grover, J., Krzic, A., & Sánchez-Soto, L. L. (2018). Optimal measurements for quantum spatial superresolution. Physical review A, 98(1), 012103.
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-metrology-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.
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.
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-metrology-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. Analyzing 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.
Estimation de paramètre expérimentale dans les images incohérentes par décomposition en modes spatiaux La résolution des systèmes d'imagerie optique a été historiquement limitée par la diffraction et la limite de Rayleigh a longtemps été considérée comme insurmontable. Des techniques de super-résolution ont été développées pour aller au-delà de cette limite, mais elles sont adaptées spécifiquement à chaque contexte et atteindre une résolution sub-Rayleigh demeure très difficile. En examinant les problèmes d'imagerie à travers le prisme de la théorie d'estimation de paramètre, il est possible de comprendre les contraintes intrinsèques aux approches traditionnelles de super-résolution et de déterminer une méthode optimale, basée sur la détection d'intensité dans la base de modes d'Hermite-Gauss. Dans cette thèse, nous avons mis en place cette approche fournie par la métrologie quantique pour estimer la séparation entre deux sources incohérentes et nous avons atteint une sensibilité cinq ordres de grandeur au-delà du critère de Rayleigh. Avec notre dispositif expérimental, basé sur un démultiplexeur en modes spatiaux, nous avons étudié des scènes avec des sources à haut et bas flux de photons. En portant une attention particulière à l'exactitude et à la sensibilité des mesures, nous démontrons que le démultiplexage en modes spatiaux est particulièrement adapté pour effectuer des estimations de séparations sub-Rayleigh. Ce travail ouvre la voie à l'amélioration de la sensibilité des mesures dans des scènes optiques plus complexes se rapprochant de réelles situations d'imagerie.