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Asilomar Conference on Signals, Systems and Computers (ACSSC)

Robust Adaptive Quantum-Limited Super-Resolution Imaging

Tianrui Tan, Kwan Kit Lee, Amit Ashok, Animesh Datta, Boulat A. Bash

Published Oct 31, 2022• 2 citations
Publisher

Abstract

Inspired by the results from quantum information processing, spatial-mode demultiplexing offers resolution of objects at the quantum limit, below the well-known Rayleigh-Abbe diffraction limit. An intriguing aspect of these results is that, while the analysis leading to the ultimate sub-diffraction limit is quantum, semi-classical devices can be used to build “super-resolving” sensors that achieve this limit. Therefore, these developments have potential to significantly improve the quality of imaging systems in the near term. However, these quantum-inspired systems are sensitive to fluctuation in nuisance parameters, whether they are natural or adversarial. In this paper we analyze the impact of such fluctuations and provide methods to mitigate it. We focus on a problem of resolving two point sources, which has immediate practical applications in, e.g., space situation awareness.

DOI
10.1109/ieeeconf56349.2022.10052064

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Inspired by the results from quantum information processing, spatial-mode demultiplexing offers resolution of objects at the quantum limit, below the well-known Rayleigh-Abbe diffraction limit. An intriguing aspect of these results is that, while the analysis leading to the ultimate sub-diffraction limit is quantum, semi-classical devices can be used to build “super-resolving” sensors that achieve this limit. Therefore, these developments have potential to significantly improve the quality of imaging systems in the near term. However, these quantum-inspired systems are sensitive to fluctuation in nuisance parameters, whether they are natural or adversarial. In this paper we analyze the impact of such fluctuations and provide methods to mitigate it. We focus on a problem of resolving two point sources, which has immediate practical applications in, e.g., space situation awareness.
We investigate analytically and numerically the role of quantum fluctuations in reconstruction of optical objects from diffraction-limited images. Taking as example of an input object two closely spaced Gaussian peaks, we demonstrate that one can improve the resolution in the reconstructed object over the classical Rayleigh limit. We show that the ultimate quantum limit of resolution in such a reconstruction procedure is determined not by diffraction but by the signal-to-noise ratio in the input object. We formulate a quantitative measure of super-resolution in terms of the optical point-spread function of the system.
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.
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.
Resolving sources beyond the diffraction limit is important in imaging, communications, and metrology. Current image-based methods of super-resolution require phase information (either of the source points or an added filter) and perfect alignment with the centroid of the object. Both inhibit the practical application of these methods, as uniform motion and/or relative jitter destroy their assumptions. Here, we show that measuring intensity in the Fourier plane enables super-resolution without any of the issues of image-based methods. We start with the shift-invariance of the Fourier transform and the observation that the two-point position problem x1,x2{x_1,x_2}x1​,x2​ in the near field corresponds to the single-point wavenumber problem k =2π/(x2−x1)k\ =2π/(x_2-x_1)k =2π/(x2​−x1​) in the far field. We consider the full range of mutual coherence and show that for fully coherent sources, the Fourier method saturates the quantum limit, i.e. it gives the best possible measurement. Similar results hold for sub-Rayleigh constellations of NNN sources, which can act collectively as a spatially averaged metasurface and/or individually as elements of a phased-array antenna. The theory paves the way to merge Fourier optics with super-resolution techniques, enabling experimental devices that are both simpler and more robust than previous designs.
Discriminating two spatially separated sources is one of the most fundamental problems in imaging.Recent research based on quantum parameter estimation theory shows that the resolution limit of two incoherent point sources given by Rayleigh can be broken.However, in realistic optical systems, there often exists coherence in the imaging light field, and there have been efforts to analyze the optical resolution in the presence of partial coherence.Nevertheless, how the degree of coherence between two point sources affects the resolution has not been fully understood.Here, we analyze the quantum-limited resolution of two partially coherent point sources by explicitly relating the state after evolution through the optical systems to the coherence of the sources.In particular, we consider the situation in which coherence varies with the separation.We propose a feasible experiment scheme to realize the nearly optimal measurement, which adaptively chooses the binary spatial-mode demultiplexing measurement and direct imaging.Our results will have wide applications in imaging involving coherence of light.