• Photonics Research
  • Vol. 9, Issue 8, 08001522 (2021)
Ben Wang, Liang Xu, Jun-chi Li, and Lijian Zhang*
Author Affiliations
  • National Laboratory of Solid State Microstructures and College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
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    Abstract

    As a method to extract information from optical systems, imaging can be viewed as a parameter estimation problem. The fundamental precision in locating one emitter or estimating the separation between two incoherent emitters is bounded below by the multiparameter quantum Cramér-Rao bound (QCRB). Multiparameter QCRB gives an intrinsic bound in parameter estimation. We determine the ultimate potential of quantum-limited imaging for improving the resolution of a far-field, diffraction-limited optical field within the paraxial approximation. We show that the quantum Fisher information matrix (QFIm) in about one emitter’s position is independent on its true value. We calculate the QFIm of two unequal-brightness emitters’ relative positions and intensities; the results show that only when the relative intensity and centroids of two-point sources, including longitudinal and transverse directions, are known exactly, the separation in different directions can be estimated simultaneously with finite precision. Our results give the upper bounds on certain far-field imaging technology and will find wide use in applications from microscopy to astrometry.
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    Ben Wang, Liang Xu, Jun-chi Li, Lijian Zhang. Quantum-limited localization and resolution in three dimensions[J]. Photonics Research, 2021, 9(8): 08001522
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    Received: Dec. 16, 2020
    Accepted: May. 21, 2021
    Posted: Jun. 9, 2021
    Published Online: Jul. 22, 2021
    The Author Email: Lijian Zhang (lijian.zhang@nju.edu.cn)