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Optics Communications

Quantum theory of super-resolution for optical systems with circular apertures

Mikhail I. Kolobov, Vladislav N. Beskrovnyy

Published Mar 1, 2006• 19 citations
Publisher
DOI
10.1016/j.optcom.2006.02.019

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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.
Heisenberg’s uncertainty principle tells us that it is impossible to determine simultaneously the position of a photon crossing a telescope’s aperture and its momentum. Super-resolution imaging techniques rely on modification of the observed sample or on entangling photons. In astronomy, we have no access to the object, but resolution may be improved by optical amplification. Unfortunately, spontaneous emission contributes noise and negates the possible gain from stimulated emissions. We show that it is possible to increase the weight of the stimulated photons by considering photon statistics and observe an improvement in resolution. Most importantly, we demonstrate a method that can apply for all imaging purposes.