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Frontiers in Optics

Super-resolution of two unbalanced sources

Abdelali Sajia, Xiao‐Feng Qian

Published Jan 1, 2021• 0 citations
Publisher

Abstract

Estimation of arbitrary separations between two unbalanced point sources is studied by including the spatial property’s entangled partner. Super-resolution is shown to be achievable with high accuracy through finite values of Fisher information.
DOI
10.1364/fio.2021.jw7a.7

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When two point sources are separated by less than the Abbe-Rayleigh limit, conventional resolution methods fail to distinguish whether there is one source or two. Consequently, it becomes nearly impossible to resolve important relative properties of the two sources, such as mutual coherence, relative phase, and brightness contrast. In this regime, the incoming composite quantum signal must be treated as a single entity described by an overall quantum wave function. In this study, we explore the superresolution of such two-point sources by examining a special wave property, i.e., entanglement between spatial degree of freedom (DoF) and remaining DoFs (both internal and external). Remarkably, we find that increasing this inter-DoF entanglement enhances the precision of superresolution, as quantified by the quantum Fisher information (QFI) in single-parameter estimation. Moreover, we show that this entanglement reliably ensures a nonvanishing QFI in two-parameter estimation, highlighting its role as a valuable resource for quantum superresolution.
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The diffraction, or Rayleigh, limit was long thought to determine the ultimate resolving power of optical imaging devices. Using techniques from quantum statistical inference, Tsang et al. [1] demonstrated that this limit can be circumvented, and derived an alternative measurement strategy capable of resolving two incoherent point sources no matter how arbitrarily small their separation is. However, these measurements require perfect knowledge of the sources centroid position, and are extremely sensitive to any source of misalignment about this position [2] , [3] . In this work, we study the problem of super-resolution from a more global point of view.
Sub-diffraction-limit resolution, or superresolution, has been successfully demonstrated in recent theoretical and experimental studies for two equal-brightness and incoherent point sources. However, practical situations of either nonequal brightness (i.e., unbalancedness) or partial coherence are shown to have fatal effects on such superresolution. As a step towards resolving such issues, we consider the effects of both unbalancedness and a form of partial coherence (i.e., quantum state coherence) together by including an entangled degree of freedom of the two point sources. Unexpectedly, it is found that the two negative effects can counteraffect each other, thus permitting credible superresolution, when the measurement is analyzed in the entangled partner's rotated basis. The least resolvable non-zero two-source separation is also identified analytically. Our result represents useful guidance towards the realization of superresolution for practical point sources. The vector-structure analog of quantum and classical light sources also suggests that our analysis applies to both contexts.