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Conference on Lasers and Electro-Optics

Quantum-Optimal Binary Object Classification in Sub-Diffraction Incoherent Imaging

Michael R. Grace, Saikat Guha

Published Jan 1, 2021• 1 citation
Publisher

Abstract

We derive the quantum limit on average error for hypothesis tests between any two incoherent, diffraction-limited objects and identify quantum-optimal measurements that achieve a quadratic scaling improvement over direct imaging.
DOI
10.1364/cleo_qels.2021.fw3n.4

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We consider imaging tasks involving discrimination between known objects and investigate the best possible accuracy with which the correct object can be identified. Using the quantum Chernoff bound, we analytically find the ultimate achievable asymptotic error rate for symmetric hypothesis tests between \emph{any} two incoherent 2D objects when the imaging system is dominated by optical diffraction. Furthermore, we show that linear-optical demultiplexing of the spatial modes of the collected light exactly saturates this ultimate performance limit, enabling a quadratic improvement over the asymptotic error rate achieved by direct imaging as the objects become more severely diffraction-limited. We extend our results to identify the quantum limit and optimal measurement for discrimination between an arbitrary number of candidate objects. Our work constitutes a complete theoretical treatment of the ultimate quantitative limits on passive, sub-diffraction, incoherent object discrimination and is readily applicable to a multitude of real-world applications.
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The spatial resolution of an imaging apparatus is limited by the Rayleigh diffraction bound, a consequence of the imager's finite spatial extent. We show some NNN-photon strategies that permit resolution of details that are smaller than this bound, attaining either a 1∕N1∕\sqrt{N}1∕N​ enhancement (standard quantum limit) or a 1∕N1∕N1∕N enhancement (Heisenberg-like scaling) over standard techniques. In the incoherent imaging regime, the methods presented are loss resistant, since classical light sources suffice. Our results may be of importance in many applications: microscopy, telescopy, lithography, metrology, etc.
In a previous paper [M. Tsang, Phys. Rev. A 99, 012305 (2019)], I proposed a quantum limit to the estimation of object moments in subdiffraction incoherent optical imaging. In this sequel, I prove the quantum limit rigorously by infinite-dimensional analysis. A key to the proof is the choice of an unfavorable parametric submodel to give a bound for the semiparametric problem. By generalizing the quantum limit for a larger class of moments, I also prove that the measurement method of spatial-mode demultiplexing with just one or two modes is able to achieve the quantum limit. For comparison, I derive a classical bound for direct imaging using the parametric-submodel approach, which suggests that direct imaging is substantially inferior.