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Optica

Quantum-inspired superresolution for incoherent imaging

Xiaojie Tan, Qi Luo, Lianwei Chen, Aaron James Danner, Pakorn Kanchanawong, Mankei Tsang

Published Jul 27, 2023• 33 citations

Abstract

Optical measurements that can achieve the fundamental quantum limits have the potential to improve the imaging of subdiffraction objects in important applications, including optical astronomy and fluorescence microscopy. Working towards the goal of implementing such quantum-inspired measurements for real applications, we experimentally demonstrate the localization of two incoherent optical point sources and the semiparametric estimation of object moments in the subdiffraction regime via spatial-mode demultiplexing (SPADE). In the case of two sources, we are able to estimate both of their locations accurately, not just their separation, by exploiting the asymmetric response of our SPADE device. In the case of semiparametric estimation, we demonstrate that, even if the source number is unknown, the moments of the source distribution can still be estimated accurately. Our demonstration paves the way towards the use of SPADE for optical superresolution in practical scenarios, where adaptive measurements are difficult and many parameters are unknown.

DOI: 10.1364/optica.493227

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I propose a spatial-mode demultiplexing (SPADE) measurement scheme for the far-field imaging of spatially incoherent optical sources. For any object too small to be resolved by direct imaging under the diffraction limit, I show that SPADE can estimate its second or higher moments much more precisely than direct imaging can fundamentally do in the presence of photon shot noise. I also prove that SPADE can approach the optimal precision allowed by quantum mechanics in estimating the location and scale parameters of a subdiffraction object. Realizable with far-field linear optics and photon counting, SPADE is expected to find applications in both fluorescence microscopy and astronomy.

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I present a semiclassical analysis of a spatial-mode demultiplexing (SPADE) measurement scheme for far-field incoherent optical imaging under the effects of diffraction and photon shot noise. Building on previous results that assume two point sources or the Gaussian point-spread function, I generalize SPADE for a larger class of point-spread functions and evaluate its errors in estimating the moments of an arbitrary subdiffraction object. Compared with the limits to direct imaging set by the Cram\'er-Rao bounds, the results show that SPADE can offer far superior accuracy in estimating second- and higher-order moments.

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