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SPIE Quantum Technologies for Defence and Security

Single-photon superresolution imaging and spectroscopy

Luigi Santamaria Amato, Francesco Di Lena, Fabrizio Sgobba, Roberto Gabriel Aiello, P. Maddaloni, Danilo Triggiani, Cosmo Lupo

Published Oct 29, 2025• 0 citations
Publisher

Abstract

The resolution of direct imaging, the most common method for remote observation in the optical domain, is inherently constrained by diffraction. Recent studies have demonstrated that this diffraction limit can be surpassed, even with passive optics, through interferometric far-field techniques such as spatial mode demultiplexing (SPADE) or super localization by image inversion interferometry (SLIVER). We share our findings on sub-diffraction imaging of two incoherent point-like sources using SPADE and SLIVER.

DOI
10.1117/12.3069609

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The resolution of direct imaging, the most common method for remote observation in the optical domain, is inherently constrained by diffraction. Recent studies have demonstrated that this diffraction limit can be surpassed, even with passive optics, through interferometric far-field techniques such as spatial mode demultiplexing (SPADE) or super localization by image inversion interferometry (SLIVER). We share our findings on sub-diffraction imaging of two incoherent point-like sources using SPADE and SLIVER.
The resolution of direct imaging, which is the most widespread technique for remote observation in the optical domain, is fundamentally limited by diffraction. It has been recently shown that the diffraction limit can be overcome, even with passive optics, using interferometric far-field techniques like spatial mode demultiplexing (SPADE). We present our results on sub-diffraction imaging and spectroscopy of a pair of incoherent point-like emitters using SPADE in the single-photon regime. A theoretical analysis provides a comparison with direct imaging and explains the improvement in terms of signal-to-noise ratio. The application of single-photon SPADE for detection of more complex objects beyond a pair of point-emitters is underway for deployment in earth observation and object detection. The results are presented in the framework of the Quantum Imaging for Exoplanet detection (QUEXO) project.
Recent works employing tools from quantum optics and quantum metrology proposed a new passive imaging technique that allows to resolve details far below the diffraction limit. This technique is based on replacing standard spatially-resolved intensity measurements, e.g. at each pixel of a camera, with spatial-mode demultiplexing (SpaDe) measurements that allow to acquire information in a more efficient way. In this contribution, we want to provide an intuitive explanation of why such a SpaDe approach is so effective, and illustrate how we used these idea to discriminate one point source from two, and to estimate the separation between two incoherent sources.
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.
For more than a century, the diffraction limit has defined the resolution achievable by passive optical imaging systems. Although some resolution improvement can be gained through classical data processing of the image, it is limited by the noise arising from quantum nature of light. Minimizing the effect of this noise requires quantum treatment of optical imaging. By reformulating imaging as a problem of quantum measurement and estimation, it becomes possible to identify optimal detection strategies that recover spatial information previously thought inaccessible. This review summarizes the theoretical framework that underpins this development, from the formulation of quantum Cramer-Rao bounds and Chernoff bounds to the construction of receivers that attain them, such as those based on spatial-mode demultiplexing. We show how these methods can beat conventional imaging in the classification, localization, and imaging of sub-Rayleigh incoherent sources. We then discuss extensions to multiparameter and partially coherent scenarios, and highlight the unifying connections between estimation and discrimination tasks. Finally, we survey recent experimental demonstrations that approach quantum-limited resolution and outline emerging applications in microscopy, astronomy, and optical sensing.
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.
Remarkable resolution improvement has been achieved in super-resolution imaging [1]–[4], but all of the techniques possess the shortcoming of not being able to passively image the sample. In 2015 Tsang et al. [5]–[7] showed that the diffraction limit can be overcome for estimating the distance between two incoherent point sources. Our group extended his framework into complete far-field, linear-optical, and passive 2D imaging, deemed Hermite-Gaussian imaging (HGI), by measuring Hermite-Gaussian (HG) modes in the image plane and shown a two-fold resolution improvement for reconstructing coherent objects [8]–[9].