Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Optics Express

Spatial mode demultiplexing for super-resolved source parameter estimation

John S. Wallis, David R. Gozzard, Alex M. Frost, Joshua J. Collier, Nicolas G. J. Maron, Benjamin P. Dix-Matthews

Published Jul 16, 2025• 3 citations
Publisher

Abstract

We present the use of a multi-planar light converter (MPLC) to perform spatial mode demultiplexing (SPADE) for optical source parameter estimation. This technique has been extended to use higher-order Hermite-Gaussian modes for the purposes of estimating the separation of a pair of incoherent sources, both above and below the diffraction limit. We resolve these sources at separations 90× lower than the diffraction limit. We also show our system is capable of simultaneous separation estimation and relative power estimation while maintaining super-resolving capabilities, with relative power differences as large as 20 dB by using the additional information gained by incorporation of the higher order modes. These results support the potential use of SPADE for astronomical imaging of binary systems.

DOI
10.1364/oe.563503

Related papers

Multiparameter estimation for the superresolution of two incoherent sources

Antonin Grateau, Alexander Boeschoten, Tanguy Favin-Lévêque +2 more

We experimentally demonstrate the simultaneous estimation of the three parameters characterizing a pair of incoherent optical sources in the sub-Rayleigh regime, enabling super-resolved scene characterization. Using spatial-mode demultiplexing (SPADE) with two demultiplexers--one deliberately shifted--we determine separations well below the diffraction limit and achieve sensitive joint estimation of separation, centroid, and relative brightness over a broad range of scene configurations in a single experimental setting. We benchmark our performance using Fisher-information-based Cramér-Rao bounds, and discuss the corresponding quantum limits. We investigate two complementary scenarios: a realistic case with slightly non-identical sources, and an idealized case of indistinguishable sources.

quant-pharXiv:2601.14876•Physical Review Letters•Jan 22, 2026•0 citations

Sub-Rayleigh Imaging of Unequal-Intensity Sources: Near-Quantum-Limit Multiparameter Estimation

Y. Batuhan Yilmaz, Kent A. G. Bonsma-Fisher, Muhammad Mohid +3 more

In optical imaging, diffraction strongly degrades the performance of conventional intensity-based estimation once the separation between two sources is below the Rayleigh-Abbe limit. Recent developments showed that this limitation can be surpassed using spatial-mode demultiplexing (SPADE), and this was demonstrated in several experiments for two equal-intensity spots of unknown separation. When there are multiple unknown parameters, as in the case of several unequal sources with unknown intensities and unknown separation, cross-talk among the parameters makes the multi-parameter estimation problem significantly more challenging. In this paper, we adapt super-resolved position localization by inversion of coherence along an edge (SPLICE) to estimate both the separation and relative intensity of two incoherent sources simultaneously. We demonstrate a clear advantage over direct imaging (DI), achieving a root mean squared error (RMSE) approximately $50 \%$ larger than the quantum limit and a sixfold improvement over DI within the range of parameters we tested. This improvement can be even greater for smaller separations and larger intensity imbalances when crosstalk is suppressed.

physics.opticsCross-listedarXiv:2608.07868•Aug 11, 2026•0 citations

Parameter estimation approach to super resolution

Alexander Boeschoten, Antonin Grateau, Clémentine Rouvière +7 more

The resolution of optical systems, formulated as the smallest possible distance between two point sources for which they still can be dissolved, was for a long time believed to be limited by diffraction, formulated by the Rayleigh criterion. Recent advancements in quantum metrology have shown, by evaluation of the Quantum Cramér Rao bound (QCRB), that the Rayleigh criterion is not a fundamental limit. In our experiment, spatial mode demultiplexing (SPADE) is used to estimate the separation of the sources orders of magnitude below the Rayleigh limit. The experiment is extended to incorporate the measurement of additional parameters, such as power imbalance and centroid position of the two sources, bringing it closer to real-world applicability.

SPIE Quantum Technologies for Defence and Security•Nov 15, 2024•0 citations

Resolution limits of spatial mode demultiplexing with noisy detection

Yink Loong Len, Chandan Datta, Michal P. Parniak +1 more

We consider the problem of estimating the spatial separation between two mutually incoherent point light sources using the super-resolution imaging technique based on spatial mode demultiplexing (SPADE) with noisy detectors. We show that in the presence of noise, the resolution of the measurement is limited by the signal-to-noise ratio (SNR) and the minimum resolvable spatial separation has a characteristic dependence of [Formula: see text]. Several detection techniques, including direct photon counting, as well as homodyne and heterodyne detection are considered.

arXiv:1911.04744•International Journal of Quantum Information•Jan 31, 2020•51 citations

A Multimode Quantum Optics Approach to Incoherent Imaging

Giacomo Sorelli

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.

London Imaging Meeting•Jun 27, 2024•0 citations

Subdiffraction incoherent optical imaging via spatial-mode demultiplexing

Mankei Tsang

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.

arXiv:1608.03211•New Journal of Physics•Feb 16, 2017•113 citations
We present the use of a multi-planar light converter (MPLC) to perform spatial mode demultiplexing (SPADE) for optical source parameter estimation. This technique has been extended to use higher-order Hermite-Gaussian modes for the purposes of estimating the separation of a pair of incoherent sources, both above and below the diffraction limit. We resolve these sources at separations 90× lower than the diffraction limit. We also show our system is capable of simultaneous separation estimation and relative power estimation while maintaining super-resolving capabilities, with relative power differences as large as 20 dB by using the additional information gained by incorporation of the higher order modes. These results support the potential use of SPADE for astronomical imaging of binary systems.
We experimentally demonstrate the simultaneous estimation of the three parameters characterizing a pair of incoherent optical sources in the sub-Rayleigh regime, enabling super-resolved scene characterization. Using spatial-mode demultiplexing (SPADE) with two demultiplexers--one deliberately shifted--we determine separations well below the diffraction limit and achieve sensitive joint estimation of separation, centroid, and relative brightness over a broad range of scene configurations in a single experimental setting. We benchmark our performance using Fisher-information-based Cramér-Rao bounds, and discuss the corresponding quantum limits. We investigate two complementary scenarios: a realistic case with slightly non-identical sources, and an idealized case of indistinguishable sources.
In optical imaging, diffraction strongly degrades the performance of conventional intensity-based estimation once the separation between two sources is below the Rayleigh-Abbe limit. Recent developments showed that this limitation can be surpassed using spatial-mode demultiplexing (SPADE), and this was demonstrated in several experiments for two equal-intensity spots of unknown separation. When there are multiple unknown parameters, as in the case of several unequal sources with unknown intensities and unknown separation, cross-talk among the parameters makes the multi-parameter estimation problem significantly more challenging. In this paper, we adapt super-resolved position localization by inversion of coherence along an edge (SPLICE) to estimate both the separation and relative intensity of two incoherent sources simultaneously. We demonstrate a clear advantage over direct imaging (DI), achieving a root mean squared error (RMSE) approximately 50%50 \%50% larger than the quantum limit and a sixfold improvement over DI within the range of parameters we tested. This improvement can be even greater for smaller separations and larger intensity imbalances when crosstalk is suppressed.
The resolution of optical systems, formulated as the smallest possible distance between two point sources for which they still can be dissolved, was for a long time believed to be limited by diffraction, formulated by the Rayleigh criterion. Recent advancements in quantum metrology have shown, by evaluation of the Quantum Cramér Rao bound (QCRB), that the Rayleigh criterion is not a fundamental limit. In our experiment, spatial mode demultiplexing (SPADE) is used to estimate the separation of the sources orders of magnitude below the Rayleigh limit. The experiment is extended to incorporate the measurement of additional parameters, such as power imbalance and centroid position of the two sources, bringing it closer to real-world applicability.
We consider the problem of estimating the spatial separation between two mutually incoherent point light sources using the super-resolution imaging technique based on spatial mode demultiplexing (SPADE) with noisy detectors. We show that in the presence of noise, the resolution of the measurement is limited by the signal-to-noise ratio (SNR) and the minimum resolvable spatial separation has a characteristic dependence of [Formula: see text]. Several detection techniques, including direct photon counting, as well as homodyne and heterodyne detection are considered.
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.