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Optics Continuum

Reconstruction algorithm for g 2 (0) correlation maps using compressively sensed imaging in single-photon emitters

Sonali Gupta, Kiran Bajar, Alexander McFarland, Amit Kumar, Subhas Manna, Sushil A. Mujumdar

Published Aug 3, 2026• 0 citations
Publisher

Abstract

Optical imaging of quantum emitters is essential for a wide range of quantum applications. Conventional confocal imaging relies on point-by-point raster scanning, which is inherently time-consuming, particularly for sparse emitter distributions and photon-limited samples. Here, we demonstrate a compressive-sensing-based fluorescence imaging approach in which spatially structured wide-field excitation is used to acquire multiplexed measurements of sparse emitters. In our implementation, random binary patterns are projected onto the sample, and the spatial fluorescence distribution is reconstructed from the measured signals using a gradient projection for a sparse reconstruction algorithm with Barzilai Borwein step size (GPSR-BB). We experimentally demonstrate this approach using nitrogen-vacancy (NV) centers in diamond as a representative platform, achieving high-fidelity image reconstruction using only approximately 20% of the measurements required for conventional raster scanning. Beyond intensity reconstruction, we develop a compressive correlation-reconstruction model for recovering spatial maps of the second-order correlation function g (2) (0) from photon-correlation measurements. Through numerical simulations, we show that the reconstructed g (2) (0) maps can identify single-photon-emitter locations using the antibunching criterion g (2) (0) < 0.5. These results demonstrate that compressive sampling can reduce measurement overhead while preserving spatial information and enabling correlation-based quantum-emitter identification.

DOI
10.1364/optcon.611909

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Optical imaging of quantum emitters is essential for a wide range of quantum applications. Conventional confocal imaging relies on point-by-point raster scanning, which is inherently time-consuming, particularly for sparse emitter distributions and photon-limited samples. Here, we demonstrate a compressive-sensing-based fluorescence imaging approach in which spatially structured wide-field excitation is used to acquire multiplexed measurements of sparse emitters. In our implementation, random binary patterns are projected onto the sample, and the spatial fluorescence distribution is reconstructed from the measured signals using a gradient projection for a sparse reconstruction algorithm with Barzilai Borwein step size (GPSR-BB). We experimentally demonstrate this approach using nitrogen-vacancy (NV) centers in diamond as a representative platform, achieving high-fidelity image reconstruction using only approximately 20% of the measurements required for conventional raster scanning. Beyond intensity reconstruction, we develop a compressive correlation-reconstruction model for recovering spatial maps of the second-order correlation function g (2) (0) from photon-correlation measurements. Through numerical simulations, we show that the reconstructed g (2) (0) maps can identify single-photon-emitter locations using the antibunching criterion g (2) (0) < 0.5. These results demonstrate that compressive sampling can reduce measurement overhead while preserving spatial information and enabling correlation-based quantum-emitter identification.
Optical imaging of quantum emitters is essential for a wide range of quantum applications. Conventional confocal imaging relies on point-by-point raster scanning, which is inherently time-consuming and photon-inefficient, particularly for sparse emitter distributions and photon-limited samples. Here, we demonstrate a compressive sensing-based imaging approach, where spatially structured wide-field excitation replaces raster scanning, enabling reconstruction of sparse emitters. In our implementation, random binary patterns are used to acquire compressive measurements, from which the spatial fluorescence distribution is reconstructed using a GPSR-BB algorithm. We experimentally demonstrate this approach using nitrogen-vacancy (NV) centers in diamond as a representative platform, with high-fidelity image reconstruction achieved using only approximately 20%20\%20% of the measurements required for conventional raster scanning. In addition to intensity reconstruction, we extend this framework to reconstruct spatial maps of the second-order correlation function g(2)(0)g^{(2)}(0)g(2)(0) from compressive measurements. This enables identification of single-photon emitters through antibunching signatures using significantly reduced data.
Super-resolved reconstruction of single-photon emitter locations from g(2)(0)g^{(2)}(0)g(2)(0) maps
Single-photon sources are vital for emerging quantum technologies. In particular, Nitrogen-vacancy (NV) centers in diamond are promising due to their room-temperature stability, long spin coherence, and compatibility with nanophotonic structures. A key challenge, however, is the reliable identification of isolated NV centers, since conventional confocal microscopy is diffraction-limited and cannot resolve emitter distributions within a focal spot. Besides, the associated intensity scanning is a time-expensive procedure. Here, we introduce a raster-scanned g(2)(0)g^{(2)}(0)g(2)(0) mapping technique combined with an inversion-based reconstruction algorithm. By directly measuring local photon antibunching across the field of view, we extract the effective emitter number within each focal spot and reconstruct occupancy maps on a sub-focal-spot grid. This enables recovery of the number and spatial distribution of emitters within regions smaller than the confocal focal spot, thereby offering possibilities of going beyond the diffraction limit. Our simulations confirm robust reconstruction of NV-center distributions. The method provides a practical diagnostic tool for locating single-photon sources in an efficient and accurate manner, at much lesser time and effort compared to conventional intensity scanning. It offers valuable feedback for nanophotonic device fabrication, supporting more precise and scalable integration of NV-based quantum photonic technologies.
Single-photon sources are vital for emerging quantum technologies. In particular, Nitrogen-vacancy (NV) centers in diamond are promising due to their room-temperature stability, long spin coherence, and compatibility with nanophotonic structures. A key challenge, however, is the reliable identification of isolated NV centers, since conventional confocal microscopy is diffraction-limited and cannot resolve emitter distributions within a focal spot. Besides, the associated intensity scanning is a time-expensive procedure. Here, we introduce a simulation-based raster-scanned g ( 2 ) ( 0 ) mapping technique combined with an inversion-based reconstruction algorithm. Using synthetically generated photon-timestamp data for randomly distributed NV centers under a scanned Gaussian excitation profile, by directly measuring local photon antibunching across the field of view, we extract the effective emitter number within each focal spot and reconstruct occupancy maps on a sub-focal-spot grid. This enables recovery of the number and spatial distribution of emitters within regions smaller than the confocal focal spot, thereby offering possibilities of going beyond the diffraction limit. Simulations confirm robust reconstruction of NV-center distributions. The method reduces experimental effort in identifying isolated emitters by inferring the effective emitter number and sub-diffraction occupancy within each focal spot in a single scan, thereby avoiding unnecessary searches in regions that do not contain single emitters, as commonly encountered in intensity-based scanning approaches. It offers valuable feedback for nanophotonic device fabrication, supporting more precise and scalable integration of NV-based quantum photonic technologies.
Quantum imaging protocols have traditionally relied on spatially resolving detector arrays or multi-pixel cameras whose noise floors, limited detection efficiencies, and timing jitter fundamentally constrain image quality. Here we report a fibre-integrated architecture that reconstructs full two-dimensional quantum images using only a single superconducting nanowire single-photon detector, replacing spatial resolution with temporal multiplexing and compressive measurement. Correlated photon pairs generated by parametric down-conversion illuminate the target through one arm while the partner photon is retained as a temporal reference; non-local dispersion engineered across the two arms suppresses uncorrelated background while preserving pair timing. A compressive sensing algorithm exploiting sparsity in the Fourier domain then recovers 50×50-pixel images from far fewer measurements than conventional raster scanning would require. Operating over several kilometres of standard single-mode fibre at the eye-safe wavelength of 1550 nm, the system produces images of comparable fidelity to classical illumination while using 95 dB less optical power, achieves sub-shot-noise performance with a 7.9 dB signal-to-noise ratio improvement, and sustains useful image quality under injected noise exceeding the signal by 10 dB. The same temporal correlation data yield a timing precision of 1.2 ps, corresponding to sub-millimetre ranging resolution. These results establish single-detector temporal multiplexing as a viable and scalable route to practical quantum imaging over deployed telecommunications infrastructure.
We implement a double-pixel compressive-sensing camera to efficiently characterize, at high resolution, the spatially entangled fields that are produced by spontaneous parametric down-conversion.This technique leverages sparsity in spatial correlations between entangled photons to improve acquisition times over raster scanning by a scaling factor up to n 2 = logðnÞ for n-dimensional images.We image at resolutions up to 1024 dimensions per detector and demonstrate a channel capacity of 8.4 bits per photon.By comparing the entangled photons' classical mutual information in conjugate bases, we violate an entropic Einstein-Podolsky-Rosen separability criterion for all measured resolutions.More broadly, our result indicates that compressive sensing can be especially effective for higher-order measurements on correlated systems.
Temporal photon correlations have been a crucial resource for quantum and quantum-enabled optical science for over half a century. However, attaining non-classical information through these correlations has typically been limited to a single point (or, at best, a few points) at a time. Here, we perform a massively multiplexed wide-field photon correlation measurement using a large single-photon avalanche diode array, the SwissSPAD3. We demonstrate the performance of this apparatus by acquiring wide-field photon correlation measurements of single-photon emitters and illustrate two applications of the attained quantum information: wide-field emitter counting and quantum-enabled super-resolution imaging (by a factor of 500×500). The considerations and limitations of applying this technique in a practical context are discussed. Ultimately, the realization of massively multiplexed wide-field photon correlation measurements can accelerate quantum sensing protocols and quantum-enabled imaging techniques by orders of magnitude.