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Science Advances

Using cyclic Hadamard masks for single-pixel quantum imaging under entangled photon illumination

Shu-Hang 书航 Bie 别, Xiaoxi Tong, Ziyang Lv, Hanyu Ye, Tun Cao

Published Aug 20, 2025• 13 citations
Publisher

Abstract

Quantum imaging, operating at extremely low photon flux and accommodating nondegenerate imaging wavelengths, offers a unique approach for imaging light-sensitive structures. Conventional quantum imaging systems often require costly intensified charge-coupled devices together with complex delay line and triggering electronics, limiting broader applications. In this work, we propose an approach for quantum imaging that uses a simple rotating mask coded with cyclic Hadamard patterns, together with single-pixel detectors, eliminating the need for the abovementioned specialized devices. Single-pixel quantum imaging with a resolution of 41 pixels by 43 pixels is performed, and its noise-resistant performance is further studied with an improved gate time of 1 nanosecond using time-correlated single-photon counting. An imaging speed up to 2 frames per second can be achieved, corresponding to a spatial modulation rate of 3.8 kilohertz. Furthermore, quantum ghost imaging with the object and the mask modulation in separate beams is also demonstrated, showing the potential of our system for high-speed, low-cost, and noise-resistant quantum imaging applications.

DOI
10.1126/sciadv.adw4799

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Quantum imaging, operating at extremely low photon flux and accommodating nondegenerate imaging wavelengths, offers a unique approach for imaging light-sensitive structures. Conventional quantum imaging systems often require costly intensified charge-coupled devices together with complex delay line and triggering electronics, limiting broader applications. In this work, we propose an approach for quantum imaging that uses a simple rotating mask coded with cyclic Hadamard patterns, together with single-pixel detectors, eliminating the need for the abovementioned specialized devices. Single-pixel quantum imaging with a resolution of 41 pixels by 43 pixels is performed, and its noise-resistant performance is further studied with an improved gate time of 1 nanosecond using time-correlated single-photon counting. An imaging speed up to 2 frames per second can be achieved, corresponding to a spatial modulation rate of 3.8 kilohertz. Furthermore, quantum ghost imaging with the object and the mask modulation in separate beams is also demonstrated, showing the potential of our system for high-speed, low-cost, and noise-resistant quantum imaging applications.
Quantum ghost imaging harnesses entangled photon pairs to form images using light that never directly interacts with the object. Conventional approaches rely on pixelated detectors or spatial masks, where the resolution is fundamentally limited by the pixel size and thus bounded by the Rayleigh criterion. In this work, we present a modal approach that replaces pixel-based detection with measurements in a basis of structured modes. By reconstructing images through tailored spatial modes, we decouple resolution from the physical limitations of detectors and instead tie it to the system’s optical precision and computational control. We demonstrate that even non-orthogonal modal sets can achieve high fidelity image reconstruction by exploiting modal sparsity, significantly reducing the number of required measurements. Using phase-only approximations of Hermite-Gaussian modes, we avoid the loss associated with complex amplitude modulation while retaining high reconstruction fidelity. The result is a high-resolution, high-efficiency quantum ghost imaging technique powered by structured light, opening new possibilities for photon-efficient imaging in low-light and quantum-limited regimes, such as biological microscopy and remote sensing.
Single-pixel quantum ghost imaging involves the exploitation of non-local photon spatial correlations to image objects with light that has not interacted with them and, using intelligent spatial scanning with projective masks, reduces detection to a single pixel. Despite many applications, extension to complex amplitude objects remains challenging. Here, we reveal that the necessary interference for phase retrieval is naturally embedded in the correlation measurements formed from traditional projective masks in bi-photon quantum ghost imaging. Using this, we develop a simple approach to obtain the full phase and amplitude information of complex objects. We demonstrate straightforward reconstruction without ambiguity using objects exhibiting spatially varying structures from phase steps to gradients as well as complex amplitudes. This technique could be an important step toward imaging the phase of light-sensitive structures in biological matter.
Pairs of entangled photos are used to reconstruct an image in the application area known as quantum ghost imaging. It is the correlation between the photon pair that allows for the reconstruction of the image, as opposed to single photon detection. The entangled photons are spatially separated into two independent paths, one to illuminate the object and the other which is collected by a spatially resolving detector. Initially, ghost imaging experiments accomplished spatially resolving detectors by moving a single-pixel detector throughout a transverse scanning area. Advancements consisted of using ultra-sensitive cameras to avoid a system consisting of physically moving detectors. Ultra-sensitive cameras are, however, expensive and have limited spectral sensitivity. Here we demonstrate an alternative by utilising a spatial light modulator and a bucket detector to spatially resolve what is detected. Importantly, the masks displayed on the spatial light modulator must constitute a complete basis to acquire a completely reconstructed image. Historically, imaging speeds have been slow and inefficient due to the quadratic increase in the scanning capability for spatially resolved detectors and the low light levels associated with quantum experiments. Here we additionally utilise machine and deep learning algorithms to improve both image reconstruction time and resolution. We demonstrate this with a non-degenerate ghost imaging setup where the physical parameters such as the mask type and resolution are varied and controlled on a spatial light modulator. Thereby answering the question: can we image an object without using a camera?
Correlated photon imaging, popularly known as ghost imaging, is a technique whereby an image is formed from light that has never interacted with the object. In ghost imaging experiments, two correlated light fields are produced. One of these fields illuminates the object, and the other field is measured by a spatially resolving detector. In the quantum regime, these correlated light fields are produced by entangled photons created by spontaneous parametric down-conversion. To date, all correlated photon ghost imaging experiments have scanned a single-pixel detector through the field of view to obtain spatial information. However, scanning leads to poor sampling efficiency, which scales inversely with the number of pixels, N , in the image. In this work, we overcome this limitation by using a time-gated camera to record the single-photon events across the full scene. We obtain high-contrast images, 90%, in either the image plane or the far field of the photon pair source, taking advantage of the Einstein–Podolsky–Rosen-like correlations in position and momentum of the photon pairs. Our images contain a large number of modes, >500, creating opportunities in low-light-level imaging and in quantum information processing.
Entangled photons have the remarkable ability to be more sensitive to signal and less sensitive to noise than classical light. Joint photons can sample an object collectively, resulting in faster phase accumulation and higher spatial resolution, while common components of noise can be subtracted. Even more, they can accomplish this while physically separate, due to the nonlocal properties of quantum mechanics. Indeed, nearly all quantum optics experiments rely on this separation, using individual point detectors that are scanned to measure coincidence counts and correlations. Scanning, however, is tedious, time consuming, and ill-suited for imaging. Moreover, the separation of beam paths adds complexity to the system while reducing the number of photons available for sampling, and the multiplicity of detectors does not scale well for greater numbers of photons and higher orders of entanglement. We bypass all of these problems here by directly imaging collinear photon pairs with an electron-multiplying CCD camera. We show explicitly the benefits of quantum nonlocality by engineering the spatial entanglement of the illuminating photons and introduce a new method of correlation measurement by converting time-domain coincidence counting into spatial-domain detection of selected pixels. We show that classical transport-of-intensity methods are applicable in the quantum domain and experimentally demonstrate nearly optimal (Heisenberg-limited) phase measurement for the given quantum illumination. The methods show the power of direct imaging and hold much potential for more general types of quantum information processing and control.
Correlated-photon imaging, popularly known as ghost imaging, is a technique whereby an image is formed from light that has never interacted with the object. In ghost imaging experiments two correlated light fields are produced. One of these fields illuminates the object, and the other field is measured by a spatially resolving detector. In the quantum regime, these correlated light fields are produced by entangled photons created by spontaneous parametric down-conversion. To date, all correlated-photon ghost-imaging experiments have scanned a single-pixel detector through the field of view to obtain the spatial information. However, scanning leads to a poor sampling efficiency, which scales inversely with the number of pixels, N, in the image. In this work we overcome this limitation by using a time-gated camera to record the single-photon events across the full scene. We obtain high-contrast images, 90%, in either the image plane or the far-field of the photon pair source, taking advantage of the EPR-like correlations in position and momentum of the photon pairs. Our images contain a large number of modes, >500, creating opportunities in low-light-level imaging and in quantum information processing.