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Scientific Reports

Single-pixel quantum ghost imaging using generalized Ising model

Hamidreza Oliaei-Moghadam, Mahmood Hosseini Farzad, Najmeh Tabebordbar

Published Jul 1, 2025• 3 citations
Publisher

Abstract

In advanced single-pixel imaging systems that use spatial light modulators (SLMs), the scene needs to be illuminated by numerous different patterns that are coded into the SLM to gather information about the object. The appropriate choice of pattern set and reconstruction algorithm are essential for rapid reconstruction of a high-quality image. For single-pixel quantum ghost imaging (QGI) systems, we introduce an adaptive pattern generation method based on the generalized Ising model. The 2D Ising model describes an array of spins arranged in a lattice, where each spin in the lattice can interact with its adjacent spins and also can be influenced by an external magnetic field. By modeling spin values (up or down) as pixel states of the SLM (on or off) and using the Ising model, we can generate binary patterns that closely resemble the object's shape. Imaging using patterns generated by our proposed method can reduce the number of measurements required for high-quality image reconstruction.

DOI
10.1038/s41598-025-08851-0

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In advanced single-pixel imaging systems that use spatial light modulators (SLMs), the scene needs to be illuminated by numerous different patterns that are coded into the SLM to gather information about the object. The appropriate choice of pattern set and reconstruction algorithm are essential for rapid reconstruction of a high-quality image. For single-pixel quantum ghost imaging (QGI) systems, we introduce an adaptive pattern generation method based on the generalized Ising model. The 2D Ising model describes an array of spins arranged in a lattice, where each spin in the lattice can interact with its adjacent spins and also can be influenced by an external magnetic field. By modeling spin values (up or down) as pixel states of the SLM (on or off) and using the Ising model, we can generate binary patterns that closely resemble the object's shape. Imaging using patterns generated by our proposed method can reduce the number of measurements required for high-quality image reconstruction.
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.
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.
The process of image recording is arguably one of the most prevalent technology in modern society and continues to inspire vast swathes of research due to its widespread applications spanning military, medical and consumer spheres. The danger present in a field so broad is that separate niches of research can become isolated with critical advancements struggling to traverse the gulfs between. Unifying the field is the omnipresent drive to acquire an ever increasing quality of images at the lowest possible cost, a goal which warrants continual fundamental research. Quantum entanglement exhibits many intriguing characteristics which make it a suitable tool for such fundamental investigations. The process of spontaneous parametric down- conversion has offered a yet unbeaten strength of photon correlations with the quantum nature of their production providing a reliable and controllable source of single-photons. Arising from these attributes is the technique known as ghost imaging. Though now known to be classically possible, the strength of entanglement generated correlations is yet to be surpassed. This thesis implemented this technique in tandem with the cutting edge detector technology in order to probe the fundamentals of image formation. This form of imaging allowed us to subject an object to a known number of photons whilst acquiring structural information from spatially separate, correlated photons which never interact with the object. The strength of the produced correlations allow us to acquire low background, high resolution images with far less light than traditional techniques and affords many novel benefits. The possibility of incorporating this technique with pre-existent regimes allowed me to draw from advancements made across the landscape of imaging research. Although referred to as “quantum ghost imaging” throughout this work, it should be noted that the intrinsic quantum nature of the correlations was not directly relied upon but provided an ideal source of strongly correlated photons. In order to determine the limits of a traditional imaging system this thesis first sought to answer the question: “can an image of an object be reconstructed from fewer photons than ii pixels in the image?” In chapter 3 I approached this from the perspective of compression, which minimises redundant information within a signal. This lead to the development of an imaging regime capable of imaging with far fewer photons than pixels in the image. By employing assumptions about the sparsity of natural images I was able to reconstruct an image of a biological sample containing an average of less than one photon per image pixel. Having reduced the number of photons necessary to form an image I then considered alternative methods for reducing the optical energy impinging on a sample. I sought to answer the question: “can non-degenerate ghost imaging reduce the optical energy impinged upon an object during imaging”. The photons produced in SPDC need not be of similar wavelengths, however may be chosen far from degeneracy, i.e. non-degenerate. In Chapter 4 I presented a ghost imaging system which illuminated the object with infrared light whilst recording the structural information via entangled visible photons. This allowed for objects opaque to visible light to be imaged in high quality without the need for a spatially resolving infrared detector, the state of the art of which lags behind their silicon based visible counterparts. I presented the systems capabilities by imaging objects which were etched into a gold substrate layered on to silicon, both of which are opaque to visible light. Not only did a reduction in energy deposition arise from the lower energy probe wavelength but applying the reconstruction techniques from the previous chapter brought that down to as low as ≈16 nJcm−2s−1. Seeking to expand the repertoire of applications, the low-light capabilities of my ghost imaging were applied to the technique of phase-contrast microscopy in chapter 5. Typically applied to translucent objects, phase-contrast imaging transfers phase information, i.e. the refractive index changed within the object, into an intensity distribution through the use of a phase-filter. In many of these applications the objects tend to be biological in nature, where high optical exposure can result in bleaching or damage. By applying the phase-filter non- locally, i.e. to the photons correlated to those probing the object, I acquired edge-enhanced images of a phase object whilst illuminating with significantly fewer photons than standard phase-contrast techniques. Having displayed the broad applicability of our low-light ghost imaging system, I then sought to determine the optical resolution in chapter 6. The resolution limits of ghost imaging are not clear at first glance owing to the resolutions dependence upon the strength of spatial correlations. As the length over which the spatial correlations are produced can be brought below the standard diffraction limit, it would seem the resolution of the system could be brought similarly low. To clarify this I artificially restricted the number of spatial modes in each of the correlated beams to uncover the physically realisable resolution. I show that although the resolution of a ghost imaging system to be fundamentally determined by the strength of the correlations, this can never be reached due to the inherent limitations of the intervening imaging system.
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 (QGI) leverages correlations between entangled photon pairs to reconstruct an image using light that has never physically interacted with an object. Despite extensive research interest, this technique has long been hindered by slow acquisition speeds, due to the use of raster-scanned detectors or the slow response of intensified cameras. Here, we utilize a single-photon-sensitive time-stamping camera to perform QGI at ultra-low-light levels with rapid data acquisition and processing times, achieving high-resolution and high-contrast images in under 1 min. Our work addresses the trade-off between image quality, optical power, data acquisition time, and data processing time in QGI, paving the way for practical applications in biomedical and quantum-secured imaging.