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Ising Patterns for All-Digital Quantum GI System Imaging

In an article recently published in the journal Optics & Laser Technology, researchers discussed the utility of Ising model-generated patterns for all-digital quantum ghost imaging.

Study: Patterns for all-digital quantum ghost imaging generated by the Ising model. Image Credit: BokehStore/

Ghost Imaging (GI)

GI is known as a different imaging method that can be applied to imaging in both the quantum and classical regimes. It has garnered a lot of interest in recent decades due to its advantages over traditional imaging, including super-resolution, greater image quality in a challenging optical environment, and higher detection sensitivity. Using correlation data from two light beams—the object beam and the reference beam—the standard ghost imaging technique reconstructs an image of the object or scene.

The spatial correlation among the two beams makes it possible to rebuild the image of the item using data from both detectors, even though none of the detectors can independently discern the spatial information of the object. A raster-scanned imaging detector, the only component used in conventional quantum ghost imaging, drastically reduces the system's total effective quantum efficiency in terms of the number of pixels in the image. A detector array would make the perfect image detector, but the cumulative noise of such arrays prevents precise measurement of a single photon's position inside the field of view.

Drawbacks of GI

Even with all its advantages, GI has a major disadvantage. Reconstructing the image requires many measurements, indicating that the imaging speed is inadequate. Many initiatives have been made to increase GI speed by enhancing imaging techniques and image reconstruction algorithms. With single-pixel imaging systems, the illumination pattern selected can significantly affect the quality and speed of the reconstructed images. When employing random patterns, too many measurements will be required to reconstruct an image with good accuracy.

Caustic patterns can be created by progressively changing random phase masks. These patterns could be used for imaging over a wide range of length scales and wavelengths and could be utilized to estimate binary images with improved edges when using a small number of samples.

Illumination Patterns for GI Systems

In this study, the authors discussed the development of novel illumination patterns for single-pixel imaging in all-digital quantum GI systems. The Ising model, a ferromagnetic model, was used to create the digital patterns, which were then written as computer-generated holograms on spatial light modulators (SLM). Temperature (T) and magnetic field (H) were two variables that had an impact on the Ising patterns. To develop a technique for utilizing Ising patterns to reconstruct high-quality ghost images with very minimal background noise, the magnetic field was set to zero, and the temperature values were changed. Also, the experimental verification for applying these Ising masks in quantum GI was provided.

A selection of Ising patterns with temperatures that tended to infinity was established as random binary patterns. At various temperatures above the critical temperature, Ising patterns were produced with the magnetic field at zero. For different inverse temperature parameters, ��′ = 0, 0.3, 0.5, 0.75, and 0.9, N equals 64 x 64-pixel ising patterns were produced to evaluate their application in ghost imaging. In the initial stage of the simulation, ghost images of two separate objects were created using 0.01 N, 0.05 N, 0.25 N, 0.5 N, N, and 2 N samples. The simulation's outcomes were obtained by applying  ��′= 0.75 and ��′ = 0.

An experiment was performed to assess the application of Ising patterns in an optical quantum ghost imaging setup. The results of the simulation were compared to the experimental ghost images. The difference between the maximum and least pixel intensities was computed to determine the image contrast. For a more in-depth analysis, the quality of the captured ghost images using Pearson's correlation coefficient (PCC) and mean square error (MSE) was evaluated, and the quality variables were plotted against the sample count. The findings were contrasted with those attained by the use of Hadamard sampling.

Experimental Observations and Results

Speckles of various sizes were observed in the designs formed close to the critical temperature. Though the patterns obtained at higher temperatures could be used to extract the specifics of the item, the Ising patterns obtained at lower temperatures were ideal for immediate identification of the location and approximate size of the object.  Using high ��′ Ising patterns as opposed to random patterns (��′ = 0) produced ghost images with a darker background and less noise. In other words, there was more contrast in the image between the central object and the background. Ising patterns were found to be suitable for identifying the position and size of items in a scene.

With a limited number of measurements, the quality factors demonstrated that Ising patterns with high ��' were preferable to random patterns. This made it difficult to estimate basic details about the scene, such as the size and placement of the objects, utilizing a limited number of measurements employing higher ��′ patterns. The resultant image could be binarized using a global threshold to create masks with zero values everywhere else but the potential locations of items. The correlation coefficients for the images with ��′ = 0.9 and ��′ = 0.5 were 0.949 and 0.951, respectively, for a total of 1025 patterns. Their correlation coefficients were 0.987 and 0.989, respectively.

The image could be entirely sampled using orthogonal Hadamard patterns, and a noiseless sampling replicated the ground truth image. The PCC for Hadamard ghost images increased to 0.915 and 0.869, respectively, by raising the sampling rate to M = 2048. These findings demonstrated that, for low sample rates, the proposed method could outperform Hadamard patterns. With slowly fluctuating random phase masks, caustic patterns could be created and used for imaging over a broad range of length scales and wavelengths.


In conclusion, this study elucidated that the caustic and Ising techniques both outperformed random patterns when using a limited number of samples. While Ising patterns could be used to estimate binary images with enhanced contrast, caustic patterns could estimate binary images with enhanced edges.

The authors demonstrated that it was possible to estimate the picture of the object with strong contrast and relatively little background noise by applying patterns with greater ��′.

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Oliaei-Moghadam, H., Moodley, C., Hosseini-Farzad, M., Patterns for all-digital quantum ghost imaging generated by the Ising model. Optics & Laser Technology, 163, 109392 (2023).

Surbhi Jain

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Surbhi Jain

Surbhi Jain is a freelance Technical writer based in Delhi, India. She holds a Ph.D. in Physics from the University of Delhi and has participated in several scientific, cultural, and sports events. Her academic background is in Material Science research with a specialization in the development of optical devices and sensors. She has extensive experience in content writing, editing, experimental data analysis, and project management and has published 7 research papers in Scopus-indexed journals and filed 2 Indian patents based on her research work. She is passionate about reading, writing, research, and technology, and enjoys cooking, acting, gardening, and sports.


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