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Moscow University Physics Bulletin

Mathematical Processing of Quantum Images in a Biphoton Setup via Measurement Reduction

Dmitriy A. Balakin, Aleksandr V. Belinsky

Published Jul 1, 2020• 6 citations
Publisher

Abstract

Abstract We investigate the possibilities of increasing the measurement accuracy and creating the least-damaging regime of object illumination by mathematical simulation of the process of generating paired images, that is, a ghost image and a regular image, using a new scheme with quantum biphoton generation. It is shown that diffraction and non-unit quantum efficiency of the sensors in traditional ghost imaging cause missing some information carried by the object arm photons. Forming an image of the studied object in the object arm and registering it makes it possible to weaken the influence of these factors on the measurement result when using the developed version of the method of measurement reduction to the form that is typical for measuring the transparency distribution of the object for processing a pair of obtained images.

DOI
10.3103/s0027134920040037

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Abstract We investigate the possibilities of increasing the measurement accuracy and creating the least-damaging regime of object illumination by mathematical simulation of the process of generating paired images, that is, a ghost image and a regular image, using a new scheme with quantum biphoton generation. It is shown that diffraction and non-unit quantum efficiency of the sensors in traditional ghost imaging cause missing some information carried by the object arm photons. Forming an image of the studied object in the object arm and registering it makes it possible to weaken the influence of these factors on the measurement result when using the developed version of the method of measurement reduction to the form that is typical for measuring the transparency distribution of the object for processing a pair of obtained images.
Ghost imaging allows extracting information about an object from the spatial correlation function between the photons that interacted with an object and the photons in the reference arm(s). The reference beam does not interact with the object; however, it is measured by a CCD matrix. The mathematical method of measurement reduction allows using both the mutual correlations of multiplexed ghost images and prior information about how the image of the research object can look in order to improve the quality of the reconstructed image. The information about the object is the sparsity of its transparency distribution under a given transform. Computer modelling of image reconstruction using multiplexed ghost images formed by four-mode entangled quantum light states confirms the efficiency of the proposed algorithm even with a small number of photons that illuminate the research object.
Abstract A modification of the classical scheme of the quantum ghost image formation is considered, in which an image of the object under study is formed and recorded in the object channel. This image is used together with the ghost image to construct an estimate of the transparency distribution of the object. It is shown that this technique reduces the image quality worsening associated with the non-unit quantum efficiency of the sensors, even when the quantum image obtained in the object channel is additionally distorted by noise due to photons that did not interact with the object.
Ghost imaging allows one to obtain information on an object from the spatial correlation function between photons propagating through or reflected from the object and photons of the reference arm. In this case, detection in the object arm is performed over the entire aperture of the beam and, therefore, it does not give information on the object. The reference beam does not interact with the object, but is recorded with a scanning point detector or a CCD array permitting the measurement of the spatial correlation function of photons in two arms. The use of multimode entangled quantum light beams by illuminating the object by one beam and orienting other beams to reference arms makes it possible to obtain simultaneously several ghost images (GIs). Cross correlations of multiplexed GIs (MGIs) are determined by eighth-order field correlation functions. A special algorithm is developed for calculating higher-order correlations of Bose operators. The presence of GI cross correlations is used for improving the quality of the reconstructed object’s image by their processing using the measurement reduction method. An example of the computer simulation of the image reconstruction by MGIs formed in the field of four-frequency entangled quantum states is considered. It is found that in this case the reduced GI has a signal-to-noise ratio several times higher than that of GIs.
Correlated light (either classical or quantum) can be employed in various ways to improve resolution and measurement sensitivity. In an “interaction-free” measurement, a single photon can be used to reveal the presence of an object placed within one arm of an interferometer without being absorbed by it. This method has previously been applied to imaging. With a technique known as “ghost imaging”, entangled photon pairs are used for detecting an opaque object with significantly improved signal-to-noise ratio while preventing over-illumination. Here, we integrate these two methods to obtain a new imaging technique which we term “interaction-free ghost-imaging” that possesses the benefits of both techniques. While improving the image quality of conventional ghost-imaging, this new technique is also sensitive to phase and polarization changes in the photons introduced by a structured object. Furthermore, thanks to the “interaction-free” nature of this new technique, it is possible to reduce the number of photons required to produce a clear image of the object (which could be otherwise damaged by the photons) making this technique superior for probing light-sensitive materials and eventually biological tissues. If time allows, I will discuss some follow-up works involving partial measurements and remote erasure/completion of images. The latter techniques can help to suppress various types of noise during the imaging process.
Quantum ghost imaging is a nonlocal imaging technique in which the image or diffraction pattern of an object illuminated by photon pairs can be observed through the correlation measurement. This study theoretically demonstrates the cloaking effect of such a quantum imaging. Quantum ghost imaging completely offsets two objects that are placed at proper positions in the interferometer. Furthermore, illusion of quantum imaging, where an object transforms into another object, has also been observed. This phenomenon can be understood by quantum interferences in the correlation measurement.
Quantum ghost imaging (GI) has significantly advanced the research and application of spatially entangled photon pairs over the past three decades. Nevertheless, existing works predominantly concentrate on qualitative analyses of GI results. The absence of rigorous theoretical models limits the capability of GI to address quantitative problems, which is essential in complex scenarios. Here, we present a comprehensive theoretical model that describes the evolution of the biphoton state throughout the GI process. Based on this model, we can explicitly analyze how the biphoton state evolves, and how object information is encoded into two-photon correlation measurements. We further introduce a virtual single-arm (VSA) operator, which maps the effects of two-arm optical elements into an equivalent single-arm representation, enabling a more intuitive analysis of biphoton-state evolution. Experimental validation is performed using a GI system based on an intensified charge-coupled device (ICCD) camera with multiple objects placed at different longitudinal positions. The excellent agreement between experimental and simulation results confirms the validity of the theoretical framework. This work clarifies the evolution of the biphoton states in quantum GI and opens new avenues for its applications in GI and broader quantum information tasks.