鬼成像的物理原理与信息论描述
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1.核生化灾害防护化学全国重点实验室,北京,102205;2.国科大杭州高等研究院,浙江杭州,310024;3.国防科技大学理学院,湖南长沙,410073

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国家自然科学基金(62201165);国家重点研发计划(2024YFF0505601)。


Physical Principles and Information-Theoretic Description of Ghost Imaging
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State Key Laboratory of Chemistry for NBC Hazards Protection, Beijing 102205, China

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    摘要:

    本文综述了鬼成像(ghost imaging)这一基于光场高阶关联的成像技术的物理原理及其信息论描述。首先,介绍了鬼成像的物理原理,阐述了光场关联函数与一阶、二阶相干性的基本概念,分析了相干态、热光(赝热光)与纠缠光子对等典型光源的高阶统计关联特性,探讨了在纠缠光子对与(赝)热光两类光源下,光场二阶相干度均呈单峰分布,从而在物面与像面建立点对点映射关系的成像机理,以及 Klyshko等效光路的统一解释;随后从信息论角度,将鬼成像过程等效为信息在“信源—信道—信宿”模型中的传递过程,分析了互信息、信道容量、Fisher 信息与 Cramér–Rao 界等经典信息度量方法在成像性能评估中的适用条件与内在联系,对信息度量指导下的编码优化与解码优化技术路线进行了分类比较与评述,并探讨了引入量子互信息、量子 Fisher 信息等量子信息论工具的适用条件和可行路径。指出光场二阶关联函数的统计结构决定成像系统的信息获取能力,同时信息度量方法正由“事后评价”走向“事前设计”;得出互信息、信道容量与 Fisher 信息分别从信息获取效率、信道传输潜能与参数估计精度三个层面刻画成像性能且互为补充的结论;提出未来可在编码优化与解码优化的协同设计、解码算法性能与信息论极限的定量对比、非经典光源鬼成像的量子信道建模以及面向弱信号与特殊波段应用等方向深化研究,进一步揭示鬼成像过程中的信息传递规律,提升成像系统的信息传输效率与图像重建精度,推动相关技术在生物医学成像、雷达探测等领域的应用与发展。

    Abstract:

    This paper reviews the physical principles and information-theoretic description of ghost imaging, an imaging technique based on the high-order statistical correlation of optical fields. First, the physical principles of ghost imaging are introduced: the fundamental concepts of optical field correlation functions and first- and second-order coherence are expounded, and the high-order statistical correlation characteristics of typical light sources, including coherent states, thermal (pseudo-thermal) light, and entangled photon pairs, are analyzed. The imaging mechanism in which the degree of second-order coherence of the optical field exhibits a single-peaked distribution under both entangled photon-pair and (pseudo-)thermal light illumination, thereby establishing a point-to-point mapping between the object plane and the image plane, is discussed, together with the unified interpretation offered by the Klyshko equivalent optical path. Subsequently, from the information-theoretic perspective, the ghost imaging process is modeled as the transmission of information in a “source–channel–sink” model: the applicable conditions and internal relations of classical information metrics, including mutual information, channel capacity, Fisher information, and the Cramér–Rao bound, in imaging performance evaluation are analyzed; the encoding optimization and decoding optimization approaches guided by information metrics are classified, compared, and reviewed; and the applicable conditions and feasible paths for introducing quantum information-theoretic tools such as quantum mutual information and quantum Fisher information are explored. It is pointed out that the statistical structure of the second-order correlation function of the optical field determines the information acquisition capability of the imaging system, and that information metrics are evolving from “post-hoc evaluation” toward “a priori design”. It is concluded that mutual information, channel capacity, and Fisher information characterize imaging performance in terms of information acquisition efficiency, channel transmission potential, and parameter estimation precision, respectively, and are mutually complementary. It is proposed that future research be deepened in directions such as the collaborative design of encoding and decoding optimization, the quantitative comparison between the performance of decoding algorithms and information-theoretic limits, quantum channel modeling for ghost imaging with non-classical light sources, and applications oriented toward weak signals and special bands, so as to further reveal the mechanisms of information transfer in the ghost imaging process, enhance the information transmission efficiency and image reconstruction accuracy of imaging systems, and promote the application and development of related technologies in biomedical imaging, radar detection, and other fields.

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  • 收稿日期:2026-08-24
  • 最后修改日期:2026-10-19
  • 录用日期:2026-10-23
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