Article(id=1319955590084931591, tenantId=1146029695717560320, journalId=1278651732997652489, issueId=1319955241370502145, articleNumber=null, orderNo=null, doi=10.12086/oee.2026.250209, pmid=null, cstr=32245.14.oee.2026.250209, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1752595200000, receivedDateStr=2025-07-16, revisedDate=1756656000000, revisedDateStr=2025-09-01, acceptedDate=1756828800000, acceptedDateStr=2025-09-03, onlineDate=1792631536264, onlineDateStr=2026-10-22, pubDate=1769270400000, pubDateStr=2026-01-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1792631536264, onlineIssueDateStr=2026-10-22, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1792631536264, creator=13701087609, updateTime=1792631536264, updator=13701087609, issue=Issue{id=1319955241370502145, tenantId=1146029695717560320, journalId=1278651732997652489, year='2026', volume='53', issue='1', pageStart='250064', pageEnd='1', issueExtLink='null', onlineDate='null', pubDate='1769270400000', pubDateStr='2026-01-25', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1792631453125, creator='13701087609', updateTime=1792631453125, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=250209, endPage=1, ext={EN=ArticleExt(id=1319955591703932936, articleId=1319955590084931591, tenantId=1146029695717560320, journalId=1278651732997652489, language=EN, title=Multidimensional optical sensing via single-shot of a single-layer metasurface, columnId=1279511634116841602, journalTitle=Opto-Electronic Engineering, columnName=Article, runingTitle=null, highlight=null, articleAbstract=
Objective

Light is the most fundamental medium through which humans perceive the objective world, encompassing multiple physical dimensions such as amplitude, phase, and polarization, and these dimensions carry abundant information after light interacts with matter, making their rapid and accurate sensing of great scientific significance and application value. For highly transparent materials such as living cells, variations in the transmitted light field are mainly manifested in the phase dimension, and therefore the development of highly sensitive quantitative phase imaging techniques is crucial for fast and accurate biological tissue analysis and pathological diagnosis. When light interacts with a medium, its polarization state often changes due to the dielectric properties, microstructure, and morphological characteristics of the material, and measuring the polarization state of transmitted or reflected light not only enables the perception of material properties but also enhances optical sensing capabilities in special environments such as nighttime, fog, or haze. Consequently, improving the ability to simultaneously sense multiple physical dimensions of the light field, including amplitude, phase, and polarization, has long been one of the core research directions in optical imaging. While the amplitude of a light field can be directly obtained using photoelectric detectors due to its quadratic relationship with intensity, phase and polarization information are inherently difficult to measure directly. Existing approaches for quantitative phase sensing mainly include interferometric methods, such as digital holographic interferometry, and non-interferometric phase retrieval techniques based on Hartmann wavefront sensing and the transport of intensity equation (TIE). Polarization measurement is typically realized with waveplates, polarizers, and other bulk optical components through time-division, amplitude-division, or polarization-channel-division acquisition of multiple sets of orthogonally polarized images. However, such systems are usually constrained by complex optical layouts and the size of conventional components, which hinders efficient integration and miniaturization, and in particular, time-division imaging severely limits sensing speed and temporal resolution. The emergence of optical metasurfaces provides a promising solution to these challenges, as their ability to manipulate multiple wavefront parameters of light at subwavelength scales enables substantial reduction of imaging system volume while maintaining high imaging quality. Although significant progress has been achieved in metasurface-based imaging and extensive efforts have been devoted to realizing multidimensional light-field imaging using metasurfaces, it remains challenging to develop a compact, easily integrable multidimensional imaging system that is robust and adaptable to complex imaging scenarios.

Methods

To address these issues, this work proposes a 4f optical architecture for multidimensional imaging based on a single-layer metasurface and single-shot acquisition. By employing a space- and polarization-multiplexed multi-channel metasurface, three-dimensional spatial decoupling of the orthogonal circular polarization components of the incident light field is achieved, enabling four-channel imaging with jointly controllable defocus and off-axis distances. Four intensity images are simultaneously recorded at the image plane in a single exposure, and through accurate cropping, calibration, and matching of these images, the complex amplitudes of the orthogonal circular polarization components are precisely reconstructed using the transport of intensity equation. Without the need for interferometric reference beams, the proposed architecture enables the simultaneous acquisition of intensity, phase, and polarization ellipticity information of the light field in a single exposure, significantly improving imaging efficiency and system robustness. The non-interferometric multidimensional imaging architecture is further integrated into a commercial microscope platform, demonstrating its compatibility with existing optical systems.

Results and Discussions

Quantitative phase imaging of a microlens array is performed to verify phase reconstruction accuracy, and polarization imaging of murine tendon tissue is conducted to demonstrate its capability for revealing birefringent and anisotropic structures in biological samples. Experimental results confirm that the proposed system enables label-free, fast, and multidimensional imaging of biological tissues and cells, effectively overcoming limitations of conventional imaging approaches for highly transparent samples and biological specimens, such as limited imaging dimensionality, high system complexity, and restricted applicability to in vivo measurements. Moreover, the proposed architecture introduces a system design concept that balances miniaturization, functional integration, and imaging performance, providing a practical pathway toward compact multidimensional optical imaging systems.

Conclusions

In principle, the proposed framework can achieve full Stokes parameter sensing based on TIE-derived phase and intensity information of orthogonal polarization components. However, in practical experiments, noise, model mismatch, and uncertainties in boundary conditions make it difficult for existing algorithms to accurately reconstruct the phase of complex tissues, especially in regions with large intensity gradients, where distortions and blurring are prone to occur, thereby hindering the reliable determination of the Stokes parameters s1 and s2. Future work will therefore focus on improving TIE-based phase retrieval algorithms to enhance reconstruction accuracy and robustness, as well as optimizing the matching and registration of intensity images acquired from different off-axis directions to mitigate off-axis effects, with the aim of further extending the applicability of the proposed metasurface-based multidimensional imaging architecture to complex biological, medical, and environmental sensing scenarios.

, authors=Kang Ren, Xuanguang Wu, Bingyan Wei, Sheng Liu, Jianlin Zhao, Peng Li, authorsList=Kang Ren, Xuanguang Wu, Bingyan Wei, Sheng Liu, Jianlin Zhao, Peng Li, authorCompany=null, correspAuthors=Peng Li, authorNote=null, correspAuthorsNote=
, copyrightStatement=Copyright © 2026 Opto-Electronic Engineering. All rights reserved., copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1319955597118779431, articleId=1319955590084931591, tenantId=1146029695717560320, journalId=1278651732997652489, language=CN, title=单层超表面单次曝光实现光学多维感知, columnId=1319955120360636489, journalTitle=光电工程, columnName=研究论文, runingTitle=null, highlight=null, articleAbstract=

光场蕴含着振幅、相位和偏振等多个物理维度,突破传统光电探测的维度极限并快速精准获取更多维度信息,对光学感知具有重要意义,并且在机器视觉、生物医学等领域中展现了极大的应用价值。光学超表面以其优异的光波前多维调控能力,推动光学多维成像架构向小型化和集成化的快速变革。本文提出一种基于单层超表面单次曝光实现光学多维成像的新架构,利用四通道偏振编码超表面对正交圆偏振分量进行空间和偏振复用,实现焦距独立调控的分焦面成像。利用光强传输方程实现正交圆偏振分量的定量相位复原,在单次曝光下同时获取了光场的强度、相位和偏振椭圆度多维信息。将该架构集成到商用显微镜中,实现了液晶微透镜阵列的定量相位复原和小鼠肌腱组织的偏振成像。本文的研究工作在活细胞检测、临床检测和诊断等领域中具有潜在的应用价值。

, authors=任康, 武炫光, 魏冰妍, 刘圣, 赵建林, 李鹏*, *, authorsList=任康, 武炫光, 魏冰妍, 刘圣, 赵建林, 李鹏, authorCompany=null, correspAuthors=李鹏, authorNote=

作者贡献

任康:文献调研、分析,多维成像架构设计、搭建与实验表征,论文写作与修改;武炫光:超表面设计与加工;魏冰妍:指导论文选题、实验表征;刘圣:指导论文选题、论文修改;赵建林:指导论文选题、论文修改;李鹏:论文选题、实验设计与表征、论文修改。

任康(2001-),男,硕士研究生,主要从事基于超表面的相位复原和偏振成像技术方面的研究。E-mail:

李鹏(1984-),男,博士,西北工业大学物理科学与技术学院教授,博士生导师,主要开展多维光场调控与光信息探测研究。E-mail:

, correspAuthorsNote=
李鹏,
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李鹏(1984-),男,博士,西北工业大学物理科学与技术学院教授,博士生导师,主要开展多维光场调控与光信息探测研究。E-mail:

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李鹏(1984-),男,博士,西北工业大学物理科学与技术学院教授,博士生导师,主要开展多维光场调控与光信息探测研究。E-mail:

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单层超表面单次曝光实现光学多维感知
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任康 , 武炫光 , 魏冰妍 , 刘圣 , 赵建林 , 李鹏 *, *
光电工程 | 研究论文 2026,53(1): 250209-1
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单层超表面单次曝光实现光学多维感知
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任康(2001-),男,硕士研究生,主要从事基于超表面的相位复原和偏振成像技术方面的研究。E-mail:

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李鹏(1984-),男,博士,西北工业大学物理科学与技术学院教授,博士生导师,主要开展多维光场调控与光信息探测研究。E-mail:

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李鹏(1984-),男,博士,西北工业大学物理科学与技术学院教授,博士生导师,主要开展多维光场调控与光信息探测研究。E-mail:

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任康 , 武炫光, 魏冰妍, 刘圣, 赵建林, 李鹏*, *
作者信息
  • 西北工业大学物理科学与技术学院,光场调控与信息感知工业和信息化部重点实验室陕西省光信息技术重点实验室,陕西 西安 710129
通讯作者:
作者简介:

作者贡献

任康:文献调研、分析,多维成像架构设计、搭建与实验表征,论文写作与修改;武炫光:超表面设计与加工;魏冰妍:指导论文选题、实验表征;刘圣:指导论文选题、论文修改;赵建林:指导论文选题、论文修改;李鹏:论文选题、实验设计与表征、论文修改。

任康(2001-),男,硕士研究生,主要从事基于超表面的相位复原和偏振成像技术方面的研究。E-mail:

李鹏(1984-),男,博士,西北工业大学物理科学与技术学院教授,博士生导师,主要开展多维光场调控与光信息探测研究。E-mail:

Multidimensional optical sensing via single-shot of a single-layer metasurface
Kang Ren , Xuanguang Wu, Bingyan Wei, Sheng Liu, Jianlin Zhao, Peng Li
Affiliations
  • Key Laboratory of Light Field Manipulation and Information Acquisition Ministry of Industry and Information Technology, Shaanxi Key Laboratory of Optical Information Technology, School of Physics Science and Technology, Northwest University of Technology, Xi'an, Shaanxi 710129, China
  • Corresponding Author:
出版时间: 2026-01-25 doi: 10.12086/oee.2026.250209
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光场蕴含着振幅、相位和偏振等多个物理维度,突破传统光电探测的维度极限并快速精准获取更多维度信息,对光学感知具有重要意义,并且在机器视觉、生物医学等领域中展现了极大的应用价值。光学超表面以其优异的光波前多维调控能力,推动光学多维成像架构向小型化和集成化的快速变革。本文提出一种基于单层超表面单次曝光实现光学多维成像的新架构,利用四通道偏振编码超表面对正交圆偏振分量进行空间和偏振复用,实现焦距独立调控的分焦面成像。利用光强传输方程实现正交圆偏振分量的定量相位复原,在单次曝光下同时获取了光场的强度、相位和偏振椭圆度多维信息。将该架构集成到商用显微镜中,实现了液晶微透镜阵列的定量相位复原和小鼠肌腱组织的偏振成像。本文的研究工作在活细胞检测、临床检测和诊断等领域中具有潜在的应用价值。

超表面  /  多维成像  /  光强传输方程  /  偏振
Objective

Light is the most fundamental medium through which humans perceive the objective world, encompassing multiple physical dimensions such as amplitude, phase, and polarization, and these dimensions carry abundant information after light interacts with matter, making their rapid and accurate sensing of great scientific significance and application value. For highly transparent materials such as living cells, variations in the transmitted light field are mainly manifested in the phase dimension, and therefore the development of highly sensitive quantitative phase imaging techniques is crucial for fast and accurate biological tissue analysis and pathological diagnosis. When light interacts with a medium, its polarization state often changes due to the dielectric properties, microstructure, and morphological characteristics of the material, and measuring the polarization state of transmitted or reflected light not only enables the perception of material properties but also enhances optical sensing capabilities in special environments such as nighttime, fog, or haze. Consequently, improving the ability to simultaneously sense multiple physical dimensions of the light field, including amplitude, phase, and polarization, has long been one of the core research directions in optical imaging. While the amplitude of a light field can be directly obtained using photoelectric detectors due to its quadratic relationship with intensity, phase and polarization information are inherently difficult to measure directly. Existing approaches for quantitative phase sensing mainly include interferometric methods, such as digital holographic interferometry, and non-interferometric phase retrieval techniques based on Hartmann wavefront sensing and the transport of intensity equation (TIE). Polarization measurement is typically realized with waveplates, polarizers, and other bulk optical components through time-division, amplitude-division, or polarization-channel-division acquisition of multiple sets of orthogonally polarized images. However, such systems are usually constrained by complex optical layouts and the size of conventional components, which hinders efficient integration and miniaturization, and in particular, time-division imaging severely limits sensing speed and temporal resolution. The emergence of optical metasurfaces provides a promising solution to these challenges, as their ability to manipulate multiple wavefront parameters of light at subwavelength scales enables substantial reduction of imaging system volume while maintaining high imaging quality. Although significant progress has been achieved in metasurface-based imaging and extensive efforts have been devoted to realizing multidimensional light-field imaging using metasurfaces, it remains challenging to develop a compact, easily integrable multidimensional imaging system that is robust and adaptable to complex imaging scenarios.

Methods

To address these issues, this work proposes a 4f optical architecture for multidimensional imaging based on a single-layer metasurface and single-shot acquisition. By employing a space- and polarization-multiplexed multi-channel metasurface, three-dimensional spatial decoupling of the orthogonal circular polarization components of the incident light field is achieved, enabling four-channel imaging with jointly controllable defocus and off-axis distances. Four intensity images are simultaneously recorded at the image plane in a single exposure, and through accurate cropping, calibration, and matching of these images, the complex amplitudes of the orthogonal circular polarization components are precisely reconstructed using the transport of intensity equation. Without the need for interferometric reference beams, the proposed architecture enables the simultaneous acquisition of intensity, phase, and polarization ellipticity information of the light field in a single exposure, significantly improving imaging efficiency and system robustness. The non-interferometric multidimensional imaging architecture is further integrated into a commercial microscope platform, demonstrating its compatibility with existing optical systems.

Results and Discussions

Quantitative phase imaging of a microlens array is performed to verify phase reconstruction accuracy, and polarization imaging of murine tendon tissue is conducted to demonstrate its capability for revealing birefringent and anisotropic structures in biological samples. Experimental results confirm that the proposed system enables label-free, fast, and multidimensional imaging of biological tissues and cells, effectively overcoming limitations of conventional imaging approaches for highly transparent samples and biological specimens, such as limited imaging dimensionality, high system complexity, and restricted applicability to in vivo measurements. Moreover, the proposed architecture introduces a system design concept that balances miniaturization, functional integration, and imaging performance, providing a practical pathway toward compact multidimensional optical imaging systems.

Conclusions

In principle, the proposed framework can achieve full Stokes parameter sensing based on TIE-derived phase and intensity information of orthogonal polarization components. However, in practical experiments, noise, model mismatch, and uncertainties in boundary conditions make it difficult for existing algorithms to accurately reconstruct the phase of complex tissues, especially in regions with large intensity gradients, where distortions and blurring are prone to occur, thereby hindering the reliable determination of the Stokes parameters s1 and s2. Future work will therefore focus on improving TIE-based phase retrieval algorithms to enhance reconstruction accuracy and robustness, as well as optimizing the matching and registration of intensity images acquired from different off-axis directions to mitigate off-axis effects, with the aim of further extending the applicability of the proposed metasurface-based multidimensional imaging architecture to complex biological, medical, and environmental sensing scenarios.

metasurface  /  multidimensional imaging  /  transport of intensity equation  /  polarization
任康, 武炫光, 魏冰妍, 刘圣, 赵建林, 李鹏. 单层超表面单次曝光实现光学多维感知. 光电工程, 2026 , 53 (1) : 250209 -1 . DOI: 10.12086/oee.2026.250209
Kang Ren, Xuanguang Wu, Bingyan Wei, Sheng Liu, Jianlin Zhao, Peng Li. Multidimensional optical sensing via single-shot of a single-layer metasurface[J]. Opto-Electronic Engineering, 2026 , 53 (1) : 250209 -1 . DOI: 10.12086/oee.2026.250209
光是人类感知客观世界的最基础媒介,包含了振幅、相位、偏振等多个物理维度,这些物理维度在光与物质相互作用后承载了丰富的信息,对这些维度的快速精准感知具有重要的科学意义和应用价值。例如,对于活细胞等高透过率物质,透射光场的变化则主要体现在相位上,发展高灵敏度的定量相位成像技术对快速精准的生物组织分析[1]、病理诊断等具有重要意义[2]。当光与介质相互作用时,其偏振态常因材料介电特性、结构形貌等发生改变,通过对介质透/反射光的偏振态测量,不仅能够感知介质属性[3-4],还可增强夜间[5]、雾霾[6-7]等特殊环境下的光学感知能力。因此,增强光场振幅、相位和偏振等多个物理维度的同时感知能力一直是光学成像领域的核心研究之一。光场的振幅信息因为与强度有直接平方关系,可通过光电耦合探测器直接获取,而相位和偏振信息则难以实现直接获取。实现定量相位感知的途径主要有以数字全息干涉[8-9]为代表的干涉法、以哈特曼波前传感[10]和以光强传输方程为基础的非干涉法复原相位[11]。而偏振测量则借助波片和偏振片等器件,通过分时、分偏振通道的多组正交偏振图像同步采集[12-16]实现。然而,此类系统普遍受限于复杂的光路和传统器件尺寸,难以满足高效集成需求,特别是分时成像极大限制了感知速率。
光学超表面的出现为解决这一问题提供了一种新的途径,其展现的亚波长尺度定制光场波前多维参量的能力[17-19],在保证成像质量的同时大幅缩小了成像系统的体积。例如,2021年,Engay等[20]通过TE和TM偏振通道编码两个不同焦距的超透镜,实现了单次曝光下正交偏振通道中在焦和离焦图像的同时采集,并利用光强传输方程实现了定量相位成像;2018年,Arbabi等[21]通过多路复用超表面同步获取6种偏振态数据,实现了全斯托克斯矢量解析。随着超表面在定量相位和偏振成像领域的快速发展[22-26],多维成像超表面成为新的研究热点。例如,2018年,杨振宇等[27]结合哈特曼波前传感和斯托克斯矢量测量原理,提出了一种基于超透镜阵列的光学多维成像方法,实现了对光束强度、相位、偏振3个多维信息的实时成像。2025年,包燕军等[28]利用超表面优化算法产生参考光分量并调控正交偏振分量的衍射及与参考光的干涉,成功实现了单次曝光下多种不同输入光场强度、相位、偏振信息的重建。
本文提出一种基于单层超表面单次曝光实现光学多维成像的新架构,其原理如图1所示,利用偏振和空间复用的多通道超表面对入射光正交圆偏振分量进行三维空间解耦,可实现离焦、离轴距离独立调控的四通道成像。通过光强传输方程精准重建正交圆偏振分量的复振幅,无需干涉即可在单次曝光下同时获取光场的强度、相位和偏振椭圆率信息。将这种非干涉的多维成像架构集成到商用显微镜中,通过对液晶微透镜阵列的定量相位成像和小鼠肌腱组织的偏振成像,验证了其在生物组织和细胞的无标记、快速、多维成像中的应用可能,克服了传统高透明样品及生物组织成像方法中存在的成像维度单一、系统复杂性高、活体检测受限等难题,也为基于光学多维成像的病理分析、医疗诊断提供了新的实现方案。
超表面的单个电介质结构可等效为一个双折射元件,能够对沿其快、慢轴方向上的线偏振分量施加不同的振幅、相位调制作用,其传输特性可用琼斯矩阵[29]表示为
$ \mathbf{J}=T\mathrm{e}^{\mathrm{i}\varphi_0}\left[\begin{array}{cc}\cos\dfrac{\delta}{2} & \mathrm{i}\sin\dfrac{\delta}{2}\mathrm{e}^{-\mathrm{i}2\theta} \\ \mathrm{i}\sin\dfrac{\delta}{2}\mathrm{e}^{\mathrm{i}2\theta} & \cos\dfrac{\delta}{2}\end{array}\right]\; , $
式中:i为虚数单位;θ为单元结构的偏转角度;φ0为传输相位;δ为快轴和慢轴之间的相位延迟;T为振幅透过率。当圆偏振光E=[1 ±i]T入射时,出射光场为
$ {{\boldsymbol{E}}}_{\text {out}} = T \exp \left(\mathrm{i} \varphi_0\right)\left(\cos \dfrac{\delta}{2}\left[\begin{array}{c}1 \\\pm \mathrm{i}\end{array}\right] + \mathrm{i} \sin \dfrac{\delta}{2} \exp (\mp \mathrm{i} 2 \theta)\left[\begin{array}{c}1 \\\mp \mathrm{i}\end{array}\right]\right)\;. $
出射光场由两个正交偏振分量组成,即同偏振分量[1 ±i]T和交叉偏振分量$ [1\; \mp\mathrm{i}] $T。两个偏振分量具有共同的传输相位exp(iφ0),以及互补的强度分布。同偏振分量和交叉偏振分量的强度比值取决于光场快、慢轴之间的相位延迟量δ。此外,交叉偏振分量还存在一个相位项exp(±i2θ),其为偏振态转化所引入的几何相位,大小取决于单元结构的旋转角度θ。
当严格控制快、慢轴之间的相位延迟量δ=π,且忽略共同的传输相位exp(iφ0)和振幅透过率T时,出射光仅包含交叉偏振分量。对于任意偏振态的光场,可将其采用右、左旋圆偏振分量表示为E=[ER EL]T,其中ER、EL分别为右、左旋圆偏振分离的复振幅。于是,透过超表面的出射光场可表示为
$ {\boldsymbol{E}}_{{\text{out}}} = {E_{\text{R}}}\exp \left( { - {\text{i2}}\theta } \right)\left[ {\begin{array}{*{20}{c}} 1 \\ { - {\text{i}}} \end{array}} \right] + {E_{\text{L}}}\exp \left( {{\text{i2}}\theta } \right)\left[ {\begin{array}{*{20}{c}} 1 \\ {\text{i}} \end{array}} \right]\;. $
由式(3)可知,光场的左、右旋圆偏振分量在出射时将获得共轭的几何相位φ=±2θ。利用该原理,将超表面的几何相位设计为
$ \begin{split} \varphi = &\arg \Bigg( {\text{exp}}\left( {{\text{i}}k\left( {x{\text{ + }}y} \right)\tan \alpha } \right)\exp \left( { - {\mathrm{i}k}\frac{{{r^2}}}{{2f\left( {f/\Delta {\textit{z}}} \right)}}} \right)\\&+ {\text{exp}}\left( {{\text{i}}k\left( {x - y} \right)\tan \alpha } \right) \Bigg)\;,\end{split} $
式中:k=2π/λ为波数;(x, y)为面内坐标变量,r2=x2+y2;f为成像透镜的焦距;∆z为设计的离焦距离;tanα为空间复用两个正交圆偏振态时所引入的线性相移梯度。
将式(4)所对应的几何相位超表面放置于一个焦距为f的4f系统频谱面时,透过超表面的线偏振光的左、右旋圆偏振分量将获得几何相位±φ。该相位函数包含两项,第一项集合了诱导45°方向位移的线性相位和离焦调制的二次相位,在其调制作用下,入射光的左、右旋圆偏振分量在像面产生沿45°方向和轴向相反的位移(±∆x, ±∆y, ±∆z);第二项则仅包含诱导135°方向位移的线性相位,在其调制作用下,入射光的左、右旋分量在像面产生沿135°方向分离的在焦图像。因而,左旋圆偏振分量在+φ的调制作用下,4f系统将产生两个点扩散函数(point spread functions, PSFs),其相对像面的三维位移分别为(x, −y, 0)和(x, y, ∆z)。相反地,透过超表面的右旋圆偏振分量受到−φ的调制作用所产生的两个点扩散函数相对像面的三维位移分别为(−x, y, 0)和(−x, −y, −∆z)。由此可知,对于任意输入图像,成像系统的像平面处将同时产生4个在焦和离焦的左、右旋圆偏振图像,其光强分别表示为IL、IR和IL(∆z)、IR(−∆z)。其中,左、右旋圆偏振分量的离焦量符号相反。
将上述4个空间和偏振复用的强度图像通过棋盘格图案进行精准对准和几何校正,代入如下光强传输方程:
$ -k \frac{\partial I_{\mathrm{L}, \mathrm{R}}(x, y, {\textit{z}})}{\partial {\textit{z}}}=\nabla \cdot\left[I_{\mathrm{L}, \mathrm{R}}(x, y, {\textit{z}}) \nabla \varphi_{\mathrm{L}, \mathrm{R}}(x, y)\right]\;, $
式中:$\nabla $为哈密顿算符;φL,R(x, y)为像面处左、右旋圆偏振分量的相位分布。两个圆偏振分量的强度图像IL,R(x, y, z)的纵向微分分别由四个图像IL和IL(∆z)、IR和IR(−∆z)获得。利用快速傅里叶变换法并引入辅助函数[11],通过下式可重建两个圆偏振分量的相位,表达式为
$ {\varphi _{{\text{L,R}}}}\left( {x,y} \right) = - k\nabla _{{\mathrm{FFT}}}^{ - 2}{\nabla _{{\mathrm{FFT}}}}\left[ {I_{{\text{L,R}}}^{ - 1}\left( {x,y} \right){\nabla _{{\mathrm{FFT}}}}\nabla _{{\mathrm{FFT}}}^{ - 2}\frac{{\partial {I_{{\text{L,R}}}}\left( {x,y} \right)}}{{\partial {\textit{z}}}}} \right] \;. $
值得注意的是,设计过程中应采取合适且较小的离焦距离Δz来提高近似微分的精度。进一步,将重建的左、右旋圆偏振分量的相位与直接采集的强度结合,即可重建出光场的斯托克斯参量,从而实现出射光强度、相位和偏振椭圆度感知。
根据设计的几何相位φ,利用图2(a)所示的单元结构设计超表面。该单元结构由多晶硅纳米柱以及二氧化硅衬底组成,纳米柱高度H恒定为600 nm,周期P为450 nm。利用有限差分时域(FDTD)模拟在633 nm光入射下,这种多晶硅纳米柱沿x方向的相位透过率φx和振幅透过率Tx与其几何长度L和宽度W的关系分别如图2(b)和图2(c)所示。根据超表面几何相位调控原理,仅需控制单元结构的旋向,就可以实现对入射光左、右旋圆偏振分量的共轭相位调制作用。并且,因为单元结构的几何尺寸完全一致,超表面具有全局相同的振幅透射率。在实验中,超表面采用标准的电子束刻蚀工艺制作[30-31],其扫描电子显微镜图像如图2(d)和图2(e)所示。超表面尺寸为1 mm×1 mm,设计的离焦距离∆z为3 mm。
将制备的基于超表面的多维感知架构集成于商业显微镜中,如图3(a1)所示。超表面被固定在4f透镜系统(f=7.5 mm)的共焦平面,如图3(a2)所示。基于该显微成像系统对液晶微透镜阵列进行表面形貌表征,在水平线偏振光入射情况下,采集到的在焦、离焦左、右旋圆偏振分量图像分别如图3(b1-b4)所示。利用式(6)所述光强传输方程对左、右旋圆偏振分量分别进行相位复原,重建的两个圆偏振分量的相位图像如图3(c1)和图3(c2)所示。为了验证这种方法重建相位的准确性,采用数字全息干涉法对该微透镜阵列进行了定量相位成像测量,所重建的相位如图3(c3)所示。图3(c4)展示了二维分布相位图中沿标注黑线的剖面数据对比。结果表明,数字全息干涉法重建的相位具有空间一致性,且与微透镜阵列调制的波前相位高度吻合,而基于光强传输方程复原的相位存在非均匀的微小误差。产生这种现象的主要原因是,该方法相位复原结果的准确性极大地依赖于两幅强度图像的匹配和离焦距离∆z的选取,前者受到像差和离焦效应的影响,使得离焦和在焦图像难以实现理想配准,后者虽然可以通过减小离焦距离∆z在一定程度上提升结果的准确性,但同时也会放大噪声对结果的影响。另一方面,受限于超表面的尺寸大小,只能对光场的部分频率信息进行调控,在丢失高频信息的情况下,求解相位的精度也相应降低。尽管存在上述局限,利用该显微成像系统仍能有效重建微透镜阵列的核心形貌特征,且对于无偏振响应的介质,左、右旋圆偏振分量的相位复原结果呈现一致性。鉴于快速傅里叶变换法在求解光强传输方程时未引入边界条件约束,所以均截取实验过程中视场中央的部分图像进行相位复原。在显微镜10×物镜配置下,实验测量该系统的强度和相位成像空间分辨率分别为4.55 μm和7.14 μm。对比分析表明,强度分辨率主要受限于超表面调制效率;相位分辨率则同时受算法误差和调制效率的双重影响。
对于具有光学各向异性响应的介质,尤其是具有双折射特性的样品,本系统同样具备偏振成像的能力。为评估该能力,将离体小鼠的肌腱组织作为样品进行成像分析。水平线偏振光入射时,采集到的右、左旋圆偏振分量的在焦图像分别如图4(a1)、图4(a2)所示。基于IR和IL计算得到的斯托克斯参量s0和s3分布如图4(b1)、图4(c1)所示,将其与图4(b2)、图4(c2)所示的传统偏振测量方法所获取的s0和s3图像进行对比。结果显示,两种成像方法获取的s0和s3分布图像在空间分布上呈现高度一致性,能够清晰地区分小鼠肌腱组织的不同结构域。然而,两种方法所测得的具体数值存在一定差异。其原因主要是超表面对左、右旋圆偏振分量的调制效率不同,导致其测得的对应强度图像存在误差,且由于超表面的尺寸限制,高频信息的丢失,造成了强度图像中肌腱组织不同结构之间边界模糊,进而影响了测量结果。理论上,根据斯托克斯参量与入射光左、右旋分量强度和相位的关系可以进一步求解s1和s2,但在实际的实验过程中,由于小鼠肌腱组织本身相位分布的复杂性和成像架构视场大小受限,且受到噪声和边界条件不确定的限制,在现有算法的基础上,重建的相位分布与传统方法获得的结果之间存在显著差异,进而影响了s1和s2的准确重建。
本文提出了一种偏振和空间复用的超表面结构,能够对入射光场两个正交圆偏振分量进行四通道相位调控,基于该超表面设计了多维成像超表面架构,能够对两个正交圆偏振分量进行三维空间解耦调控,实现了焦距独立调控的四焦点分焦面成像。结合光强传输方程,还能够在单次曝光下重建正交偏振分量的复振幅。进而将这种超表面成像架构集成到商用显微镜后,借助定量相位成像原理实现了液晶微透镜阵列的表面形貌表征,并且获得了与数字全息干涉测量一致的实验结果。最后,利用该系统对小鼠肌腱组织进行偏振成像,进一步证实了这种多通道超表面架构的多维感知能力。理论上,该架构可基于TIE实现全斯托克斯参量感知,但是受噪声和边界条件不确定的制约,现有的算法难以准确复原复杂组织的相位,阻碍了斯托克斯参量s1和s2的可靠求解,为突破该瓶颈,可通过引入线偏振通道直接实现全斯托克斯参量重建,或通过改进相位复原算法提升相位估计精度,从而间接实现高准确度的全参量恢复。

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2026年第53卷第1期
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doi: 10.12086/oee.2026.250209
  • 接收时间:2025-07-16
  • 首发时间:2026-10-22
  • 出版时间:2026-01-25
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  • 收稿日期:2025-07-16
  • 修回日期:2025-09-01
  • 录用日期:2025-09-03
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    西北工业大学物理科学与技术学院,光场调控与信息感知工业和信息化部重点实验室陕西省光信息技术重点实验室,陕西 西安 710129

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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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