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Reinforcement Learning Environment for Wavefront Sensorless Adaptive Optics in Single-Mode Fiber Coupled Optical Satellite Communications Downlinks 单模光纤耦合光学卫星通信下行链路中波前无传感器自适应光学的强化学习环境
IF 2.4 4区 物理与天体物理
Photonics Pub Date : 2023-12-13 DOI: 10.3390/photonics10121371
Payam Parvizi, Runnan Zou, Colin Bellinger, R. Cheriton, Davide Spinello
{"title":"Reinforcement Learning Environment for Wavefront Sensorless Adaptive Optics in Single-Mode Fiber Coupled Optical Satellite Communications Downlinks","authors":"Payam Parvizi, Runnan Zou, Colin Bellinger, R. Cheriton, Davide Spinello","doi":"10.3390/photonics10121371","DOIUrl":"https://doi.org/10.3390/photonics10121371","url":null,"abstract":"Optical satellite communications (OSC) downlinks can support much higher bandwidths than radio-frequency channels. However, atmospheric turbulence degrades the optical beam wavefront, leading to reduced data transfer rates. In this study, we propose using reinforcement learning (RL) as a lower-cost alternative to standard wavefront sensor-based solutions. We estimate that RL has the potential to reduce system latency, while lowering system costs by omitting the wavefront sensor and low-latency wavefront processing electronics. This is achieved by adopting a control policy learned through interactions with a cost-effective and ultra-fast readout of a low-dimensional photodetector array, rather than relying on a wavefront phase profiling camera. However, RL-based wavefront sensorless adaptive optics (AO) for OSC downlinks faces challenges relating to prediction latency, sample efficiency, and adaptability. To gain a deeper insight into these challenges, we have developed and shared the first OSC downlink RL environment and evaluated a diverse set of deep RL algorithms in the environment. Our results indicate that the Proximal Policy Optimization (PPO) algorithm outperforms the Soft Actor–Critic (SAC) and Deep Deterministic Policy Gradient (DDPG) algorithms. Moreover, PPO converges to within 86% of the maximum performance achievable by the predominant Shack–Hartmann wavefront sensor-based AO system. Our findings indicate the potential of RL in replacing wavefront sensor-based AO while reducing the cost of OSC downlinks.","PeriodicalId":20154,"journal":{"name":"Photonics","volume":"119 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139004486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Extension of Fiber Bragg Grating Ultrasound Sensor Network by Adhesive Couplers 通过粘合耦合器扩展光纤布拉格光栅超声波传感器网络
IF 2.4 4区 物理与天体物理
Photonics Pub Date : 2023-12-12 DOI: 10.3390/photonics10121366
J. Kim, S. Aboubakr, Kara Peters
{"title":"Extension of Fiber Bragg Grating Ultrasound Sensor Network by Adhesive Couplers","authors":"J. Kim, S. Aboubakr, Kara Peters","doi":"10.3390/photonics10121366","DOIUrl":"https://doi.org/10.3390/photonics10121366","url":null,"abstract":"Previous studies demonstrated coupling of acoustic guided waves from one optical fiber to another through a simple adhesive bond coupler. This paper experimentally utilizes such an adhesive bond coupler to easily extend an already existing sensor network. We experimentally demonstrate this concept for detecting simulated cracks growing from circular holes in a thin aluminum plate. A single, remotely bonded FBG sensor is used to detect the original crack growth, followed by the addition of other optical fiber segments using adhesive couplers to detect new crack growth locations on the plate. A laser Doppler vibrometer is also used to measure the guided wave propagation through the plate to verify that the changes in the FBG sensor measurements are due to the growth of the cracks.","PeriodicalId":20154,"journal":{"name":"Photonics","volume":"7 9","pages":""},"PeriodicalIF":2.4,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139009685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Measurement of the Optical Path Difference Caused by Steering Mirror Using an Equal-Arm Heterodyne Interferometer 利用等臂异调干涉仪测量转向镜造成的光程差
IF 2.4 4区 物理与天体物理
Photonics Pub Date : 2023-12-11 DOI: 10.3390/photonics10121365
Weizhou Zhu, Yue Guo, Qiyi Jin, Xue Wang, Xingguang Qian, Yong Xie, Lingqiang Meng, Jianjun Jia
{"title":"Measurement of the Optical Path Difference Caused by Steering Mirror Using an Equal-Arm Heterodyne Interferometer","authors":"Weizhou Zhu, Yue Guo, Qiyi Jin, Xue Wang, Xingguang Qian, Yong Xie, Lingqiang Meng, Jianjun Jia","doi":"10.3390/photonics10121365","DOIUrl":"https://doi.org/10.3390/photonics10121365","url":null,"abstract":"In space gravitational wave detection, the inter-satellite link-building process requires a type of steering mirror to achieve point-ahead angle pointing. To verify that the background noise does not drown out the gravitational wave signal, this paper designed a laser heterodyne interferometer specifically designed to measure the optical path difference of the steering mirror. Theoretically, the impact of angle and position jitter is analyzed, which is called tilt-to-length (TTL) coupling. This interferometer is based on the design concept of equal-arm length. In a vacuum (10−3 Pa), vibration isolation (up to 1 Hz), and temperature-controlled (approximately 10 mK) experimental environment, the accuracy is increased by about four orders of magnitude through a common-mode suppression approach and can reach 390 pm/Hz when the frequency is between 1 mHz and 1 HZ. By analogy, the optical path difference caused by the steering mirror reaches 5 pm/Hz in the 1 mHz to 1 Hz frequency band. The proposed TTL noise model is subsequently verified.","PeriodicalId":20154,"journal":{"name":"Photonics","volume":"8 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138979832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Physical and Technological Aspects of Laser-Induced Damage of ZGP Single Crystals under Periodically Pulsed Laser Irradiation at 2.1 μm 2.1 μm 周期性脉冲激光辐照下 ZGP 单晶体激光诱导损伤的物理和技术问题
IF 2.4 4区 物理与天体物理
Photonics Pub Date : 2023-12-11 DOI: 10.3390/photonics10121364
N. Yudin, Victor Dyomin, Alexander Gribenyukov, Oleg Antipov, Andrei Khudoley, I. Kinyaevskiy, Mikhail Zinovev, S. Podzyvalov, V. Kuznetsov, E. Slyunko, Alexey Lysenko, A. Kalsin, I. Eranov, H. Baalbaki
{"title":"Physical and Technological Aspects of Laser-Induced Damage of ZGP Single Crystals under Periodically Pulsed Laser Irradiation at 2.1 μm","authors":"N. Yudin, Victor Dyomin, Alexander Gribenyukov, Oleg Antipov, Andrei Khudoley, I. Kinyaevskiy, Mikhail Zinovev, S. Podzyvalov, V. Kuznetsov, E. Slyunko, Alexey Lysenko, A. Kalsin, I. Eranov, H. Baalbaki","doi":"10.3390/photonics10121364","DOIUrl":"https://doi.org/10.3390/photonics10121364","url":null,"abstract":"The nonlinear properties of zinc germanium diphosphide (ZGP) crystals enable their applications in powerful mid-IR optical parametric oscillators and second-harmonic generators. This paper summarizes the mechanisms of the laser-induced damage (LID) of high-purity ZGP crystals under periodically pulsed nanosecond irradiation by a Ho3+:YAG laser at 2.1 μm. The ZGP samples were manufactured by “LOC” Ent., Tomsk, Russia, or the Harbin Institute of Technology, China. The impact of processing techniques and the post-growing methods for polishing and anti-reflective coatings on the LID threshold are discussed. The importance of the defect structure of the crystal lattice and the parameters of transparent coatings for increasing the LID threshold are also discussed. The impact of the test laser parameters on the LID threshold and the transient area near the LID threshold obtained using digital holography are analyzed. The influence of the pre-damage processes on the optical parametric oscillations is reported. Lastly, the prospects for improving ZGP crystals to further increase the LID threshold are discussed.","PeriodicalId":20154,"journal":{"name":"Photonics","volume":"55 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139010409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Simulation Test of The Aerodynamic Environment of A Missile-Borne Pulsed Laser Forward Detection System at High Flight Speed 导弹携带式脉冲激光前向探测系统高速飞行时的空气动力环境模拟测试
IF 2.4 4区 物理与天体物理
Photonics Pub Date : 2023-12-10 DOI: 10.3390/photonics10121363
Peng Liu, Jian Li, Tuan Hua, He Zhang
{"title":"Simulation Test of The Aerodynamic Environment of A Missile-Borne Pulsed Laser Forward Detection System at High Flight Speed","authors":"Peng Liu, Jian Li, Tuan Hua, He Zhang","doi":"10.3390/photonics10121363","DOIUrl":"https://doi.org/10.3390/photonics10121363","url":null,"abstract":"When a missile-borne pulsed laser forward detection system flies at supersonic speed, the laser beam will be distorted by the uneven outflow field, resulting in a significant reduction in ranging accuracy. In this paper, the impact of high flight speed on a pulsed laser detection system is studied. First, a new ray tracing method with adaptive step size adjustment is proposed, which greatly improves the computational efficiency. Second, the aerodynamic environment of a munition flying at high speed is simulated by an intermittent transonic and supersonic wind tunnel to obtain the schlieren data of the flow field at various Mach numbers. The schlieren data present a shock wave structure similar to that of the simulation. In addition, the variation patterns of the pulsed laser echo waveform of the model under different aerodynamic conditions are studied to evaluate the detectability and operational stability of the laser detection system under static conditions. The test results match the simulation results well, and the two offer relatively consistent shock wave structures, which verifies the correctness and effectiveness of the flow field simulation model. The test echo waveforms are in good agreement with the simulated echo waveforms; the relative errors between the peak values of test and simulated echo waveforms at various Mach numbers do not exceed 20%, and the correlation coefficients between the test and simulated echo waveforms all exceed 0.7, indicating high correlations between the two.","PeriodicalId":20154,"journal":{"name":"Photonics","volume":"222 ","pages":""},"PeriodicalIF":2.4,"publicationDate":"2023-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138982430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Signal-to-Noise Ratio Improvement for Phase-Sensitive Optical Time-Domain Reflectometry Using a Genetic Least Mean Square Method 利用遗传最小均方法提高相位敏感光学时域反射测量法的信噪比
IF 2.4 4区 物理与天体物理
Photonics Pub Date : 2023-12-09 DOI: 10.3390/photonics10121362
Xin Liu, Zhihua Liu, Xiaoxu Zhou, Yu Wang, Qing Bai, Bao-quan Jin
{"title":"Signal-to-Noise Ratio Improvement for Phase-Sensitive Optical Time-Domain Reflectometry Using a Genetic Least Mean Square Method","authors":"Xin Liu, Zhihua Liu, Xiaoxu Zhou, Yu Wang, Qing Bai, Bao-quan Jin","doi":"10.3390/photonics10121362","DOIUrl":"https://doi.org/10.3390/photonics10121362","url":null,"abstract":"In this paper, a genetic least mean square (GLMS) method is proposed to improve the signal-to-noise ratio (SNR) of acoustic signal reconstruction in a phase-sensitive optical time-domain reflectometry system. The raw demodulated signal is processed via applying the least mean square criterion. The SNR of the processed signal was calculated and served as the objective function in the fitness evaluation procedure. The genetic operations of the population selection, crossover, and mutation are sequentially performed and repeated until the suspensive condition is reached. Through multiple iterations, the GLMS method continuously optimized the population to find the optimal solution. Experimental results demonstrate that the SNR is substantially improved by 14.37–23.60 dB in the monotonic scale audio signal test from 60 to 1000 Hz. Furthermore, the improvement of the phase reconstruction of a human voice audio signal is also validated by exploiting the proposed GLMS method.","PeriodicalId":20154,"journal":{"name":"Photonics","volume":"243 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138983230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optical Phased Array-Based Laser Beam Array Subdivide Pixel Method for Improving Three-Dimensional Imaging Resolution 基于光学相控阵的激光束阵列细分像素法提高三维成像分辨率
IF 2.4 4区 物理与天体物理
Photonics Pub Date : 2023-12-09 DOI: 10.3390/photonics10121360
Shuai Wang, Gang Yuan, Kun-Peng Wang, Guang-De Sun, Lei Liu, Ling Li, Bing Zhang, Lin Quan
{"title":"Optical Phased Array-Based Laser Beam Array Subdivide Pixel Method for Improving Three-Dimensional Imaging Resolution","authors":"Shuai Wang, Gang Yuan, Kun-Peng Wang, Guang-De Sun, Lei Liu, Ling Li, Bing Zhang, Lin Quan","doi":"10.3390/photonics10121360","DOIUrl":"https://doi.org/10.3390/photonics10121360","url":null,"abstract":"The small number of pixels in the current linear mode avalanche photodiode (LM-APD) array limits its three-dimensional (3D) imaging resolution. We use an optical phased array-based beam array subdivided pixel method to improve the 3D imaging resolution, using an optical phased array to generate a beam array with the same number of pixels as the LM-APD array and matching positions and controlling each sub-beam in the beam array to scan in the field of view of the corresponding pixel. The sub-beam divergence angle in the beam array is smaller than the instantaneous field of view angle of a single pixel in the LM-APD array. The sub-beam scanning in a single pixel’s field of view realizes the multiple acquisition of the target 3D information by the LM-APD array, thus improving the resolution of the LM-APD array. The distribution of the beam array in the far field is simulated, and the main performance parameters of 3D imaging are analyzed. Finally, a liquid crystal phase modulator is used as an optical phased array device to conduct experiments on a target 20 m away, and the results prove that our method can improve the resolution from 4 × 4 to 8 × 8, which can be improved at least four times.","PeriodicalId":20154,"journal":{"name":"Photonics","volume":"389 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138983141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mueller-Polarimetry of Barley Leaves I: Depolarization Metrics 大麦叶片的穆勒极化测量法 I:去极化指标
IF 2.4 4区 物理与天体物理
Photonics Pub Date : 2023-12-09 DOI: 10.3390/photonics10121361
S. Savenkov, Y. Oberemok, I. Kolomiets, R. Muttiah
{"title":"Mueller-Polarimetry of Barley Leaves I: Depolarization Metrics","authors":"S. Savenkov, Y. Oberemok, I. Kolomiets, R. Muttiah","doi":"10.3390/photonics10121361","DOIUrl":"https://doi.org/10.3390/photonics10121361","url":null,"abstract":"In this paper, Mueller polarimetry is applied to study the three groups of common barley leaf samples (Hordeum vulgare) in the visible spectrum (λ = 632.8 nm): Chlorina mutant, Chlorina etiolated mutant and Cesaer varieties. These samples differed in internal leaf structure from genetic mutation or by illumination during growth. Our main concern is to discriminate and characterize these three groups of leaf samples by depolarization metrics: degree of polarization (DoP), average degree of polarization (Average DoP), depolarization index (DI(M)), and Q(M) and R(M) metrics. The results obtained show that all depolarization metrics are sensitive to the sample’s polarization properties. The most effective observable is the Q(M) metric in both forward and backward scattering. The DoP metric showed presence of depolarization anisotropy, which is significantly different for forward and backward scattering for all three groups of samples. Dichroism is observed for both forward and backward scattering, with lower dichroism in forward scattering.","PeriodicalId":20154,"journal":{"name":"Photonics","volume":"564 ","pages":""},"PeriodicalIF":2.4,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138983156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spin-Hall Effect of Cylindrical Vector Vortex Beams 圆柱矢量涡束的自旋-霍尔效应
IF 2.4 4区 物理与天体物理
Photonics Pub Date : 2023-12-08 DOI: 10.3390/photonics10121356
Xuyao Zhang, Shuo Wang, Jinhong Liu, Jinze Wu, Jinhong Li
{"title":"Spin-Hall Effect of Cylindrical Vector Vortex Beams","authors":"Xuyao Zhang, Shuo Wang, Jinhong Liu, Jinze Wu, Jinhong Li","doi":"10.3390/photonics10121356","DOIUrl":"https://doi.org/10.3390/photonics10121356","url":null,"abstract":"Spin-Hall effect (SHE) of light is one of the main manifestations of the spin-orbit interaction of photons, and has been extensively studied for optical beams with homogeneous polarization. Here, we present a theoretical study of the SHE of cylindrical vector vortex beams (CVVBs) possessing inhomogeneous polarization. We derive the analytical expressions of the SHE of CVVBs reflected and refracted at a dielectric interface with radial and azimuthal polarization of incidence. The spin-dependent shifts of the SHE of light linearly depend on the topological charge of the CVVBs. In contrast to the conventional SHE of horizontally or vertically polarized beams, the SHE shifts of the CVVBs are asymmetrical when the topological charge is nonzero. This asymmetry results in the transverse Imbert–Fedorov (IF) shifts that are proportional to the topological charge. Furthermore, based on weak measurement, we propose an experimental scheme to enhance the SHE and related IF shifts with proper pre- and post-selection polarization states. Our results advance the study of the SHE of structured light and may find applications in SHE-based techniques such as precision measurement.","PeriodicalId":20154,"journal":{"name":"Photonics","volume":"46 23","pages":""},"PeriodicalIF":2.4,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138588353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Deep Mutual Learning-Based Mode Recognition of Orbital Angular Momentum 基于深度互学的轨道角动量模式识别
IF 2.4 4区 物理与天体物理
Photonics Pub Date : 2023-12-08 DOI: 10.3390/photonics10121357
T. Qu, Zhiming Zhao, Yan Zhang, Jiaji Wu, Zhensen Wu
{"title":"Deep Mutual Learning-Based Mode Recognition of Orbital Angular Momentum","authors":"T. Qu, Zhiming Zhao, Yan Zhang, Jiaji Wu, Zhensen Wu","doi":"10.3390/photonics10121357","DOIUrl":"https://doi.org/10.3390/photonics10121357","url":null,"abstract":"Due to its orbital angular momentum (OAM), optical vortex has been widely used in communications and LIDAR target detection. The OAM mode recognition based on deep learning is mostly based on the basic convolutional neural network. To ensure high-precision OAM state detection, a deeper network structure is required to overcome the problem of similar light intensity distribution of different superimposed vortex beams and the effect of atmospheric turbulence disturbance. However, the large number of parameters and the computation of the OAM state detection network conflict with the requirements of deploying optical communication system equipment. In this paper, an online knowledge distillation scheme is selected to achieve an end-to-end single-stage training and the inter-class dark knowledge of similar modes are fully utilized. An optical vortex OAM state detection technique based on deep mutual learning (DML) is proposed. The simulation results show that after mutual learning training, a small detection network with higher accuracy can be obtained, which is more suitable for terminal deployment. Based on the scalability of the number of networks in the DML queue, it provides a new possibility to further improve the detection accuracy of the optical communication.","PeriodicalId":20154,"journal":{"name":"Photonics","volume":"165 ","pages":""},"PeriodicalIF":2.4,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139011449","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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