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Keywords = electro-optic coefficient

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20 pages, 790 KB  
Article
Electro-Optical Properties of Excitons in CdSe Nanoplatelets
by Gerard Czajkowski
Symmetry 2026, 18(2), 386; https://doi.org/10.3390/sym18020386 - 22 Feb 2026
Viewed by 148
Abstract
Applying a constant external electric field to a semiconductor nanostructure with Wannier–Mott excitons, in which the electron and hole interact via a centrally symmetric Coulomb potential, alters the symmetry of the system. When the electric field is applied parallel to the z-axis, [...] Read more.
Applying a constant external electric field to a semiconductor nanostructure with Wannier–Mott excitons, in which the electron and hole interact via a centrally symmetric Coulomb potential, alters the symmetry of the system. When the electric field is applied parallel to the z-axis, the system exhibits cylindrical symmetry; when the field lies in the xy plane, the symmetry is broken. These symmetry changes affect the optical properties of the system. We present a theoretical calculation that yields analytical expressions for the optical functions of CdSe Nanoplatelets—reflectivity, transmissivity, and the absorption coefficient—in an external homogeneous electric field. From these, we focus on the absorption coefficient. We consider various configurations, with the external field oriented perpendicular and parallel to the platelet planes. Using the real density matrix approach, we calculate the linear electro-optical functions of CdSe nanoplatelets, taking into account the effect of dielectric confinement on excitonic states. We also discuss the impact of platelet geometry (thickness and lateral dimensions) and applied field strength on the spectrum. Full article
(This article belongs to the Special Issue Symmetry and Nonlinearity in Optics)
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10 pages, 1893 KB  
Article
Design of a High-Efficiency Hydrogenated Amorphous Silicon Electro-Absorption Modulator with Embedded Graphene Capacitor
by Babak Hashemi, Sandro Rao, Maurizio Casalino and Francesco Giuseppe Della Corte
Photonics 2025, 12(9), 916; https://doi.org/10.3390/photonics12090916 - 13 Sep 2025
Viewed by 1093
Abstract
Waveguide-integrated electro-optical modulators play a crucial role in the design of new-generation photonic integrated circuits. The target of this paper is to demonstrate the potential offered by the association of graphene (Gr) and hydrogenated amorphous silicon (a-Si:H) in enhancing silicon photonics technology, enabling, [...] Read more.
Waveguide-integrated electro-optical modulators play a crucial role in the design of new-generation photonic integrated circuits. The target of this paper is to demonstrate the potential offered by the association of graphene (Gr) and hydrogenated amorphous silicon (a-Si:H) in enhancing silicon photonics technology, enabling, in particular, the fabrication of efficient, wide-bandwidth, highly compact active devices. The design of the proposed electro-optic modulator is based on accurate numerical simulations where Gr is explored as the active material, absorbing (or not) the light propagating along the waveguide core, with its absorption coefficient being tunable through the application of an external electric bias. By strategically embedding two Gr monolayers where the propagating optical field is at its maximum, the performance of the modulator is maximized, resulting in a 39.5 GHz 3 dB bandwidth, corresponding to a 0.34 dB/µm modulation depth. The straightforward feasibility of the proposed structure is bolstered by the use of the Plasma-Enhanced Chemical Vapor Deposition technique, which allows for the deposition of a-Si:H on a silicon-on-insulator platform as a post-processing phase, ensuring potential scalability and practical implementation for advanced photonics. Full article
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28 pages, 23013 KB  
Review
On-Chip OPA: Progress and Prospects in Liquid Crystal, Lithium Niobate, and Silicon Material Platforms
by Xiaobin Wang, Junliang Guo, Zixin Yang, Yuqiu Zhang, Jinyong Leng, Qiang Yu and Jian Wu
Nanomaterials 2025, 15(17), 1374; https://doi.org/10.3390/nano15171374 - 5 Sep 2025
Viewed by 2108
Abstract
Non-mechanical beam steering is required for holographic displays, free-space optical communication, and chip-scale LiDAR. Optical phased arrays (OPAs), which allow for inertia-free, high-speed beam control via electronic phase control, are an important research topic. The present study investigates the primary material platform for [...] Read more.
Non-mechanical beam steering is required for holographic displays, free-space optical communication, and chip-scale LiDAR. Optical phased arrays (OPAs), which allow for inertia-free, high-speed beam control via electronic phase control, are an important research topic. The present study investigates the primary material platform for on-chip OPAs: Liquid crystal OPAs (LC-OPAs) employ electrically tunable refractive indices for low-voltage operation; lithium niobate OPAs (LN-OPAs) utilize high electro-optic coefficients for high-speed, low-power consumption, and large-bandwidth operation; and silicon-based OPAs (Si-OPAs) apply mature photonic integration to achieve high integration density and GHz-range steering. The paper thoroughly examines OPA basics, recent material-specific advancements, performance benchmarks, outstanding issues, and future prospects. Full article
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29 pages, 12480 KB  
Review
Advances of Welding Technology of Glass for Electrical Applications
by Dejun Yan, Lili Ma, Jiaqi Lu, Dasen Wang and Xiaopeng Li
Materials 2025, 18(17), 4096; https://doi.org/10.3390/ma18174096 - 1 Sep 2025
Cited by 1 | Viewed by 4464
Abstract
Glass, as an amorphous material with excellent optical transparency and chemical stability, plays an irreplaceable role in modern engineering and technology fields such as semiconductor manufacturing and micro-electro-mechanical systems (MEMS). For example, borosilicate glass, with a coefficient of thermal expansion (CTE) that is [...] Read more.
Glass, as an amorphous material with excellent optical transparency and chemical stability, plays an irreplaceable role in modern engineering and technology fields such as semiconductor manufacturing and micro-electro-mechanical systems (MEMS). For example, borosilicate glass, with a coefficient of thermal expansion (CTE) that is close to having good thermal shock resistance and chemical stability, can be applied to MEMS packaging and aerospace fields. SiO2 glass exhibits excellent thermal stability, extremely low optical absorption, and high light transmittance, while also possessing strong chemical stability and extremely low dielectric loss. It is widely used in semiconductors, photolithography, and micro-optical devices. However, the stress sensitivity of traditional mechanical joints and the poor weather resistance of adhesive bonding make conventional methods unsuitable for glass joining. Welding technology, with its advantages of high joint strength, structural integrity, and scalability for mass production, has emerged as a key approach for precision glass joining. In the field of glass welding, technologies such as glass brazing, ultrasonic welding, anodic bonding, and laser welding are being widely studied and applied. With the advancement of laser technology, laser welding has emerged as a key solution to overcoming the bottlenecks of conventional processes. This paper, along with the application cases for these technologies, includes an in-depth study of common issues in glass welding, such as residual stress management and interface compatibility design, as well as prospects for the future development of glass welding technology. Full article
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25 pages, 3030 KB  
Review
Lithium Niobate Crystal Preparation, Properties, and Its Application in Electro-Optical Devices
by Yan Zhang, Xuefeng Xiao, Jiayi Chen, Han Zhang, Yan Huang, Jiashun Si, Shuaijie Liang, Qingyan Xu, Huan Zhang, Lingling Ma, Cui Yang and Xuefeng Zhang
Inorganics 2025, 13(9), 278; https://doi.org/10.3390/inorganics13090278 - 22 Aug 2025
Cited by 3 | Viewed by 2831
Abstract
Lithium Niobate (LiNbO3, LN) crystals are multifunctional optical materials with excellent electro-optical, acousto-optical, and nonlinear optical properties, and their broad spectral transparency makes them widely used in electro-optical modulators, tunable filters, and beam deflectors. Near Stoichiometric Lithium Niobate (NSLN) crystals have [...] Read more.
Lithium Niobate (LiNbO3, LN) crystals are multifunctional optical materials with excellent electro-optical, acousto-optical, and nonlinear optical properties, and their broad spectral transparency makes them widely used in electro-optical modulators, tunable filters, and beam deflectors. Near Stoichiometric Lithium Niobate (NSLN) crystals have a lithium to niobium ratio ([Li]/[Nb]) close to 1:1,demonstrate superior performance characteristics compared to composition lithium niobate (Congruent Lithium Niobate (CLN), [Li]/[Nb] = 48.5:51.5) crystals. NSLN crystals have a lower coercive field (~4 kV/mm), higher electro-optic coefficient (γ33 = 38.3 pm/V), and better nonlinear optical properties. This paper systematically reviews the research progress on preparation methods, the physical properties of LN and NSLN crystals, and their applications in devices such as electro-optical modulators, optical micro-ring resonators, and holographic storage. Finally, the future development direction of NSLN crystals in the preparation process (large-size single-crystal growth and defect control) and new electro-optical devices (low voltage deflectors based on domain engineering) is envisioned. Full article
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12 pages, 1298 KB  
Article
Effect of Deuteration on the Temperature Dependence of the Quadratic Electro-Optic Effect in KDP Crystals
by Marek Izdebski and Rafał Ledzion
Materials 2025, 18(14), 3290; https://doi.org/10.3390/ma18143290 - 12 Jul 2025
Viewed by 745
Abstract
The results of precise measurements of the temperature dependencies of quadratic electro-optic coefficients, namely g1111g1122 and no3g1111ne3g3311, in KH2PO4 (KDP) and KD2PO4 [...] Read more.
The results of precise measurements of the temperature dependencies of quadratic electro-optic coefficients, namely g1111g1122 and no3g1111ne3g3311, in KH2PO4 (KDP) and KD2PO4 (DKDP) crystals at a wavelength of 632.8 nm are presented. We consider electro-optic coefficients describing changes in the optical impenetrability tensor resulting from an applied electric field, as well as intrinsic electro-optic coefficients defined in terms of induced polarization. The results show significant differences in the values of the analogous coefficients for the KDP and DKDP crystals and their temperature dependencies. Therefore, the quadratic electro-optic effect in KDP-type crystals cannot be easily described based solely on the contribution of PO4 tetrahedra, as assumed in current models of the linear effect. Moreover, the values of the intrinsic coefficients in the KDP and DKDP crystals differ even more than the corresponding usual electro-optic coefficients, which contradicts the conventional belief in their lower variability. Full article
(This article belongs to the Section Optical and Photonic Materials)
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16 pages, 5900 KB  
Article
Tuning Transmission Properties of Two-Dimensional Photonic Crystal Waveguides Using Functional Dielectric Cavities
by Siqi Zhang, Feng Yang, Wenying Zhang, Wei Zhao, Luhe Yang and Hong Li
Micromachines 2025, 16(5), 597; https://doi.org/10.3390/mi16050597 - 20 May 2025
Cited by 1 | Viewed by 1369
Abstract
In this study, the photonic band structure, transmissivity, and electric field distribution of a two-dimensional photonic crystal coupled waveguide structure are calculated using the supercell technique and finite element method. The waveguide consists of circular KNbO3 and functional dielectric [...] Read more.
In this study, the photonic band structure, transmissivity, and electric field distribution of a two-dimensional photonic crystal coupled waveguide structure are calculated using the supercell technique and finite element method. The waveguide consists of circular KNbO3 and functional dielectric cylinders embedded in air. The dielectric constant of a functional medium cylinder is spatially dependent, which is realized through the electro-optic and Kerr effects. The dielectric constant function is defined as εc(r)=k·r+b (0rrc), where the coefficient k and parameter b can be adjusted by an external electric field. By tuning k and b, the transmission characteristics of the waveguide, including the propagation direction and light field distribution, exhibit significant adjustability. Specifically, parameter b enhances or suppresses the transmissivity at output ports 1 and 2. By utilizing the regulatory capability of functional media on waveguide transmission characteristics, optical filters with specific filtering functions can be designed. These findings provide novel design strategies for advanced optical devices. Full article
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12 pages, 2802 KB  
Article
Research on the Fabrication of X-Cut Near Stoichiometric Lithium Niobate Wafers
by Zixuan Dong, Qingyan Xu, Shuaijie Liang, Jiashun Si, Mengfan Wang, Xuefeng Zhang and Jilin He
Crystals 2025, 15(3), 282; https://doi.org/10.3390/cryst15030282 - 19 Mar 2025
Cited by 2 | Viewed by 1228
Abstract
This article discusses the preparation of twin free X-cut lithium niobate wafers using the diffusion method. The liquid electrode method was used to eliminate parasitic microdomains at dislocations. According to research, the Li-rich lithium niobate polycrystalline material contains (Li0.941Nb0.059) [...] Read more.
This article discusses the preparation of twin free X-cut lithium niobate wafers using the diffusion method. The liquid electrode method was used to eliminate parasitic microdomains at dislocations. According to research, the Li-rich lithium niobate polycrystalline material contains (Li0.941Nb0.059) Nb0.9528O3 and Li3NbO4 phases, and the diffused near-stoichiometric lithium niobate wafer exhibits a monodomain state. The piezoelectric coefficient (d33) of near-stoichiometric lithium niobate after eliminating microdomains increased by 12% compared to congruent lithium niobate. The Curie temperature of near-stoichiometric lithium niobate wafers can reach 1198 °C, and the UV absorption spectrum of near-stoichiometric lithium niobate is blue shifted by 10 nm compared to congruent lithium niobate wafers, making it more suitable for fabricating electro-optic and micro nano electronics devices. Full article
(This article belongs to the Section Industrial Crystallization)
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12 pages, 2778 KB  
Article
High Reflectivity, Compact, and Widely Tunable Distributed Bragg Reflector Based on Silicon-Rich SiNx-SiOy at 80 °C PECVD
by Irene Rodríguez Lamoso and Sascha Preu
Appl. Sci. 2025, 15(6), 3330; https://doi.org/10.3390/app15063330 - 18 Mar 2025
Cited by 2 | Viewed by 4201
Abstract
This study investigates the mechanical and optical characteristics of silicon nitride thin films deposited with PECVD at 80 °C for tunable silicon-rich SiNx-SiOy-based MEMS optical cavities. Varying the deposition parameters using SiH4 and N2 as precursor gases [...] Read more.
This study investigates the mechanical and optical characteristics of silicon nitride thin films deposited with PECVD at 80 °C for tunable silicon-rich SiNx-SiOy-based MEMS optical cavities. Varying the deposition parameters using SiH4 and N2 as precursor gases for silicon-rich SiNx thin films allows us to tune the refractive index to a value as high as 2.40 ± 0.013 at an extinction coefficient of only 0.008, an extremely low surface roughness of only 0.26 nm, and a compressive stress of about 150 MPa. We deposited 6.5-layer pairs of silicon-rich SiNx/SiOy-distributed Bragg reflector (DBR) micro-electro-mechanical system (MEMS) mirror that covers the whole 1300 and 1550 nm range. Cavity architectures of 6.5 top and 6 bottom layer-pairs were fabricated in the clean room providing a variety of cavity lengths between 0.615 µm and 2.85 µm. These lengths were then simulated in order to estimate the Young’s Modulus of silicon-rich SiNx, obtaining values from 56 to 92 GPa. One of the designs was characterised electro-thermally providing a tuning range of at least 86.7 nm centred at 1585 nm. The tunable filters are well suitable for implementation as tuning element in lasers for optical coherence tomography. Full article
(This article belongs to the Special Issue Interdisciplinary Approaches and Applications of Optics & Photonics)
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18 pages, 1880 KB  
Article
Proposal for a Battery to Evaluate Functional Capacity in Older Adults with Disabilities
by Josu Ascondo, Iñaki Llodio, Bingen Marcos-Rivero, Cristina Granados, Sheila Romero, Aitor Iturricastillo and Javier Yanci
Sensors 2025, 25(6), 1813; https://doi.org/10.3390/s25061813 - 14 Mar 2025
Cited by 1 | Viewed by 1135
Abstract
The purpose was to design and validate a battery of physical tests, called EFEPD-1.0, adapted to assess functionality in people with disabilities. In addition, we sought to analyze the validity and reliability of this battery both for the total group and differentiated by [...] Read more.
The purpose was to design and validate a battery of physical tests, called EFEPD-1.0, adapted to assess functionality in people with disabilities. In addition, we sought to analyze the validity and reliability of this battery both for the total group and differentiated by sex. A total of 43 adults with disabilities (32 women and 11 men) participated (57.11 ± 10.12 years). The battery was composed of five blocks of functionality: neuromuscular, combined actions, acceleration, balance, and cardiovascular. The neuromuscular functionality was measured by the vertical and horizontal jump test using the optical system (Opto Jump Next®, Microgate, Bolzano, Italy) as well as the Hand Grip (HG) test using a (5030J1, Jamar®, Sammons Preston, Inc, Nottinghamshire, UK) hand dynamometer. The combined actions and balance functionality were assessed with the Time Up and Go (TUG) test, the 30 s Chair Stand (30CTS) test, and the One-Leg Stance (OLS) test measured by a manual stopwatch (HS-80TW-1EF, Casio®, Tokyo, Japan). The acceleration functionality was evaluated through 20 m sprints and the 505 change of direction (COD505) test, using the (Microgate, Witty®, Bolzano, Italy) photocell system. The cardiovascular functionality was evaluated with the Six-Minute Walking Test (6MWT), where heart rate was monitored using the (Polar Team Sport System®, Polar Electro Oy, Kempele, Finland), and additional walking mechanics were recorded with Stryd (Stryd Everest 12 Firmware 1.18 Software 3, Stryd Inc., Boulder, CO, USA). The results showed that the intraclass correlation coefficients (ICCs) ranged from moderate to almost perfect (ICC = 0.65–0.98) between test repetitions. Some tests could significantly differentiate (p < 0.05) men and women, highlighting better neuromuscular capacity in men and better balance in women. The correlations between tests showed significant convergent validity. The Evaluation of Functionality in the Disabled Population (EFEPD-1.0) battery not only consistently measures functional capacities in people with disabilities, but it can also discriminate between different subgroups within this population. Full article
(This article belongs to the Collection Sensors for Globalized Healthy Living and Wellbeing)
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9 pages, 4802 KB  
Communication
Measuring the Effective Electro-Optic Coefficient of Low-Temperature-Prepared Lead Zirconate Titanate Thin Films
by Bin Li, Hongyan Yu, Chen Yang, Jungan Wang, Yu Han and Feng Qiu
Materials 2025, 18(4), 837; https://doi.org/10.3390/ma18040837 - 14 Feb 2025
Cited by 3 | Viewed by 1405
Abstract
Developing lead zirconate titanate (PZT)-based electro-optic (EO) modulators is vital for integrated photonics. The high annealing temperature required for the processing of PZT thin films restricts their compatibility with modern complementary metal–oxide–semiconductor (CMOS) technology. In this work, high-quality PZT films were fabricated on [...] Read more.
Developing lead zirconate titanate (PZT)-based electro-optic (EO) modulators is vital for integrated photonics. The high annealing temperature required for the processing of PZT thin films restricts their compatibility with modern complementary metal–oxide–semiconductor (CMOS) technology. In this work, high-quality PZT films were fabricated on SiO2/Si substrates at a low annealing temperature of 450 °C. The PZT films demonstrated a preferential (100) orientation and were uniform and crack-free. Based on the low-temperature PZT films, we subsequently designed and fabricated a Mach–Zehnder Interferometer (MZI) waveguide modulator. The measured half-wave voltage (Vπ) was 4.8 V at a wavelength of 1550 nm, corresponding to an in-device EO coefficient as high as 66 pm/V, which shows potential use in optical devices. The results reported in this work show great promise for the integration of PZT thin films with other complex systems. Full article
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16 pages, 2157 KB  
Article
High-Voltage Measurement Infrastructure Based on Optical Technology for Transmission Lines
by Mauro Augusto da Rosa, Clayrton Monteiro Henrique, Gabriel Santos Bolacell, Hermes Irineu Del Monego and Paulo César Rodrigues de Lima Junior
Energies 2025, 18(4), 830; https://doi.org/10.3390/en18040830 - 11 Feb 2025
Cited by 2 | Viewed by 1511
Abstract
This paper introduces a singular measurement infrastructure for real-time monitoring of transmission lines, applied to a 230 kV section of the Brazilian grid. The system aimed to expand the scope of monitoring variables using new concepts of optical sensing. Thus, variables are captured [...] Read more.
This paper introduces a singular measurement infrastructure for real-time monitoring of transmission lines, applied to a 230 kV section of the Brazilian grid. The system aimed to expand the scope of monitoring variables using new concepts of optical sensing. Thus, variables are captured not only in the electrical domain but also in the mechanical, thermal, and environmental domains through optical technologies and meteorological measurement sensors strategically positioned along the transmission line. The system relies on new features, including a high-voltage polymeric insulator instrumentalized with optical fiber sensors to measure line electrical current, conductor temperature, mechanical strain, and an electro-optical signal processing unit fed by a solar system. The correlations between the monitored variables provide more complete information about what happens in the transmission line compared to the analysis of purely electrical quantities. For instance, the Spearman coefficient of 0.9909 highlights the strong correlation between anchoring force and ambient temperature. This new way of monitoring systems opens the doors to a multivariate power system analysis. Full article
(This article belongs to the Special Issue Advanced Electric Power Systems, 2nd Edition)
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13 pages, 9988 KB  
Communication
Tunable Beam Steering Metasurface Based on a PMN-PT Crystal with a High Electro-Optic Coefficient
by Huan Chen, Zixin Wang, Xin Chen and Junli Wang
Sensors 2025, 25(1), 55; https://doi.org/10.3390/s25010055 - 25 Dec 2024
Cited by 3 | Viewed by 3076
Abstract
Existing tunable optical metasurfaces based on the electro-optic effect are either complex in structure or have a limited phase modulation range. In this paper, a simple rectangular metasurface structure based on a Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT) crystal with [...] Read more.
Existing tunable optical metasurfaces based on the electro-optic effect are either complex in structure or have a limited phase modulation range. In this paper, a simple rectangular metasurface structure based on a Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT) crystal with high electro-optic coefficient of 120 pm/V was designed to demonstrate its electrically tunable performance in the optical communication band through simulations. By optimizing the structure parameters, a tunable metasurface was generated that can induce a complete 2π phase shift for beam deflection while maintaining relatively uniform transmittance. Simulations further demonstrated the electrical tunability of the beam deflection direction and operating wavelength of the metasurface. This tunable optical metasurface, with its simple and easily fabricated structure, can promote the development and application of multifunctional and controllable metasurfaces. Its adjustable beam deflection direction and operating wavelength may find applications in fields such as optical communication systems and imaging. Full article
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19 pages, 1977 KB  
Article
Measuring the Electro-Optical Kerr Effect Against the Background of Electro-Absorption Modulation in Liquids
by Rafał Ledzion, Marek Izdebski and Anita Rambo
Materials 2024, 17(21), 5346; https://doi.org/10.3390/ma17215346 - 31 Oct 2024
Cited by 2 | Viewed by 1444
Abstract
A new approach to the dynamic polarimetric method is proposed, which allows for the decoupling of electro-optical Kerr effect measurements from the electro-absorption effect in partially transparent liquids. The method is illustrated by using the results of engine oil measurements as a function [...] Read more.
A new approach to the dynamic polarimetric method is proposed, which allows for the decoupling of electro-optical Kerr effect measurements from the electro-absorption effect in partially transparent liquids. The method is illustrated by using the results of engine oil measurements as a function of temperature and modulating field frequency. It was shown that the birefringence induced in the sample, the modulation of the ordinary wave transmission, and the modulation of the extraordinary wave transmission in the sample can be shifted in phase with respect to the square of the applied alternating modulating field. Each of these three phase shifts can depend differently on the temperature and frequency. Neglecting the influence of electro-absorption on electro-optical measurements in liquids or considering electro-absorption as an effect correlated in phase with induced birefringence may lead to significant measurement errors. This indicates that the Kerr constant and the electro-absorption coefficients for an alternating electric field should be considered as complex quantities instead of real values, as they have been traditionally. The proposed approach fills an important gap in measurement techniques described in the literature, which may provide erroneous results for measurements of the Kerr constant in partially transparent liquids including many industrially important liquids. Full article
(This article belongs to the Section Optical and Photonic Materials)
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18 pages, 5824 KB  
Article
A Fusion Tracking Algorithm for Electro-Optical Theodolite Based on the Three-State Transition Model
by Shixue Zhang, Houfeng Wang, Liduo Song, Hongwen Li and Shuai Liu
Sensors 2024, 24(17), 5847; https://doi.org/10.3390/s24175847 - 9 Sep 2024
Cited by 1 | Viewed by 1513
Abstract
This study presents a novel approach to address the autonomous stable tracking issue in electro-optical theodolite operating in closed-loop mode. The proposed methodology includes a multi-sensor adaptive weighted fusion algorithm and a fusion tracking algorithm based on a three-state transition model. A refined [...] Read more.
This study presents a novel approach to address the autonomous stable tracking issue in electro-optical theodolite operating in closed-loop mode. The proposed methodology includes a multi-sensor adaptive weighted fusion algorithm and a fusion tracking algorithm based on a three-state transition model. A refined recursive formula for error covariance estimation is developed by integrating attenuation factors and least squares extrapolation. This formula is employed to formulate a multi-sensor weighted fusion algorithm that utilizes error covariance estimation. By assigning weighted coefficients to calculate the residual of the newly introduced error term and defining the sensor’s unique states based on these coefficients, a fusion tracking algorithm grounded on the three-state transition model is introduced. In cases of interference or sensor failure, the algorithm either computes the weighted fusion value of the multi-sensor measurement or triggers autonomous sensor switching to ensure the autonomous and stable measurement of the theodolite. Experimental results indicate that when a specific sensor is affected by interference or the off-target amount cannot be extracted, the algorithm can swiftly switch to an alternative sensor. This capability facilitates the precise and consistent generation of data, thereby ensuring the stable operation of the tracking system. Furthermore, the algorithm demonstrates robustness across various measurement scenarios. Full article
(This article belongs to the Section Optical Sensors)
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