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Search Results (450)

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8 pages, 1944 KiB  
Communication
Achromatic Flat Metasurface Fiber Couplers within Telecom Bands
by Jiayi Li, Rui Li, Xiaojun Xue, Xiao Jiang, Xiaoming Chen and Hsiang-Chen Chui
Photonics 2023, 10(1), 28; https://doi.org/10.3390/photonics10010028 - 27 Dec 2022
Cited by 2 | Viewed by 1922
Abstract
We proposed a single metalens for fiber coupling within telecom bands. This proposed fiber coupler combined a single layer metalens and a Polydimethylsiloxane (PDMS) layer. Instead of traditional fiber collimators, which are bulky and require complex calibration processes, we used a metalens for [...] Read more.
We proposed a single metalens for fiber coupling within telecom bands. This proposed fiber coupler combined a single layer metalens and a Polydimethylsiloxane (PDMS) layer. Instead of traditional fiber collimators, which are bulky and require complex calibration processes, we used a metalens for the focusing of incident and outgoing lasers and achieve achromatic aberration over a certain wavelength band. The focal length was kept as 514.9 μm with a 6.92-μm tolerance. The average coupling efficiency of an achromatic lens was calculated as 0.43. The different phases were produced with the nanopillar element structures. The aim is to provide an idea for creating a more convenient, integrated and efficient way of coupling fiber optics. This approach can also be applied to the design of achromatic lenses in other wavelength regions. Full article
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Figure 1

Figure 1
<p>(<b>a</b>) The optical layout of the single-mode fiber and the this designed metasurface fiber coupler; (<b>b</b>) The structure of this designed metalens fiber coupler: (1) the supported PDMS layer, (2) the SiO<sub>2</sub> layer, (3) the metasurface TiO<sub>2</sub> layer.</p>
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<p>The workflow chart for the design process of the metalens.</p>
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<p>(<b>a</b>) The nanostructured layout of the designed single-band metalens; (<b>b</b>) the lateral optical intensity distributions at 1330 nm, 1450 nm, and 1550 nm.</p>
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<p>(<b>a</b>) The nanostructured layout of the designed achromatic lens; (<b>b</b>) the lateral optical intensity distributions at 1330 nm, 1450 nm, and 1550 nm.</p>
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<p>The simulation results. (<b>a</b>) the light intensity patterns and (<b>b</b>) the focal length of achromatic metalens with different wavelengths; (<b>c</b>) the light intensity patterns and (<b>d</b>) the focal length of chromatic metalens with different wavelengths.</p>
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10 pages, 1272 KiB  
Article
Identification of Circular RNAs of Testis and Caput Epididymis and Prediction of Their Potential Functional Roles in Donkeys
by Yan Sun, Yonghui Wang, Yuhua Li, Faheem Akhtar, Changfa Wang and Qin Zhang
Genes 2023, 14(1), 66; https://doi.org/10.3390/genes14010066 - 25 Dec 2022
Cited by 2 | Viewed by 1669
Abstract
Circular RNAs (circRNAs) are a class of noncoding RNAs with a covalently closed loop. Studies have demonstrated that circRNA can function as microRNA (miRNA) sponges or competing endogenous RNAs. Although circRNA has been explored in some species and tissues, the genetic basis of [...] Read more.
Circular RNAs (circRNAs) are a class of noncoding RNAs with a covalently closed loop. Studies have demonstrated that circRNA can function as microRNA (miRNA) sponges or competing endogenous RNAs. Although circRNA has been explored in some species and tissues, the genetic basis of testis development and spermatogenesis in donkeys remain unknown. We performed RNA-seq to detect circRNA expression profiles of adult donkey testes. Length distribution and other characteristics were shown a total of 1971 circRNAs were differentially expressed and 12,648 and 6261 circRNAs were detected from the testis and caput epididymis, respectively. Among these circRNAs, 1472 circRNAs were downregulated and 499 circRNAs were upregulated in the testis. Moreover, KEGG pathway analyses and Gene Ontology were performed for host genes of circRNAs. A total of 39 upregulated circRNA host genes were annotated in spermatogenesis terms, including PIWIL2, CATSPERD, CATSPERB, SPATA6, and SYCP1. Other host genes were annotated in the focal adhesion, Rap1 signaling pathway. Downregulated expressed circRNA host genes participated in the TGF-β signaling pathway, GnRH signaling pathway, estrogen signaling pathway, and calcium signaling pathway. Our discoveries provide a solid foundation for identifying and characterizing critical circRNAs involved in testis development or spermatogenesis. Full article
(This article belongs to the Section Animal Genetics and Genomics)
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Figure 1
<p>General characteristics of circRNAs in donkey testis and caput epididymis: (<b>A</b>) chromosomal distribution of circRNAs; (<b>B</b>) length distribution of circRNAs.</p>
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<p>Differential microRNA (<b>A</b>) and circRNA (<b>B</b>) expression between testis and caput epididymis. Volcano plots showing −log<sub>10</sub> (<span class="html-italic">p</span>-value) versus log<sub>2</sub> (fold change) in RPM. Red dots denote significantly upregulated microRNAs and circRNAs, whereas green dots denote significantly downregulated microRNAs and circRNAs.</p>
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<p>Validation of DE-circRNAs by qRT-PCR. Histograms of the relative expression levels. The y-axis shows the fold change between two groups (log(−ΔΔCt,2) for qRT-PCR, log<sub>2</sub> (fold change) for sequencing). In total, the qRT-PCR results were consistent with the RNA-seq results.</p>
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22 pages, 20323 KiB  
Article
Quantifying the Influence of Surface Texture and Shape on Structure from Motion 3D Reconstructions
by Mikkel Schou Nielsen, Ivan Nikolov, Emil Krog Kruse, Jørgen Garnæs and Claus Brøndgaard Madsen
Sensors 2023, 23(1), 178; https://doi.org/10.3390/s23010178 - 24 Dec 2022
Cited by 2 | Viewed by 1999
Abstract
In general, optical methods for geometrical measurements are influenced by the surface properties of the examined object. In Structure from Motion (SfM), local variations in surface color or topography are necessary for detecting feature points for point-cloud triangulation. Thus, the level of contrast [...] Read more.
In general, optical methods for geometrical measurements are influenced by the surface properties of the examined object. In Structure from Motion (SfM), local variations in surface color or topography are necessary for detecting feature points for point-cloud triangulation. Thus, the level of contrast or texture is important for an accurate reconstruction. However, quantitative studies of the influence of surface texture on geometrical reconstruction are largely missing. This study tries to remedy that by investigating the influence of object texture levels on reconstruction accuracy using a set of reference artifacts. The artifacts are designed with well-defined surface geometries, and quantitative metrics are introduced to evaluate the lateral resolution, vertical geometric variation, and spatial–frequency information of the reconstructions. The influence of texture level is compared to variations in capturing range. For the SfM measurements, the ContextCapture software solution and a 50 Mpx DSLR camera are used. The findings are compared to results using calibrated optical microscopes. The results show that the proposed pipeline can be used for investigating the influence of texture on SfM reconstructions. The introduced metrics allow for a quantitative comparison of the reconstructions at varying texture levels and ranges. Both range and texture level are seen to affect the reconstructed geometries although in different ways. While an increase in range at a fixed focal length reduces the spatial resolution, an insufficient texture level causes an increased noise level and may introduce errors in the reconstruction. The artifacts are designed to be easily replicable, and by providing a step-by-step procedure of our testing and comparison methodology, we hope that other researchers will make use of the proposed testing pipeline. Full article
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Graphical abstract

Graphical abstract
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<p>Step-height and sandpaper artifacts used in the paper as well as the reconstructed meshes and color textures.</p>
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<p>Artifacts for validating reconstructions of the surface topography from macro- and micro-height variations. (<b>a</b>) shows the 3D-printed step artifact with nominal heights: 0.63 mm, 1.25 mm, 2.5 mm, 5 mm, and 10 mm. (<b>b</b>) shows an example of a foam artifact with the P40 sandpaper attached to it.</p>
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<p>The described photogrammetry pipeline. As an input, ContextCapture takes the images (<b>a</b>), which were captured at 10-degree intervals in a semi-circle around each artifact in three heights. Features are extracted from each image, matched and a sparse point cloud and camera locations are computed; see (<b>b</b>). These are then densified and the RGB colors for each point cloud are calculated, as shown in (<b>c</b>,<b>d</b>). Finally, patches are extracted from each artifact and rasterized into depth maps; see (<b>e</b>,<b>f</b>). The subfigures are as follows: (<b>a</b>) Initial images captured from different positions. (<b>b</b>) Calculated camera positions. (<b>c</b>) Result mesh without texture. (<b>d</b>) Result mesh with texture. (<b>e</b>) Extracted patch close-up. (<b>f</b>) Rasterized depth map.</p>
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<p>Illustration of the image segmentation of P80 sandpaper. (<b>A</b>) The topographic map after filtering to remove low-frequency variations. (<b>B</b>) The segmentation result after the adaptive thresholding is shown in green overlaid on the topographic map. (<b>C</b>) The coloring shows the labeling of the individual particles after applying the modified watershed algorithm to the segmentation. The width of the scale bar is 0.5 mm.</p>
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<p>The reconstructed step-height artifact. The reconstructions in (<b>a</b>) at 1.5 m and in (<b>b</b>) at 2.0 m range are of the manually marked artifact. In (<b>c</b>), the reconstruction using a projected pattern over the artifact is shown. The top and middle row shows the reconstruction with and without color texture. In the bottom row, a line profile is shown across the artifact with the position indicated by the line in the middle row.</p>
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<p>Step height artifact parameters from FVM, SfM marked pattern at 1.5 m and 2.0 and SfM projected pattern at 1.5 m. (<b>A</b>) SD of measured step height. Note that the SD of the 10 mm step of the SfM projected pattern was cropped off at 0.5 mm for better visual comparison. (<b>B</b>) measured ER with the SD as errorbar. (<b>C</b>) Power spectral density (PSD) analysis of the full reconstructed step-height artifact. Both intensity and frequency are shown on a log-scale. SfM measurements are compared to a nominal PSD based on the design geometry.</p>
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<p>SfM reconstructions of the seven grit sizes at 1.7 m range. (Leftmost) P40 with close up of the geometry. (<b>Top</b> row) P60, P80, P100 and (<b>bottom</b> row) P120, P180, P240. The P120, P180 and P240 reconstructions show darker areas with erroneous color texture. These areas are marked with red.</p>
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<p>Topographic maps of sandpaper artifacts with grits P40, P80 and P180. CM (top row), SfM (middle row) at 1.7 m range, and fCM (bottom row) after Gaussian filtering with <math display="inline"><semantics> <mi>σ</mi> </semantics></math> = 0.21 mm. (<b>A</b>,<b>D</b>,<b>G</b>) P40. (<b>B</b>,<b>E</b>,<b>H</b>) P80. (<b>C</b>,<b>F</b>,<b>I</b>) P180. The width of the scale bar is 0.5 mm in all panels. Note that CM and SfM have been measured at different sample locations.</p>
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<p>(<b>A</b>–<b>C</b>) Height distributions for SfM, CM and fCM particle analysis. (<b>A</b>) SfM, (<b>B</b>) CM, (<b>C</b>) fCM, (<b>D</b>) Mean measured height values versus the nominal grain diameter. The SfM range was 1.7 m.</p>
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<p>PSD analysis of CM (dotted line), SfM at 1.7 m range (full line), and fCM (dashed line) topographies of sandpaper artifacts of grit sizes P60–P240. The average of 1D PSD curves for each line in the DEM is shown on a log–log scale. (<b>A</b>) P60. (<b>B</b>) P80. (<b>C</b>) P100. (<b>D</b>) P120. (<b>E</b>) P180. (<b>F</b>) P240.</p>
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<p>Particle height for P40 artifact at varying capture distance. (<b>A</b>) SfM distributions. (<b>B</b>) fCM distributions. (<b>C</b>) Mean height vs range.</p>
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<p>PSD analysis of P40 grit size at varying range or filtering level. CM (dotted line), SfM (full line), and fCM (dashed line). The average of 1D PSD curves for each line in the DEM is shown on a log–log scale. (<b>A</b>) 1.5 m. (<b>B</b>) 1.7 m. (<b>C</b>) 2.0 m. (<b>D</b>) 2.2 m.</p>
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14 pages, 3602 KiB  
Article
Generalized Scale Factor Calibration Method for an Off-Axis Digital Image Correlation-Based Video Deflectometer
by Long Tian, Tong Ding and Bing Pan
Sensors 2022, 22(24), 10010; https://doi.org/10.3390/s222410010 - 19 Dec 2022
Cited by 3 | Viewed by 1437
Abstract
When using off-axis digital image correlation (DIC) for non-contact, remote, and multipoint deflection monitoring of engineering structures, accurate calibration of the scale factor (SF), which converts image displacement to physical displacement for each measurement point, is critical to realize high-quality displacement measurement. In [...] Read more.
When using off-axis digital image correlation (DIC) for non-contact, remote, and multipoint deflection monitoring of engineering structures, accurate calibration of the scale factor (SF), which converts image displacement to physical displacement for each measurement point, is critical to realize high-quality displacement measurement. In this work, based on the distortion-free pinhole imaging model, a generalized SF calibration model is proposed for an off-axis DIC-based video deflectometer. Then, the transversal relationship between the proposed SF calibration method and three commonly used SF calibration methods was discussed. The accuracy of these SF calibration methods was also compared using indoor rigid body translation experiments. It is proved that the proposed method can be degraded to one of the existing calibration methods in most cases, but will provide more accurate results under the following four conditions: (1) the camera’s pitch angle is more than 20°, (2) the focal length is more than 25 mm, (3) the pixel size of the camera sensor is more than 5 um, and (4) the image y-coordinate corresponding to the measurement point after deformation is far from the image center. Full article
(This article belongs to the Collection Vision Sensors and Systems in Structural Health Monitoring)
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Figure 1
<p>Schematic illustration of off-axis DIC-based video deflectometer for deflection monitoring.</p>
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<p>Imaging model of off-axis DIC: (<b>a</b>) geometric model with off-axis imaging of camera; (<b>b</b>) the off-axis imaging relation diagram of the measurement point.</p>
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<p>Schematic of the two distance representation methods.</p>
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<p>Schematic diagram of camera roll angle correction: (<b>a</b>) original model; (<b>b</b>) corrected model.</p>
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<p>The video deflectometer and high-precision vertical displacement platform.</p>
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<p>Experiment setup of laboratory verification tests.</p>
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<p>Image displacement of two camera lenses with different focal lengths: (<b>a</b>) <span class="html-italic">f</span> = 8 mm, (<b>b</b>) <span class="html-italic">f</span> = 50 mm.</p>
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<p>Displacement was calculated by three calibration methods and two different lenses.</p>
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<p>SF variation with the camera and lens parameters: (<b>a</b>) SF-pitch angle curve for different focal lengths of the lens, (<b>b</b>) SF-pitch angle curve for different pixel sizes.</p>
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<p>Simulated results of full-field SFs before and after deformation for two calibration methods: (<b>a</b>) the proposed calibration method before deformation, (<b>b</b>) Pan’s calibration method before deformation, (<b>c</b>) the proposed calibration method after vertical translation 100 pixels, (<b>d</b>) difference between the proposed and Pan’s calibration after vertical translation 100 pixels.</p>
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13 pages, 4019 KiB  
Article
Sub-Diffraction Focusing Using Metamaterial-Based Terahertz Super-Oscillatory Lens
by Ayato Iba, Makoto Ikeda, Valynn Katrine Mag-usara, Verdad C. Agulto and Makoto Nakajima
Appl. Sci. 2022, 12(24), 12770; https://doi.org/10.3390/app122412770 - 13 Dec 2022
Cited by 4 | Viewed by 1496
Abstract
This paper presents a metamaterial-based super-oscillatory lens (SOL) fabricated by photolithography on a glass substrate and designed to operate at sub-terahertz (sub-THz) frequencies. The lens consists of repeating crisscross patterns of five-ring slits with sub-wavelength diameter. The lens is capable of generating multiple [...] Read more.
This paper presents a metamaterial-based super-oscillatory lens (SOL) fabricated by photolithography on a glass substrate and designed to operate at sub-terahertz (sub-THz) frequencies. The lens consists of repeating crisscross patterns of five-ring slits with sub-wavelength diameter. The lens is capable of generating multiple focal points smaller than the diffraction limit, thereby allowing many points to be inspected simultaneously with sub-wavelength resolution. After elucidating the influence of the lens parameters on light collection through calculations by the finite element method, the fabricated lens was then evaluated through actual experiments and found to have a focal length of 7.5 mm (2.5λ) and a hot spot size of 2.01 mm (0.67λ) at 0.1 THz (λ = 3 mm), which is 0.27 times the diffraction limit of the lens. This demonstrated sub-diffraction focusing capability is highly effective for industrial inspection applications utilizing terahertz waves. Full article
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<p>Schematic of the generation of focal spots using a metamaterial-based SOL.</p>
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<p>Schematic of the lens: (<b>a</b>) circular unit pattern and (<b>b</b>) square unit pattern, where <span class="html-italic">l</span> is the distance between each unit slit and <span class="html-italic">D</span> is the diameter (for circular patterns) or the diagonal (for square patterns). <span class="html-italic">A</span> is the distance between the centers of unit patterns.</p>
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<p>Calculation results: (<b>a</b>) intensity distribution through the square patterns; (<b>b</b>) the intensity distribution and phase distribution through the circular patterns; (<b>c</b>) spot width of the square patterns (blue dots) and circular patterns (red dots); and (<b>d</b>) intensity distribution due to the 3 × 3 circular unit patterns at 8-mm distance from the lens.</p>
Full article ">Figure 3 Cont.
<p>Calculation results: (<b>a</b>) intensity distribution through the square patterns; (<b>b</b>) the intensity distribution and phase distribution through the circular patterns; (<b>c</b>) spot width of the square patterns (blue dots) and circular patterns (red dots); and (<b>d</b>) intensity distribution due to the 3 × 3 circular unit patterns at 8-mm distance from the lens.</p>
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<p>Calculation results of using square patterns with a linearly polarized beam along the y direction: intensity distribution on (<b>a</b>) the plane parallel to the polarization (yz plane) and (<b>b</b>) the plane perpendicular to the polarization (xz plane); (<b>c</b>) spot widths on the plane parallel to the polarization (blue dots) and the plane perpendicular to the polarization (red dots).</p>
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<p>Calculation results of the effect of the ring diameter, slit width, and distance between rings of the lens on hot spot generation: (<b>a</b>–<b>c</b>) simulated hot spots for different ring diameters; (<b>d</b>,<b>e</b>) hot spots and their sizes for different slit widths; and (<b>f</b>,<b>g</b>) results for different distances between rings. Upper graphs in (<b>a</b>,<b>d</b>,<b>f</b>) also show the intensity distribution after light passes through the lens when the parameter is shorter than the designed value, while the lower graphs depict the results when the parameter is longer than the designed value; (<b>b</b>,<b>e</b>,<b>g</b>) show the spot size along the z axis.</p>
Full article ">Figure 5 Cont.
<p>Calculation results of the effect of the ring diameter, slit width, and distance between rings of the lens on hot spot generation: (<b>a</b>–<b>c</b>) simulated hot spots for different ring diameters; (<b>d</b>,<b>e</b>) hot spots and their sizes for different slit widths; and (<b>f</b>,<b>g</b>) results for different distances between rings. Upper graphs in (<b>a</b>,<b>d</b>,<b>f</b>) also show the intensity distribution after light passes through the lens when the parameter is shorter than the designed value, while the lower graphs depict the results when the parameter is longer than the designed value; (<b>b</b>,<b>e</b>,<b>g</b>) show the spot size along the z axis.</p>
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<p>(<b>a</b>) Image of the fabricated super-oscillatory lens (SOL) with circular patterns; (<b>b</b>) schematic of the cross-section of the SOL; (<b>c</b>) microscopical image of the fabricated slit.</p>
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<p>Schematic of the experimental setup.</p>
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<p>Experimental results: (<b>a</b>) intensity distribution through the SOL; (<b>b</b>) spot size: red line (calculation) and blue dots (experimental); (<b>c</b>) normalized intensity along the z direction; and (<b>d</b>) normalized intensity on x = 0 mm or y = 0 mm at z = 8 mm.</p>
Full article ">Figure 8 Cont.
<p>Experimental results: (<b>a</b>) intensity distribution through the SOL; (<b>b</b>) spot size: red line (calculation) and blue dots (experimental); (<b>c</b>) normalized intensity along the z direction; and (<b>d</b>) normalized intensity on x = 0 mm or y = 0 mm at z = 8 mm.</p>
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<p>Frequency dependence of the lens: (<b>a</b>,<b>b</b>) calculation results using (<b>a</b>) 0.097 THz and (<b>b</b>) 0.103 THz incident beams; (<b>c</b>,<b>d</b>) experimental results using (<b>c</b>) 0.097 THz and (<b>d</b>) 0.103 THz; and (<b>e</b>) frequency dependence of the interval between focal points: black line represents the calculated results using the Talbot principle while the red squares show the calculated results by the finite element method. The green circle shows the experimental results.</p>
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15 pages, 3268 KiB  
Article
Holographic Lens Resolution Using the Convolution Theorem
by Tomás Lloret, Marta Morales-Vidal, Víctor Navarro-Fuster, Manuel G. Ramírez, Augusto Beléndez and Inmaculada Pascual
Polymers 2022, 14(24), 5426; https://doi.org/10.3390/polym14245426 - 11 Dec 2022
Cited by 3 | Viewed by 1422
Abstract
The similarity between object and image of negative asymmetrical holographic lenses (HLs) stored in a low-toxicity photopolymer has been evaluated theoretically and experimentally. Asymmetrical experimental setups with negative focal lengths have been used to obtain HLs. For this purpose, the resolution of the [...] Read more.
The similarity between object and image of negative asymmetrical holographic lenses (HLs) stored in a low-toxicity photopolymer has been evaluated theoretically and experimentally. Asymmetrical experimental setups with negative focal lengths have been used to obtain HLs. For this purpose, the resolution of the HLs was calculated using the convolution theorem. A USAF 1951 test was used as an object and the impulse responses of the HLs, which in this case was the amplitude spread function (ASF), were obtained with two different methods: using a CCD sensor and a Hartmann Shack (HS) wavefront sensor. For a negative asymmetrically recorded HL a maximum resolution of 11.31 lp/mm was obtained. It was evaluated at 473 nm wavelength. A theoretical study of object-image similarity had carried out using the MSE (mean squared error) metric to evaluate the experimental results obtained quantitatively. Full article
(This article belongs to the Section Polymer Applications)
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<p>Biophotopol chemical structures of the prepolymer components. PVA: polyvinyl alcohol, NaAO: sodium acrylate, TEA: triethanolamine, RF: riboflavin 5’- monophosphate sodium salt.</p>
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<p>(<b>a</b>) Experimental setup for the HLs resolution evaluation. F: filter, SF: spatial filter, L: lens, D: diaphragm, HL: holographic lens, CCD Sensor: Charge Coupled Device. (<b>b</b>) Real photo of the experimental setup. (<b>c</b>) Picture of HL stored on the photopolymer layer. Video of HL stored on the photopolymer layer can be seen in <a href="#app1-polymers-14-05426" class="html-app">S1</a>.</p>
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<p>Geometry for obtaining the impulse response (ASF) of the HLs.</p>
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<p>Geometry for the relation between the ideal sagittal, the real sagittal and the wave aberration function (<span class="html-italic">W</span>). The wave aberration (<span class="html-italic">W</span>) is also related to the ray aberration (<math display="inline"><semantics> <mrow> <mo>Δ</mo> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> </semantics></math>).</p>
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<p>Simulated convolution for negative asymmetrical HLs, with ASF obtained with the HS wavefront sensor, reconstructed at (<b>a</b>) 473 nm and (<b>b</b>) 633 nm.</p>
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<p>Simulated convolution for negative asymmetrical HLs, with ASF obtained with the CCD sensor, reconstructed at: (<b>a</b>) 473 nm, (<b>b</b>) 633 nm.</p>
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<p>Image obtained with the CCD sensor illuminated at: (<b>a</b>) 473 nm, (<b>b</b>) 633 nm.</p>
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<p>Convolution simulations of an object test (University of Alicante logo) with the ASFs obtained by the different methods (HS wavefront sensor and CCD sensor) using as reconstruction wavelength: (<b>a</b>) 473 nm and (<b>b</b>) 633 nm.</p>
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<p>Convolution simulations of an object test (University of Alicante logo) with the ASFs obtained by the different methods: HS wavefront sensor and CCD sensor.</p>
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12 pages, 2895 KiB  
Article
Mid-Infrared Continuous Varifocal Metalens with Adjustable Intensity Based on Phase Change Materials
by Liangde Shao, Kongsi Zhou, Fangfang Zhao, Yixiao Gao, Bingxia Wang and Xiang Shen
Photonics 2022, 9(12), 959; https://doi.org/10.3390/photonics9120959 - 9 Dec 2022
Cited by 2 | Viewed by 1878
Abstract
Metalenses can greatly reduce the complexity of imaging systems due to their small size and light weight and also provide a platform for the realization of multifunctional imaging devices. Achieving dynamic focus length tunability is highly important for metalens research. In this paper, [...] Read more.
Metalenses can greatly reduce the complexity of imaging systems due to their small size and light weight and also provide a platform for the realization of multifunctional imaging devices. Achieving dynamic focus length tunability is highly important for metalens research. In this paper, based on single-crystal Ge and a new low-loss phase change material Ge2Sb2Se5 (GSSe), a tunable metalens formed by a double-layer metasurface composite was realized in the mid-infrared band. The first-layer metasurface formed by Ge nanopillars combines propagation and the geometric phase (equivalent to a half-wave plate function) to produce single- or multiple-polarization-dependent foci. The second-layer metasurface formed by GSSe nanopillars provides a tunable propagation phase, and the double-layer metalens can achieve the tunability of the focus length depending on the different crystalline fractions of GSSe. The focal length varies from 62.91 to 67.13 μm under right circularly polarized light incidence and from 33.84 to 36.66 μm under left circularly polarized light incidence. Despite the difference in the crystallographic fraction, the metalens’s focusing efficiency is maintained basically around 59% and 48% when zooming under RCP and LCP wave excitation. Meanwhile, the incident wave’s ellipticity can be changed to alter the relative intensity ratios of the bifocals from 0.03 to 4.26. This continuous varifocal metalens with adjustable intensity may have potential in practical applications such as optical tomography, multiple imaging, and systems of optical communication. Full article
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Figure 1
<p>(<b>a</b>) The schematic diagram of the unit structure of the bilayer metalens. (<b>b</b>) Upper view of the GSSe unit nanopillar. (<b>c</b>) Upper view of the Ge rectangle unit nanopillar. The long and short axis of the Ge rectangle are <span class="html-italic">L</span> and <span class="html-italic">W</span>, and <span class="html-italic">θ</span> is the angle between the long axis and the horizontal direction. Artistic rendering of a bifocal varifocal metalens under <span class="html-italic">X-LP</span> wave excitations when GSSe is in the crystalline state (<b>d</b>) and the amorphous state (<b>e</b>).</p>
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<p>Transmission of cross-polarization (<b>a</b>) and co-polarization (<b>b</b>) was simulated under RCP incidence. The eight Ge nanofins marked by the red circles we selected are equivalent to the function of HWPs. (<b>c</b>) The phase change and specific transmission amplitude under RCP polarization incidence for the eight Ge cells selected (8 units in (<b>c</b>) correspond to the unit structure size marked with numbers 1-8 in (<b>a</b>)). (<b>d</b>) The phase and amplitude of GSSe cylindrical cells with different radii under the excitation of RCP polarization.</p>
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<p>The intensity of the simulated electric field under three distinct polarization excitations When the GSSe phase change material is in the crystalline (x−LP (<b>a</b>), RCP (<b>b</b>), and LCP (<b>c</b>)) and amorphous (x−LP (<b>d</b>), RCP (<b>e</b>), and LCP (<b>f</b>)) states.</p>
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<p>The optical response of the GSSe cylindrical nanopillars with different crystallization fractions m. The phase shifts (<b>a</b>) and transmission amplitudes (<b>b</b>) of the GSSe nanopillars with crystalline fraction m from 1 to 0 as a function of the nanopillars’ radius.</p>
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<p>Demonstration of electric field strength in the x−z plane under x-polarized light (<b>a</b>), right−handed circular and left−handed circular light incident (<b>b</b>) when the crystalline fraction m of GSSe varies from 0 to 1. (<b>c</b>) The focal length and FWHM of the metalens correspond to different m under the excitation of RCP and LCP. (<b>d</b>) The corresponding focusing efficiencies of the foci in (<b>c</b>).</p>
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<p>Demonstration of the intensity of the simulated metalens in the x−z and x−y planes under RCP (<b>a</b>,<b>c</b>) and LCP (<b>b</b>,<b>d</b>) incident light, when the GSSe phase change material is crystalline. (<b>e</b>,<b>f</b>) The FWHM values corresponding to the focal spot in (<b>c</b>) and (<b>d</b>) are 680 nm and 640 nm.</p>
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<p>(<b>a</b>) The relative electric field intensity profiles of two focal points in the x−z plane for the different phase difference δ. (<b>b</b>) Demonstration of intensity distribution at the longitudinal focal length.</p>
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26 pages, 10295 KiB  
Article
Interpretation and Transformation of Intrinsic Camera Parameters Used in Photogrammetry and Computer Vision
by Kuan-Ying Lin, Yi-Hsing Tseng and Kai-Wei Chiang
Sensors 2022, 22(24), 9602; https://doi.org/10.3390/s22249602 - 7 Dec 2022
Cited by 6 | Viewed by 5315
Abstract
The precision modelling of intrinsic camera geometry is a common issue in the fields of photogrammetry (PH) and computer vision (CV). However, in both fields, intrinsic camera geometry has been modelled differently, which has led researchers to adopt different definitions of intrinsic camera [...] Read more.
The precision modelling of intrinsic camera geometry is a common issue in the fields of photogrammetry (PH) and computer vision (CV). However, in both fields, intrinsic camera geometry has been modelled differently, which has led researchers to adopt different definitions of intrinsic camera parameters (ICPs), including focal length, principal point, radial distortion, decentring distortion, affinity and shear. These ICPs are indispensable for vision-based measurements. These differences can confuse researchers from one field when using ICPs obtained from a camera calibration software package developed in another field. This paper clarifies the ICP definitions used in each field and proposes an ICP transformation algorithm. The originality of this study lies in its use of least-squares adjustment, applying the image points involving ICPs defined in PH and CV image frames to convert a complete set of ICPs. This ICP transformation method is more rigorous than the simplified formulas used in conventional methods. Selecting suitable image points can increase the accuracy of the generated adjustment model. In addition, the proposed ICP transformation method enables users to apply mixed software in the fields of PH and CV. To validate the transformation algorithm, two cameras with different view angles were calibrated using typical camera calibration software packages applied in each field to obtain ICPs. Experimental results demonstrate that our proposed transformation algorithm can be used to convert ICPs derived from different software packages. Both the PH-to-CV and CV-to-PH transformation processes were executed using complete mathematical camera models. We also compared the rectified images and distortion plots generated using different ICPs. Furthermore, by comparing our method with the state of art method, we confirm the performance improvement of ICP conversions between PH and CV models. Full article
(This article belongs to the Section Physical Sensors)
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<p>Geometry of perspective projection as defined in the field of PH: (<b>a</b>) the three coordinate frames involved and (<b>b</b>) the image coordinates of the principal point.</p>
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<p>Two definitions of image frame in the field of PH: (<b>a</b>) the first: pixel unit, (<b>b</b>) the second: metric unit.</p>
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<p>Geometry of perspective projection as defined in the field of CV: (<b>a</b>) the three coordinate frames involved and (<b>b</b>) the image coordinates of the principal point.</p>
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<p>Geometry of normalized image frame in the field of CV.</p>
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<p>Workflow of transformation of PH ICPs to CV ICPs: (<b>a</b>) the description of each step and (<b>b</b>) visualized framework.</p>
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<p>Workflow of transformation of CV ICPs to PH ICPs: (<b>a</b>) the description of each step and (<b>b</b>) visualized framework.</p>
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<p>Camera calibration method tools: (<b>a</b>) rotated table with coded targets for the PH method; (<b>b</b>) checkerboard for the CV method.</p>
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<p>Selected observation points in Case 1 to 4 (Sony).</p>
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<p>Rectified images generated using different methods (Sony).</p>
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<p>Radial distortion and decentring distortion plots (Sony).</p>
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<p>Rectified images generated using different methods (GoPro).</p>
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<p>Radial distortion and decentring distortion plots (GoPro).</p>
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<p>Comparison of rectified images (Sony).</p>
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<p>Comparison of rectified images (GoPro).</p>
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<p>Visual results of corrections (Sony): (<b>a</b>) using the original ICPs (PH) (<b>b</b>) using the converted ICPs (CV to PH).</p>
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<p>Visual results of corrections (GoPro): (<b>a</b>) using PH ICPs (<b>b</b>) using CV to PH ICPs.</p>
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<p>Imagined workflow for using mixed software applied in the fields of PH and CV.</p>
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9 pages, 1982 KiB  
Article
Controlling the Abrupt Autofocusing of Circular Airy Vortex Beam via Uniaxial Crystal
by Houquan Liu, Jiawen Zhang, Huilin Pu, Jiankang Xu, Ronghui Xu and Libo Yuan
Photonics 2022, 9(12), 943; https://doi.org/10.3390/photonics9120943 - 6 Dec 2022
Cited by 7 | Viewed by 1392
Abstract
The propagation of many kinds of structured light beams in uniaxial crystal has been investigated. However, the investigation of the evolution of these structured light beams after the uniaxial crystal is lacking. In this paper, an evolution formula of a light beam after [...] Read more.
The propagation of many kinds of structured light beams in uniaxial crystal has been investigated. However, the investigation of the evolution of these structured light beams after the uniaxial crystal is lacking. In this paper, an evolution formula of a light beam after passing through a uniaxial crystal is derived. Based on the formula, controlling the autofocusing of a circular Airy vortex beam (CAVB) via a uniaxial crystal is studied. It is found that a uniaxial crystal can prolong the focal length of the autofocusing. By changing the crystal length, the relative weight of the left- and right-hand circular polarization components and the relative value between the orbital and spin angular momentum densities of the beam’s focal plane can be adjusted flexibly. In addition, other optical elements can be inserted between the crystal and the focus to further adjust the focal plane field distribution. The influences of inserting x- and y-polarization polarizers on the intensity distribution are calculated as examples. Full article
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<p>The schematic diagram of controlling the abrupt autofocusing of CAVB via uniaxial crystal when the focal point is outside the uniaxial crystal.</p>
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<p>Normalized intensity distributions during propagation under different crystal lengths. (<b>a</b>–<b>d</b>) Results for <span class="html-italic">L</span> = 0 mm, 10 mm, 20 mm and 30 mm, respectively. The white dotted lines are the output planes of the crystals, and the white arrows show the location of the focus.</p>
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<p>The relative intensity |<span class="html-italic">E</span><sub>+</sub>(<span class="html-italic">r</span><sub>⊥</sub>, <span class="html-italic">φ</span>, <span class="html-italic">z<sub>f</sub></span>)|<sup>2</sup>/max [|<span class="html-italic">E</span>(<span class="html-italic">r</span><sub>⊥</sub>, <span class="html-italic">φ</span>, 0)|<sup>2</sup>] (blue line) and |<span class="html-italic">E</span><sub>−</sub>(<span class="html-italic">r</span><sub>⊥</sub>, <span class="html-italic">φ</span>, <span class="html-italic">z<sub>f</sub></span>) |<sup>2</sup>/max [|<span class="html-italic">E</span>(<span class="html-italic">r</span><sub>⊥</sub>, <span class="html-italic">φ</span>, 0)|<sup>2</sup>] (red line) on the <span class="html-italic">r</span><sub>⊥</sub> axis under (<b>a</b>) <span class="html-italic">L</span> = 0 mm, (<b>b</b>) <span class="html-italic">L</span> = 10 mm, (<b>c</b>) <span class="html-italic">L</span> = 20 mm and (<b>d</b>) <span class="html-italic">L</span> = 30 mm.</p>
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<p>The focal plane AM density distributions on <span class="html-italic">r</span><sub>⊥</sub> axis under (<b>a</b>) <span class="html-italic">L</span> = 0 mm, (<b>b</b>) 10 mm, (<b>c</b>) 20 mm and (<b>d</b>) 30 mm. The results are relative to <span class="html-italic">ε</span><sub>0</sub>/2<span class="html-italic">ω</span>.</p>
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<p>Normalized intensity distributions on the focal plane under different crystal lengths. The first, second, and third columns correspond to the intensity distributions of the total field, the <span class="html-italic">x</span>-polarized component, and the <span class="html-italic">y</span>-polarized component, respectively. The first (<b>a1</b>,<b>b1</b>,<b>c1</b>), second (<b>a2</b>,<b>b2</b>,<b>c2</b>), and third (<b>a3</b>,<b>b3</b>,<b>c3</b>) rows correspond to <span class="html-italic">L</span> = 10 mm, 20 mm and 30 mm, respectively.</p>
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13 pages, 2752 KiB  
Article
Broadband Achromatic Metalens in the Visible Light Spectrum Based on Fresnel Zone Spatial Multiplexing
by Ruixue Shi, Shuling Hu, Chuanqi Sun, Bin Wang and Qingzhong Cai
Nanomaterials 2022, 12(23), 4298; https://doi.org/10.3390/nano12234298 - 3 Dec 2022
Cited by 3 | Viewed by 2533
Abstract
Metalenses composed of a large number of subwavelength nanostructures provide the possibility for the miniaturization and integration of the optical system. Broadband polarization-insensitive achromatic metalenses in the visible light spectrum have attracted researchers because of their wide applications in optical integrated imaging. This [...] Read more.
Metalenses composed of a large number of subwavelength nanostructures provide the possibility for the miniaturization and integration of the optical system. Broadband polarization-insensitive achromatic metalenses in the visible light spectrum have attracted researchers because of their wide applications in optical integrated imaging. This paper proposes a polarization-insensitive achromatic metalens operating over a continuous bandwidth from 470 nm to 700 nm. The silicon nitride nanopillars of 488 nm and 632.8 nm are interleaved by Fresnel zone spatial multiplexing method, and the particle swarm algorithm is used to optimize the phase compensation. The maximum time-bandwidth product in the phase library is 17.63. The designed focal length can be maintained in the visible light range from 470 nm to 700 nm. The average focusing efficiency reaches 31.71%. The metalens can achieve broadband achromatization using only one shape of nanopillar, which is simple in design and easy to fabricate. The proposed metalens is expected to play an important role in microscopic imaging, cameras, and other fields. Full article
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<p>(<b>a</b>) 3D view of the unit cells; (<b>b</b>) top view of the unit cells; (<b>c</b>) the magnetic field distribution inside the nanopillar with a diameter of 120 nm; (<b>d</b>) the phase and transmittance of the unit cell of 488 nm; (<b>e</b>) the phase and transmittance of the unit cell of 632.8 nm.</p>
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<p>Time-bandwidth products of the meta-units in the phase library.</p>
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<p>(<b>a</b>) Schematic diagram of the dual-wavelength achromatic metalens; (<b>b</b>) top view of the designed metalens.</p>
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<p>Schematic diagram of the particle swarm algorithm flow.</p>
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<p>(<b>a</b>) Normalized intensity distributions in the <span class="html-italic">x-z</span> plane at 488 nm; (<b>b</b>) normalized intensity distributions in the <span class="html-italic">x-z</span> plane at 632.8 nm; (<b>c</b>) normalized intensity distributions of focal spots in the <span class="html-italic">x-y</span> plane at 488 nm; (<b>d</b>) normalized intensity distributions of focal spots in the <span class="html-italic">x-y</span> plane at 632.8 nm; (<b>e</b>) the corresponding cross-sectional intensity cut through the focal plane at 488 nm; (<b>f</b>) the corresponding cross-sectional intensity cut through the focal plane at 632.8 nm.</p>
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<p>(<b>a</b>) Normalized intensity distributions in the <span class="html-italic">x-z</span> plane of different wavelengths; (<b>b</b>) normalized intensity distributions of focal spots in the <span class="html-italic">x-y</span> plane of different wavelengths; (<b>c</b>) the corresponding cross-sectional intensity cut through the focal planes of different wavelengths.</p>
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<p>(<b>a</b>) Focal length for the chromatic and achromatic metalens of 470–700 nm; (<b>b</b>) focusing efficiency for the achromatic metalens of 470–700 nm.</p>
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8 pages, 2406 KiB  
Communication
Dynamic Tunable Meta-Lens Based on a Single-Layer Metal Microstructure
by Xiangjun Li, Huadong Liu, Xiaomei Hou and Dexian Yan
Photonics 2022, 9(12), 917; https://doi.org/10.3390/photonics9120917 - 29 Nov 2022
Cited by 1 | Viewed by 1486
Abstract
Ultra-thin focusing meta-lenses based on the metasurface structure with adjustable focal length show important applicant value in compact systems, especially in on-chip terahertz spectroscopy, imaging systems, and communication systems. A stretchable substrate, dynamic focusing meta-lens based on the cross-polarized metal C-shaped split ring [...] Read more.
Ultra-thin focusing meta-lenses based on the metasurface structure with adjustable focal length show important applicant value in compact systems, especially in on-chip terahertz spectroscopy, imaging systems, and communication systems. A stretchable substrate, dynamic focusing meta-lens based on the cross-polarized metal C-shaped split ring resonators (SRRs) is designed and investigated. At the operation frequency of 0.1 THz, the operation characteristics of the unit cell structure and the formed meta-lens are investigated. The phase of the unit cell structures can be modulated by changing the rotation angle, width, and symmetry axis of the C-shaped metal SRRs. When the terahertz wave is incident vertically, the focusing performance can be achieved based on the specific arrangement of the metasurface unit cells. By stretching the flexible substrate of the meta-lens, the dynamic focusing effect can be realized. When the substrate stretches from 100% to 120%, the focal length changes from 59.8 mm to 125.2 mm, the dynamic focusing range is 109.4% of the minimum focal length, and the focusing efficiency changes between 5.5% and 10.5%. Full article
(This article belongs to the Special Issue Advanced Photonics Sensors, Sources, Systems and Applications)
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<p>Unit cell structure of the C-shaped metal SRR. (<b>a</b>) Three-dimensional illustration of the unit cell structure; (<b>b</b>) top view of the unit cell structure.</p>
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<p>Schematic diagram of the part single-layer metal meta-lens in the <span class="html-italic">x–y</span> plane.</p>
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<p>Schematic diagram of the change in the meta-lens before and after stretching. (<b>a</b>) Before substrate stretching; (<b>b</b>) after substrate stretching.</p>
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<p>Phase response of the single-layer metal C-shaped SRRs. (<b>a</b>) Transmission coefficients and phase responses for eight discrete unit cell structures; (<b>b</b>) relationship between the lateral distance of PDMS substrate from the origin point and the phase before and after stretching.</p>
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<p>Normalized electric field distribution of the dynamically tunable meta-lens with different stretching factors.</p>
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<p>Dynamic focusing performance of single-layer metal C-shaped SRRs at the frequency of 0.1 THz. (<b>a</b>) Normalized electric field intensity distribution along the <span class="html-italic">z</span>-axis (<span class="html-italic">x</span> = 0) when the PDMS substrate is stretched from 100% to 120%; (<b>b</b>) normalized electric field intensity distribution in the focal plane when the PDMS substrate is stretched from 100% to 120%; (<b>c</b>) the change in the focal length with different stretching factors; (<b>d</b>) the change in the focusing efficiency with different stretching factors.</p>
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16 pages, 34120 KiB  
Article
Thermooptical PDMS-Single-Layer Graphene Axicon-like Device for Tunable Submicron Long Focus Beams
by Giancarlo Margheri, André Nascimento Barbosa, Fernando Lazaro Freire and Tommaso Del Rosso
Micromachines 2022, 13(12), 2083; https://doi.org/10.3390/mi13122083 - 26 Nov 2022
Cited by 1 | Viewed by 1441
Abstract
Submicron long focusing range beams are gaining attention due to their potential applications, such as in optical manipulation, high-resolution lithography and microscopy. Here, we report on the theoretical and experimental characterization of an elastomeric polydimethylsiloxane/single layer graphene (PDMS/SLG) axicon-like tunable device, able to [...] Read more.
Submicron long focusing range beams are gaining attention due to their potential applications, such as in optical manipulation, high-resolution lithography and microscopy. Here, we report on the theoretical and experimental characterization of an elastomeric polydimethylsiloxane/single layer graphene (PDMS/SLG) axicon-like tunable device, able to generate diffraction-resistant submicrometric spots in a pump and probe configuration. The working principle is based on the phase change of an input Gaussian beam induced in the elastomer via the thermo-optical effect, while the heating power is produced by the optical absorption of the SLG. The phase-modified beam is transformed by an objective into a long focus with submicron diameter. Our foci reach an experimental full width at half maximum (FWHM) spot diameter of 0.59 μm at the wavelength of 405 nm, with the FWHM length of the focal line greater than 90 μm. Moreover, the length of the focal line and the diameter of the focus can be easily tuned by varying the pump power. The proposed thermo-optical device can thus be useful for the simple and cheap improvement of the spatial resolution on long focus lines. Full article
(This article belongs to the Special Issue Micro/Nanophotonic Devices in Europe)
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<p>Working principle of the PDMS/SLG thermo-optical device. The absorbed pump heats up the PDMS locally, creating a refractive index profile Δn characteristic of a negative axicon. The input beam is focused into a light ring by an objective. The successive propagation produces the sub-micrometric LFRB.</p>
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<p>Geometry of the thermo-optical model, completed with the boundary conditions used in the COMSOL code. The convective parameter is h = 10 W/m<sup>2</sup>K.</p>
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<p>Results of the thermo−optical modeling. (<b>a</b>) Spatial variation of the refractive index due to the thermo-optical effect. In the inset, the apex distribution is shown. (<b>b</b>) Variation of |Δn(0,0)| with the heating power. (<b>c</b>) Radial distribution of the modulus on the graphene layer surface for several heating powers and (<b>d</b>) its axial distribution for the same powers.</p>
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<p>Propagation of the electromagnetic field through the optical chain. The input field E<sub>0</sub> acquires two phase delays, ΔΦ and ΔΦ<sub>lens</sub>, due to the refractive index gradient in the PDMS and the lens, respectively. The objective is located at distance <span class="html-italic">d</span> from the sample of about 15 mm. The beam is finally transformed into a long focusing range beam. See text for further details.</p>
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<p>Upper part: Theoretical far field at three different heating powers P<sub>h</sub> at the wavelength of 633 nm. Lower part: definition of the polar angle.</p>
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<p>(<b>a</b>–<b>d</b>) Theoretical normalized light distributions beyond the focusing optics (focal length, origin of the x-axis = 2.6 mm) for three heating powers P<sub>4</sub> = 4 mW, 8 mW, 16 mW. Upper row (<b>a</b>,<b>b</b>): <span class="html-italic">λ</span><sub>1</sub> = 633 nm; lower row (<b>c</b>,<b>d</b>): <span class="html-italic">λ</span><sub>2</sub> = 405 nm. (<b>a</b>,<b>c</b>) Axial and (<b>b</b>,<b>d</b>) radial intensities. In (<b>b</b>,<b>d</b>), only the radial FWHMs relative to P<sub>h</sub> = 16 mW are reported. The other parameters are listed in <a href="#micromachines-13-02083-t001" class="html-table">Table 1</a> for a simpler comparison. (<b>e</b>) Computed light intensities for the same heating powers for two wavelengths <span class="html-italic">λ</span><sub>1</sub> (left side) and <span class="html-italic">λ</span><sub>2</sub> (right side). The light propagates from left to right. Notice the converging ring on the left of each focal line that evolves in the long range focus.</p>
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<p>Focal line length (FWHM<sub>line</sub>) and maximum on-axis intensity vs. the heating power P<sub>h</sub> for <span class="html-italic">λ</span><sub>2</sub> = 405 nm. The focal length of the focusing lens is 2.6 mm. The increase in FWHM<sub>line</sub> is accompanied by a reduction in the intensity. See text for details.</p>
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<p>Experimental apparatus. The input probe beam travels through the heated PDMS, which modifies and transmits it to the focusing objective Obj<sub>1</sub> (focal length 2.6 mm), mounted on a three-axis piezo. The focusing action determines the formation of a superposition volume (evidenced in the red box and exploded in the upper part) where the long focus develops. The section of the focus located on the plane π<sub>im</sub> is conjugated onto the observation screen by a 2-stage optical magnifier, composed of an objective Obj<sub>2</sub> (focal length 2.6 mm, measured magnification 110x, and a 20x Galilean telescope. The focus image, magnified 2200 times, is then projected onto the screen and imaged by a CCD camera. An image processing software permits checking the image intensity on a given line in real time, allowing the monitoring of the change in the spot dimensions in response to changes in P<sub>h</sub>, obtained with a variable attenuator. The measure of the far field annular distributions is performed without Obj<sub>1</sub> and the 2200x magnification system (green frame in the upper left side).</p>
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<p>(<b>a</b>) Annular rings produced at 350 mm distance from the sample at <span class="html-italic">λ</span><sub>1</sub> = 633 nm (upper part of the photo) and <span class="html-italic">λ</span><sub>2</sub> = 405 nm (lower part) for different heating powers. (<b>b</b>) The ring diameter, intended as the distance between the maxima directly measured on a diametric scanning line (see caption of <a href="#micromachines-13-02083-f007" class="html-fig">Figure 7</a>), vs. the heating power P<sub>h</sub>.</p>
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<p>Upper part: photos of the focal LFRB spots magnified 2200 times at different heating powers at <span class="html-italic">λ</span><sub>1</sub> = 633 nm. The scale bar indicates the effective dimensions of the focal cross−section. Lower part: Corresponding measured diametric light distributions.</p>
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<p>Upper part: Photos of the focal LFRB spots magnified 2200 times at different heating powers at <span class="html-italic">λ</span><sub>2</sub> = 405 nm. The scale bar represents the actual dimensions of the focal cross-section. Lower part: Corresponding measured diametric light distributions.</p>
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<p>Upper part: Measured (black dots) and theoretical (red dots) light distributions in the focal lines for (<b>a</b>) <span class="html-italic">λ</span><sub>1</sub> = 633 nm and (<b>b</b>) <span class="html-italic">λ</span><sub>2</sub> = 405 nm. (<b>c</b>) Definition of the focal LFRB line P<sub>1</sub>P<sub>2</sub>, within which the FWHM spot diameter is submicrometric.</p>
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21 pages, 5897 KiB  
Article
Circular Subaperture Stitching Interferometry Based on Polarization Grating and Virtual–Real Combination Interferometer
by Yao Hu, Zhen Wang and Qun Hao
Sensors 2022, 22(23), 9129; https://doi.org/10.3390/s22239129 - 24 Nov 2022
Cited by 2 | Viewed by 1574
Abstract
This paper presents a polarization grating based circular subaperture stitching interferometer. The system can be used for small F/# concave surface tests with a large F/# transmission sphere, where F/# is the ratio of focal length to aperture. A polarization grating was employed [...] Read more.
This paper presents a polarization grating based circular subaperture stitching interferometer. The system can be used for small F/# concave surface tests with a large F/# transmission sphere, where F/# is the ratio of focal length to aperture. A polarization grating was employed to deflect the incident beam for subaperture scanning by its axial rotation instead of a multi-axis motion-control system. Compared with the traditional subaperture stitching interferometric system, the system proposed in this paper is smaller in size and reduces the measurement error introduced by mechanical adjustment. Using a virtual interferometer model and a virtual–real combination algorithm to remove the retrace error, the full-aperture figure error can be directly obtained without the need for a complex stitching algorithm. The feasibility of the algorithm was verified, and the measurement error caused by the modeling error was analyzed by simulation. The capability of the polarization grating to scan subapertures was experimentally confirmed, and possible solutions to some engineering challenges were pointed out. The research in this paper has pioneering and guiding significance for the application of polarization grating in interferometry. Full article
(This article belongs to the Section Optical Sensors)
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<p>(<b>a</b>) Schematic diagram of PG-CSSI. (<b>b</b>) The function of PG in PG-CSSI.</p>
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<p>(<b>a</b>) Optical path diagram of the off-axis subaperture (between the focus O of the TS and the SUT). (<b>b</b>) Schematic diagram of the subaperture layout. O is the focus of the TS. <span class="html-italic">θ</span> is PG’s deflection angle to the chief ray. <span class="html-italic">R</span> is the radius of curvature of the SUT. <span class="html-italic">h</span> is the center distance between the off-axis subaperture and the center subaperture. <span class="html-italic">β</span> is the rotation stepping angle of the PG. <span class="html-italic">D</span><sub>sub</sub> is the diameter of the central subaperture. <span class="html-italic">D</span><sub>full</sub> is the diameter of the SUT.</p>
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<p>(<b>a</b>) Front-view and (<b>b</b>) top-view of the microstructure of PG. The blue rod-like structures in the figure are LC molecules. <span class="html-italic">d</span> is the thickness of the LC layer. <span class="html-italic">Λ</span> is the space period of PG.</p>
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<p>Schematic diagram of the virtual interferometer.</p>
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<p>(<b>a</b>) True figure error. (<b>b</b>) Schematic diagram of subaperture layout.</p>
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<p>The simulated image plane wavefront of subaperture No. 6 of the (<b>a</b>) aspheric surface with R/D = 2.5, K = 2, and (<b>b</b>) spherical surface with R/D = 1.</p>
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<p>(<b>a</b>) The test result of the figure error of the SUTs with different surface parameters. (<b>b</b>) The difference between the test results and the true value.</p>
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<p>Variations of the Zernike coefficients describing the image plane wavefront of the subaperture No. 3 in <a href="#sensors-22-09129-f007" class="html-fig">Figure 7</a>b caused by the SUT’s lateral translation error.</p>
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<p>(<b>a</b>,<b>c</b>) Figure error test results under different Δ<span class="html-italic">Z</span><sub>3</sub> and (<b>b</b>,<b>d</b>) the test errors. Δ<span class="html-italic">Z</span><sub>3</sub> is the error of optimization object <span class="html-italic">Z</span><sub>3</sub>.</p>
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<p>Experimental setup of PG-CSSI. LP is the linear polarizer. PG is the polarization grating. QWP is the λ/4 wave plate. SUT is the surface under test.</p>
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<p>Full-aperture figure error of the spherical SUT.</p>
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<p>Interferograms captured during the process of system adjustment. The interferograms have been enhanced for better visual effects. (<b>a</b>) Stray fringes caused by scanning structure. (<b>b</b>) Dense interferogram with aliasing artifacts captured by the detector when the scanning structure was not perpendicular to the optical axis. (<b>c</b>) Sparse interferogram after adjusting the SUT.</p>
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<p>(<b>a</b>) Zernike coefficient of image plane wavefront. (<b>b</b>) Image plane wavefront.</p>
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<p>Wavefront maps of the off-axis subapertures in the (<b>a</b>) real interferometer and (<b>b</b>) virtual interferometer.</p>
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15 pages, 6195 KiB  
Article
Movable and Focus-Tunable Lens Based on Electrically Controllable Liquid: A Lattice Boltzmann Study
by Fei Wang, Zijian Zhuang, Zhangrong Qin and Binghai Wen
Entropy 2022, 24(12), 1714; https://doi.org/10.3390/e24121714 - 24 Nov 2022
Cited by 3 | Viewed by 1707
Abstract
Adjusting the focal length by changing the liquid interface of the liquid lens has become a potential method. In this paper, the lattice-Boltzmann-electrodynamic (LB-ED) method is used to numerically investigate the zooming process of a movable and focus-tunable electrowetting-on-dielectrics (EWOD) liquid lens by [...] Read more.
Adjusting the focal length by changing the liquid interface of the liquid lens has become a potential method. In this paper, the lattice-Boltzmann-electrodynamic (LB-ED) method is used to numerically investigate the zooming process of a movable and focus-tunable electrowetting-on-dielectrics (EWOD) liquid lens by combining the LBM chemical potential model and the electrodynamic model. The LB method is used to solve the Navier–Stokes equation, and the Poisson–Boltzmann (PB) equation is introduced to solve the electric field distribution. The experimental results are consistent with the theoretical results of the Lippmann–Young equation. Through the simulation of a liquid lens zoom driven by EWOD, it is found that the lens changes from a convex lens to a concave lens with the voltage increases. The focal length change rate in the convex lens stage gradually increases with voltage. In the concave lens stage, the focal length change rate is opposite to that in the convex lens stage. During the zooming process, the low-viscosity liquid exhibits oscillation, and the high-viscosity liquid appears as overdamping. Additionally, methods were proposed to accelerate lens stabilization at low and high viscosities, achieving speed improvements of about 30% and 50%, respectively. Simulations of lens motion at different viscosities demonstrate that higher-viscosity liquids require higher voltages to achieve the same movement speed. Full article
(This article belongs to the Section Complexity)
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<p>EWOD schematic diagram.</p>
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<p>Schematic diagram of the electrowetting lens structure.</p>
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<p>Contact angle variation with voltage on different hydrophilic substrates and compared with Lippmann–Young’s analytical solution.</p>
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<p>The numerical focal length on different wettability substrates and voltages compared with the theoretical focal length in initial contact angles 110°, 130°, 150°, and 170°.</p>
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<p>The thickness of the center of the lens changes with time under different viscosity conditions.</p>
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<p>Variations of lens center height during applied voltage for high viscosity liquid lens. Take points b, c, and d as dividing lines, the left side is overvoltage, and the right side is target voltage. Point a is the initial state, and point e is the final steady state after applying the target voltage.</p>
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<p>Variations of lens center height with time during applied voltage in a low viscosity liquid lens. The blue line depicts the modified zoom method, where a low voltage is applied and then switched to the target voltage at point b. Insets (a–c) show the lens’s state diagram at different times at two voltages. Inset (d) shows the state diagram at 35 ms under a single voltage.</p>
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<p>Variation of lens movement speed with voltage for different viscosity liquids.</p>
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10 pages, 2924 KiB  
Article
Simultaneous Beam Forming and Focusing Using a Checkerboard Anisotropic Surface
by Jeong-Hyun Park and Jae-Gon Lee
Electronics 2022, 11(22), 3823; https://doi.org/10.3390/electronics11223823 - 21 Nov 2022
Viewed by 1401
Abstract
A novel design method of simultaneous beam forming and focusing using a checkerboard anisotropic surface is proposed and verified in this paper. The proposed multibeam control regardless of far and near regions can easily be achieved through a rearrangement of the checkerboard structure. [...] Read more.
A novel design method of simultaneous beam forming and focusing using a checkerboard anisotropic surface is proposed and verified in this paper. The proposed multibeam control regardless of far and near regions can easily be achieved through a rearrangement of the checkerboard structure. The unit cell of the utilized anisotropic surface consists of two identical metallic structures divided by a dielectric material. When the EM wave with a circular polarization (CP) is incident on the unit cell, the maximum transmission phase variation of the unit cell is 360 degrees by half rotation of the unit cell. A microstrip patch antenna with trimmed corners is used to launch the CP wave and the distance between the microstrip patch antenna and anisotropic surface is about 2 wavelengths considering the optimized spillover and taper efficiencies. After designing each anisotropic surface for beam forming and focusing, the unit cells of the surface are rearranged in the form of a checkerboard. The feasibility of the proposed method is confirmed by full-wave simulation and measurement for anisotropic surface with a beam forming angle of 30 degrees and beam focusing point 60 mm away from center at 5.8 GHz. The forming angle and focal length are simulated and measured to be 28 degrees and about 65 mm, respectively. Full article
(This article belongs to the Section Microwave and Wireless Communications)
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<p>Unit cell of the metasurface (Top view).</p>
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<p>Full-wave simulated transmission responses of the unit cell of anisotropic surface. (<b>a</b>) Magnitude (<b>b</b>) Phase.</p>
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<p>Relation between beam and transmitted phase through anisotropic surface.</p>
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<p>Full-wave simulated transmission phases of anisotropic surface. (<b>a</b>) Beam forming of 30 degrees (<b>b</b>) Beam focusing (Focal length = 60 mm) (<b>c</b>) Simultaneous beam forming and focusing.</p>
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<p>Photographs of fabricated transmitarray antenna. (<b>a</b>) source antenna (<b>b</b>) Anisotropic antenna (<b>c</b>) Transmitarray antenna.</p>
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<p>Photographs of fabricated transmitarray antenna. (<b>a</b>) source antenna (<b>b</b>) Anisotropic antenna (<b>c</b>) Transmitarray antenna.</p>
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<p>Simulation and experiment setup for verification of beam focusing. (<b>a</b>) Simulation (<b>b</b>) Experiment.</p>
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<p>Performance of proposed antenna in far and near regions. (<b>a</b>) Far-field radiation pattern (<span class="html-italic">ϕ</span> = 0°) (<b>b</b>) Normalized E-field intensity at <span class="html-italic">x</span>-axis.</p>
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