Journal articles: 'F-θ lens'

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Huang, Kuang-Lung, Mei Chu, Cheng-Huan Chen, Yu-Chung Lin, Min-Kai Lee, and Sung-Ho Liu. "Enlarging lens design with f-Θ lens for real time laser lithography inspections." Optical Review 18, no. 1 (January 2011): 72–75. http://dx.doi.org/10.1007/s10043-011-0034-y.

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Rez, Peter. "Analytic integration of contrast transfer functions." Proceedings, annual meeting, Electron Microscopy Society of America 46 (1988): 822–23. http://dx.doi.org/10.1017/s042482010010617x.

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In high resolution microscopy the image amplitude is given by the convolution of the specimen exit surface wave function and the microscope objective lens transfer function. This is usually done by multiplying the wave function and the transfer function in reciprocal space and integrating over the effective aperture. For very thin specimens the scattering can be represented by a weak phase object and the amplitude observed in the image plane is1where fe (Θ) is the electron scattering factor, r is a postition variable, Θ a scattering angle and x(Θ) the lens transfer function. x(Θ) is given by2where Cs is the objective lens spherical aberration coefficient, the wavelength, and f the defocus.We shall consider one dimensional scattering that might arise from a cross sectional specimen containing disordered planes of a heavy element stacked in a regular sequence among planes of lighter elements. In a direction parallel to the disordered planes there will be a continuous distribution of scattering angle.

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Yang, Su, An Zhi-yong, Li Qi, and Xu Miao. "Optical design of wide-angle large-relative-aperture f-θ lens." Journal of Applied Optics 36, no. 3 (2015): 376–80. http://dx.doi.org/10.5768/jao201536.0301007.

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Ning, Chen Wei, Cao Jian Zhong, Yang Hong Tao, Zhang Jian, Fan Zhe Yuan, Wu Li, Zhang Hui, and Lei Yang Jie. "Target Optimization Design of Cam Curve in Zoom System." Key Engineering Materials 552 (May 2013): 44–51. http://dx.doi.org/10.4028/www.scientific.net/kem.552.44.

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Zoom lens has been widely applied in all kinds of fields, and its cam optimization is the key to actualizing the performance of its optical design and the zooming process, while the smoothness and speediness of zooming movement must be considered for military and civilian use. With the incremental use of environmental requirements, it puts forward higher requests to the cam performance of lens. In order to guarantee that the cam has good stiffness in the case of vibration and shock environment, in the process of cam design, it not only requires curve optimal, but also needs to consider influence on the performance which is caused by reduced cam stiffness of the zoom system. A fine curve can ensure that the cam pressure angle α is smaller, and to ensure the cam follower maintains the uniform velocity and smaller acceleration in zooming process, and make the zoom system produce little impact, and whole zooming process smooth and fluent, it can reduce the zoom systems driving moment M, and can ensure the stability imaging of the zoom system. Good cam stiffness K can make the zoom lens have good stability in vibration environment, and make sure that the image quality. M and K respectively up to the pressure angle α of zoom curve and the rotation angle θ of zoom curve in cam. In the new cam design process, considering the whole influence on the performance that is caused by K and M to cam, we construct the function expressions K = f (α, θ) and M = f (α, θ), and then, build target optimization function with K and M, optimize the relationship between pressure angle α of zoom curve and rotation angle θ, looking for the optimal value for the stiffness K and the cam system driving moment M , and improve overall performance of the zoom cam .

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Yuanyuan, LI, WANG Chunyan, and WANG Zhiqiang. "F-θ lens design for high-precision semiconductor laser marking machine." Journal of Applied Optics 41, no. 1 (2020): 202–8. http://dx.doi.org/10.5768/jao202041.0107003.

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May, Karl Henrik, Shiva Mohammadzadeh, Andreas Keil, Georg von Freymann, and Fabian Friederich. "Coherent Off-Axis Terahertz Tomography with a Multi-Channel Array and f-theta Optics." Sensors 24, no. 2 (January 15, 2024): 529. http://dx.doi.org/10.3390/s24020529.

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Terahertz tomography is a promising method among non-destructive inspection techniques to detect faults and defects in dielectric samples. Recently, image quality was improved significantly through the incorporation of a priori information and off-axis data. However, this improvement has come at the cost of increased measurement time. To aim toward industrial applications, it is therefore necessary to speed up the measurement by parallelizing the data acquisition employing multi-channel setups. In this work, we present two tomographic frequency-modulated continuous wave (FMCW) systems working at a bandwidth of 230–320 GHz, equipped with an eight-channel detector array, and we compare their imaging results with those of a single-pixel setup. While in the first system the additional channels are used exclusively to detect radiation refracted by the sample, the second system features an f-θ lens, focusing the beam at different positions on its flat focal plane, and thus utilizing the whole detector array directly. The usage of the f-θ lens in combination with a scanning mirror eliminates the necessity of the formerly used slow translation of a single-pixel transmitter. This opens up the potential for a significant increase in acquisition speed, in our case by a factor of four to five, respectively.

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Tien, Chuen-Lin, Chun-Yu Chiang, and Wen-Shing Sun. "Design of a Miniaturized Wide-Angle Fisheye Lens Based on Deep Learning and Optimization Techniques." Micromachines 13, no. 9 (August 27, 2022): 1409. http://dx.doi.org/10.3390/mi13091409.

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This paper presents the optimization design of a miniaturized five-element wide-angle fisheye lens using a deep learning algorithm. Zemax optical design software was used to simulate and optimize the wide-angle fisheye lens. A deep learning algorithm helped to find the best combination of different lens materials. We first used six lens elements as an initial configuration to design miniaturized wide-angle fisheye lenses using the optimization process. The optical system components were gradually decreased to five lens elements. Both OKP4HT and polymethyl methacrylate (PMMA) plastic aspheric lenses were selected to replace the second spherical glass lens in the original design. We propose two types of wide-angle fisheye lens designs with four spherical lenses and one aspheric lens. The results for these designs indicated a viewing angle of 174°, a total length of less than 15 mm, a spot size of less than 6 μm, lateral color within ±1 μm, field curvature within ±0.02 mm, and F-θ distortion of ±3.5%. In addition, the MTF value was larger than 0.4 at the spatial frequency of 100 cycles/mm.

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Volyar, Alexander, Eugeny Abramochkin, Yana Akimova, and Mikhail Bretsko. "Astigmatic-Invariant Structured Singular Beams." Photonics 9, no. 11 (November 8, 2022): 842. http://dx.doi.org/10.3390/photonics9110842.

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We investigate the transformation of structured Laguerre–Gaussian (sLG) beams after passing through a cylindrical lens. The resulting beam, ab astigmatic structured Laguerre–Gaussian (asLG) beam, depends on quantum numbers (n,ℓ) and three parameters. Two of them are control parameters of the initial sLG beam, the amplitude ϵ and phase θ. The third one is the ratio of the Rayleigh length z0 and the focal length f of the cylindrical lens. It was theoretically revealed and experimentally confirmed that the asLG beam keeps the intensity shape of the initial sLG beam when the parameters satisfy simple conditions: ϵ is unity and the tangent of the phase parameter θ/2 is equal to the above ratio. We also found sharp bursts and dips of the orbital angular momentum (OAM) in the asLG beams in the vicinity of the point where the OAM turns to zero. The heights and depths of these bursts and dips significantly exceed the OAM maximum and minimum values of the initial sLG beam and are controlled by the radial number n.

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Wang Chunhui, 王春晖, 季一勤 Ji Yiqin, 高龙 Gao Long, 李彦超 Li Yanchao, and 曲杨 Qu Yang. "Optical Design of Large Working Area f-θ Scanning Lens for 2 μm Laser Heterodyne Interferometry System." Chinese Journal of Lasers 38, no. 12 (2011): 1216002. http://dx.doi.org/10.3788/cjl201138.1216002.

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Pang, Yajun, Kai Zhang, Zhenxu Bai, Youchun Sun, and Meiling Yao. "Design Study of a Large-Angle Optical Scanning System for MEMS LIDAR." Applied Sciences 12, no. 3 (January 25, 2022): 1283. http://dx.doi.org/10.3390/app12031283.

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MEMS-based LIDAR has the advantages of fast-scanning, simple structure, small volume, and light weight, which make it a hot topic for 3D imaging. In order to overcome the limited scanning angle of the current MEMS mirrors, a large angle MEMS-based optical scanning system was designed using telephoto structure. In this design an f-θ lens group is used for flat field scanning and a symmetrical cemented lens group is used for angle expansion. The principle of this system is discussed in detail and an optical design is implemented by ZEMAX software. The designed system realized a scanning angle as large as 57° and is in excellent linear relation with the tilt angle of the MEMS mirror. At the target distance of 100 m, the maximum RMS radius of the light spot is only 7 cm. This optical scanning system shows a significant application potentiality for 3D imaging LIDAR.

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Zhang, Jialei, Yaoke Xue, Canglong Zhou, Shangmin Lin, and Meiying Liu. "Athermalization of Optical System with Large Field of View for Image Navigation." Journal of Physics: Conference Series 2617, no. 1 (October 1, 2023): 012007. http://dx.doi.org/10.1088/1742-6596/2617/1/012007.

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Abstract Image navigation sensor is one of the most important sensing means for human to explore the extraterrestrial space environment, and optical system is a key component of image navigation sensor, directly determines the amount of information perceived. The optical system requirements of image navigation sensors are gradually developing towards large field of view and miniaturization. The fisheye lens is the first choice for large field of view imaging by selecting the appropriate optical structure, without adding other additional components, and has the advantages of small size and strong perception energy. However, as the image surface illuminance of fisheye lens will decrease sharply with the increase of the field of view, the change of temperature will also degrade the imaging quality of the system, and strong stray light sources such as the sun will easily enter the field of view, which will greatly affect the perception ability of the system. Because of this, effective design of these systems is quite difficult. In this paper, a reverse-telephoto structure was used for large-field imaging, and the degradation of imaging quality caused by temperature changes was eliminated by selecting appropriate optical and mechanical materials. Designed with a focal length of 6.7mm, an F number of 3.6, a viewing angle of 130°, a working band of 0.45μm to 0.65μm, an after work distance of 7mm, a total system length≤60mm, we tested our system in a -40°C to +60°C temperature range and measured the image quality. Through simulation analysis, the system in the whole field of view within our spot diagrams was≤5.5μm, optical transfer function was greater than 0.2 at 90lp/mm, and no vignetting occurred. Furthermore, the imaging illumination of the edge field of view was 0.72 times that of the center field of view, the f – tan (θ) relative distortion value of the center field of view was≤2.3%, and the f – θ relative distortion value of the edge field of view was≤2.7%. Compared to normal temperatures, the optical transfer function changes at -20°C and +40°C were 0.02 and 0.01, respectively. Thus, the system displayed the characteristics of excellent image quality, small size, high energy utilization rate and good non-thermal performance.

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Chang, Sung Ho, Young Moo Heo, G. H. Shin, Young Min Lee, Jeong Jin Kang, and T. S. Jung. "An Experimental Study on Flow Characteristics of PBK-40 for Glass Molding Press Simulation." Key Engineering Materials 364-366 (December 2007): 476–81. http://dx.doi.org/10.4028/www.scientific.net/kem.364-366.476.

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Remarkable progress had been made in both technology and production of optical elements including aspheric lens. Especially, requirements for machining glass materials have been increasing in terms of limitation on using environment, flexibility of material selection and surface accuracy. In the past, precision optical glass lenses were produced through multiple processes such as grinding and polishing, but mass production of aspheric lenses requiring high accuracy and having complex profile was rather difficult. Against such a background, the high-precision optical GMP process was developed with an eye on mass production of precision optical glass pasts by molding press. This GMP process can produce with precision and good repeatability special form lenses such as for cameras, video cameras, aspheric lenses for laser pickup, f-θ lens for laser printer and prism, and fine glass parts including diffraction grating and V-grooved base. Generally, GMP process can be classified into batch and progressive type. In these types, because progressive type has many merits in that productivity is higher and repair/retouch of mold is easier than batch type, progressive GMP process is mainly used to produce aspheric glass lenses these days. In this paper, as a fundamental study to develop the multi-cavity mold for higher productivity of progressive GMP process used in fabrication of aspheric glass lens, compression tests for K-PBK40, which is the material of aspheric glass lens, were conducted at high temperature. As a result, flow characteristics of K-PBK40 were obtained for aspheric glass lens press simulation.

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Harris, Zachery B., Arjun Virk, Mahmoud E. Khani, and M. Hassan Arbab. "Terahertz time-domain spectral imaging using telecentric beam steering and an f-θ scanning lens: distortion compensation and determination of resolution limits." Optics Express 28, no. 18 (August 25, 2020): 26612. http://dx.doi.org/10.1364/oe.398706.

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14

Borges, Carlos R. "LECs, Local Mixers, Topological Groups and Special Products." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 44, no. 2 (April 1988): 252–58. http://dx.doi.org/10.1017/s1446788700029839.

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AbstractWe prove that every (locally) contractible topological group is (L)EC and apply these results to homeomorphism groups, free topological groups, reduced products and symmetric products. Our main results are: The free topological group of a θ-contractible space is equiconnected. A paracompact and weakly locally contractible space is locally equiconnected if and only if it has a local mixer. There exist compact metric contractible spaces X whose reduced (symmetric) products are not retracts of the Graev free topological groups F(X) (A(X)) (thus correcting results we published ibidem).

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BOISSONNAT, JEAN-DANIEL, OLIVIER DEVILLERS, LEONBATTISTA DONATI, and FRANCO P. PREPARATA. "MOTION PLANNING OF LEGGED ROBOTS: THE SPIDER ROBOT PROBLEM." International Journal of Computational Geometry & Applications 05, no. 01n02 (March 1995): 3–20. http://dx.doi.org/10.1142/s0218195995000027.

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We consider the problem of planning motions of a simple legged robot called the spider robot. The robot is modelled as a point where all its legs are attached, and the footholds where the robot can securely place its feet consist of a set of n points in the plane. We show that the space F of admissible and stable placements of such robots has size Θ(n2) and can be constructed in O(n2 log n) time and O(n2) space. Once F has been constructed, we can efficiently solve several problems related to motion planning.

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Liu, Meng, and Xuan Zheng. "Improving the Light Extraction Efficiency of GaN-Based Thin-Film Flip-Chip Micro-LEDs through Inclined Sidewall and Photonic Crystals." Electronics 13, no. 18 (September 21, 2024): 3750. http://dx.doi.org/10.3390/electronics13183750.

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Low light extraction efficiency (LEE) remains a critical bottleneck in the performance of contemporary micro-light-emitting diodes (micro-LEDs). This study presents an innovative approach to improve the LEE of Gallium nitride (GaN)-based thin-film flip-chip (TFFC) micro-LEDs by integrating an inclined sidewall with photonic crystals (PhCs). Three-dimensional finite-difference time-domain (FDTD) simulations reveal that the inclined sidewall design significantly increases the escape probability of light, thereby improving LEE. Additionally, the PhCs’ structure further improves LEE by enabling more light to propagate into the escape cones through diffraction. Optimal results are achieved when the inclined sidewall angle (θ) is 28° and the PhCs exhibit a period (a) of 220 nm, a filling factor (f) of 0.8, and a depth (d) of 3 μm, resulting in a maximum LEE of 36.47%, substantially surpassing the LEE of conventional planar TFFC micro-LEDs. These results provide valuable design guidelines for the development of high-efficiency GaN-based micro-LEDs.

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Larson, D. J., K. F. Russell, and M. K. Miller. "Effect of Specimen Aspect Ratio on the Reconstruction of Atom Probe Tomography Data." Microscopy and Microanalysis 5, S2 (August 1999): 930–31. http://dx.doi.org/10.1017/s1431927600017979.

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The field ion microscope is a point projection microscope, with the magnification inversely proportional to the radius of curvature (R) of the needle-shaped tip which comprises the specimen. The electric field at the specimen apex, which determines the trajectories of field evaporated ions, is given by F=V/(kR), where V is the specimen voltage and k is a geometric field reduction factor which increases with the specimen taper angle, θ. In the reconstruction of atom probe tomography (APT) data, the magnification, and thus the lateral extent of the analyzed region, is determined primarily by the specimen radius and taper angle. Asymmetric specimens may often be fabricated, even from materials which lend themselves to straightforward preparation. In addition, in certain materials, specimens with high aspect ratios may result from crystallographic preferential electropolishing. For accurate data reconstruction, it is important to know not only the specimen radius, but also, ideally, the degree of anisotropy (aspect ratio taper angle in orthogonal directions) of the specimen.

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Shadle, Christine H. "Alternatives to moments for characterizing fricatives: Reconsidering Forrest et al. (1988)." Journal of the Acoustical Society of America 153, no. 2 (February 2023): 1412–26. http://dx.doi.org/10.1121/10.0017231.

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Means of characterizing acoustic signals of fricatives with a few parameters have long been sought. When Forrest, Weismer, Milenkovic, and Dougall [(1988) J. Acoust. Soc. Am. 84, 115–123] described their system of treating spectra as probability density functions and computing the first four spectral moments, others quickly adopted their clearly described method, although it did not distinguish /f/ and /θ/. Various problems with their method are described, including the lack of spectral averaging, the necessity of normalizing the amplitude, and correlation between pairs of moments. Even when these issues are rectified by alternative methods, the fact remains that moments are not ideal descriptors because they can only describe departures from the shape of a normal Gaussian distribution. Fricative spectra, particularly of non-sibilants, are often quite dissimilar in shape from Gaussians. Furthermore, shape descriptors do not lend themselves to direct inferences about the production variables that caused the acoustic effects. Here, alternative parameters are defined, it is shown how to adapt them to specific experimental conditions, and tests of efficacy are proposed. These parameters are strongly linked to the articulatory and aerodynamic variables that underlie fricative production.

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Kuchev, D. N. "Mathematical Model Development of an In-Line Robotic Complex Mechanical System." Vestnik IzhGTU imeni M.T. Kalashnikova 27, no. 1 (March 30, 2024): 4–13. http://dx.doi.org/10.22213/2413-1172-2024-1-4-13.

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The article considers the problem of pipeline inspection of the Russian Federation, provides brief statistics on failures of various purpose industrial pipelines, presents the causes of accidents, analyzes technical solutions for pipeline timely inspection using in-line robotic devices, proposes a new design of an in-line robotic complex with the possibility of movement along complex geometry sections, a study presents the mathematical description development of an in-line robotic complex mechanical system for the subsequent creation of a motion control system for the device moving inside the pipeline. The research uses methods of analysis, synthesis, generalization of scientific experience in the field of automated in-tube devices, methods of theoretical mechanics, mechatronics and robotics. As a result, a mathematical description of a statically balanced mechanical system transition into the movement of the device is obtained when тяги расч с ;F F> relations of design parameters and its orientation on scalar values of wheel propeller reaction forces are obtained; thus, for a device weight of 12 kg, the orientation of the pipeline inclination angle of 0 degrees and the minimum clamping force of wheel propellers, the resulting reaction forces of the supports is 117.6 N. The obtained relations make it possible to determine the gravity distribution between the supporting legs with respect to design parameters of an automated device, as well as its orientation, while the wheel propeller reaction forces are the main component in determining the device traction force. In turn, this allows calculation of the required forces on the supporting legs to maintain the device spatial position with respect to the orientation angles ( ),,θ α to move the inspecting equipment of the device to the required diagnostic position relative to the pipeline and to select an electric motor. The results of the study can be used in the development of in-line robotic devices of the push-pull type.

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Danel, Zoriana, Joanna Halun, and Pawel Karbowniczek. "Analytical and Numerical Investigation of Star Polymers in Confined Geometries." International Journal of Molecular Sciences 25, no. 17 (September 3, 2024): 9561. http://dx.doi.org/10.3390/ijms25179561.

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The analysis of the impact of the star polymer topology on depletion interaction potentials, depletion forces, and monomer density profiles is carried out analytically using field theory methods and techniques as well as molecular dynamic simulations. The dimensionless depletion interaction potentials and the dimensionless depletion forces for a dilute solution of ideal star polymers with three and five legs (arms) in a Θ-solvent confined in a slit between two parallel walls with repulsive surfaces and for the case where one of the surfaces is repulsive and the other inert are obtained. Furthermore, the dimensionless layer monomer density profiles for ideal star polymers with an odd number (f˜ = 3, 5) of arms immersed in a dilute solution of big colloidal particles with different adsorbing or repelling properties in respect of polymers are calculated, bearing in mind the Derjaguin approximation. Molecular dynamic simulations of a dilute solution of star-shaped polymers in a good solvent with N = 901 (3 × 300 + 1 -star polymer with three arms) and 1501 (5 × 300 + 1 -star polymer with five arms) beads accordingly confined in a slit with different boundary conditions are performed, and the results of the monomer density profiles for the above-mentioned cases are obtained. The numerical calculation of the radius of gyration for star polymers with f˜ = 3, 5 arms and the ratio of the perpendicular to parallel components of the radius of gyration with respect to the wall orientation for the above-mentioned cases is performed. The obtained analytical and numerical results for star polymers with an odd number (f˜ = 3, 5) of arms are compared with our previous results for linear polymers in confined geometries. The acquired results show that a dilute solution of star polymer chains can be applied in the production of new functional materials, because the behavior of these solutions is strictly correlated with the topology of polymers and also with the nature and geometry of confined surfaces. The above-mentioned properties can find extensive practical application in materials engineering, as well as in biotechnology and medicine for drug and gene transmission.

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Kaye, Stephen B., Jamila Surti, and James S. Wolffsohn. "Average paraxial power of a lens and visual acuity." Scientific Reports 13, no. 1 (May 2, 2023). http://dx.doi.org/10.1038/s41598-023-34010-4.

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AbstractTo provide a solution for average paraxial lens power (ApP) of a lens. Orthogonal and oblique sections through a lens of power $$F$$ F were reduced to a paraxial representation of lens power followed by integration. Visual acuity was measured using lenses of different powers (cylinders of − 1.0 and − 2.0D) and axes, mean spherical equivalent (MSE) of S + C/2, ApP and a toric correction, with the order of correction randomised. A digital screen at 6 m was used on which a Landolt C with crowding bars was displayed for 0.3 s before vanishing. The general equation for a symmetrical lens of refractive index (n), radius of curvature R, in medium of refractive index n1, through orthogonal ($$\theta$$ θ ) and oblique meridians ($$\gamma$$ γ ) as a function of the angle of incidence ($$\alpha$$ α ) reduces for paraxial rays ($$\alpha \sim 0$$ α ∼ 0 ) to $$F_{n,R} \left( {\alpha ,\theta ,\gamma } \right)\left. \right|_{\alpha \sim 0} = \frac{{n - n_{1} }}{R}\cos^{2} \theta \cos^{2} \gamma$$ F n , R α , θ , γ α ∼ 0 = n - n 1 R cos 2 θ cos 2 γ . The average of this function is $$F_{n,R} \left( {\alpha ,\theta ,\gamma } \right)\left. \right|_{\alpha \sim 0} = \frac{{n - n_{1} }}{4R} $$ F n , R α , θ , γ α ∼ 0 = n - n 1 4 R providing a solution of $$\frac{F}{4}$$ F 4 for ApP.For central (p = 0.04), but not peripheral (p = 0.17) viewing, correction with ApP was associated with better visual acuity than a MSE across all tested refractive errors (p = 0.04). These findings suggest that $$\frac{F}{4}$$ F 4 may be a more inclusive representation of the average paraxial power of a cylindrical lens than the MSE.

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Mohammadzadeh, Shiva, Raphael Hussung, Andreas Keil, Sven Leuchs, Christian Krebs, Dirk Nüßler, Jörg Seewig, Georg von Freymann, and Fabian Friederich. "Compact hand-guided 3D scanning terahertz sensor platforms with 3D-printed aspherical telecentric f-θ lens." International Journal of Microwave and Wireless Technologies, April 26, 2023, 1–11. http://dx.doi.org/10.1017/s1759078723000259.

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Abstract We report on the development of a handheld three-dimensional (3D) terahertz scanning system with an aspherical telecentric 3D-printed f-θ lens using selective laser sintering. The lens covers a broader scan line of 50 mm with its larger aperture, compared to the 20 mm range in our initial work, which was presented at the European Microwave Week 2021. In order to evaluate the adaptability of the optomechanical components with different sensor units, two different integrated frequency-modulated continuous wave radar modules based on monolithic microwave integrated circuit technology, operating in W- and D-bands are tested within the measurement scheme. The optomechanical part consists of a galvanometer scanner mirror and the f-θ lens. The optical system enables B-scans perpendicular to the manual translational movement of the sensor unit by its user. An integrated guiding wheel system with rotary encoder makes it possible to correlate the measurement points to their respective locations, enabling complete 3D volumetric inspection of the corresponding structures, which is particularly useful for the inspection along cracks and welds.

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-, Sagar Sars Maithil. "Drive Formula for Sars Length of Wire Hanging Between Two Electric Poles and Some Applications." International Journal For Multidisciplinary Research 6, no. 1 (January 30, 2024). http://dx.doi.org/10.36948/ijfmr.2024.v06i01.12541.

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Base on sars length of wire hanging between two electric poles makes angles θ & ∝ with horizontal. Drive the formula for sars length of wire makes angles with horizontal θ & ∝ where (θ > ∝). Find the volume, Sars surface area,Total surface area of many kinds of Sars cuboid and Sars cube like as LL-Sars cuboid, UU-Sars cuboid, LU-Sars cuboid, LL-Sars cube, UU-Sars cube, LU-Sars cube . All kind of Sars cuboid and Sars cube used in optics instruments like as Sars lens, Sars mirror. When a ray of light incident on the Sars surface area then it is refracted or reflected depending on the sars surface area and angles θ&∝. Base on Sars length of wire used 170 applications and more. But in this paper some application are used. To find the Sars length of wire hanging between two electric poles. If f(x) is a smooth curve on [a, b] and length of curve y=f(x) from a to b.

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Zhang, Jingwei, Jingpei Hu, Zenghui Yang, Aijun Zeng, and Huijie Huang. "Angle monitor of micromirror array for freeform illumination in lithography systems." AIP Advances 14, no. 1 (January 1, 2024). http://dx.doi.org/10.1063/5.0186334.

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Source and mask optimization is a critical technique for further resolution enhancement in immersion lithography systems, wherein the optimal illumination source shape is widely generated by the micromirror array. Accordingly, the accurate achievement of the allocated angles of micromirrors is a key prerequisite for the implementation of arbitrary illumination patterns. In this paper, we propose an angle monitor to ensure the high-precision tilting of thousands of biaxial micromirrors. As one of the critical modules for closed-loop control of the two-dimensional micromirror array, the online monitor feeds the monitored high-precision tilt angle back to the processing system. The angle monitor mainly consists of the spot scanning module and the angle detection module. Among them, an f-θ lens and a Fourier transform lens with satisfied performances are designed and evaluated by CODE V. Furthermore, a galvanometer and the designed f-θ lens are adopted for the generation of the spot array irradiated on the electrostatic actuated mirrors. Meanwhile, the designed Fourier transform lenses are employed to detect the corresponding tilt angles. In addition, the performance of the proposed system is identified by simulations and experiments individually. It is demonstrated that the monitorable biaxial tilt range of the system is (−2.5°, +2.5°) with a repeatability of better than 0.005°. The large-format micromirror array can be monitored completely without optical cross-talk. Through the device, a 16 × 16 micromirror array is monitored, where the initial angle with no bias voltage applied is captured and the voltage–angle relation for individual micromirrors is obtained. In general, the proposed system can be utilized in the illumination system, providing an efficient and reliable method for complex source shape generation.

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Khani, Mahmoud E., Zachery B. Harris, Omar B. Osman, Juin W. Zhou, Andrew Chen, Adam J. Singer, and M. Hassan Arbab. "Supervised machine learning for automatic classification of in vivo scald and contact burn injuries using the terahertz Portable Handheld Spectral Reflection (PHASR) Scanner." Scientific Reports 12, no. 1 (March 24, 2022). http://dx.doi.org/10.1038/s41598-022-08940-4.

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AbstractWe present an automatic classification strategy for early and accurate assessment of burn injuries using terahertz (THz) time-domain spectroscopic imaging. Burn injuries of different severity grades, representing superficial partial-thickness (SPT), deep partial-thickness (DPT), and full-thickness (FT) wounds, were created by a standardized porcine scald model. THz spectroscopic imaging was performed using our new fiber-coupled Portable HAndheld Spectral Reflection Scanner, incorporating a telecentric beam steering configuration and an f-$$\theta$$ θ scanning lens. ASynchronous Optical Sampling in a dual-fiber-laser THz spectrometer with 100 MHz repetition rate enabled high-speed spectroscopic measurements. Given twenty-four different samples composed of ten scald and ten contact burns and four healthy samples, supervised machine learning algorithms using THz-TDS spectra achieved areas under the receiver operating characteristic curves of 0.88, 0.93, and 0.93 when differentiating between SPT, DPT, and FT burns, respectively, as determined by independent histological assessments. These results show the potential utility of our new broadband THz PHASR Scanner for early and accurate triage of burn injuries.

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Journal articles on the topic 'F-θ lens'

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