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1
Kotlyar, Victor V., Alexey A. Kovalev, Alexey M. Telegin, et al. "Transverse Spin Hall Effect and Twisted Polarization Ribbons at the Sharp Focus." Applied Sciences 14, no. 9 (2024): 3926. http://dx.doi.org/10.3390/app14093926.
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In this work, using a Richards-Wolf formalism, we derive explicit analytical relationships to describe vectors of the major and minor axes of polarization ellipses centered in the focal plane when focusing a cylindrical vector beam of integer order n. In these beams, the major axis of a polarization ellipse is found to lie in the focal plane, with the minor axis being perpendicular to the focal plane. This means that the polarization ellipse is perpendicular to the focal plane, with its polarization vector rotating either clockwise or anticlockwise and forming “photonic wheels”. Considering that the wave vector is also perpendicular to the focal plane, we conclude that the polarization ellipse and the wave vector are in the same plane, so that at some point these can coincide, which is uncharacteristic of transverse electromagnetic oscillations. In a cylindrical vector beam, the spin angular momentum vector lies in the focal plane, so when making a circle centered on the optical axis, at some sections, the handedness of the spin vector and circular motion are the same, being opposite elsewhere. This effect may be called an azimuthal transverse spin Hall effect, unlike the familiar longitudinal spin Hall effect found at the sharp focus. The longitudinal spin Hall effect occurs when opposite-sign longitudinal projections of the spin angular momentum vector are spatially separated in the focal plane. In this work, we show that for the latter, there are always an even number of spatially separated regions and that, when making an axis-centered circle, the major-axis vector of polarization ellipse forms a two-sided twisted surface with an even number of twists.
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Kotlyar, V. V., A. A. Kovalev, A. M. Telegin, and E. S. Kozlova. "Transverse spin Hall effect and polarization twist ribbon at the sharp focus." Computer Optics 48, no. 6 (2024): 822–31. https://doi.org/10.18287/2412-6179-co-1504.
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In this work, using the Richards-Wolf formalism, we found explicit analytical expressions for the coordinates of the major and minor axes of the polarization ellipse centered in the focal plane for a cylindrical vector beam of integer order n. For such a beam, the major axis of the polarization ellipse lies in the focal plane, whereas the minor axis is perpendicular to the focal plane. Therefore, the polarization ellipse is perpendicular to the focal plane, with the polarization vector rotating clockwise or counterclockwise in this plane (producing 'optical wheels'). Considering that the wave vector is also perpendicular to the focal plane, the polarization ellipse and the wave vector turn out to lie in the same plane, so that at some point of time the polarization vector can coincide with the wave vector, which is not usual for transverse electromagnetic oscillations. For a cylindrical vector beam, the spin angular momentum vector lies in the focal plane. So, when going around a certain circle with the center on the optical axis, the spin vector is directed counterclockwise in some sections of the circle, and clockwise in other sections. This effect can be called the transverse (azimuthal) optical spin Hall effect, in contrast to the well-known longitudinal optical spin Hall effect at the sharp focus. The longitudinal spin Hall effect is understood as the separation in the focal plane of regions with different signs of the longitudinal projection of the spin angular momentum vector. This work shows that there is always an even number of such regions and that when going around a circle, the vector of the major axis of the polarization ellipse forms a two-sided twist surface with an even number of turns.
3
Kkallas, Ch, C. B. Papazachos, E. M. Scordilis, and B. N. Margaris. "Re-examining the stress field of the broader southern Aegean subduction area using an updated focal mechanism database." Bulletin of the Geological Society of Greece 47, no. 2 (2017): 563. http://dx.doi.org/10.12681/bgsg.11083.
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We have employed the data of EGELADOS temporary network (October 2005-April 2007) to determine 88 focal mechanism solutions from Southern Aegean Sea using the RAPIDINV algorithm (Cesca et al., 2010). The new focal mechanism solutions determined, complemented with the previously available ones for Southern Aegean Seα provide the basis for a detailed examination of the stress field, using the distribution of P and T axes. To obtain the stress field we applied the method of Gephart and Forsyth (1984), namely the grid search inversion approach of Gephart (1990a,b), which incorporates the P and T axes of selected focal mechanisms. For the inversion, the initial stress solutions were computed by the “average” kinematic P and T-axis approach of Papazachos and Kiratzi (1992). The stress-inversion allows choosing the "ideal" fault plane corresponding to the minimum misfit rotation about an axis of general orientation which is needed to match an observed fault plane/slip direction with one consistent with the final stress model.
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Kotlyar, Victor V., Alexey A. Kovalev, Anton G. Nalimov, Sergey S. Stafeev, and Alexey M. Telegin. "Transverse and Longitudinal Energy Flows in a Sharp Focus of Vortex and Cylindrical Vector Beams." Applied Sciences 14, no. 14 (2024): 6305. http://dx.doi.org/10.3390/app14146305.
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It is shown in this work that, with strong focusing of a beam with optical vortex and circular polarization, three energy flows take place in the focal plane: direct longitudinal, reverse longitudinal and azimuthal transverse flows. Calculations are made analytically using the Richards–Wolf formalism and by numerical simulation. Moreover, the energy rotation at different lengths from the optical axis occurs in different directions. Therefore, the focal plane intersects along the optical axis only part of the initial beam energy per unit time. The same energy part (other things being equal) intersects the focal plane along the positive direction of the optical axis when an optical vortex with cylindrical polarization is focused. The difference is that, if an optical vortex is present, then the transverse energy flux at the focus rotates around the optical axis. If an optical vortex is not present (a beam with only cylindrical polarization), then the average transverse flow in the focal plane is zero, though, in some regions in the focal plane, the flow is directed towards the optical axis and, in other regions, away from it. This behavior of the transverse energy flow at the focus (flow direction towards the optical axis and away from the optical axis) of a cylindrical vector beam can be deemed another kind of Hall effect.
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Ebel, John E., and Bruce R. Bouck. "New Focal Mechanisms for the New England Region: Constrains on the Regional Stress Regime." Seismological Research Letters 59, no. 4 (1988): 183–87. http://dx.doi.org/10.1785/gssrl.59.4.183.
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Abstract Single-event focal mechanisms for fifteen earthquakes in New England and New York have been determined. Thirteen of these are new focal mechanisms, while two are redeterminations for events with previously reported solutions. The focal mechanisms display considerable scatter in P-axis orientation, as has been reported in earlier studies. Some areas within the region, such as central New Hampshire and northeastern Massachusetts, show locally consistent principal stress directions. Other areas, such as central Maine, do not. All but one or two of the new focal mechanisms have P-axis and T-axis orientations which fall within the range of values calculated by Gephart and Forsyth (1985) for a regional stress field of horizontal, E-W maximum stress and vertical minimum stress in New England.
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Andrés, P., M. Martínez-Corral, and J. Ojeda-Castañeda. "Off-axis focal shift for rotationally nonsymmetric screens." Optics Letters 18, no. 16 (1993): 1290. http://dx.doi.org/10.1364/ol.18.001290.
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TAHIR, N. A., A. SHUTOV, D. VARENTSOV, et al. "High-energy-density matter research at GSI Darmstadt using intense heavy ion beams." Laser and Particle Beams 20, no. 3 (2002): 393–97. http://dx.doi.org/10.1017/s0263034602203043.
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This paper presents two-dimensional numerical simulations of heating of matter with intense heavy ion beams. It has been shown that it is very advantageous to irradiate the target with two different beams simultaneously, a main high intensity bunched beam of a heavy element like uranium and an unbunched low intensity beam of a lighter element like argon. The main beam is used to heat the target while the second beam is used as a diagnostic tool.Influence of the shape of the focal spot on compression and heating of matter has also been studied using an elliptic focal spot with an ellipticity of 1.5 (semimajor axis is along y-axis and is 1.5 times the semiminor axis which is along x-axis). It has been found that the temporal behavior of the development of density, pressure, and temperature profiles along different directions is quite different, which is not the case with a circular focal spot.
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Kotlyar, V. V., S. S. Stafeev, M. A. Telegin, and E. S. Kozlova. "Superposition of an optical vortex and a plane wave with linear polarization states at the tight focus." Computer Optics 48, no. 6 (2024): 851–57. https://doi.org/10.18287/2412-6179-co-1502.
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We analyze the sharp focusing of the superposition of a vortex laser beam with topological charge n and linear polarization and a plane wave with the same linear polarization directed along the horizontal axis. Using the Richards-Wolf formalism, analytical expressions are obtained for the intensity distribution and longitudinal projection of the spin angular momentum (SAM) in the focal plane. It is shown that for even and odd numbers n the intensity and SAM have different symmetries: for even n they are symmetric with respect to both Cartesian axes, and for odd n they are symmetric only with respect to the vertical axis. The intensity distribution has 2n local maxima at the focus, and the intensity on the optical axis is nonzero for any n. The distribution of the longitudinal SAM (spin density) in the focal plane has (n+2) subwavelength regions with a positive SAM and (n+2) regions with a negative SAM, the centers of which alternately locate on a circle of a certain radius centered at the optical axis. Such an alternating-spin pattern demonstrates the spin Hall effect at the focus. At the focus, the negative and positive spins are mutually compensated, meaning that the total spin is zero.
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Zheng, Guoliang, Qingyang Wu, Tiefeng He, and Xuhui Zhang. "Propagation Characteristics of Circular Airy Vortex Beams in a Uniaxial Crystal along the Optical Axis." Micromachines 13, no. 7 (2022): 1006. http://dx.doi.org/10.3390/mi13071006.
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Circular airy vortex beams (CAVBs) have attracted much attention due to their “abruptly autofocusing” effect, phase singularity, and their potential applications in optical micromanipulation, communication, etc. In this paper, we numerically investigated the propagation properties of circular airy beams (CABs) imposed with different optical vortices (OVs) along the optical axis of a uniaxial crystal for the first time. Like other common beams, a left-hand circular polarized (LHCP) CAVB, propagating along the optical axis in a uniaxial crystal, can excite a right-hand circular polarized (RHCP) component superimposed with an on-axis vortex of topological charge (TC) number of 2. When the incident beam is an LHCP CAB imposed with an on-axis vortex of TC number of l = 1, both of the two components have an axisymmetric intensity distribution during propagation and form hollow beams near the focal plane because of the phase singularity. The phase pattern shows that the LHCP component carries an on-axis vortex of TC number of l = 1, while the RHCP component carries an on-axis vortex of TC number of l = 3. With a larger TC number (l = 3), the RHCP component has a larger hollow region in the focal plane compared to the LHCP component. We also studied cases of CABs imposed with one and two off-axis OVs. The off-axis OV makes the CAVB’s profile remain asymmetric throughout the propagation. As the propagation distance increases, the off-axis OVs move near the center of the beam and overlap, resulting in a special intensity and phase distribution near the focal plane.
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Chabou, Saoussen, and Abdelhalim Bencheikh. "The on-axis intensity behavior of the diffracted Laguerre-Gaussian beam, LGp , by an opaque disk." Journal of Physical & Chemical Research 1, no. 1 (2022): 18–25. http://dx.doi.org/10.58452/jpcr.v1i1.26.
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In this work, we present a detailed study of the on-axis intensitydistribution of the Laguerre-Gaussian beam with no azimuthal index,diffracted by an opaque disk, by means of numerical simulation ofFresnel-Kirchhoff diffraction integral. We investigate the effect of theopaque disk size, the beam order, the beam waist, and the focal length.The results show that different focal phenomena may occur includingthe focal shift, focal split, and focal switch.
 
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Krylov, A. A., L. I. Lobkovsky, S. A. Kovachev, et al. "GEODYNAMIC REGIMES IN THE LAPTEV SEA REGION ACCORDING TO THE LATEST SEISMOLOGICAL DATA." Доклады Российской академии наук. Науки о Земле 513, no. 2 (2023): 224–30. http://dx.doi.org/10.31857/s2686739723601783.
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The results of the analysis of focal mechanisms and the general distribution of earthquake epicenters in the Laptev Sea region were presented. For four groups of clusters of events with known focal mechanisms, the directions of the principal stress axes were calculated by the formal stress inversion method. The distributions of earthquake epicenters and crustal thickness were compared. It has been revealed that, according to seismological data, the prolongation of the extension axis of the Gakkel Ridge on the Laptev Sea shelf is currently located in the vicinity of the group of extension detachments, which is extended along the eastern boundary of the Anisin, Zarya, and Belkovsko-Svyatonossky rift chains. The older extension axis, located along the group detachments marking the eastern boundary of the Ust-Lena and Omoloy rift systems, and continuing the axis of the Gakkel Ridge, is currently much less active, realizing residual stresses near its intersection with the Khatanga-Lomonosov fault zone in the northwestern parts of the shelf and with the Lena-Taimyr zone of boundary uplifts – in the southwestern. Near the Lena delta extension axes are oriented along the Olenekskaya and Bykovskaya channels and the border of the Siberian Platform, forming the extension conditions in the eastern part and the strike-slip regime in the western part of the vicinity of the Lena delta.
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Kotlyar, V. V., S. S. Stafeev, and A. A. Kovalev. "Sharp focusing of a light field with polarization and phase singularities of an arbitrary order." Computer Optics 43, no. 3 (2019): 337–46. http://dx.doi.org/10.18287/2412-6179-2019-43-3-337-346.
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Using the Richards-Wolf formalism, we obtain general expressions for all components of the electric and magnetic strength vectors near the sharp focus of an optical vortex with the topological charge m and nth-order azimuthal polarization. From these equations, simple consequences are derived for different values of m and n. If m=n>1, there is a non-zero intensity on the optical axis, like the one observed when focusing a vortex-free circularly polarized light field. If n=m+2, there is a reverse flux of light energy near the optical axis in the focal plane. The derived expressions can be used both for simulating the sharp focusing of optical fields with the double singularity (phase and polarization) and for a theoretical analysis of focal distributions of the intensity and the Poynting vector, allowing one to reveal the presence of rotational symmetry or the on-axis reverse energy flux, as well as the focal spot shape (a circle or a doughnut).
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Chen, Ruixiang, Tiegen Song, Yuee Luo, Hehe Li, and Xinzhong Li. "Inverse Energy Flux in Tight Focusing of Vector Vortex Beam." Photonics 10, no. 7 (2023): 743. http://dx.doi.org/10.3390/photonics10070743.
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In this paper, we focus on the study of the negative energy flow in the tight focusing of a radially polarized vortex beam. We know that, because of the coupling of the polarization state and the vortex charge, the on-axis energy flow in the focal region can be well modulated by changing the polarization order and the vortex charge of the incident vector beam. This shows that when the polarization order and the vortex charge satisfy the specific relation, the on-axis negative energy flow can be obtained in the focal region. Moreover, the initial phases of two polarization unit vectors also affect the evolution of the on-axis negative energy flow in the tight focusing of the radially polarized beam. The phase difference modulation of the two polarization unit vectors indicates two different modulations of the polarization state. Our work provides a more flexible modulation method for focal shaping and optical modulation.
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Zapata-Rodrı́guez, Carlos J., Genaro Saavedra, and Manuel Martı́nez-Corral. "Focal shift in optical waves with off-axis focus." Optics Communications 216, no. 1-3 (2003): 11–17. http://dx.doi.org/10.1016/s0030-4018(02)02280-0.
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Surashev, Nurgali, Michael Dudkin, Darkhan Yelemes, and Aziza Kalieva. "The Planetary Vibroexciter with Elliptic Inner Race." Advanced Materials Research 694-697 (May 2013): 229–32. http://dx.doi.org/10.4028/www.scientific.net/amr.694-697.229.
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We present a method determining analysis of workflow of the planetary vibroexciter, allowing by constructing three-dimensional graphs obtained in MathCAD, combine several line graphs in one. Improves the availability the results of theoretical analysis, the influence of the main parameters of the vibroexciter on its dynamic characteristics. The use of a planetary vibroexciter with elliptic inner race gives substantial advantage in generated driving force against an analog vibroexciter, equipped with a round inner race with the same dimensions and initial parameters. Selecting the mode of setting the spider axis of a planetary vibroexciter in one of focal points of elliptic inner race leads to the increase of generated driving force, 2.2 times on abscissa axis and 2.4 times on ordinate axis, against the central position of the spider axis. This proves the effectiveness of the elliptic planetary vibroexciter use. 1.6 times increase of focal length results in directly proportional increase of driving force projection on ordinate axis, and 2.1 times increase of driving force projection on abscissa axis.
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Liao, Che-Wei, Ming-Tzu Tsai, Heng-Li Huang, et al. "Geometrical Calibration of a 2.5D Periapical Radiography System." Applied Sciences 10, no. 3 (2020): 906. http://dx.doi.org/10.3390/app10030906.
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The objective of this study was to develop a geometrical calibration method applicable to the 2.5D prototype Periapical Radiography System and estimate component position errors. A two-steel-ball phantom with a precisely known position was placed in front of a digital X-ray sensor for two-stage calibration. In the first stage, the following three parameters were estimated: (1) r, the distance between the focal spot and the rotation axis of the X-ray tube; (2) ψ, the included angle between the straight line formed by the X-ray tube’s focal spot and rotation axis and the straight line of the orthogonal sensor; and (3) L4, the distance between the rotation axis and the plane where the two steel balls were positioned. In the second stage, the steel balls’ positions were determined to calculate the positions of the X-ray tube on the x, y, and z axes. Computer simulation was used to verify the accuracy of the calibration method. The results indicate that for the calibration approach proposed in this study, the differences between the estimated errors and setting errors were smaller than 0.15% in the first and second stages, which is highly accurate, verifying its applicability to accurate calibration of the 2.5D Periapical Radiography System.
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Han, Lei, Jiale Qi, Chuchu Gao, and Fuli Li. "Controllable reverse energy flow in the focus of tightly focused hybrid vector beams." Optics Express 32, no. 21 (2024): 36865. http://dx.doi.org/10.1364/oe.536888.
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We demonstrate analytically and numerically that the reverse energy flow is able to appear around the optical axis in the focal region of tightly focused hybrid vector beams. Theoretically, we derive and obtain the general expression of the longitudinal component of the Poynting vector in the focal plane for hybrid vector beams having circular polarization mapping tracks on the Poincaré sphere under xy basis vectors. Following from the obtained expression and the numerical simulation results, the on-axis and near-axis reverse energy flow behaviors are proved. We also reveal that the relative phase of xy basis vectors can be adopted to conveniently control the reverse energy flow. Furthermore, we show that the concerned hybrid vector beams can meanwhile induce the nonzero transverse energy flow in the focal plane, while the previously reported cases with locally linear polarization states cannot. More strikingly, further simulation results indicate that one can observe the reverse energy flow phenomena for the hybrid vector beams under circular and elliptical polarization basis vectors. The results provide a fresh method for achieving and controlling the reverse energy flow.
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Pavlov, Milen. "On the focal surfaces of helical surfaces." Proceedings. College Dobrich IX (December 25, 2016): 126–33. https://doi.org/10.5281/zenodo.10032932.
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Generalized helical surfaces are obtained from the helical surfaces by replacing straight line, which rotates with arbitrary plane curve. Surfaces of revolution belong to the generalized helical surfaces. Surfaces of revolution with one axis are discussed and the their focal surfaces are presented. Their properties and applications are also studied.
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Kang, Chanchan, Yao Fang, Huawei Wang, Feng Zhou, Zeyue Ren, and Feixiang Han. "Online Optical Axis Parallelism Measurement Method for Continuous Zoom Camera Based on High-Precision Spot Center Positioning Algorithm." Photonics 11, no. 11 (2024): 1017. http://dx.doi.org/10.3390/photonics11111017.
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Ensuring precise alignment of the optical axis is critical for achieving high-quality imaging in continuous zoom cameras. However, existing methods for measuring optical axis parallelism often lack accuracy and fail to assess parallelism across the entire focal range. This study introduces an online measurement method designed to address these limitations by incorporating two enhancements. First, image processing methodologies enable sub-pixel-level extraction of the spot center, achieved through improved morphological processing and the incorporation of an edge tracing algorithm. Second, measurement software developed using Qt Creator can output real-time data on optical axis parallelism across the full focal range post-measurement. This software features a multi-threaded architecture that facilitates the concurrent execution of image acquisition, data processing, and serial communication. Experimental results derived from simulations and real data indicate that the maximum average error in extracting the center of the spot is 0.13 pixels. The proposed system provides critical data for optical axis calibration during camera adjustment and inspection.
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Taqwim, Moh Ahsanit, Imam Sucahyo, and Meta Yantidewi. "RANCANG BANGUN ALAT PENENTU PANJANG FOKUS PADA LENSA BIKONVEKS MENGGUNAKAN SENSOR TEMT6000 DAN MOTOR STEPPER." Inovasi Fisika Indonesia 10, no. 2 (2021): 81–86. http://dx.doi.org/10.26740/ifi.v10n2.p81-86.
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Abstrak
 Penelitian ini bertujuan untuk merancang instrumen pengukuran panjang fokus lensa bikonveks secara otomatis. Dengan menerapkan sifat lensa bikonveks dimana berkas-berkas sinar yang paralel terhadap sumbu lensa akan dibiaskan dan berpotongan pada titik fokus. Titik fokus lensa ditentukan menggunakan sensor TEMT6000 dan panjang fokusnya diukur meggunakan motor stepper. Sinar dari dua buah laser dioda yang dipasang sejajar terhadap sumbu lensa akan berpotongan pada titik fokus sehingga intensitas di titik tersebut akan maksimum. Sensor TEMT6000 yang terhubung dengan motor stepper bergerak linier sesumbu dengan sumbu lensa dan berhenti pada titik fokus lensa karena hasil pembacaan sensor bernilai maksimum pada titik tersebut. Mikrokontroler akan menghitung jarak yang ditempuh sensor dan menampilkannya pada display sebagai panjang fokus lensa. Instrumen ini akan diujicobakan pada tiga buah lensa yang memiliki spesifikasi panjang fokus 100 mm, 150 mm, 200 mm, 250 mm dan 300 mm. Berdasarkan penelitian yang dilakukan, panjang fokus hasil pengukuran secara otomatis adalah: 103,8 mm untuk lensa berspesifikasi panjang fokus 100 mm dengan tingkat kesalahan 3,8%, 153,1 mm untuk lensa berspesifikasi panjang fokus 150 mm dengan tingkat kesalahan 2,1%, 203,2 mm untuk lensa berspesifikasi panjang fokus 200 mm dengan tingkat kesalahan 1,6%, 253,2 mm untuk lensa berspesifikasi panjang fokus 250 mm dengan tingkat kesalahan 1,3%, 303,5 mm untuk lensa berspesifikasi panjang fokus 300 mm dengan tingkat kesalahan 1,1%. Penyebab terjadinya penyimpangan titik fokus adalah berkas sinar yang berasal dari laser tidak sejajar dengan sumbu lensa dikarenakan terjadi penyimpangan sudut tembak laser.
 Kata Kunci: panjang fokus lensa bikonveks, sensor TEMT6000, motor stepper
 
 Abstract
 This study aims to design an automatic instrument for measuring the focal length of biconvex lens. By applying the property of a biconvex lens, the rays parralel to the axis of the lens will be refracted and intersect at the focal point. The focal point of the lens was determined using a TEMT6000 sensor and the focal length measured using a stepper motor. The rays from the two laser diodes that were placed parallel to the lens axis would intersect at the focal point so that the intensity at that point would be maximum. TEMT6000 sensor which is connected to the stepper motor moves linearly about the lens axis and stops at the focal point of the lens because the sensor reading is maximum at that point. Microcontroller would calculate the distance travelled by the sensor and show it on the display as the focal length of the lens. The instrument would be tested on five lenses that have focal length specifications of 100 mm, 150 mm, 200 mm, 250 mm and 300 mm. Based on the research wich has been done, focal length of the automatic measurement results is: 103,8 mm for the lens with the specification of focal length 100 mm and the error was 3,8%, 153,1 mm for the lens with the specification of focal length 150 mm and the error percentage is 2,1%, 203,2 mm for the lens with the specification of focal length 200 mm and the error percentage was 1,6%, 253,2 mm for the lens with the specification of focal length 250 mm and the error percentage was 1,3%, 303,5 mm for the lens with the specification of focal length 300 mm and the error percentage was 1,1%. The cause of focal point deviation is, ray from the laser was not parallel to the lens axis due to laser beam angle deviation.
 Keywords: focal length of biconvex lens, TEMT6000 sensor, stepper motor
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Kotlyar, V. V., S. S. Stafeev, and A. M. Telegin. "Spin angular momentum at the sharp focus of a cylindrical vector vortex beam." Computer Optics 47, no. 6 (2023): 875–83. http://dx.doi.org/10.18287/2412-6179-co-1347.
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Sharp focusing of a light field with double (phase and polarization) singularity is studied. Using the Richards-Wolf method, an exact analytical expression for the longitudinal projection of the spin angular momentum (SAM) vector at the focus is obtained. The expression derived suggests that 4 (n –1) subwavelength regions are formed at the focus, where n is the cylindrical vector beam order, with their centers located on a certain circle centered on the optical axis. Notably, the SAM projections are found to have the opposite sign in the neighboring regions. This means that in the neighboring focal regions, the light has alternating left or right elliptical polarization (manifestation of a spin Hall effect). At the center of the focal spot near the optical axis, the field is right-handed elliptically polarized at m > 0, or left-handed elliptically polarized at m < 0, where m is the vortex charge. The total longitudinal spin, i.e., the longitudinal SAM component averaged over the beam-cross section, is zero and preserved upon focusing. Due to the beam containing an optical vortex with charge m, the transverse energy flow rotates on a spiral path near the focal plane, rotating on a circle in the focal plane. The rotation direction near the optical axis is counterclockwise for m > 0, and clockwise for m < 0.
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K. Gokulakrishnan and T. V. Sivasubramonia Pillai. "Investigation of Azimuthally Polarized Bessel-modulated Gaussian Beam with Annular Obstruction." Journal of Environmental Nanotechnology 4, no. 1 (2015): 32–36. http://dx.doi.org/10.13074/jent.2015.03.144119.
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Investigation of annular obstructed azimuthally polarized Bessel-modulated Gaussian beam (QBG) in the focal region of high NA lens, based on vectorial diffraction theory. The numerical results show that the intensity distribution in focal region of the incident beam can be altered considerably by changing beam parameter (μ) and introducing annular apodization (δ). Beam parameter induces the focal splitting in transverse direction, while annular apodization leads to change in focal pattern along optical axis of the focusing system. More interesting, the focal splitting may be in continuous in certain case of incident beam propagating through aligned optical system which is suitable for application such as optical manipulation and optical trapping.
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Kotlyar, Victor V., Sergey S. Stafeev, Alexey M. Telegin, and Elena S. Kozlova. "Spin Angular Momentum at the Focus of a Superposition of an Optical Vortex and a Plane Wave with Linear Polarizations." Photonics 11, no. 4 (2024): 330. http://dx.doi.org/10.3390/photonics11040330.
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In this paper, tight focusing of a superposition of a vortex laser beam with topological charge n with linear polarization and a plane wave with the same linear polarization directed along the horizontal axis is considered. Using the Richards–Wolf formalism, analytical expressions are obtained for the intensity distribution and longitudinal projection of the spin angular momentum in the focal plane. It is shown that for even and odd numbers n, the intensity and the spin angular momentum have different symmetries: for even n they are symmetric about both Cartesian axes, and for odd n they are symmetric only about the vertical axis. The intensity distribution has n local maxima at the focus, and it is nonzero on the optical axis for any n. The distribution of the longitudinal spin angular momentum (spin density) in the focal plane has (n + 2) subwavelength regions with a positive spin angular momentum and (n + 2) regions with a negative spin angular momentum, the centers of which alternately lie on a circle of a certain radius with a center on the optical axis. This spin distribution with different signs demonstrates the spin Hall effect at the focus. Negative and positive spins are mutually compensated, and the total spin is equal to zero at the focus. We have shown that by changing the topological charge of the optical vortex, it is possible to control the spin Hall effect at the focus, that is, to change the number of regions with spins of different signs.
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Naresh, V., Naveen Shamnur, NK Lokesh, KVV Pratapvarma, C. Srikrishna, and V. Goutham Chakravarthy. "Cephalometric Assessment of Effect of Head Rotation toward Focal Spot on Lateral Cephalometric Radiographs." Journal of Contemporary Dental Practice 14, no. 2 (2013): 202–7. http://dx.doi.org/10.5005/jp-journals-10024-1300.
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ABSTRACT Introduction The patient's head can be slightly rotated sagittally vertically or transversely with the head holding device. Because of such improper positions due to head rotation, an error can occur in cephalometric measurements. The purpose of this study was to identify the projection errors of lateral cephalometric radiograph due to head rotation in the vertical Z-axis toward the focal spot. Materials and methods Ten human dry skulls with permanent dentition were collected. Each dry skull was rotated from 0° to +20° at 5° intervals. A vertical axis, the Z-axis, was used as a rotational axis to have 50 lateral cephalometric radiographs exposed. Four linear (S-N, Go-Me, N-Me, S-Go) and six angular measurements (SNA, SNB, N-S-Ar, S-Ar-Go, Ar-Go-Me, ABmandibular plane angle) were calculated manually. Results The findings were that: (1) Angular measurements have fewer projection errors than linear measurements. (2) The greater the number of landmarks on the midsagittal plane that are included in angular measurements, the fewer the projection errors occurring. (3) Horizontal linear measurements have more projection errors than vertical linear measurements. Conclusion The angular measurements of lateral cephalometric radiographs are more useful than linear measurements in minimizing the projection errors associated with head rotation on a vertical axis toward the focal spot. How to cite this article Naresh V, Lokesh NK, Pratapvarma KVV, Srikrishna C, Chakravarthy VG, Shamnur N. Cephalometric Assessment of Effect of Head Rotation toward Focal Spot on Lateral Cephalometric Radiographs. J Contemp Dent Pract 2013;14(2):202-207.
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Luo Xi, 罗曦, 陈培锋 Chen Peifeng, and 王英 Wang Ying. "Analysis of 90° Off-Axis Parabolic Mirror Focal Spot Characteristic." Acta Optica Sinica 29, no. 3 (2009): 682–87. http://dx.doi.org/10.3788/aos20092903.0682.
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Nicola, S. De. "On-axis focal shift effects in focused truncated Bessel beams." Pure and Applied Optics: Journal of the European Optical Society Part A 5, no. 6 (1996): 827–31. http://dx.doi.org/10.1088/0963-9659/5/6/008.
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Quatrano, Ralph S., Leigh Brian, Joyce Aldridge, and Thomas Schultz. "Polar axis fixation in Fucus zygotes: components of the cytoskeleton and extracellular matrix." Development 113, Supplement_1 (1991): 11–16. http://dx.doi.org/10.1242/dev.113.supplement_1.11.
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Polar axis formation and polar axis stabilization (or fixation) can be separated and analyzed in synchronously developing zygotes of the brown alga Fucus. Extensive experimental evidence points to a role for both the cytoskeleton and the extracellular matrix (ECM) in the process of axis fixation in Fucus. A structural complex composed of the cytoskeleton and the ECM has been postulated to stabilize membrane asymmetries generated as a result of axis-forming vectors. This axis stabilizing complex (ASC) may take the form of transmembrane connections between the cytoskeleton on the cytoplasmic face and the ECM on the external side of the plasma membrane, similar to focal contacts in animal cells. At present we know of two components in the proposed ASC of Fucus: an adhesive sulfated glycoprotein which is localized in the ECM, and an actin network which is localized on the adjoining cytoplasmic face. This preliminary report describes evidence for the presence of molecules in two-celled Fucus embryos that are similar to those found in focal contacts in animal cells, i.e. vinculin, integrin and vitronectin. However, their localization and interaction with each other relative to the polar axis has yet to be determined. These initial observations will provide the basis to pursue further an analysis of these components in the process of polar axis fixation.
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Stafeev, S. S., and V. D. Zaicev. "A minimal subwavelength focal spot for the energy flux." Computer Optics 5, no. 45 (2021): 685–91. http://dx.doi.org/10.18287/2412-6179-co-908.
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It is shown theoretically and numerically that circularly and linearly polarized incident beams produce at the tight focus identical circularly symmetric distributions of an on-axis energy flux. It is also shown that the on-axis energy fluxes from radially and azimuthally polarized optical vortices with unit topological charge are equal to each other. An optical vortex with azimuthal polarization is found to generate the minimum focal spot measured for the intensity (all other parameters being equal). Slightly larger (by a fraction of a percent) is the spot size calculated for the energy flux for the circularly and linearly polarized light. The spot size in terms of intensity is of importance in light-matter interaction, whereas the spot size in terms of energy flux affects the resolution in optical microscopy.
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Stafeev, S. S., and V. D. Zaicev. "A minimal subwavelength focal spot for the energy flux." Computer Optics 5, no. 45 (2021): 685–91. http://dx.doi.org/10.18287/2412-6179-co-908.
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It is shown theoretically and numerically that circularly and linearly polarized incident beams produce at the tight focus identical circularly symmetric distributions of an on-axis energy flux. It is also shown that the on-axis energy fluxes from radially and azimuthally polarized optical vortices with unit topological charge are equal to each other. An optical vortex with azimuthal polarization is found to generate the minimum focal spot measured for the intensity (all other parameters being equal). Slightly larger (by a fraction of a percent) is the spot size calculated for the energy flux for the circularly and linearly polarized light. The spot size in terms of intensity is of importance in light-matter interaction, whereas the spot size in terms of energy flux affects the resolution in optical microscopy.
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Lalithambigai, K., R. C. Saraswathi, P. M. Anbarasan, K. B. Rajesh, and Z. Jaroszewicz. "Generation of Multiple Focal Hole Segments Using Double-Ring Shaped Azimuthally Polarized Beam." Journal of Atomic and Molecular Physics 2013 (June 5, 2013): 1–4. http://dx.doi.org/10.1155/2013/451715.
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We investigated the focusing properties of a double-ring-shaped azimuthally polarized beam tightly focused with a high NA lens and a binary phase filter. We observe that by using 3 belts and 5 belts binary phase filters novel focal patterns including splitting of focal rings and multiring focus are obtained. We also found that a suitably designed phase structure can shift the focal rings along optical axis. The author expects such investigation is worthwhile for optical manipulation and material processing technologies.
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He, Jun Feng, and Chang Chun Huang. "Large Amount of Off-Axis Machining Ellipsoidal Reflector." Applied Mechanics and Materials 484-485 (January 2014): 254–58. http://dx.doi.org/10.4028/www.scientific.net/amm.484-485.254.
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The article introduces the off-axis ellipsoidal mirror processing and testing, and uses AutoCAD software to calculate the maximum aspheric mirrors degrees. After processing the off-axis ellipsoidal reflector inclination error of 1.55arcsec, root mean square roughness ((RMS) of 3.21nn, focal length error is less than 1mm, and the surface accuracy can reach λ / 6 (0.51-0.98 μ m).
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Telegin, A. M., A. A. Kovalev, and V. V. Kotlyar. "Polarization Möbius strip at the tight focus of a generalized Poincaré beam." Computer Optics 48, no. 4 (2024): 519–24. http://dx.doi.org/10.18287/2412-6179-co-1487.
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Based on the Richards-Wolf formalism, we investigate tight focusing of a generalized Poincaré beam. Analytical expressions are derived for all components of the electric field strength vector in the focal plane. For superposition of a right-handed circularly polarized plane wave with a left-handed circularly polarized optical vortex with topological charge –1, we obtain expressions for the intensity distribution and the longitudinal component of the spin angular momentum vector at the tight focus. We demonstrate both theoretically and numerically that the initial beam has topological charge –1/2 and, in the center of the focal plane, there is a C-point (a point with circular polarization which makes a C-line along the optical axis) with the singularity index of –1/2 (star), whereas the vector of major axis of the polarization ellipse makes along a certain-radius circle around the optical axis a single-side polarization Möbius stripe of the order –3/2, which has three half-turnovers and one stitching, where two opposite major axis vectors of the polarization ellipse meet.
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Luan, Guangrui, and Jian Lin. "Versatile focal field design using cascaded artificial neural network." AIP Advances 12, no. 12 (2022): 125015. http://dx.doi.org/10.1063/5.0130517.
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Both forward and inverse design methods have been developed for focal field engineering, which has applications in many areas including super-resolution imaging and optical lithography, high-density optical storage, and particle manipulation. However, a certain method is normally targeted at a unique focal field distribution. Here, we report on a versatile focal field design method based on a cascaded artificial neural network (CANN) for the inverse design of focal field distributions in a high numerical aperture focusing system. The CANN consists of a forward and an inverse artificial neural network. Once trained properly, the CANN can predict modulation phase patterns for multiple focal field distributions. We demonstrate the effectiveness of the CANN by the design of focal field distributions along the optical axis including a uniform optical needle and an anti-point spread function with lengths up to 14 wavelengths and multiple focal spots with controllable intensities as well as those in the focal plane including flat-top and sub-diffraction focal spots.
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Kotlyar, V. V., S. S. Stafeev, and A. G. Nalimov. "Vortex energy flow in the tight focus of a non-vortex field with circular polarization." Computer Optics 44, no. 1 (2020): 5–11. http://dx.doi.org/10.18287/2412-6179-co-582.
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Using Richards-Wolf formulas, we show that an axisymmetric circularly polarized vortex-free field can be focused into a sharp subwavelength focal spot, around which there is a region where the light energy flow propagates along a spiral. This effect can be explained by the conversion of the spin angular momentum of the circularly polarized field into the orbital angular momentum near the focus, although the on-axis orbital angular momentum remains zero. It is also shown that a linearly polarized optical vortex with topological charge 2 forms near the focal plane an on-axis reverse energy flow (defined by the negative longitudinal component of the Poynting vector) whose amplitude is comparable with the direct energy flow.
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Leake, Carl, David Arnas, and Daniele Mortari. "Non-Dimensional Star-Identification." Sensors 20, no. 9 (2020): 2697. http://dx.doi.org/10.3390/s20092697.
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This study introduces a new “Non-Dimensional” star identification algorithm to reliably identify the stars observed by a wide field-of-view star tracker when the focal length and optical axis offset values are known with poor accuracy. This algorithm is particularly suited to complement nominal lost-in-space algorithms, which may identify stars incorrectly when the focal length and/or optical axis offset deviate from their nominal operational ranges. These deviations may be caused, for example, by launch vibrations or thermal variations in orbit. The algorithm performance is compared in terms of accuracy, speed, and robustness to the Pyramid algorithm. These comparisons highlight the clear advantages that a combined approach of these methodologies provides.
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Zaitsev, V. D., S. S. Stafeev, and V. V. Kotlyar. "Tight focusing of circularly polarized light limited by semicircular aperture." Journal of Physics: Conference Series 2103, no. 1 (2021): 012164. http://dx.doi.org/10.1088/1742-6596/2103/1/012164.
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Abstract In this work, the focusing of a circularly polarized plane wave (wavelength 532 nm) was simulated by a lens with a numerical aperture NA = 0.95. The wave front was considered flat. When integrating according to the Richards-Wolf formulas, the semicircular aperture was set by limiting the azimuthal angle from 0 to π. It was shown that when focusing light with right and left circular polarization, the focal spot turns out to be elliptical - elongated along the y axis, and, depending on the direction of polarization, its center shifts by about 0.05 μm in different directions along the x axis. It was also shown that the reverse flow region is located near the focal spot (at a distance of 0.25 μm from the center). Depending on the direction of polarization, it is located either to the right or to the left of the focal spot. Thus, the polarization state of the incident radiation can be determined from the displacement of the spot in focus.
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Roman, R. Jose, J. E. Peterson, and D. Y. Goswami. "An Off-Axis Cassegrain Optimal Design for Short Focal Length Parabolic Solar Concentrators." Journal of Solar Energy Engineering 117, no. 1 (1995): 51–56. http://dx.doi.org/10.1115/1.2847742.
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The present work addresses an off-axis Cassegrain optical concentration system. The specific primary collector analyzed, a short focal length parabolic concentrator, is at the University of Florida’s Energy Park. A secondary hyperbolic reflective element was designed to redirect the solar radiation from the primary focal plane to an off-axis target on the polar axis of the primary concentrator. This ground level target will be required for planned experimental work. The analysis was performed using a numerical ray tracing procedure that incorporates both random and systematic errors due to slope and surface irregularities. The optimization process varied secondary element size, curvature, and offset angle, and yielded information required for optimum design. As a single secondary element was found impractical, three elements were designed for use at various times of the year. The numerical analysis predicts that typically 70 to 75 percent of the solar flux incident on the primary concentrator aperture was focused within a 0.5-meter radius. During the design, it was found that this type of compact concentration system is a practical alternative. The optical system is also shown to have advantages that are generally applicable for problems involving short focal length primary concentrators, or when the solar apparatus is to be placed outside the primary collector aperture.
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Kotlyar, V. V., S. S. Stafeev, A. G. Nalimov, A. A. Kovalev, and A. P. Porfirev. "Experimental investigation of the energy backflow in the tight focal spot." Computer Optics 44, no. 6 (2020): 863–70. http://dx.doi.org/10.18287/2412-6179-co-763.
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Using two identical microobjectives with a numerical aperture NA = 0.95, we experimentally demonstrate that the on-axis intensity near the tight focal spot of an optical vortex with a topological charge 2 is zero for right-handed circular polarization and nonzero for left-handed circular polarization. This serves to confirm that in the latter case there is a reverse energy flow on the optical axis, as testified by a very weak local maximum (the Arago spot) detected at the center of the measured energy flow distribution, caused by diffraction of the direct energy flow by a 300 nm circle (the diameter of a reverse energy flow tube). The comparison of numerical and experimental intensity distributions shows that it is possible to determine the diameter of the reverse energy flow "tube", which is equal to the distance between the adjacent intensity nulls. For NA = 0.95 and a 532 nm incident wavelength, the diameter of the on-axis reverse energy flow "tube" is measured to be 300 nm. It is also experimentally shown that when an optical beam with second-order cylindrical polarization is focused with a lens with NA = 0.95, there is a circularly symmetric energy flow in the focus with a very weak maximum in the center (the Arago spot), whose distribution is determined by diffraction of the direct energy flow by a 300 nm circular region, where the energy flow is reverse. This also confirms that in this case, there is a reverse energy flow on the optical axis.
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Nalimov, A. G., and S. S. Stafeev. "Linear to circular polarization conversion in the sharp focus of an optical vortex." Computer Optics 45, no. 1 (2021): 13–18. http://dx.doi.org/10.18287/2412-6179-co-778.
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We have shown that when sharply focusing a linearly polarized optical vortex with topological charge 2, in the near-axis region of the focal plane, not only does a reverse energy flow (the negative on-axis projection of the Poynting vector) occur, but also the right-handed circular polariza-tion of light. Moreover, due to spin-orbital angular momentum conversion, the on-axis polarization vector and the transverse energy flow rotate around the optical axis in the same direction (counter-clockwise). If an absorbing spherical microparticle is put in the focus on the optical axis, it will rotate around the axis and around its center of mass counterclockwise. Numerical simulation results confirms the theoretical predictions.
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BEAZLEY, KAREN, and NATHAN CARDINAL. "A systematic approach for selecting focal species for conservation in the forests of Nova Scotia and Maine." Environmental Conservation 31, no. 2 (2004): 91–101. http://dx.doi.org/10.1017/s0376892904001249.
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Focal species are a critical component of conservation planning, along with representation of ecosystems, special elements and ecologically sustainable management. They warrant conservation attention because they are functionally important, wide-ranging or space-demanding, habitat-quality indicators, ‘flagship’, and/or vulnerable or special populations. A delphi survey matrix-based approach, involving regional experts in the selection of potential focal species, was applied in Nova Scotia, Canada and Maine, USA. Matrices with native species on one axis and selection characteristics on the other axis were used to summarize expert knowledge and judgment. Characteristics were related to biological traits and habitat requirements that make some species more vulnerable than others in human-modified landscapes. In Nova Scotia and Maine, 19 and 11 experts, respectively, completed the matrices, which were subsequently numerically assessed. Species with the highest scores were identified as potential focal species, including wolf, cougar, lynx, river otter, eastern pipistrelle, wood turtle, four-toed salamander, golden eagle and Atlantic salmon. Concerns remain around the lack of representation of some classes of species, subjectivity in selecting and weighting characteristics, and the relative nature of assessing species against the characteristics. Accordingly, potential focal species should be subject to verification through more rigorous and quantitative analysis and monitoring. Nonetheless, if applied with care, the matrix-based approach can provide a relatively systematic and effective way of engaging regional experts in focal species selection.
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Banghar, A. R. "Mechanism Solution of Nepal-Bihar Eartbquake of August 20, 1988." Journal Geological Society of India 37, no. 1 (1991): 25–30. http://dx.doi.org/10.17491/jgsi/1991/370103.
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Abstract This paper presents the focal mechanism solution of the Nepal Bihar earthquake of August 20, 1988. Use was made of the first motions of P waves and polarization (or first motions) of S waves. The mechanism solution is characterized by a predominent component of strike-slip faulting. The deduced orientation of the axis of compression is nearly north south. This orientation of the axis of compression is in agreement with the axis of compression deduced from the mechanism studies for Himalayan earthquakes.
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Manawadu, Mayura, and Soon-Yong Park. "6DoF Object Pose and Focal Length Estimation from Single RGB Images in Uncontrolled Environments." Sensors 24, no. 17 (2024): 5474. http://dx.doi.org/10.3390/s24175474.
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Accurate 6DoF (degrees of freedom) pose and focal length estimation are important in extended reality (XR) applications, enabling precise object alignment and projection scaling, thereby enhancing user experiences. This study focuses on improving 6DoF pose estimation using single RGB images of unknown camera metadata. Estimating the 6DoF pose and focal length from an uncontrolled RGB image, obtained from the internet, is challenging because it often lacks crucial metadata. Existing methods such as FocalPose and Focalpose++ have made progress in this domain but still face challenges due to the projection scale ambiguity between the translation of an object along the z-axis (tz) and the camera’s focal length. To overcome this, we propose a two-stage strategy that decouples the projection scaling ambiguity in the estimation of z-axis translation and focal length. In the first stage, tz is set arbitrarily, and we predict all the other pose parameters and focal length relative to the fixed tz. In the second stage, we predict the true value of tz while scaling the focal length based on the tz update. The proposed two-stage method reduces projection scale ambiguity in RGB images and improves pose estimation accuracy. The iterative update rules constrained to the first stage and tailored loss functions including Huber loss in the second stage enhance the accuracy in both 6DoF pose and focal length estimation. Experimental results using benchmark datasets show significant improvements in terms of median rotation and translation errors, as well as better projection accuracy compared to the existing state-of-the-art methods. In an evaluation across the Pix3D datasets (chair, sofa, table, and bed), the proposed two-stage method improves projection accuracy by approximately 7.19%. Additionally, the incorporation of Huber loss resulted in a significant reduction in translation and focal length errors by 20.27% and 6.65%, respectively, in comparison to the Focalpose++ method.
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Minin, Igor V., and Oleg V. Minin. "FOCUSING OF TERAHERTZ RADIATION WITH A MESOSCALE CUBOID LENS MADE OF ARTIFICIAL DIELECTRIC." Vestnik SSUGT (Siberian State University of Geosystems and Technologies) 26, no. 6 (2021): 155–63. http://dx.doi.org/10.33764/2411-1759-2021-26-6-155-163.
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The aim of this work is to study a new dimensionless cuboid lens made of artificial dielectric for the terahertz wavelength range. The research method is mathematical modeling of the process. It is es-tablished that a lens made of anisotropic artificial dielectric along the optical axis with a characteristic size of 3λ is able to focus terahertz radiation at the calculated frequency of 0.15 THz into a focal spot with a transverse size equal to the diffraction limit. The focus area is located along the optical axis of the lens. The ability to focus radiation remains in a wide range of effective refractive index, at least from 1.4 to 1.7, while the value of the focal length does not change significantly.
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Hu, Xiao, Jiu Li, Jin Feng Liu, and Zi Qiang Huang. "Design and Analysis of Novel Four-Quadrant Double Liquid Lens Based on EWOD." Advanced Materials Research 403-408 (November 2011): 4388–97. http://dx.doi.org/10.4028/www.scientific.net/amr.403-408.4388.
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A novel double liquid lens based on Electrowetting-On-Dielectric (EWOD) is presented and analyzed. The special construction is that the lens was divided into four quadrants. The particular fabrication process is presented to achieve the structure. It was proved that the lens not only expressed the electric zoom character but also shifted focal point away from optical axis. It also achieved an infinite focal length under zero electric field. The paper presented the relationship between the focus length and applied voltage, also gave the association between focus length and the applied voltage from 0V to 80V. We analyzed how the optical axis shifted according to the voltage difference between quadrants, furthermore, explained the new function that the focus object was away from center of lens.
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Över, Semir, Süha Özden, Esra Kalkan Ertan, Fatih Turhan, Zeynep Coşkun, and Ali Pınar. "20 July 2017 Bodrum-Kos Earthquake (Mw:6.6) in southwestern Anatolia, Turkey." Earth Sciences Research Journal 25, no. 3 (2021): 309–21. http://dx.doi.org/10.15446/esrj.v25n3.87080.
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In the Aegean Sea, the western part of Gökova Gulf, Kos and Bodrum were struck by a 6.6 (Mw) earthquake on July 20, 2017. The fault plane solution for the main shock shows an E-W striking normal type fault with approximately N-S (N4°E) tensional axis (T-axis). Fault plane solutions of 33 aftershocks show two groups of normal type fault with E-W and NE-SW to ENE-WSW orientations. The inversion of the focal mechanisms of the aftershocks yields two different normal faulting stress regimes: one is characterized by an approximately N-S (N5°E) σ3 axis (minimum horizontal stress axis). This extension is obtained from 13 focal mechanisms of aftershocks with approximately E-W direction. The other is characterized by approximately NW-SE (N330°E) σ3 axis. The latter is calculated from 21 seismic faults of aftershocks with approximately NE-SW direction. These aftershocks occurred on relatively small-scale faults that were directed from NE-SW to ENE-WSW, and possibly contributed to expansion of the basin in the west. The 24 focal mechanisms of earthquakes which occurred since 1933 in and around Gökova Basin are introduced into the inversion analysis to obtain the stress state effective in a wider region. The inversion yields an extensional stress regime characterized by an approximately N-S (N355°E) σ3 axis. The E-W directional metric faults, measured in the central part of Gökova Fault Zone bordering the Gökova Gulf in the north, also indicate N-S extension. The NE-SW extension obtained from NE-SW aftershocks appears to be more local and is responsible for the expansion of the western part of the asymmetric Gökova Basin. This N-S extension which appears to act on a regional-scale may be attributed to the geodynamic effects related to the combined forces of the southwestward extrusion of Anatolia and the roll-back process of African subduction beneath Anatolia.
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Safonov, D. A. "RECONSTRUCTION OF THE TECTONIC STRESS FIELD IN THE DEEP PARTS OF THE SOUTHERN KURIL-KAMCHATKA AND NORTHERN JAPAN SUBDUCTION ZONES." Geodynamics & Tectonophysics 11, no. 4 (2020): 743–55. http://dx.doi.org/10.5800/gt-2020-11-4-0504.
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Earthquake focal mechanisms in the Southern Kuril-Kamchatka and Northern Japan subduction zones were analysed to investigate the features of the tectonic stress field inside the Pacific lithospheric plate subducting into the upper mantle. Earthquake focal mechanism (hypocenter depths of more than 200 km) were taken from the 1966– 2018 NIED, IMGiG FEB RAS and GlobalCMT catalogues. The tectonic stress field was reconstructed by the cataclastic analysis method, using a coordinate system related to the subducting plate. In most parts of the studied seismic focal zone, the axis of the principal compression stress approximately coincides with the direction of the Pacific lithospheric plate subduction beneath the Sea of Okhotsk. It slightly deviates towards the hinge zone separating the studied regions. The principal tension stress axis is most often perpendicular to the plate movement, but less stable in direction. This leads to compression relative to the slab in some parts of the studied regions, and causes shearing in others. The hinge zone is marked by the unstable position of the tension axis and high values of the Lode–Nadai coefficient, corresponding to the conditions of uniaxial compression, while the compression direction remains the same, towards the slab movement. Two more areas of uniaxial compression are located below the Sea of Japan at depths of 400–500 km.
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Nguyen, B. V., and R. B. Herrmann. "Determination of Source Parameters for Central and Eastern North American Earthquakes (1982–1986)." Seismological Research Letters 63, no. 4 (1992): 567–86. http://dx.doi.org/10.1785/gssrl.63.4.567.
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Abstract A search technique is applied to determine focal mechanisms from the surface-wave spectral amplitudes of recent earthquakes in the eastern U. S. and Canada. The technique provides the five source parameters of dip, slip, strike, depth, and seismic moment through a combination of criteria requiring best correlation coefficients, least residuals between theoretical and observed spectral-amplitudes and equality between independent seismic moment estimates from Love and Rayleigh wave data. This technique is applied to eight earthquakes of mb ≈ 5 that occurred in the North American continent in recent years. The focal mechanism results, constrained by P-wave first motions, indicate that near horizontal pressure axes are in the ENE-WSW for the 1982 Miramichi, New Brunswick (Canada) mainshock and one large aftershock (another large aftershock has ESE-WNW P-axis), the 1982 Gaza, New Hampshire mainshock, the 1982 Arkansas mainshock, the 1983 Goodnow, New York mainshock, and the 1986 Perry, Ohio mainshock. On the other hand a near horizontal tension axis in the direction NNE-SSW is found for the 1984 Wyoming mainshock in the western part of North American continent. The results obtained are consistent with the regional stress patterns and generally agree with the solutions of other investigators who used other aspects of the seismic wavefield.
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Štroner, Martin, Rudolf Urban, Jan Seidl, Tomáš Reindl, and Josef Brouček. "Photogrammetry Using UAV-Mounted GNSS RTK: Georeferencing Strategies without GCPs." Remote Sensing 13, no. 7 (2021): 1336. http://dx.doi.org/10.3390/rs13071336.
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Georeferencing using ground control points (GCPs) is the most common strategy in photogrammetry modeling using unmanned aerial vehicle (UAV)-acquired imagery. With the increased availability of UAVs with onboard global navigation satellite system–real-time kinematic (GNSS RTK), georeferencing without GCPs is becoming a promising alternative. However, systematic elevation error remains a problem with this technique. We aimed to analyze the reasons for this systematic error and propose strategies for its elimination. Multiple flights differing in the flight altitude and image acquisition axis were performed at two real-world sites. A flight height of 100 m with a vertical (nadiral) image acquisition axis was considered primary, supplemented with flight altitudes of 75 m and 125 m with a vertical image acquisition axis and two flights at 100 m with oblique image acquisition axes (30° and 15°). Each of these flights was performed twice to produce a full double grid. Models were reconstructed from individual flights and their combinations. The elevation error from individual flights or even combinations yielded systematic elevation errors of up to several decimeters. This error was linearly dependent on the deviation of the focal length from the reference value. A combination of two flights at the same altitude (with nadiral and oblique image acquisition) was capable of reducing the systematic elevation error to less than 0.03 m. This study is the first to demonstrate the linear dependence between the systematic elevation error of the models based only on the onboard GNSS RTK data and the deviation in the determined internal orientation parameters (focal length). In addition, we have shown that a combination of two flights with different image acquisition axes can eliminate this systematic error even in real-world conditions and that georeferencing without GCPs is, therefore, a feasible alternative to the use of GCPs.
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Chen, Chong, Yuki Shimizu, Ryo Sato, Hiraku Matsukuma, and Wei Gao. "An Off-Axis Differential Method for Improvement of a Femtosecond Laser Differential Chromatic Confocal Probe." Applied Sciences 10, no. 20 (2020): 7235. http://dx.doi.org/10.3390/app10207235.
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This paper presents an off-axis differential method for the improvement of a femtosecond laser differential chromatic confocal probe having a dual-detector configuration. In the proposed off-axis differential method employing a pair of single-mode fiber detectors, a major modification is made to the conventional differential setup in such a way that the fiber detector in the reference detector is located at the focal plane of a collecting lens but with a certain amount of off-axis detector shift, while the fiber detector in the measurement detector is located on the rear focal plane without the off-axis detector shift; this setup is different from the conventional one where the difference between the two confocal detectors is provided by giving a defocus to one of the fiber detectors. The newly proposed off-axis differential method enables the differential chromatic confocal setup to obtain the normalized chromatic confocal output with a better signal-to-noise ratio and approaches a Z-directional measurement range of approximately 46 μm, as well as a measurement resolution of 20 nm, while simplifying the optical alignments in the differential chromatic confocal setup, as well as the signal processing through eliminating the complicated arithmetic operations in the determination of the peak wavelength. Numerical calculations based on a theoretical equation and experiments are carried out to verify the feasibility of the proposed off-axis differential method for the differential chromatic confocal probe with a mode-locked femtosecond laser source.
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GUO Jiang, 郭疆, 孙继明 SUN Ji-ming, 邵明东 SHAO Ming-dong, and 胡海飞 HU Hai-fei. "Calculation of focal length for off-axis TMA aerospace mapping camera." Optics and Precision Engineering 20, no. 8 (2012): 1754–58. http://dx.doi.org/10.3788/ope.20122008.1754.
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