Vectorial Doppler metrology

AbstractThe Doppler effect is a universal wave phenomenon that has spurred a myriad of applications. In early manifestations, it was implemented by interference with a reference wave to infer linear velocities along the direction of motion, and more recently lateral and angular velocities using scalar phase structured light. A consequence of the scalar wave approach is that it is technically challenging to directly deduce the motion direction of moving targets. Here we overcome this challenge using vectorially structured light with spatially variant polarization, allowing the velocity and motion direction of a moving particle to be fully determined. Using what we call a vectorial Doppler effect, we conduct a proof of principle experiment and successfully measure the rotational velocity (magnitude and direction) of a moving isotropic particle. The instantaneous position of the moving particle is also tracked under the conditions of knowing its starting position and continuous tracking. Additionally, we discuss its applicability to anisotropic particle detection, and show its potential to distinguish the rotation and spin of the anisotropic particle and measure its rotational velocity and spin speed (magnitude and direction). Our demonstration opens the path to vectorial Doppler metrology for detection of universal motion vectors with vectorially structured light.

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The Analysis of Proprioception Alteration during First Five Months after Anterior Cruciate Ligament Reconstruction

Baltic Journal of Sport and Health Sciences ◽

10.33607/bjshs.v1i84.293 ◽

2018 ◽

Vol 1 (84) ◽

Author(s):

Vilma Jurevičienė ◽

Albertas Skurvydas ◽

Juozas Belickas ◽

Giedra Bušmanienė ◽

Dovilė Kielė ◽

...

Keyword(s):

Anterior Cruciate Ligament ◽

Angular Velocity ◽

Knee Joint ◽

Cruciate Ligament ◽

Position Sense ◽

Joint Position Sense ◽

Joint Position ◽

Starting Position ◽

Angular Velocities ◽

Anterior Cruciate

Research background and hypothesis. Proprioception is important in the prevention of injuries as reduced proprioception is one of the factors contributing to injury in the knee joint, particularly the ACL. Therefore, proprioception appears not only important for the prevention of ACL injuries, but also for regaining full function after ACL reconstruction.Research aim. The aim of this study was to understand how proprioception is recovered four and five months after anterior cruciate ligament (ACL) reconstruction.Research methods. The study included 15 male subjects (age – 33.7 ± 2.49 years) who had undergone unilateral ACL reconstruction with a semitendinosus/gracilis (STG) graft in Kaunas Clinical Hospital. For proprioceptive assessment, joint position sense (JPS) was measured on both legs using an isokinetic dynamometer (Biodex), at knee flexion of 60° and 70°, and at different knee angular velocities of 2°/s and 10°/s. The patients were assessed preoperatively and after 4 and 5 months, postoperatively.Research results. Our study has shown that the JPS’s (joint position sense) error scores to a controlled active movement is significantly higher in injured ACL-deficient knee than in the contralateral knee (normal knee) before surgery and after four and five months of rehabilitation. After 4 and 5 months of rehabilitation we found significantly lower values in injured knees compared to the preoperative data. Our study has shown that in injured knee active angle reproduction errors after 4 and 5 months of rehabilitation were higher compared with the ones of the uninjured knee. Proprioceptive ability on the both legs was independent of all differences angles for target and starting position for movement. The knee joint position sense on both legs depends upon the rate of two different angular velocities and the mean active angle reproduction errors at the test of angular velocity slow speed was the highest compared with the fast angular velocity. Discussion and conclusions. In conclusion, our study shows that there was improvement in mean JPS 4 and 5 months after ACL reconstruction, but it did not return to normal indices.Keywords: knee joint, joint position sense, angular velocity, starting position for movement.

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Analysis of general creeping motion of a sphere inside a cylinder

Journal of Fluid Mechanics ◽

10.1017/s0022112009991789 ◽

2009 ◽

Vol 642 ◽

pp. 295-328 ◽

Cited By ~ 28

Author(s):

SUKALYAN BHATTACHARYA ◽

COLUMBIA MISHRA ◽

SONAL BHATTACHARYA

Keyword(s):

Vector Field ◽

Spherical Particle ◽

Asymptotic Methods ◽

Flow Equation ◽

Creeping Flow ◽

Separable Form ◽

Angular Velocities ◽

Moving Particle ◽

Parabolic Flow ◽

Quiescent Fluid

In this paper, we develop an efficient procedure to solve for the Stokesian fields around a spherical particle in viscous fluid bounded by a cylindrical confinement. We use our method to comprehensively simulate the general creeping flow involving the particle-conduit system. The calculations are based on the expansion of a vector field in terms of basis functions with separable form. The separable form can be applied to obtain general reflection relations for a vector field at simple surfaces. Such reflection relations enable us to solve the flow equation with specified conditions at different disconnected bodies like the sphere and the cylinder. The main focus of this article is to provide a complete description of the dynamics of a spherical particle in a cylindrical vessel. For this purpose, we consider the motion of a sphere in both quiescent fluid and pressure-driven parabolic flow. Firstly, we determine the force and torque on a translating-rotating particle in quiescent fluid in terms of general friction coefficients. Then we assume an impending parabolic flow, and calculate the force and torque on a fixed sphere as well as the linear and angular velocities of a freely moving particle. The results are presented for different radial positions of the particle and different ratios between the sphere and the cylinder radius. Because of the generality of the procedure, there is no restriction in relative dimensions, particle positions and directions of motion. For the limiting cases of geometric parameters, our results agree with the ones obtained by past researchers using different asymptotic methods.

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Is Direction Position? Position- and Direction-Based Correspondence Effects in Tasks with Moving Stimuli

The Quarterly Journal of Experimental Psychology Section A ◽

10.1080/02724980443000016 ◽

2005 ◽

Vol 58 (3) ◽

pp. 467-506 ◽

Cited By ~ 20

Author(s):

Simone Bosbach ◽

Wolfgang Prinz ◽

Dirk Kerzel

Keyword(s):

Eye Movements ◽

Relative Position ◽

Saccadic Eye Movements ◽

Object Motion ◽

Spatial Coding ◽

Motion Direction ◽

Directional Information ◽

Stimulus Response ◽

Starting Position ◽

Correspondence Effects

Five experiments were carried out to test whether (task-irrelevant) motion information provided by a stimulus changing its position over time would affect manual left–right responses. So far, some studies reported direction-based Simon effects whereas others did not. In Experiment 1a, a reliable direction-based effect occurred, which was not modulated by the response mode—that is, by whether participants responded by pressing one of two keys or more dynamically by moving a stylus in a certain direction. Experiments 1a, 1b, and 2 lend support to the idea that observers use the starting position of target motion as a reference for spatial coding. That is, observers might process object motion as a shift of position relative to the starting position and not as directional information. The dominance of relative position coding could also be shown in Experiment 3, in which relative position was pitted against motion direction by presenting a static and dynamic stimulus at the same time. Additionally, we explored the role of eye movements in stimulus–response compatibility and showed in Experiments 1b and 3a that the execution or preparation of saccadic eye movements—as proposed by an attention-shifting account—is not necessary for a Simon effect to occur.

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Singularity and Dexterity Analysis of the Test Tilter for the Optical Landing Aid System

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.743.22 ◽

2015 ◽

Vol 743 ◽

pp. 22-25

Author(s):

H.D. Wang ◽

Jing Sun ◽

G. Ji ◽

Y.Q. Bi

Keyword(s):

Condition Number ◽

Jacobi Matrix ◽

Rotational Velocity ◽

Vertical Motion ◽

Linear Velocity ◽

Motion Direction ◽

The Matrix

According to the kinematics equation of the test tilter for the optical landing aid system, the velocity Jacobi matrix of the tilter is established. The determinant and the condition number of Jacobi matrix based on the numeric analysis in the preset workspace, as the evaluating indicator of the singularity and the dexterity. Simulation result indicates that there is no singularity in the tilter workspace because the determinant of the matrix is not equal to zero, and the tilter has higher rotary dexterity due to the smaller condition number of the rotational velocity Jacobi matrix. At the same time, the tilter has isotropy and the best dexterity in the vertical motion direction due to the condition number of the linear velocity Jacobi matrix is equal to 1.

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RIGHTING OF CHINESE MITTEN CRABS (ERIOCHEIR SINENSIS) AND THEIR MODELS

Acta Polytechnica CTU Proceedings ◽

10.14311/app.2017.7.0053 ◽

2016 ◽

Vol 7 ◽

pp. 53

Author(s):

Tobias Riphaus ◽

Florian Hoffmann ◽

Susanna Labisch

Keyword(s):

High Speed ◽

Particle Image ◽

Numerical Models ◽

Rotational Velocity ◽

Underwater Vehicles ◽

Eriocheir Sinensis ◽

Unmanned Underwater Vehicles ◽

Starting Position ◽

Image Velocimetry ◽

Mitten Crabs

The usage of unmanned underwater vehicles for marine tasks is continuously growing and bioinspired stabilizing systems shall help them to gain and keep a stable position during work. Therefore the righting maneuver of E. sinensis has been studied. These crabs are able to perform a 180°-rotation with an angular velocity of 4.30 s−1 when falling underwater from a supine starting position. High-speed particle image velocimetry has shown, that propulsive forces with a peak of 0.021 ± 0.001 N were produced by the hind legs to initiate and stop the rotation. In a numerical multibody simulation a constant force of 0.009 N acting for 0.2 s leads to the same rotation. In order to prove this mechanism, it was implemented into a robotic system. Its mean density of 1.15 g/cm3 deviates not more than 4% from the biological and numerical models. It can complete a 180°-turn within 1.03 ± 0.12 s with a rotational velocity of up to 4.25 s−1.

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On the Distribution of Angular Velocity in the Sun

Symposium - International Astronomical Union ◽

10.1017/s0074180900008342 ◽

1976 ◽

Vol 71 ◽

pp. 415-415

Author(s):

Jaakko Tuominen

Keyword(s):

Angular Velocity ◽

Differential Rotation ◽

Rotational Velocity ◽

The Sun ◽

Large Area ◽

Heliographic Latitude ◽

Left Hand ◽

Right Hand ◽

Angular Velocities ◽

The Right

The angular velocity distribution as a function of heliographic latitude is directly observed at the solar surface. Also the dependence of the angular velocity on the distance from the solar centre can be studied observationally for the outermost layers of the Sun. But within the Sun the study of angular velocity depends very much on assumptions. One possibility to study the problem is given by the fact that in a bipolar magnetic group the leader is compact while the follower is dispersed over a large area. In Leighton's theory, following Babcock, this phenomenon is explained, in principle, in the following way: Slide 1. When a magnetic rope, as a result of magnetic buoyancy, rises to the surface, it is twisted by differential rotation. Dashed lines in the figure represent isotachial surfaces. When the rope has risen to the surface, the two ends are twisted in opposite directions. The surface differential rotation continues to twist one of the now free ends of the rope, while it untwists the other free end. Both twisting and untwisting are, in fact, very slow. They are fastest at the latitude of 35°, where the magnetic rope is rotated once in 26 days. We understand that the distribution of angular velocity within the Sun is involved in this picture. The twisting in the interior can be written equal to the untwisting of the follower spot produced by the surface differential rotation. Of course there are many solutions. Slide 2 gives two of them. The lines represent calculated isotachial surfaces and the numbers give the observed angular velocities in radians per day. In the left-hand side distribution the velocity decreases inwards, while in the right-hand side distribution it increases inwards. The right-hand side distribution is also consistent with the conclusion derived from observations that the tilt of sunspot axes from the vertical is relatively small, and with the observation that at the equatorial plane, near the surface, the rotational velocity does not vary with depth.

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Observation of the Rotational Doppler Effect With Structured Beams in Atomic Vapor

Frontiers in Physics ◽

10.3389/fphy.2021.771260 ◽

2022 ◽

Vol 9 ◽

Author(s):

Shuwei Qiu ◽

Jinwen Wang ◽

Xin Yang ◽

Mingtao Cao ◽

Shougang Zhang ◽

...

Keyword(s):

Doppler Effect ◽

Topological Charge ◽

Quantum Coherence ◽

Rotational Velocity ◽

Atomic Vapor ◽

Doppler Broadening ◽

Vortex Beam ◽

Optical Elements ◽

Vector Beam ◽

Linearly Polarized

A vector beam with the spatial variation polarization has attracted keen interest and is progressively applied in quantum information, quantum communication, precision measurement, and so on. In this letter, the spectrum observation of the rotational Doppler effect based on the coherent interaction between atoms and structured light in an atomic vapor is realized. The geometric phase and polarization of the structured beam are generated and manipulated by using a flexible and efficacious combination optical elements, converting an initial linearly polarized Gaussian beam into a phase vortex beam or an asymmetric or symmetric vector beam. These three representative types of structured beam independently interact with atoms under a longitudinal magnetic field to explore the rotational Doppler shift associated with the topological charge. We find that the rotational Doppler broadening increases obviously with the topological charge of the asymmetric and symmetric vector beam. There is no rotational Doppler broadening observed from the spectrum of the phase vortex beam, although the topological charge, and spatial profile of the beam change. This study can be applied to estimate the rotational velocity of the atom-level or molecule-level objects, measure the intensity of magnetic fields and study the quantum coherence in atomic ensembles.

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