Small Angular Deviations Research Articles

Biomechanical substantiation of the algorithm for choosing the type of corrective osteotomy of the fifth metatarsal bone in the treatment of tailor’s bunion

Background. Joint deformity between the main phalanx of the fifth toe and the fifth metatarsal bone is called tailor’s bunion. Its treatment is most often surgical. At the same time, there is no unified single approach regarding the use of osteotomies, their type and localization on the metatarsal bone (distal, diaphyseal, and proximal). Goal: based on the biomechanical studies, to substantiate the corrective possibilities of Weil and chevron distal osteotomies to correct valgus deformity of the fifth metatarsal bone depending on its geometric parameters. Materials and methods. Two types of corrective osteotomies were modeled: Weil and chevron osteotomy. We determined the maximum possible values of valgus deformity of the fifth metatarsal bone, which can be eliminated with the help of these osteotomies, depending on the geometric parameters of the fifth metatarsal bone. To determine the latter, radiometry was performed on 39 digital radiographs of the patients’ feet. Results. Taking into account the relatively small angular deviation of the fifth metatarsal bone whose value is most often observed in the range from 10 to 15° at the norm of 8°, the angular deformity can be compensated by linear displacement of the head of the metatarsal bone. Since the head displacement is performed in the horizontal plane, both osteotomies in this case work equally. The zone of maximum possible correction for deformity is determined within the range from 12°, with a length of 60 mm and a diameter of 8 mm, to 15.5°, with a length of 45 mm and a diameter of 12 mm. Given that there is some balance between bone length and diameter, the maximum deformity that can be corrected with Weil and chevron corrective osteotomies is a deformity of up to 14°. Conclusions. Weil and chevron corrective osteotomies can be used to correct the fifth metatarsal valgus deformity (tailor’s bunion) and are effective when the M4M5 angle does not exceed 14°. In cases where the M4M5 angle exceeds 15°, it is advisable to use proximal corrective osteotomies of the fifth metatarsal bone for the treatment of tailor’s bunion.

Enhanced Measurement of Vortex Beam Rotation Using Polarization-Assisted Particle Swarm Optimization for Phase Retrieval

In detecting the rotation velocity of an object employing the rotational Doppler effect of vortex beams, atmospheric turbulence can easily cause phase distortion and spiral spectrum dispersion, consequently reducing velocity measurement accuracy. This study combines adaptive optical intelligence algorithms with polarization compensation information to propose a novel approach, the Stokes–Particle swarm optimization Gerchberg–Saxton (Stokes-PSO GS) algorithm, which integrates Stokes polarization information assistance and PSO for GS phase retrieval. The algorithm adjusts the phase and amplitude of the pre-compensated phase screen of the GS algorithm utilizing Stokes information of polarized vortex beam (with lL = 5 and lR = −5) before and after distortion. The PSO is then employed to optimize the pre-compensated phase screen and perform compensations. Simulation results at zS-T = 200 m and Cn2 = 1 × 10−14 m−2/3, demonstrate that the Stokes-PSO GS algorithm exhibits strong stability (small angular spectrum purity deviation, σp, Stokes-PSO GS = 0.005675% < σp, GS = 11.62%), superior optical field recovery (well-recovered Stokes optical field, up to 33.76% improvement in angular spectrum purity), and high-velocity measurement accuracy (25.93% improvement) compared to the GS algorithm. This approach enables precise measurement of the rotation velocity of the vortex beam, demonstrating its potential in practical applications.

Navigation Path Extraction and Experimental Research of Pusher Robot Based on Binocular Vision

The pushing robot working in the complex farming environment encounters several problems. For example, the precision of its navigation path extraction is low, and its working quality is greatly affected by the weather. In view of this, a method of farm operation path extraction based on machine vision is proposed in this study in order to solve the problems above and realize the autonomous and intelligent operation of the robot. First of all, the RGB images of the working area in front of the robot are obtained by using an RGB camera installed on the machine. Then, the collected images are preprocessed by means of sky removal, denoising and grayscale transformation. After that, the image is segmented to obtain the front fence, feed belt and ground data. Finally, the navigation path is obtained by extracting the features of the feed belt. The test results show that the absolute deviation of the pushing robot at different initial lateral distances is less than ±15 cm, and the deviation between the actual navigation route and the target route is within the expected range. The absolute value of the maximum lateral deviation in five test areas is 8.9 cm, and the absolute value of the average maximum lateral deviation is 7.6 cm. These experimental results show that the pushing robot can work stably without disturbing the feeding of cows. Particle swarm optimization is used to optimize the parameters of the PID and find the optimal parameters. This makes the system balanced and more responsive. Through this test, it is found that the initial direction of the robot will have a certain impact on the path production and tracking efficiency, and this effect is more significant when the robot changes the working area or turns. In which case, the trajectory of the robot should be in such a way that it immediately faces the next row at a small angular deviation, thus ensuring smoother motion. The method proposed in this study can provide support for the automatic navigation of pushing robots in dairy farms.

Online Bayesian optimization for a recoil mass separator

The SEparator for CApture Reactions (SECAR) is a next-generation recoil separator system at the Facility for Rare Isotope Beams (FRIB) designed for the direct measurement of capture reactions on unstable nuclei in inverse kinematics. To maximize the performance of this system, stringent requirements on the beam alignment to the central beam axis and on the ion-optical settings need to be achieved. These can be difficult to attain through manual tuning by human operators without potentially leaving the system in a sub-optimal and irreproducible state. In this work, we present the first development of online Bayesian optimization with a Gaussian process model to tune an ion beam through a nuclear astrophysics recoil separator. We show that this method achieves small incoming angular deviations (\textless 1 mrad) in an efficient and reproducible manner that is at least three times faster than standard hand-tuning. Additionally, we present a Bayesian method for experimental optimization of the ion optics, and show that it validates the nominal theoretical ion-optical settings of the device, and improves the mass separation by 32\% for some beams.

Crystallographic Analysis of Plate and Lath Martensite in Fe-Ni Alloys

In the present work, we use an advanced EBSD method to analyze the two prominent types of martensite microstructures that are found in the binary Fe-Ni system, lath martensite (27.5 at.% Ni) and plate martensite (29.5 at.% Ni). We modify, document, and apply an analytical EBSD procedure, which was originally proposed by Yardley and Payton, 2014. It analyzes the distributions of the three KSI-angles (ξ1, ξ2, and ξ3, KSI after Kurdjumov and Sachs), which describe small angular deviations between crystal planes in the unit cells of martensite and austenite—which are related through specific orientation relationships. The analysis of the angular distributions can be exploited to obtain high-resolution, color-coded micrographs of martensitic microstructures, which, for example, visualize the difference between lath and plate martensite and appreciate the microstructural features, like midribs in large plate martensite crystals. The differences between the two types of martensite also manifest themselves in different distributions of the KSI-angles (wider for lath and narrower for plate martensite). Finally, our experimental results prove that local distortions result in scatter, which is larger than the differences between the orientation relationships of Kurdjumov/Sachs, Nishiyama/Wassermann, and Greninger/Troiano.

Active Mass Ejection for Asteroid Manipulation and Deflection

The dynamics of asteroid deflection and manipulation using mass ejection are examined. First, a linearized small angular velocity and inertia tensor deviation model for close-to-principal-axis rotators is developed. The model is then applied to launching boulders off of asteroid surfaces, proving that the principal-axis-rotator characteristic can be kept while removing material off the surface. Mass ejections for asteroid deflection are presented and examined. This method, dubbed mass driver deflection, uses small discrete launches of masses off an asteroid to prevent its collision with Earth. By using material from the asteroid itself, such as boulders or regolith deposits, mass driver deflection substantially reduces the required mass of the deflection system. The analysis in the paper seeks to optimize the deflection efforts while minimizing unwanted effects on the deflected asteroid’s state: both rotational and orbital. The results show that deflection is possible in timeframes of several years in a variety of scenarios and that the deflection effects on the asteroid behavior do not pose a risk of disrupting the asteroid in a catastrophic way.

Theoretical Study of Transverse Offsets of Wide Span Tractor Working Implements and Their Influence on Damage to Row Crops

Wide span tractors have a wide transversal bar, on which different implements can be mounted, while the supporting wheels follow the set traffic-lanes. The stability of wide span tractor movement is influenced by unbroken small angular deviations and transversal displacements of the machine due to several factors. These deflections from the set trajectories affect the working implements, especially the peripheral ones, which can cut the plants if wide span tractors are used to manage row crops. In this context, it needs to consider a safeguard zone that allows to reduce the probability of contact between working implements and plants. The aim of this paper was to determine the quantitative effect of transverse displacements of the working implements and the suitable size of the aforesaid safeguard zone. The magnitude of the inner and outer displacements of the working implements depends significantly on their location in relation to the center of the wide span tractor. For working implements located outside the center of the tractor, the outer safeguard zone should be larger than the inner zone. The probability of crop damage by working implements can be reduced by automated control of wide span tractor movement.

The progressive elimination task in dogs (Canis familiaris): The case of divergence

Domestic dogs (Canis familiaris) were administered progressive elimination tasks in which they had to visit and deplete either 3 or 4 baited sites. They were brought back to the starting point after each visit. When administered a 4-choice task with small angular deviation between adjacent targets, the dogs chose first an inner target (e.g., right inner target) and the opposite outer target (e.g., the left target) as a second correct choice. So they relied on divergence; that is they chose the farthest target as the next choice. Varying angular deviation did not modulate divergence. Decreasing the number of targets (3-choice task, Experiment 2) did relax divergence, though target selection was not totally random. The dogs still chose as a first choice an inner target (i.e., the middle target) when selecting the most divergent patterns of elimination. Finally, in Experiment 3, the dogs were administered a 3-choice task with large angular deviation but in which all targets had been hidden. The dogs chose first an outer target (i.e., right or left)) and the other outer target as the second correct choice. That is they relied on divergence. The results suggest that divergence is the outcome of a flexibility/cognitive load tradeoff when facing novelty and uncertainty.

Evaporation of Gold on NaCl Surfaces as a Way To Control Spatial Distribution of Nanoparticles: Insights on the Shape and Crystallographic Orientation

Herein, the growth of Au nanoparticles on NaCl surfaces as a way to control their spatial distribution is explored, giving new insights into the shape and relative orientation of the resulting nanoparticles through modern electron microscopy techniques. Their morphological features depending on the geometry of the NaCl surface site they nucleated on are described in detail. Also, hitherto unreported small but systematic angular deviations in the range of 1–4° from the exact epitaxial orientation were observed. A theoretical approach based on straightforward elastic energy considerations and yet capable of accounting for the experimental results was developed. The production of metallic nanoparticles is a fundamental subject in the development of nanotechnology, and the fine control of the shape and spatial distribution is an important issue for the applicability of nanoparticles. Furthermore, in spite of the extensive research on this topic, some key features such as the precise mechanism controlling particle shape and particle-substrate orientation are still not well understood as evidenced by the results of this work. Thus, a clear understanding of the role played by the diverse factors involved in epitaxial growth is required to produce nanoparticles with finely tailored properties.

Spin–orbit interaction of light and diffraction of polarized beams

The edge diffraction of a homogeneously polarized light beam is studied theoretically based on the paraxial optics and Fresnel–Kirchhoff approximation, and the dependence of the diffracted beam pattern of the incident beam polarization is predicted. If the incident beam is circularly polarized, the trajectory of the diffracted beam center of gravity exhibits a small angular deviation from the geometrically expected direction. The deviation is parallel to the screen edge and reverses the sign with the polarization handedness; it is explicitly calculated for the case of a Gaussian incident beam with a plane wavefront. This effect is a manifestation of the spin–orbit interaction of light and can be interpreted as a revelation of the internal spin energy flow immanent in circularly polarized beams. It also exposes the vortex character of the weak longitudinal field component associated with the circularly polarized incident beam.

Methods applied to digital processing of ultrashort pulse signals upon estimating a small angular deviation of phase-distributed radio pulses in the radiosensory vibrometrological diagnostics system

The problems concerning the vibrometric studies of the kinematic and vibrational components of mechanical structures, which are performed via the radio-wave method based on ultrashort pulses (USPs) in the field of vibrometrological diagnostics, are discussed. The principles of radio radiosensory USP probing are formulated. The advantages and features of the diagnostic method under consideration are determined and analytical model of the USP signal, as well as the scheme for detecting an unknown signal, are described. It is demonstrated that the parametric estimation of small angular deviations of phase-distributed radio pulses can be regarded as the technique by which a radio signal is indirectly converted into the mechanical-vibration function of components tested in the devices capable of generating their own mechanical oscillations or modulated by external acoustic disturbances of surroundings. Numerical digital-filtering methods (cross-correlation technique, double Fourier transform, and cepstral analysis), which rely on the windowed Fourier transform and digital signal processing aimed to estimate angular deviations, are proposed. The analytical model of test debug mode of the radiosensory system is implemented in the MATLAB environment.

Experimental investigation of laser beam diffraction on phase step and its practical applications

The change in shape of the spatial spectrum, which is a result of the interaction of a focused laser beam with a phase step structure (PSS), is investigated. As a laser beam passes through a PSS, a spatial spectrum of radiation in the form of two peaks with a deep gap in between is generated. The change in the peaks’ structure as the PSS moves relative to the optical axis of the laser beam is studied in detail. On the basis of the experimental results, a new scheme for measuring small linear and angular deviations is proposed.

High uniformity in angular correlated-color-temperature distribution of white LEDs from 2800K to 6500K

In this paper, to our best knowledge, it is the first time to present a precise simulation and detailed design of angular correlated color temperature (CCT) distribution of white LEDs covering a range of CCT from 2800K to 6500K. An optimized design of packaging structure with a silicone lens covering a phosphor dome performed an extreme small angular CCT deviation of 105K in the simulation and 182K in a corresponding real sample for a white LED with the CCT near 6500K.

Surface Morphological Effects on Subwavelength Filter of Nanoscale Grating for Near Infrared Biosensing

We modeled the effects of surface roughness (SR) on a near-infrared guided-mode resonance (GMR) biosensor. A power spectral density function was used to describe the SR with spatial autocorrelation integration through a rigorous coupled-wave analysis (RCWA), and a peak wavelength value (PWV) shift in reflectance was observed under transverse electric (TE) and transverse magnetic (TM) polarization. Sub-nanometer SR caused significant PWV shifts, leading to invalid spectral recognition. In addition to random roughness, we studied the PWV reflectance shift for SR models such as sinusoidal, rectangular, and effective medium types. All SR models showed a larger PWV shift for TM polarization than for TE polarization. Owing to SR, PWV reflectance decreased abruptly for TM polarization at small angular deviations from normal incidence. However, the symmetrically splitting of the reflectance spectra for TE polarization implied a high angular tolerance to fabrication errors. Compared to vertical sidewall roughness in our prior work, the SR is much more deleterious for GMR biosensing and should be appropriately controlled.

Surface Morphological Effects on Subwavelength Filter of Nanoscale Grating for Near Infrared Biosensing

We modeled the effects of surface roughness (SR) on a near-infrared guided-mode resonance (GMR) biosensor. A power spectral density function was used to describe the SR with spatial autocorrelation integration through a rigorous coupled-wave analysis (RCWA), and a peak wavelength value (PWV) shift in reflectance was observed under transverse electric (TE) and transverse magnetic (TM) polarization. Sub-nanometer SR caused significant PWV shifts, leading to invalid spectral recognition. In addition to random roughness, we studied the PWV reflectance shift for SR models such as sinusoidal, rectangular, and effective medium types. All SR models showed a larger PWV shift for TM polarization than for TE polarization. Owing to SR, PWV reflectance decreased abruptly for TM polarization at small angular deviations from normal incidence. However, the symmetrically splitting of the reflectance spectra for TE polarization implied a high angular tolerance to fabrication errors. Compared to vertical sidewall roughness in our prior work, the SR is much more deleterious for GMR biosensing and should be appropriately controlled.

Use of webcams as tools for alignment and supervision of a Thomson scattering system in the near infrared

The alignment stability is a major concern for Thomson scattering systems. Even small angular deviations of the laser beams crossing the plasma lead to a loss of the calibration resulting in unreliable measurements of the electron density profile. For the TCV (Tokamak à Configuration Variable) installation, the beam paths from the laser output to the vacuum chamber are ∼25 m long and include several optical components. In order to monitor the alignment on a regular basis, a set of 9 cameras has been installed at several locations along the beam path. They view the actual laser beam pattern by recording the scattered light from an intercepting optical surface (mirror or window) together with the position of markers used for reference. Small “webcams” are used for this purpose; they feature adequate intensity response at the laser wavelength of 1.06 μm, are compact, cheap and several units may be connected to a server PC simultaneously. The real-time images from all the cameras are accessible from a Web browser. This installation has proven to be extremely useful in the early detection of alignment problems and to assist the alignment procedure [1].

Residual Doppler Effect on Electromagnetically Induced Transparency in a Zeeman Sublevel System

We investigate the residual Doppler effect on the linewidth of electromagnetically induced transparency (EIT) in a Zeeman sublevel system where a careful experimental design ensures the smallest measurement error. The overall measurement error of the EIT linewidth is estimated to be less than 5%. We present the linear dependence of EIT resonance broadening at small angular deviation in detail. The theoretical analysis exploits the dependence of this feature and shows the qualitative agreement between numerical results and experimental results.

Quick Shear-Flow Alignment of Biological Filaments for X-ray Fiber Diffraction Facilitated by Methylcellulose

X-ray fiber diffraction is one of the most useful methods for examining the structural details of live biological filaments under physiological conditions. To investigate biologically active or labile materials, it is crucial to finish fiber alignment within seconds before diffraction analysis. However, the conventional methods, e.g., magnetic field alignment and low-speed centrifugations, are time-consuming and not very useful for such purposes. Here, we introduce a new alignment method using a rheometer with two parallel disks, which was applied to observe fiber diffractions of axonemes, tobacco mosaic tobamovirus, and microtubules. We found that fibers were aligned within 5 s by giving high shear flow (1000–5000 s−1) to the medium and that methylcellulose contained in the medium (∼1%) was essential to the accomplishment of uniform orientation with a small angular deviation (<5°). The new alignment method enabled us to execute structure analyses of axonemes by small-angle x-ray diffraction. Since this method was also useful for the quick alignment of purified microtubules, as well as tobacco mosaic tobamovirus, we expect that we can apply it to the structural analysis of many other biological filaments.

Observing angular deviations in the specular reflection of a light beam

The Law of Reflection of a light ray incident upon a mirror (θin = θout) was first formulated by Euclid around 300 bc in his book Catoptrics1; it has been a tenet of geometrical optics ever since. However, more recently, a small angular deviation of the Law of Reflection has been predicted for a physical light beam when this is regarded as the implementation of a ray2,3,4,5. The deviation is a diffractive consequence of the angular dependence of the reflectivity and should occur for any mirror with less than 100% reflectivity. We report here experimental proof of this angular deviation by determining the direction of an optical beam after reflection from an air–glass interface, using a position detector with nanometre resolution. Our results are relevant for angular metrology in general and cantilever-based surface microscopies in particular. Analogous angular deviations are expected for reflection of acoustic waves and quantum matter waves. A small angular deviation of the law of reflection has been previously predicted for a light beam, and is a consequence of the angular dependence of the reflectivity. Experimental proof of such a deviation at near-infrared wavelengths is now reported.

Computer-aided two-coordinate autocollimator for measuring small angular deviations

A computer-aided autocollimator for measuring small angular deviations is described. Small angular displacements are determined by the displacement of the laser beam image on a CCD array in the focal plane of a lens. Automatic control of the displacement systems allows one to test many times the systems of precision remote displacement of optical components with a minimum detectable angular deviations of about 0.2″.