Refraction Angle Research Articles

Stress field measurements using quantitative schlieren

Quantitative schlieren analysis is extended here to optically transparent solids in quasi-static and dynamic experiments to measure stress distributions. The quasi-static experiments in polymethyl methacrylate (PMMA) compared refraction angles and stress gradients calculated from schlieren images to the analytical Flamant solution of a line load on a half-space. The quantitative schlieren measurements of the stress field in the thin sample with a load compared well to the analytical solution. The analysis method was then extended to explosive induced shock waves in PMMA. The explosive induced response of PMMA was experimentally studied using high-speed schlieren to visualize the shock propagation in conjunction with Photon Doppler Velocimetry (PDV) to record surface velocity histories. The stress state estimated from the schlieren images was compared to the stress calculated from the PDV measurements. High-speed imaging limitations caused the shock wave to not be fully resolved in the images, but was resolved in the PDV measurement. The stress state behind the shock calculated from the high-speed images followed a similar trend to the stress calculated from the PDV measurements.

Simulation of horizontal refraction of continental slope in the southern continental slope of the South China Sea

Abstract Sound waves are significantly influenced by boundaries during their propagation in certain environmental conditions. The extent of this impact is related to the complexity of the boundary, such as in the case of slopes and seamounts. In these areas, sound waves may deviate from their original paths, resulting in three-dimensional effects. Recent experiments and simulations have demonstrated that three-dimensional effects occur when sound waves propagate over seamounts in the South China Sea, leading to larger acoustic shadow regions. However, there are limited studies on 3D acoustic propagation based on measured slope topography or database topography. In this study, the topography of the South China Sea area database is selected, and the measured sound velocity profile and seabed acoustic parameters in the South China Sea are taken into considered. The FOR3D sound field calculation model is used to calculate the N×2D and 3D results. The simulation results show that in the southern continental slope region of the South China Sea, when the sound source frequency is 50 Hz, the acoustic wave exhibits significant horizontal refraction with a refraction angle of approximately 13°.

Angular Deviations, Lateral Displacements, and Transversal Symmetry Breaking: An Analytical Tutorial

The study of a Gaussian laser beam interacting with an optical prism, both through reflection and transmission, provides a technical tool to examine deviations from the optical path as dictated by geometric optics principles. These deviations encompass alterations in the reflection and refraction angles, as predicted by the reflection and Snell laws, along with lateral displacements in the case of total internal reflection. The analysis of the angular distributions of both the reflected and transmitted beams allows us to understand the underlying causes of these deviations and displacements, and it aids in formulating analytic expressions that are capable of characterizing these optical phenomena. The study also extends to the examination of transverse symmetry breaking, which is a phenomenon observed in the laser beam as it traverses the oblique interface of the prism. It is essential to underscore that this analytical overview does not strive to function as an exhaustive literature review of these optical phenomena. Instead, its primary objective is to provide a comprehensive and self-referential treatment, as well as give universal analytical formulas intended to facilitate experimental validations or applications in various technological contexts.

Resonant-mode engineering for additive reflective structural colors with high brightness and high color purity

We present quad-layered reflective structural color filters generating vivid additive primary colors by controlling a mode number in a Fabry–Perot (FP) cavity and an anti-reflective (AR) coating layer, thus accomplishing high spectral contrast which is highly demanded in creating sharp colors. The reflection brightness of fabricated structural color filters is over 78% and a color gamut is comparable to the standard color gamut (sRGB). Higher-order resonant modes are exploited yielding a narrow passband with strong suppression of the reflection at shorter and longer wavelength ranges for a green color, while red and blue colors are produced by employing fundamental resonant modes. Besides, the structural color filters maintain both high brightness and high color purity at oblique incidence angles up to 40° due to a small angle of refraction by a cavity medium with high refractive index. Moreover, a large-scale fabrication is enabled owing to the simplicity of a device structure, where thin film deposition is used. The scheme presented in this work may open the door to a number of applications, such as reflective displays, imaging devices, colored photovoltaics, and decorations.

Study of the lateral shift due to atmospheric refraction: alternative analytical methods, and new results

Atmospheric refraction modifies the apparent position of objects in the sky, and also produces a progressive lateral shift of the light rays received from these objects; in the case of a spherically symmetric atmosphere, for the first time, this shift has been numerically studied in 2022, and different analytical estimators have been compared (by Labriji et al.) for the total shift. This topic is important for the reconstruction of meteor trajectories, for the analysis of wavefront sensing in adaptative optics, etc. Always in the case of a spherically symmetric atmosphere, we show two other analytical methods to study this lateral shift, and to be able to estimate it analytically in the difficult case when the celestial object is seen near the astronomical horizon. One of these methods allows us to deduce an estimator, not only of the total shift, but also of the shift of any point of the ray. We compare properties of the total lateral shift and of the refraction angle, and also the chromatism of the total lateral shift to the chromatism of the air refractivity, for rays coming from an object seen either high enough above the astronomical horizon, or on it. In this latter case, our first method shows departures from proportionality between the chromatisms of the air refractivity, of the astronomical refraction angle, and, even more, of the total lateral shift.

Deformation of solid earth by surface pressure: equivalence between Ben-Menahem and Singh’s formula and Sorrells’ formula

SUMMARY Atmospheric pressure changes on Earth’s surface can deform the solid Earth. Sorrells derived analytical formulae for displacement in a homogeneous, elastic half-space, generated by a moving surface pressure source with speed $c$. Ben-Menahem and Singh derived formulae when an atmospheric P wave impinges on Earth’s surface. For a P wave with an incident angle close to the grazing angle, which essentially meant a slow apparent velocity $c_a$ in comparison to P- ($\alpha ^{\prime }$) and S-wave velocities ($\beta ^{\prime }$) in the Earth ($c_a \ll \beta ^{\prime } \lt \alpha ^{\prime }$), they showed that their formulae for solid-Earth deformations become identical with Sorrells’ formulae if $c_a$ is replaced by $c$. But this agreement was only for the asymptotic cases ($c_a \ll \beta ^{\prime }$). The first point of this paper is that the agreement of the two solutions extends to non-asymptotic cases, or when $c_a /\beta ^{\prime }$ is not small. The second point is that the angle of incidence in Ben-Menahem and Singh’s problem does not have to be the grazing angle. As long as the incident angle exceeds the critical angle of refraction from the P wave in the atmosphere to the S wave in the solid Earth, the formulae for Ben-Menahem and Singh’s solution become identical to Sorrell’s formulae. The third point is that this solution has two different domains depending on the speed $c$ (or $c_a$) on the surface. When $c/\beta ^{\prime }$ is small, deformations consist of the evanescent waves. When $c$ approaches Rayleigh-wave phase velocity, the driven oscillation in the solid Earth turns into a free oscillation due to resonance and dominates the wavefield. The non-asymptotic analytical solutions may be useful for the initial modelling of seismic deformations by fast-moving sources, such as those generated by shock waves from meteoroids and volcanic eruptions because the condition $c / \beta ^{\prime } \ll 1$ may be violated for such fast-moving sources.

The Curriculum in NDT Training Have to Include Basics Information Technology to Accomplish Reliability of Automated NDT Result's

Automation in Non-Destructive Testing (NDT) is a reality of modern manufacturing and quality assurance. Information technology applications are simultaneously developed and applied to different fields of NDT methods. The future of doing reliability checks using automated system is inevitable. The results are important to make a variety of decisions regarding the quality of a product and/or service, hence affecting safety and reliability. Depending on artificial intelligence and quantum device development, various NDT training schemes have to adopt a new curriculum to address the issue of the basic knowledge of information technology and automation in NDT. NDT operators are basically dependent on the end results of software, in which the software developer uses a set of algorithms. These are obtained in three categories; 1) Real time database; 2) Synthetic database and 3) Hybrid or combination of them. The developers should know how the NDT systems run and NDT operators in the other hand know the mechanism of the program, so that appropriate action can be taken, in case there is a missed detection, or a detected indication is not very much detrimental to the reliability of the part (Over sizing or wrongly evaluated). For example, a set of algorithms are used to create the focal laws in a phased array ultrasonic test software in space of 1˚ beam steering. Each has a limit of maximum up to 2nd Critical angle. Operators try to copy the same algorithm and set up to 89˚ refraction angle, which will just create creep wave with unreliable results to detect effective size the reflector. Programming knowledge of the operator can effectively eliminate this type of unreliability. In various Schemes of NDT Syllabus which are in common place to employ and train plus certify operators does not have it; actually, the operators do the scope of work which does includes application of Artificial Intelligence (AI) and Software. With the development of Q coupler (Quantum Computing) system, it is obvious to adopt the upcoming technology into the application of NDT industry. Training needs to update the curriculum accordingly. The current topic has intended to focus on the training gap and to address related kind of unreliability.

Ribbed elastic metasurface with lateral scalability for flexural wave manipulation

With the goal of engineering applications, the scalability and structural portability of elastic metasurfaces have become significant and attractive. However, most existing elastic metasurfaces cannot be arbitrarily scalable, which will inevitably limit their applications. Here, a novel conceptual design of ribbed elastic metasurfaces (REMs) is proposed for anomalous wavefront manipulation of flexural waves in thin plates. Ribbed subunits, as functional subunits of REMs, are characterized by simple constructions. The phase shift mechanism for the flexural waves across the ribbed subunits is revealed by analyzing the lowest dispersion bands. The analytical model for ribbed subunits is also established based on the equivalent orthotropic plate theory and transfer matrix method (TMM) to accurately predict the phase shift and amplitude of the transmitted waves. In addition, lateral scalability can be observed when the ratio of rib width to subunit width is constant, owing to the constant equivalent bending stiffness. By considering the lateral scalability of subunits, the continuous adjustment of the refraction angle can be perfectly achieved. The deflecting and focusing functionalities of the designed REMs are numerically and experimentally demonstrated. Both simulated and experimental results are consistent with theoretical results. Since ribbed plates are typical load-bearing structures in engineering, our design has broad application prospects, including but not limited to vibration control, energy harvesting, and structural health monitoring.

A semianalytically synthesized ultrathin photolithographic metagrating for sub-THz beam splitting

Compact and efficient devices for radiation beam manipulation are in increasing demand by terahertz technologies. Herein, we introduce an ultrathin metal-polymer photolithographic metagrating operating as a transmissive beam splitter with a wide refraction angle of 58∘ at sub-THz frequencies. Harnessing this recently proposed complex media platform, composed of sparse periodic arrays of meta-atoms, constraints of conventional metasurfaces with densely packed unit cells can be alleviated. The devised splitter, synthesized semianalytically and demonstrated experimentally, features deeply subwavelength thickness due to the unique manufacturing process employed, serving as a promising alternative to thick waveguide-based metagratings previously reported for this frequency range.

Design of a Talbot phase-contrast microscopy imaging system with a digital detector for laser-driven X-ray backlighter sources

Laser-driven shock waves in matter propagate with multiple kilometers per second and therefore require sources like a laser-driven backlighter, which emit the X-rays within picoseconds, to be able to capture sharp images. The small spatial extent of shocks in low-density materials pose challenges on the imaging setup. In this work, we present a design process for a single-shot X-ray phase-contrast imaging system geared towards these objects, consisting of a two-grating Talbot interferometer and a digital X-ray detector. This imaging system is optimized with respect to the detectable refraction angle of the X-rays induced by an object, which implies a high phase sensitivity. Therefore, an optimization parameter is defined that considers experimental constraints such as the limited number of photons, the required magnification, the size and spectrum of the X-ray source, and the visibility of the moiré fringes. In this way, a large parameter space is sampled and a suitable imaging system is chosen. During a campaign at the PHELIX high-power laser facility a static test sample was imaged which is used to benchmark the optimization process and the imaging system under real conditions. The results show good agreement with the predicted performance, which demonstrates the reliability of the presented design process. Likewise, the process can be adapted to other types of laser experiments or X-ray sources and is not limited to the application presented here.

Fluctuations in Refracted Star Signals Caused by the Stratospheric Internal Gravity Waves

The application of starlight refraction navigation to spacecraft and space weapons is a significant development. However, the irregular stratospheric atmosphere can cause fluctuations in relative light intensity and refraction angles of refracted stars, which need to be analyzed to provide guidance for system design and simulation verification. The internal gravity wave (IGW) is an important component of the irregular atmosphere. Based on the Rytov approximation, closed-form approximations were obtained, which can more intuitively reveal the relationship between the IGW parameters and the star signals’ statistical characteristics. From the GOMOS observations, the influence of the stratosphere from 25 km to 35 km on the fluctuations in relative intensity and refraction angles was analyzed in this study. As the height increased, the fluctuations in starlight signals gradually weakened. Compared with the numerical solution, the error of the closed-form approximations for relative intensity fluctuations was no more than 10%, and the error for refraction angle fluctuations was 1.0%. Compared with the measured data, the error of the closed-form approximations for relative intensity was 6.3%. The proposed approximations better reflect the relationship between IGW parameters and star signal fluctuations compared to the existing approximation. The research in this article can provide a reference for application assessment based on starlight refraction navigation.

In-plane elastic waves in piezoelectric metamaterials with Parity–Time symmetry

The propagation of in-plane waves in piezoelectric metamaterials involves the coupling of longitudinal (i.e. quasi–pressure), transverse (i.e. quasi–shear) and electric potential waves, which can result in different exotic phenomena. In this study, the stiffness matrix method is used to analyze the dispersion relation, which contains anomalous propagation characteristics. With the coupling of electric potential, the frequency spectrum of in–plane wave shows new characteristics. The exceptional point caused by non–Hermitian operator that does not exist before also appears when the vertical wave number is imaginary. The oblique incidence of the in–plane wave at the interface between a homogeneous medium and phononic crystal can excite multiple refraction modes which include the negative refraction. The normal mode decomposition is developed to study the in-plane incidence of piezoelectric metamaterial and then the averaged Poynting vector is applied to obtain the refraction angle. Moreover, the defect layer is introduced into the phononic crystals to study the transmission coefficients with two different symmetrical arrangements. When the balanced gain and loss are considered in the metamaterial, the Parity–Time symmetry appears and brings in pairs of exceptional points to achieve complete transmission with unidirectional zero reflection.

Progress of CO2 Dispersion Interferometer on EAST

A CO2 Dispersion Interferometer (DI) system on the Experimental Advanced Superconducting Tokamak (EAST) was successfully operated, providing plasma electron density measurements. The DI system utilizes a continuous-wave 9.3 μm CO2 laser source to measure line-averaged electron densities. This offers significant advantages, including the ability to minimize fringe jumps and insensitivity to mechanical vibrations. These characteristics are well-suited for future high-density, long-pulse plasma discharges. The DI system provides a real-time density feedback signal to the plasma control system for routine density control during long-pulse operation. Experiments with EAST demonstrated good agreement between the density obtained by the DI system and the preset densities. The DI system also exhibited stability during long-pulse discharge. Moreover, the DI system was stable during rapid density changes and high-density pellet injections. In shot No. 120594, the DI system exhibited stable density feedback during continuous projectile injection lasting over 50 seconds; the line-averaged electron density is approximately 4×1019 m-3. In contrast to the long-wavelength source interferometer, which may deflect light from the detector owing to excessive refraction angles in larger density-gradient discharges, the DI ensured accurate density measurements. The DI system on EAST is dependable for accurately measuring the electron density.

Microwave absorption performance for Cu, Co, and Ti co-doped SrFe12O19 as a function of incident angle

Microwave-absorbing materials (MAMs) are essential for mitigating the unwanted effects of electromagnetic interference and microwave pollution. MAMs are also used in 5G technology, energy harvesting, information security, and military technology (such as reduced radar cross-section). In this work, SrFe12–2xCux/2Cox/2TixO19 samples, prepared by using a ball mill and heat treatment method, showed their superior microwave dissipation features in both effective absorption bandwidth (EAB) and reflection loss (RL) values for the microwave incident angle of 0°, where EAB and RL values reached 15.90 GHz and −42.86 dB, respectively. The optimum RL values would change with the variation of the incident microwave angle. RL values at a specific oblique angle could exhibit better RL values for both transverse electric (TE) and transverse magnetic (TM) polarization modes, except for the x = 0.15 (SrM15) sample for TE mode. In detail, the x = 0 (SrM0) sample achieved the lowest RL value of −71.28 dB for the incident angle of 20° in the TE polarization mode, which was much better than that of the normal incident. The RL of the SrM15 sample in TM mode was significantly enhanced and reached a value of −66.48 dB for an incident angle of 10°. The increase in the RL values resulted from the superior values of complex permittivity and permeability and their matching. In addition, the improvement in RL values could be attributed to the increase in incident and refraction angles as well as the longer pathway of the microwave inside the samples. These discoveries also illustrate that SrFe12–2xCux/2Cox/2TixO19 samples hold promise for various everyday applications, even when exposed to oblique angle variation.

Quantum imaging of biological organisms through spatial and polarization entanglement.

Quantum imaging holds potential benefits over classical imaging but has faced challenges such as poor signal-to-noise ratios, low resolvable pixel counts, difficulty in imaging biological organisms, and inability to quantify full birefringence properties. Here, we introduce quantum imaging by coincidence from entanglement (ICE), using spatially and polarization-entangled photon pairs to overcome these challenges. With spatial entanglement, ICE offers higher signal-to-noise ratios, greater resolvable pixel counts, and the ability to image biological organisms. With polarization entanglement, ICE provides quantitative quantum birefringence imaging capability, where both the phase retardation and the principal refractive index axis angle of an object can be remotely and instantly quantified without changing the polarization states of the photons incident on the object. Furthermore, ICE enables 25 times greater suppression of stray light than classical imaging. ICE has the potential to pave the way for quantum imaging in diverse fields, such as life sciences and remote sensing.

Reliable extraction of x-ray refraction and dark-field signals with a large field of view, multi-modal scanning system at spectral energies up to 150 kVp

Abstract Multi-modal x-ray scanning allows the simultaneous acquisition of attenuation, refraction and ultra-small angle scattering or dark field images. While many examples of multi-modal x-ray scanning exist in the literature, extension to high x-ray energy, necessary to investigate dense and high-Z materials, still poses challenges. We present the investigation of attenuation, refraction and dark field images taken at 90, 120 and 150 kVp, using a scanning, large field of view multi-modal imaging system. Increases in tube voltage reduce both contrast and signal to noise but still produce satisfactory results suitable for quantitative analysis. On top of benchmarking against phantoms made of known materials, we illustrate this by scanning a 9 V PP3 battery; a highly absorbing sample which causes photon starvation at lower energies.

A new method for high-precision starlight refraction indirect horizon-sensing positioning of atmospheric flight vehicles

The starlight refraction indirect horizon-sensing positioning method is a new type of autonomous celestial navigation method with broad application prospects. In view of this method currently being limited to the spacecraft outside the atmosphere, this article derives and establishes a starlight refraction indirect horizon-sensing positioning model between the starlight refraction angle and the flight vehicle’s position inside the atmosphere. Based on this model, a new starlight refraction indirect horizon-sensing positioning method for the flight vehicle inside the atmosphere is proposed. According to the atmospheric refraction law and the spherical atmospheric model, the refracted optical path of starlight entering the atmosphere and reaching the flight vehicle is traced, so as to establish a starlight refraction positioning model that reflects the relationship between the refraction angle and the 3-D position of the flight vehicle inside the atmosphere. Subsequently, by employing star sensors on the flight vehicle to measure the starlight refraction angle, and combining the starlight refraction positioning model that maps the starlight refraction angle and the flight vehicle’s position, a starlight refraction indirect horizon-sensing autonomous celestial positioning method, tailored for the flight within the atmosphere, is proposed. Finally, the effectiveness of the proposed method is verified through ground semi physical experiments, and an analysis is conducted to explore the factors that affect the positioning accuracy of the starlight refraction indirect horizon-sensing positioning method within the atmosphere.

Polarization-independent full mode-converting elastic metasurfaces

This investigation proposes a novel elastic metasurface tailored to convert a longitudinal wave into a transverse wave and vice versa at an arbitrary refraction angle with full (100 %) conversion efficiency. The previous mode-converting elastic metasurface based on Snell's critical angle can convert a longitudinal wave into a transverse wave, but the refraction angle of the transverse wave cannot be smaller than the critical angle. In addition, the previous metasurface cannot convert a transverse wave into a longitudinal wave without generating a parasitic transverse wave. Here, we propose an elastic metasurface that enables full mode-converting transmission at an arbitrary refraction angle, regardless of whether the incident wave's polarization is longitudinal or transverse. To this end, we present a novel strategy to design unit cells that yield total mode-conversion efficiency as well as the desired phase shifts covering the entire 2π range. Shape optimization and geometry-flipping strategies were employed to design the unit cells constituting the metasurface. The concept of the unit cell's effective length was useful for the unit cell design. The designed metasurfaces were then used for various applications, such as longitudinal-to-transverse and transverse-to-longitudinal wave steering, splitting, and focusing. The performance of our metasurface was verified by ultrasonic experiments performed on an aluminum plate with the designed metasurface embedded. The realized full mode-converting transmission applicable for an arbitrary angle is expected to be critically valuable for nondestructive testing and medical ultrasounds requiring a specific elastic wave mode of the desired arbitrary beam pattern.

The optical possibilities of gelatin

Contact lenses have traditionally been manufactured using a variety of plastics: polymers for soft lenses and acrylic or polymethyl methacrylate for hard lenses. There is emerging interest in the use of gelatin for lenses to increase malleability, water solubility, and sustainability as a non-plastic. A predicted difficulty in the use of gelatin is the reduced refractive index (RI). We looked at how acrylic or gelatin changes the RI and focal length in order to see how gelatin lenses would have to be altered for more severe prescriptions. We tested the refractive rays of gelatin and acrylic with both convex and concave lens types to investigate which produced smaller angles of refraction and correspondingly greater focal length. The average RI of the biconvex and biconcave acrylic without Pam, acrylic with Pam, and gelatin were 1.47, 1.496 and 1.36, respectively. Gelatin’s lesser angles of refraction produced a longer focal length. The lower RI of the gelatin (0.11–0.136 less than acrylic) directly correlated with its lesser angles of refraction, which produced an overall greater focal length (3.51– 4.38 more than acrylic). Gelatin needs to be thickened, increased in curvature, or mixed with crosslinkers to strengthen the lens. Lens makers will face similar challenges with the switch to gelatin lenses, so they may need to incorporate a larger percentage of solid gelatin concentrate or a plastic alloy in the gelatin to increase the RI, decrease the focal length, and improve the stability of the gelatin.

"The effect of gravity on the evolution of life on earth based on general relativity and the low of free fall "

The radius of the universe can be determined by combining the Einstein formulas, which determine the degree of gravitational redshift and describe the angle of refraction of a beam of light running along celestial bodies. The relationship between the two equations is made by the ratio of the total angle to the angle of deflection of the beam of light passing by the Earth according to the rules of Euclidean geometry (2∙π/α). The so-called Darwinian evolutionary distances measured from the color changes of the respiratory pigments of biological creatures (in connection with the phase of their circulation) can be paralleled with this. It is possible to measure these to the radius of the universe determined in this way. During the nearly 4-billion-year uninterrupted process of Darwinian evolution, living organisms presumably adapted to surface gravity during mutations as well as to any other environmental factor. In this way, they can accelerate continuously along the imaginary straight line from the origin of life to the appearance of the human race, i.e., within the short evolutionary distance, due to the attractive effect of gravity. During the free fall from the past to the present, the curvature of space-time may gradually appear in their physiological processes and anatomical structure. Specifically in their circulatory system, the rate of evolution would correspond to the most qualitatively advanced level, i.e., the velocity of human blood circulation. In this way, the evolution accelerating to almost the speed of light is reduced to 5.23 cm/s due to an enormous time dilation (as a proportion of angles; α/2/π). With this average human blood flow velocity, together with data from cardiac and circulatory procedures, a toroidal, or even more refined, ‘interlocking figure 8 model’ can be constructed. It reflects the dimensions, flow and pressure conditions of the pulmonary and systemic circulation, as well as the work of the heart.