Spatial Phase Shift Research Articles

Spatial phase-shift dual-beam speckle interferometry.

The spatial phase-shift technique has been successfully applied to an out-of-plane speckle interferometry system. Its application to a pure in-plane sensitive system has not been reported yet. This paper presents a novel optical configuration that enables the application of the spatial phase-shift technique to pure in-plane sensitive dual-beam speckle interferometry. The new spatial phase-shift dual-beam speckle interferometry (SPS-DBSP) uses a dual-beam in-plane electronic speckle pattern interferometry configuration with individual aperture shears, avoiding the interference in the object plane by the use of a low-coherence source, and different optical paths. The measured object is illuminated by two incoherent beams that are generated by a delay line, which is larger than the coherence length of the laser. The two beams reflected from the object surface interfere with each other at the CCD plane because of different optical paths. A spatial phase shift is introduced by the angle between the two apertures when they are mapped to the same optical axis. The phase of the in-plane deformation can directly be extracted from the speckle patterns by the Fourier transform method. The capability of SPS-DBSI is demonstrated by theoretical discussion as well as experiments.

Secret Key Exchange and Authentication via Randomized Spatial Modulation and Phase Shifting

Advances in physical layer security techniques have increasingly demonstrated their potential to replace security functionalities that are traditionally included in the upper layers of the Open Systems Interconnection model. This has made it possible for devices with limited layer structures or/and restricted hardware components to offer security measures. In this paper, we consider spatial modulation (SM) systems and propose a unique physical layer technique that uses a random constellation mapping criterion for secret key exchange. The principle idea here is to exploit the inherent symbol-antenna mapping feature of the SM technique to encode the secret key. Specifically, a random phase shift is imposed on each of the modulated symbols using a channel driven approach to uniquely authenticate the transmitted key bits or/and the encrypted confidential data. The results demonstrate that the proposed technique is superior to benchmark techniques in terms of computational complexity and key bit error rate. It will also be shown that the proposed technique offers greater flexibility in terms of the authentication process preference, which is normally unattainable in most of the key exchange proposed techniques.

Highly noise-tolerant hybrid algorithm for phase retrieval from a single-shot spatial carrier fringe pattern

A highly noise-tolerant hybrid algorithm (NTHA) is proposed in this study for phase retrieval from a single-shot spatial carrier fringe pattern (SCFP), which effectively combines the merits of spatial carrier phase shift method and two dimensional continuous wavelet transform (2D-CWT). NTHA firstly extracts three phase-shifted fringe patterns from the SCFP with one pixel malposition; then calculates phase gradients by subtracting the reference phase from the other two target phases, which are retrieved respectively from three phase-shifted fringe patterns by 2D-CWT; finally, reconstructs the phase map by a least square gradient integration method. Its typical characters include but not limited to: (1) doesn't require the spatial carrier to be constant; (2) the subtraction mitigates edge errors of 2D-CWT; (3) highly noise-tolerant, because not only 2D-CWT is noise-insensitive, but also the noise in the fringe pattern doesn't directly take part in the phase reconstruction as in previous hybrid algorithm. Its feasibility and performances are validated extensively by simulations and contrastive experiments to temporal phase shift method, Fourier transform and 2D-CWT methods.

Dynamic measurement of first-order spatial derivatives of deformations by digital shearography

This paper presents a simple spatial phase shift shearography based on the Michelson interferometer. A novel digital shearography set-up with a large angle of view, which is based on a 4f system is demonstrated. In the system, the Michelson interferometer is used as a shearing device to generate a shearing distance by tilting a small angle in one of the two mirrors. In fact spherical wave fronts become plane after going through the first lens in 4f system. Tilting the mirror in the Michelson interferometer also generates spatial carrier frequency. Sinusoid fitting method is applied to evaluate the phase. This system can generate a phase map of shearography by using only a single image. The effects of shearing angle, the choice of algorithm and comparison result are discussed in detail. The theory and the application are presented.

General spatial phase-shifting interferometry by optimizing the signal retrieving function.

A general spatial phase-shifting (GSPS) interferometry method is proposed to achieve phase retrieval from one-frame spatial carrier frequency interferogram. By optimizing the internal signal retrieving function of the spatial phase-shifting (SPS) method, the accuracy, anti-noise ability and speed of phase retrieval can be significantly improved, meanwhile the corresponding local calculation property is reserved. Especially, in the case that the ratio of the spatial carrier to the phase variation rate are small, the proposed method reveals obvious advantage in the accuracy improvement relative to the conventional SPS methods, so the more details of measured sample can be effectively reserved through introducing smaller spatial carrier frequency, and this will facilitate its application in interference microscopy. The principle analysis, numerical simulation and experimental result are employed to verify the performance of the proposed GSPS method.

Hybrid algorithm for phase retrieval from a single spatial carrier fringe pattern.

A hybrid algorithm is proposed in this study for demodulating a single spatial carrier fringe pattern (FP) of interferometric measurement, which essentially combines the spatial carrier phase shift (SCPS) method and Fourier transform (FT) method. It firstly extracts three phase-shifted FPs from a single spatial carrier FP, then employs the FT method and a subtraction operation to determine the phase shift of three phase-shifted FPs, and finally retrieves the phase map using a least-square phase shift algorithm. The subtraction operation could considerably mitigate the inherent edge error of the FT method, resulting in an increase of accuracy compared with the FT method. It also does not require the background and modulation amplitude of the spatial carrier FP to be constant; thus it is robust and quite suitable for engineering. The factors that may influence the performance of the proposed algorithm are analyzed, including the random and speckle noise, carrier frequency, shape of the background, and modulation amplitude. The feasibility of the proposed algorithm is validated by two experiments, comparing them with the temporal phase-shifted method. The proposed algorithm is expected to be used in interferometric measurement under adverse environments.

Polarized digital shearography for simultaneous dual shearing directions measurements.

The selection of the direction of sensitivity for digital shearography is determined by its shearing direction. As a result, directionally shaped defects could be missed in non-destructive testing using a digital shearography system with only one shearing direction. This paper reports a polarized digital shearography system based on two Mach-Zehnder interferometers, which can create two orthogonal shearing directions and record shearograms in the two orthogonal directions simultaneously. The two shearograms are separated from each other by proper polarization design so that no cross interference occurs. The phase maps of the shearograms are generated by spatial phase shift methods through the introduction of different carrier frequencies in the two orthogonal shearograms and use of the Fourier transform method. This enabled simultaneous dual directional non-destructive testing during continuous loading. Theory derivation, spectrum analysis, and non-destructive testing application results are shown in detail.

Calculation of tip vortex cavitation flows around three-dimensional hydrofoils and propellers using a nonlinear k-ɛ turbulence model

Simulations of tip vortex wetted flows and cavitating flows are carried out by using a RANS model. Two types of turbule- nce models, with and without the Boussinesq turbulent-viscosity hypothesis, are adopted in comparing with experimental results regarding the vorticity, the strain rate and the Reynolds shear stress distributions in the vortex region. The numerical results imply that the spatial phase shift between the mean strain rate and the Reynolds stresses can be accurately modeled by the nonlinear k-ɛ turbulence model, the tip vortex cavitation region can only be predicted using the nonlinear k-ɛ turbulence model. The mecha- nism of the over-dissipation due to the turbulence model is analyzed in terms of the turbulence production, which is one of the dominant source terms in the transport equations of energy.

Simultaneous dual directional strain measurement using spatial phase-shift digital shearography

This paper presents a Dual Directional Sheared Spatial Phase-Shift Digital Shearography (DDS-SPS-DS) system for simultaneous measurement of strains/displacement derivative in two directions. Two Michelson Interferometers are used as the shearing device to create two shearograms, one in the x-shearing direction and one in the y-shearing direction, which are recorded by a single CCD camera. Two lasers with different wavelengths are used for illumination, and corresponding band pass filters are applied in front of each Michelson Interferometer to avoid cross-interference between the two shearing direction channels. Two perpendicular shearing directions in the two measurement channels introduce two different spatial frequency carriers whose spectrums are orientated in different directions after Fourier Transform. Phase maps of the recorded two shearograms can be obtained by applying a windowed inverse Fourier transform, which enables simultaneous measurement of dual directional strains/displacement derivatives. The new system is well suited for nondestructive testing and strain measurement with a continuous or dynamic load. The capability of the dual directional spatial phase-shift digital shearography system is described by theoretical discussions as well as experiments.

Simulations of tip vortex cavitation flows with nonlinear k-ε model

Effects of turbulence models on the simulations of tip vortex wetted flows and cavitating flows are studied. Two types RANS turbulence models, with and beyond the Boussinesq turbulent-viscosity hypothesis, are investigated by examining experimental results regarding strain rate and Reynolds shear stress distributions in the vortex region. The numerical results imply that the spatial phase shift between the mean strain rate and Reynolds stresses can be accurately modeled by the nonlinear k-ε turbulence model; the tip vortex cavitation region can only be predicted using the nonlinear turbulence model. The mechanism of the over-dissipation due to the turbulence model is analyzed in terms of the turbulence production, which is one of the dominant source terms in the transport equations of energy. The numerical results imply that the nonlinear k-ε model is a promising candidate for predicting tip vortex cavitation flows in practical applications at a reasonable computational cost.

Hydrodynamic schooling of flapping swimmers.

Fish schools and bird flocks are fascinating examples of collective behaviours in which many individuals generate and interact with complex flows. Motivated by animal groups on the move, here we explore how the locomotion of many bodies emerges from their flow-mediated interactions. Through experiments and simulations of arrays of flapping wings that propel within a collective wake, we discover distinct modes characterized by the group swimming speed and the spatial phase shift between trajectories of neighbouring wings. For identical flapping motions, slow and fast modes coexist and correspond to constructive and destructive wing–wake interactions. Simulations show that swimming in a group can enhance speed and save power, and we capture the key phenomena in a mathematical model based on memory or the storage and recollection of information in the flow field. These results also show that fluid dynamic interactions alone are sufficient to generate coherent collective locomotion, and thus might suggest new ways to characterize the role of flows in animal groups.

A fabrication process for the monolithic integration of magnetoelastic actuators and silicon sensors

This paper describes a microfabrication process that accommodates the design considerations of wirelessly actuated magnetoelastic traveling wave and standing wave motors that are integrated with capacitive position sensors on a silicon substrate. The process—which incorporates AuIn eutectic bonding, multiple deep reactive ion etching steps, and metal electrode deposition and etching—addresses the challenges of magnetoelastic layer attachment, multi-layer structures, and robust electrode isolation. Measurements of successfully fabricated devices show that the typical resonant frequencies of the clockwise and counterclockwise modes for the standing wave stators existed at 12.1 and 22.4 kHz with 0.44 µm and 0.4 µm out-of-plane amplitudes, respectively, when a ≈2 Oe amplitude ac magnetic field and a ≈6.5 Oe dc magnetic bias field were applied. For the as-fabricated traveling wave motors, two desired mode shapes with π/2 spatial phase shift existed at typical frequencies of 28.4 and 29.9 kHz, with typical out-of-plane amplitudes of 74 and 70 nm, respectively, when a ≈6 Oe amplitude ac magnetic field and a ≈3 Oe dc magnetic bias field were applied. The frequencies were tuned with added mass, resulting in a shift to 28.37 and 28.33 kHz with out-of-plane amplitudes of 80 and 60 nm for the two modes, respectively. After tuning, a traveling wave with a continuous direction of propagation was successfully demonstrated. The capacitive position sensing scheme showed a sensitivity of ≈0.5 pF per degree over 8°.

Nonlinear response of magnetic islands to localized electron cyclotron current injection

The magnetic island evolution under the action of a current generated externally by electron cyclotron wave beams is studied using a reduced resistive magnetohydrodynamics plasma model. The use of a two-dimensional reconnection model shows novel features of the actual nonlinear evolution as compared to the zero-dimensional model of the generalized Rutherford equation. When the radio frequency control is applied to a small magnetic island, the complete annihilation of the island width is followed by a spatial phase shift of the island, referred as “flip” instability. On the other hand, a current-drive injection in a large nonlinear island can be accompanied by the occurrence of a Kelvin-Helmholtz instability. These effects need to be taken into account in designing tearing mode control systems based on radio frequency current-drive.

Thermokinetic Origin of Luminescent Traveling Fronts in the H2O2–NaOH–SCN––Cu2+ Homogeneous Oscillator: Experiments and Model

According to our original discovery, the oscillatory course of the Cu(2+)-catalyzed oxidation of thiocyanate ions with hydrogen peroxide, in nonstirred medium and upon the addition of luminol as an indicator, can be a source of a novel type of dissipative patterns--luminescent traveling waves. The formation of these fronts, contrary to the patterns associated with the Belousov-Zhabotinsky reaction, cannot be explained in terms of coupled homogeneous kinetics and diffusion, and under isothermal conditions. Both experimental studies and numerical simulations of the kinetic mechanism suggest that the spatial progress of these waves requires mainly the temperature gradient in the solution, which affects the local chemical reaction rate (and thus the oscillation period), with practically negligible contribution from diffusion of reagents. As a consequence of this thermokinetic coupling, the observed traveling patterns are thus essentially the phase (or kinematic) waves, formed due to the spatial phase shift of the oscillations caused by differences in chemical reaction rates. The temperature gradient, caused by the significant heat effect of exothermic oxidation of thiocyanate by hydrogen peroxide, can emerge spontaneously as a local fluctuation or can be forced externally, if the control of progress of the luminescent waves is to be achieved.

Granular transport in a horizontally vibrated sawtooth channel

We present a new mode of transport of spherical particles in a horizontally vibrated channel with sawtooth-shaped side walls. The underlying driving mechanism is based on an interplay of directional energy injection transformed by the sidewall collisions and density-dependent interparticle collisions. Experiments and matching numerics show that the average particle velocity reaches a maximum at 60% of the maximal filling density. Introducing a spatial phase shift between the channel boundaries increases the transport velocity by an order of magnitude.

Michelson interferometer based spatial phase shift shearography

This paper presents a simple spatial phase shift shearography based on the Michelson interferometer. The Michelson interferometer based shearographic system has been widely utilized in industry as a practical nondestructive test tool. In the system, the Michelson interferometer is used as a shearing device to generate a shearing distance by tilting a small angle in one of the two mirrors. In fact, tilting the mirror in the Michelson interferometer also generates spatial frequency shift. Based on this feature, we introduce a simple Michelson interferometer based spatial phase shift shearography. The Fourier transform (FT) method is applied to separate the spectrum on the spatial frequency domain. The phase change due to the loading can be evaluated using a properly selected windowed inverse-FT. This system can generate a phase map of shearography by using only a single image. The effects of shearing angle, spatial resolution of couple charge device camera, and filter methods are discussed in detail. The theory and the experimental results are presented.

Combustion in the Me1-Me2-N2 system: Unconventional macrostructure of combustion products

Multiwave combustion in the Me1-Me2-N2 system is rationalized in terms of catalytic combustion mechanism, without formation of planar combustion front, but via numerous combustion waves with different spatial configuration and phase shift. The process of afterburning involves formation of new waves or warm-up with the torches of burning gaseous products. The latter ones form outlet craters on the surface of burned samples.

The simultaneous suppression of phase shift error and harmonics in the phase shifting interferometry using carrier squeezing interferometry

The phase shift errors and the harmonics are the most common types of errors in the phase shifting interferometry. Although there are many suppression techniques for these two errors, it is hard to suppress them simultaneously. In this paper the carrier squeezing interferometry is used to solve this problem, where the data of phase shifting interferograms with linear carrier are re-arranged to acquire a spatial–temporal fringes image. In the frequency domain of the image the lobes of harmonics and phase shift errors and the lobe of the phase are separated, so the correct phase can be extracted by filtering. The algorithm is validated by both simulations and the experiments, with the phase retrieving accuracy greater than λ/400 and λ/200 (RMS value), respectively. The spatial uniform phase shift errors and harmonics can be suppressed by this method, using only four phase shifting interferograms.

Illusory patterns are fishy for fish, too

It has been widely recognized that size,shape, and distance perception are not themere translation of images in the eyes, asretinal images are inherently ambiguous.Some form of knowledge and/or assump-tions by unconscious inductive inferenceseems to be necessary (Gregory, 1997).With respect to this topic, visual illusionsare a valuable tool for understanding theneuro-cognitive systems underlying visualperception by indirectly revealing the hid-den constraints of the perceptual systemin a way that normal perception cannot.In humans, such constraints have beenoftensummarizedastheso-called“Gestaltprinciples,” which can be briefly describedby the motto “the whole is greater thanthe sum of its parts” (Wertheimer, 1938).Almost a century of experimental inves-tigation on visual illusions has broad-ened ourcomprehensionofthe perceptualmechanisms that enableus to perceive fig-ures and forms instead of just a collectionof lines and curves. Such mechanisms arehighly adaptive, as they allow for a quickand stable picture of the environment,enablinganappropriatemotorresponseinevery context (Ikinand Turner, 1972).Given their high ecological value, thereislittlereasontobelievethatselective pres-surestodevelopavisualsystemthatisableto segregate objects from the backgroundhaveacted onlyonhominids. Indeed, overthe lastdecade,research hasdemonstratedthat both apes and monkeys are deceivedbyillusorypatterns. Forinstance, baboonsperceive the Zollner illusion (Benhar andSamuel, 1982), capuchin monkeys per-ceive the Muller-Lyer illusion (Suganumaet al., 2007), and rhesus monkeys per-ceive numerosity illusion (Beran, 2006;Beran and Parrish, 2013), thus showingthattheorganizationofvisualinformationissimilarbetweenhumanandnon-humanprimates.Despite the existence of a large num-ber of studies, it is still unclear to whatextent previous experience plays a role inhow the brain/mind interprets and recon-structs physical reality (Hebb, 1949; Bod,2002; Quinn and Bhatt, 2006). For prac-tical and ethical reasons, it is very difficulttomanipulateexperiences duringdevelop-mental periodsinhumanandnon-humanprimates. Furthermore, as primates lackindependence at birth, different proce-dures are used for studying newborns,juveniles, or adults, presenting one of themajordrawbackswhenstudyingthedevel-opment of visual perception in primates,i.e., the difficulty of devising experimen-tal paradigms applicable to different ages(Bisazza et al., 2010). The recent dis-covery that even relatively simple organ-isms like fish, whose divergence seeminglyoccurred approximately 450 million yearsago (Kumar and Hedges, 1998), also per-ceive visual illusions, as humans do, pavesthe way for the use of new animal modelsto investigate the relative contribution ofgenes and experience.Redtailsplitfin,forinstance,wasshownto be able to perceive illusory contours(Sovrano and Bisazza, 2009). Fish wererequired to discriminate between a squareor a triangle and the corresponding back-ground. After reaching a learning crite-rion, subjects performed test trials in thepresence of two stimuli: one consisted ofasubjectivefigure(triangleorsquare)induced by interruption or spatial phase-shift of diagonal lines; the other consistedof a series of diagonal lines only. In a sub-sequent test, two figures were presented:one in which pacmen were positionedin order to reproduce the Kanizsa tri-angle or square, and one in which thesame pacmen were scrambled in differentpositions so as to prevent an impressionof a subjective figure. Discrimination oforientation, rather than discrimination ofshape, was also tested in a second exper-iment. Subjects were initially trained todiscriminatebetween averticalandahori-zontal line with real physical contours. Intest trials vertically and horizontally ori-ented illusory lines were presented, cre-ated either through interruption or spatialphase-shift of diagonal lines (see

Magnetic island evolution under the action of electron cyclotron current drive

The magnetic island evolution under the action of an externally current generated by electron cyclotron (ECCD) wave beams is studied using a reduced resistive magnetohydrodynamics (RRMHD) plasma model. We found interesting and somewhat unexpected features of the actual nonlinear 2-D evolution of the magnetic perturbation depending on the injection time of the radio frequency control. In particular in the linear phase of the magnetic island growth we observe that the complete annihilation of the island width is followed by a spatial phase shift of the island, referred as "flip"instability. On the other hand, a current drive deposition in the Rutherford regime can be accompained by the occurrence of a Kelvin-Helmholtz type shear flow instability, responsible for the onset of a plasma turbulent behavior.