Spatial Phase Shift Research Articles

Precise localization of a two-level atom by the superposition of two standing-wave fields

A scheme is proposed to achieve one-dimensional localization of a two-level atom moving through a standing wave regime constructed by two classical standing-wave fields. Precise position information of the atom can be obtained by measuring resonant absorption of a weak coherent field probing the transition strongly driven by the resonant standing-wave fields. Behavior of atomic localization has been shown for symmetric superposition of the standing-wave fields arranged in two distinct configurations: (i) parallel and (ii) cross. In the cross-configuration, we have shown 100% detection probability of the atom within one wavelength range with the evolution of single localization peak in the sub-half-wavelength range due to the variation of spatial phase shift of one of the standing-wave fields. In case of nonresonant coupling of the atom with the standing-wave fields, a single localization peak in the sub-half-wavelength range can be obtained by changing the relative detuning of frequency of the probe field. For achieving high resolution single-peak localization of a two-level atom, the present scheme would be of great interest from the experimental point of view.

Simultaneous measurement of deformation and the first derivative with spatial phase-shift digital shearography

This paper presents a spatial phase-shift digital shearography system based on a modified Michelson Interferometer, which is capable of measuring out-of-plane deformation and its first derivative simultaneously. A reference beam is introduced into the Michelson Interferometer using an optical fiber. Two sheared images from the Michelson Interferometer are combined with the reference beam to generate two holograms and one shearogram. The Fourier Transform method is utilized to calculate the phase difference. To separate the spectrum in the Fourier Domain, the reference beam is tilted a small angle to create a spatial phase shift. An out-of-plane deformation and its first derivative can then be determined simultaneously from a single speckle interferogram by properly selecting filters for the spectrum image. The theory and the experimental results are presented.

First observation of a transverse vertical oscillation during the formation of a hot post-flare loop

Aims. We report and analyse the first observation of a transverse oscillation in a hot coronal loop with the Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory (SDO), following a linked coronal-flare mass-ejection event on the 3 November 2010. The oscillating coronal loop is observed off the east solar limb and exclusively in the 131 A and 94 A bandpasses, indicating a loop plasma of temperature in the range of 9-11 MK. Furthermore, the loop is not observed to cool into the other AIA channels, but just disappears from all bandpasses at the end of the oscillation. Methods. A time series analysis of the loop oscillation is conducted by taking several cuts at different positions along the loop, estimating the transverse displacements over time for two strands in the loop and fitting those with a damped cosine curve. Intensity time variations, both along the loop and for a series of cut cross-sections, are investigated. Using a three-dimensional loop geometry obtained from a comparison of STEREO-B/EUVI and AIA images, we model different modes of transverse oscillations in the uniformly filled loop. Results. Our time series analysis reveals a period of 302 ± 14 s (291 ± 9 s) and a damping time of 306 ± 43 s (487 ± 125 s) for the first (second) loop strand. A spatial phase shift along the loop of approximately 180° suggests that we observe a higher order harmonic. Intensity oscillations are consistent with an interpretation in terms of a vertically polarised mode. Our forward modelling suggests that the loop oscillates as either a second or third order harmonic of this mode. Conclusions. This is the first observation of a transverse loop oscillation observed exclusively in the hot coronal lines. The loop oscillation is vertically polarised and is dominated by a higher order harmonic mode. We conclude that the excitation mechanism of this 5 min period oscillation is directly connected with the reconnection processes that form the post flare loop, which differs from the blast wave excitation mechanism often proposed as the cause of cooler transverse loop oscillations. © 2012 ESO.

Imaging the Gouy phase shift in photonic jets with a wavefront sensor

A wavefront sensor is used as a direct observation tool to image the Gouy phase shift in photonic nanojets created by micrometer-sized dielectric spheres. The amplitude and phase distributions of light are found in good agreement with a rigorous electromagnetic computation. Interestingly the observed phase shift when travelling through the photonic jet is a combination of the awaited π Gouy shift and a phase shift induced by the bead refraction. Such direct spatial phase shift observation using wavefront sensors would find applications in microscopy, diffractive optics, optical trapping, and point spread function engineering.

Miniaturization of the Quasi-Traveling Wave Ultrasonic Linear Motor Using a Ring Type Rectangular Vibrator

Ultrasonic linear motor, Piezoelectricity, Rectangular vibrator, Traveling wave Abstract. With the aim of realizing quasi-traveling wave drive in ultrasonic linear micro motors, a novel quasi-traveling wave ultrasonic linear motor using a ring type rectangular vibrator with the sizes of 39mm×6mm×12.7mm is proposed. The quasi-traveling wave is excited and propagates along the ring type rectangular vibrator depending on the superposition of two orthogonal flexural-vibration modes with a spatial phase shift of 90 degrees. 7 piezoelectric ceramic elements are used to excite two working modes of the vibrator. The vibrator structure was designed and eigenfrequency degeneration was realized by Finite Element Analysis (FEA) method. The modal test shows that the design scheme was tenable. The excitation and propagation of quasi-traveling wave were proved by laser vibration test. The trial motor gave a maximum driving velocity of 162.5mm/s and a maximum load of 8.5N, while the excitation frequency was 66 KHz and voltage was 160Vpp.

非局域椭圆厄米高斯空间光孤子与相移

非局域椭圆厄米高斯空间光孤子与相移

Zonal flow in a tokamak pedestal

Neoclassical shielding is the dominant mechanism reducing the collisionless zonal flow in a tokamak. Previously, this phenomenon was analyzed in the case of an essentially homogeneous equilibrium since the wavelength of the zonal flow perturbation was assumed to be much less than the scale length of background plasma parameters. This assumption is not appropriate in a tokamak pedestal. Therefore the pedestal neoclassical polarization and the zonal flow residual differ from the conventional results. This change is due to the strong electric field intrinsic to a subsonic pedestal that modifies neoclassical ion orbits so that their response to a zonal flow perturbation is qualitatively different from that in the core. In addition to orbit squeezing, we find a spatial phase shift between the initial and final zonal flow potentials—an effect absent in previous works. Moreover, we demonstrate that because of orbit modification neoclassical phenomena disappear in the large electric field limit making the residual close to one.

UV-photorefractive effect in LiNbO 3:Ce:Mn single crystal

In this paper, the ultraviolet (UV) photorefraction effect of lithium niobate doubly doped with Ce and Mn has been investigated. It is found the diffraction efficiency shows oscillating behavior under UV-light-recording. A model based on electrons and holes as the dominant carriers is proposed to study the oscillatory behavior of the diffraction efficiency. On the basis of the material equations and the coupled-wave equations, we found that the oscillatory behavior is due to the oscillation of the relative spatial phase shift Φ. And the electron–hole competition may cause the oscillation of the relative spatial phase shift. This oscillation behavior is different from that caused by very high-strength space electric field. UV recording can suppress the beam-fanning perfectly, and the most important is the high sensitivity.

Perception of Subjective Contours in Fish

The ability of fish to perceive subjective (or illusory) contours, ie contours that lack a physical counterpart in terms of luminance contrast gradients, was investigated. In the first experiment, redtail splitfins (Xenotoca eiseni), family Goodeidae, were trained to discriminate between a geometric figure (a triangle or a square) on various backgrounds and a background without any figure. Thereafter, the fish performed test trials in which illusory squares or triangles were obtained by (i) interruptions of a background of diagonal lines, (ii) phase-shifting of a background of diagonal lines, and (iii) pacmen spatially arranged to induce perception of Kanizsa subjective surfaces. In all three conditions, fish seemed to generalise their responses to stimuli perceived as subjective contours by humans. Fish chose, correctly, squares or triangles made of interrupted or phase-shifted diagonal lines from uniform backgrounds of diagonal lines, as well as illusory square or triangle Kanizsa figures from figures in which the inducing pacmen were scrambled. In the second experiment, fish were trained to discriminate between a vertical and a horizontal bar with luminance contrast gradients, and then tested with vertically and horizontally oriented illusory bars, created either through interruption or spatial phase-shift of inducing diagonal lines. Fish appeared to be able to generalise the orientation discrimination to illusory contours. These results demonstrate that redtail splitfins are capable of perceiving illusory contours.

Alignment measurement method for imprint lithography using moiré fringe pattern

A simple and high-accuracy alignment measurement method based on a moire fringe pattern is proposed. It involves relative rotation positioning and relative linear displacement measurement. Taking full advantage of the magnification effect of moire fringe in angular and linear displacement, the relative rotation between the template and the wafer is determined first by measuring the inclination of the moire fringe, and then the relative linear displacement between them is acquired by evaluating the spatial phase shift of two matched moire fringes. The frequency components in the orthogonal directions of the fringe image obtained by a fast Fourier transform (FFT) and zooming process are used to measure the inclination of the moire fringe. By selecting different orthogonal directions, a moire fringe with any inclination can be measured accurately. When gratings are adjusted to parallel, a frequency-domain analysis is also used to extract the spatial phase of fringes at a given frequency. According to the relationship between spatial phase and linear displacement, the misalignment is detected. In experiments, the repeatability for the misalignment measurement has reached 4.8 nm (3).

Spatial shift of spatially modulated light projected on turbid media

This work extends modulated imaging, a recently developed technique based on the projection of structured light on a turbid medium that is able to measure optical properties of the high-scattering medium and perform tomography. We observe that structured light obliquely projected on a turbid medium undergoes a spatial shift during propagation. We propose a method to measure the spatial phase shift of a sinusoidal fringe pattern projected in a turbid medium, and we present a model derived from the diffusion approximation to describe the light propagation. Experimental validation by measurements performed on liquid phantoms is presented.

A comparison of temporal, spatial and parallel phase shifting algorithms for digital image plane holography

This paper investigates the performance of several phase shifting (PS) techniques when using digital image plane holography (DIPH) as a fluid velocimetry technique. The main focus is on increasing the recording system aperture in order to overcome the limitation on the little light available in fluid applications. Some experiments with small rotations of a fluid-like solid object have been used to test the ability of PS-DIPH to faithfully reconstruct the object complex amplitude. Holograms for several apertures and for different defocusing distances have been recorded using spatial phase shifting (SPS) or temporal phase shifting (TPS) techniques. The parallel phase shifted holograms (HPPS) have been generated from the TPS holograms (HTPS). The data obtained from TPS-DIPH have been taken as the true object complex amplitude, which is used to benchmark that recovered using the other techniques. The findings of this work show that SPS and PPS are very similar indeed, and suggest that both can work for bigger apertures yet retain phase information.

Digital speckle pattern interferometry using spatial phase shifting: influence of intensity and phase gradients

Spatial phase shifting technique in digital speckle pattern interferometry (DSPI) and digital shearography (DS) provides the phase information due to the object displacement from two images, one stored before and other after loading. The technique needs a carrier fringe system. The double aperture mask in front of the imaging system is one of the methods for introducing the spatial carrier frequency for phase evaluation. The size of the apertures and their separation are important criteria to obtain appropriate phase shift/column within the desired size of the speckle for phase retrieval. The assumptions of constant intensity and phase on adjacent pixels of the camera while calculating phase in spatial phase shifting (SPS) are not met as the speckled object wave contains intensity and phase gradients, resulting in distortions in the calculated phase profiles. In this paper we discuss a strategy to overcome these problems. The contrast of the correlation fringe obtained using this approach is much improved. It also eliminates the distortion in the unwrapped phase map like wave ripples. The experimental results on an edge clamped circular plate loaded at the center are presented.

Modified temporal-phase-unwrapping method for measuring in real time the out-of-plane displacements of the tympanic membrane of Mongolian Gerbil

A technique for measuring in real-time continuous out-of-plane displacements of delicate objects is proposed, and demonstrated on the tympanic membrane of Mongolian Gerbil. The technique is based on the combination of two methods: the spatial phase shifting (SPS) and the modified temporal phase unwrapping (TPU). The combination allows to obtain, in several steps, the phase values of the points that undergo out-of-plane displacement as the object is deformed. The technique reduces the frame acquisition time of the standard TPU used in moiré interferometry by a factor of 4, which is important to diminish post-mortem artifacts during in-vitro experiments and to reduce motion artifacts in in-vivo tests. The proposed technique is robust against problems associated with the temporal phase-shifting method, such as nonlinear phase shift and noise. The advantages and disadvantages are discussed.

Modeling the effect of nonuniform sediment on the dynamics of offshore tidal sandbanks

Tidal sandbanks are large‐scale bed features present in many shallow shelf seas. Here we investigate the effect of nonuniform sediment on their dynamics, with a particular aim to explain observed surficial grain size variations over tidal sandbanks from a process‐based modeling perspective. To this end, we use a linear stability analysis that describes the positive feedback mechanism between hydrodynamics, sediment, and the seabed responsible for sandbank formation on a horizontal shelf. In this model the sediment transport and bed evolution modules are extended by introducing an active layer and a bimodal sediment mixture. We include a dynamic hiding/exposure description of sediment transport, enhancing the transport of coarse grains and inhibiting the transport of finer grains. The model results show that for symmetrical tidal conditions, coarse grains tend to accumulate at the bank crests. Moreover, the growth rates of the perturbations increase compared to the case of uniform sediment, while the preferred wavelength and bank orientation remain unchanged. For asymmetrical tidal conditions we find a spatial phase shift between topography and the mean grain size fraction, indicating an accumulation of coarse grains on the lee side of the bank. The model results qualitatively agree with observations from banks on the Belgian continental shelf.

Wavefront reconstruction by spatial-phase-shift imaging interferometry

Common-path imaging interferometers offer some advantages over other interferometers, such as insensitivity to vibrations and the ability to be attached to any optical system to analyze an imaged wavefront. We introduce the spatial-phase-shift imaging interferometry technique for surface measurements and wavefront analysis in which different parts of the wavefront undergo certain manipulations in a certain plane along the optical axis. These manipulations replace the reference-beam phase shifting of existing interferometry methods. We present the mathematical algorithm for reconstructing the wavefront from the interference patterns and detail the optical considerations for implementing the optical system. We implemented the spatial phase shift into a working system and used it to measure a variety of objects. Measurement results and comparison with other measurement methods indicate that this approach improves measurement accuracy with respect to existing quantitative phase-measurement methods.

Use of spatial phase shifting technique in digital speckle pattern interferometry (DSPI) and digital shearography (DS)

Digital speckle pattern interferometry (DSPI) and digital shearography (DS) are well known optical tools for qualitative as well as quantitative measurements of displacement components and its derivatives of engineering structures subjected either static or dynamic load. Spatial phase shifting (SPS) technique is useful for extracting quantitative displacement data from the system with only two frames. Optical configurations for DSPI and DS with a double aperture mask in front of the imaging lens for spatial phase shifting are proposed in this paper for the measurement of out-of-plane displacement and its first order derivative (slope) respectively. An error compensating four-phase step algorithm is used for quantitative fringe analysis.

Study of oscillatory behavior of recording process arising from electron–hole competition in strongly oxidized LiNbO 3:Ce:Cu

We have investigated ultraviolet (UV) photorefractive effect of lithium niobate doubly doped with Ce and Cu. It is found the diffraction efficiency shows oscillating behavior under UV-light-recording. A model in which electrons and holes can be excited from impurity centers in the UV region is proposed to study the oscillatory behavior of the diffraction efficiency. On the basis of the material equations and the coupled-wave equations, we found that the oscillatory behavior is due to the oscillation of the relative spatial phase shift Φ. And the electron–hole competition may cause the oscillation of the relative spatial phase shift. A switch point from electron grating to hole grating is chosen to realize nonvolatile readout by a red light with high sensitivity (0.4 cm/J).

Time series of high resolution photospheric spectra in a quiet region of the Sun

From the inversion of a time series of high resolution slit spectrograms obtained from the quiet sun, the spatial and temporal distribution of the thermodynamical quantities and the vertical flow velocity is derived as a function of logarithmic optical depth and geometrical height. Spatial coherence and phase shift analyzes between temperature and vertical velocity depict the height variation of these physical quantities for structures of different size. An average granular cell model is presented, showing the granule-intergranular lane stratification of temperature, vertical velocity, gas pressure and density as a function of logarithmic optical depth and geometrical height. Studies of a specific small and a specific large granular cell complement these results. A strong decay of the temperature fluctuations with increasing height together with a less efficient penetration of smaller cells is revealed. The T -T coherence at all granular scales is broken already at log tau =-1 or z~170 km. At the layers beyond, an inversion of the temperature contrast is revealed. Vertical velocities are in phase throughout the photosphere and penetrate into the highest layers under study.

Vortex dynamics of fiber-laden free shear flows

The objective of this study is to investigate the effects of high aspect-ratio fiber additives on the temporal hydrodynamic instabilities of free shear flows. Nonlinear numerical simulations are conducted on a two-dimensional semi-dilute fiber-laden flow model coupled with a three-dimensional orientation distribution. An averaged-based approach is adopted to describe the orientation of the fiber using orientation tensors defined as moments of the orientation distribution function. The resulting system of differential equations is solved using a combination of a pseudo-spectral method based on the Hartley transform and a finite difference technique. The results of the study show that higher volume fraction and/or larger fiber aspect-ratio weaken the roll-up of the flow. More importantly, it is found that weak hydrodynamic interactions lead to fundamental structural changes in the flow and result in either a spatial phase shift of the vorticity or the growth of higher harmonics that compete with the fundamental and prevent the completion of the roll-up. A detailed analysis of the distribution of the fiber stresses and orientation allowed us to explain the physical mechanisms responsible for the observed changes in the structures of the flow. These mechanisms are compared to those developing in a polymer flow in order to understand the similarities and differences in the effects of these two additives on the mechanisms of transition to turbulence in free shear flows.