Local Phase Shifts Research Articles

Spatial carrier phase-shifting algorithm based on least-squares iteration

An advanced spatial carrier phase-shifting (SCPS) algorithm based on least-squares iteration is proposed to extract the phase distribution from a single spatial carrier interferogram. The proposed algorithm divides the spatial carrier interferogram into four phase-shifted interferograms. By compensating for the effects of the variations of phase shifts between pixels and the variations of background and contrast, the proposed algorithm determines the local phase shifts and phase distribution simultaneously and accurately. Numerical simulations show that the accuracy of the proposed algorithm is obviously improved by compensating for the effects of background and contrast variations. The peak to valley of the residual phase error remains less than 0.002 rad when the magnitude of spatial carrier is in the range from pi/5 to pi/2 and the direction of the spatial carrier is in the range from 25 degrees to 65 degrees. Numerical simulations and experiments demonstrate that the proposed algorithm exhibits higher precision than the existing SCPS algorithms. The proposed algorithm is sensitive to random noise, but the error can be reduced by N times if N measurements are taken and averaged.

Stimulus-induced Rotary Saturation (SIRS): A potential method for the detection of neuronal currents with MRI

Neuronal currents produce local transient and oscillatory magnetic fields that can be readily detected by MEG. Previous work attempting to detect these magnetic fields with MR focused on detecting local phase shifts and dephasing in T2 or T2⁎-weighted images. For temporally biphasic and multi-phasic local currents the sensitivity of these methods can be reduced through the cancellation of the accrued phase induced by positive and negative episodes of the neuronal current. The magnitude of the phase shift is also dependent on the distribution of the current within the voxel. Since spins on one side of a current source develop an opposite phase shift relative to those on the other side, there is likely to be significant cancellation within the voxel.We introduce a potential method for detecting neuronal currents though their resonant T1ρ saturation during a spin-lock preparation period. The method is insensitive to the temporal and spatial cancellation effects since it utilizes the multi-phasic nature of the neuronal currents and thus is not sensitive to the sign of the local field. To produce a T1ρ reduction, the Larmor frequency in the rotating frame, which is set by γB1lock (typically 20 Hz–5 kHz), must match the major frequency components of the stimulus-induced neuronal currents. We validate the method in MRI phantom studies. The rotary saturation spectra showed a sharp resonance when a current dipole within the phantom was driven at the Larmor frequency in the rotating frame. A 7 min block-design experiment was found to be sensitive to a current dipole strength of 56 nAm, an approximate magnetic field of 1 nT at 1.5 mm from the dipole. This dipole moment is similar to that seen using the phase shift method in a similar experimental setup by Konn et al. [Konn, D., Gowland, P., Bowtell, R., 2003. MRI detection of weak magnetic fields due to an extended current dipole in a conducting sphere: a model for direct detection of neuronal currents in the brain. Magn. Reson. Med. 50, 40–49], but is potentially less encumbered by temporal and spatial cancellation effects.

Iterative algorithm for phase extraction from interferograms with random and spatially nonuniform phase shifts

An advanced iterative algorithm is presented to extract phase distribution from randomly and spatially nonuniform phase-shifted interferograms. The proposed algorithm divides the interferograms into small blocks and retrieves local phase shifts accurately by iterations. Therefore, the phase distribution can be calculated with high precision by eliminating the effect of tilts occurring during phase shifting. Simulated results and experiments demonstrate that the proposed algorithm exhibits high precision and converges faster than previous algorithms even when the tilt errors are up to 27.6% of the normal phase step.

COMPARATIVE DEMODULATION RESULTS FOR SIX-PORT AND CONVENTIONAL 60 GHZ DIRECT CONVERSION RECEIVERS

Two 60 GHz homodyne receivers dedicated for high-speed short-range communication systems are presented. The receivers are based on six-port and conventional (anti-parallel diodes) mixers, respectively. Comparative bit error rate results, function of local oscillator power, phase, and frequency shift over the operating bandwidth, are presented and discussed.

Non-equilibrium coherence dynamics in one-dimensional Bose gases

Low-dimensional systems provide beautiful examples of many-body quantum physics. For one-dimensional (1D) systems, the Luttinger liquid approach provides insight into universal properties. Much is known of the equilibrium state, both in the weakly and strongly interacting regimes. However, it remains a challenge to probe the dynamics by which this equilibrium state is reached. Here we present a direct experimental study of the coherence dynamics in both isolated and coupled degenerate 1D Bose gases. Dynamic splitting is used to create two 1D systems in a phase coherent state. The time evolution of the coherence is revealed through local phase shifts of the subsequently observed interference patterns. Completely isolated 1D Bose gases are observed to exhibit universal sub-exponential coherence decay, in excellent agreement with recent predictions. For two coupled 1D Bose gases, the coherence factor is observed to approach a non-zero equilibrium value, as predicted by a Bogoliubov approach. This coupled-system decay to finite coherence is the matter wave equivalent of phase-locking two lasers by injection. The non-equilibrium dynamics of superfluids has an important role in a wide range of physical systems, such as superconductors, quantum Hall systems, superfluid helium and spin systems. Our experiments studying coherence dynamics show that 1D Bose gases are ideally suited for investigating this class of phenomena.

Entanglement condition via su(2) and su(1,1) algebra using Schrödinger-Robertson uncertainty relation

The Schrodinger-Robertson inequality generally provides a stronger bound on the product of uncertainties for two noncommuting observables than the Heisenberg uncertainty relation, and as such it can yield a stricter separability condition in conjunction with partial transposition. In this paper, using the Schrodinger-Robertson uncertainty relation, the separability condition previously derived from the su(2) and su(1,1) algebra is made stricter and refined to a form invariant with respect to local phase shifts. Furthermore, a linear optical scheme is proposed to test this invariant separability condition.

Manifestation of the Arctic Oscillation and El Niño-Southern Oscillation in the tropical stratosphere

Characteristics of the Arctic Oscillation and El Nino-Southern Oscillation effects manifested on interannual scales in the equatorial stratosphere are determined. Wavelet analysis of local phase shifts, coherence, and correlation is used to obtain correlation portraits of the largest factors of climate variability against the background of coherent variations in the equatorial stratospheric wind speed at the 50- and 15-hPa pressure levels. It is shown that the Arctic Oscillation and El Nino-Southern Oscillation signals may reach the tropical stratosphere. The signals are easily identified in a wide range of scales, including quasi-biennial, 3-to 5-year, and 10-to 11-year periods. The results obtained reflect a coherent pattern of the manifestation of these signals at the selected stratospheric levels. It is found that the El Nino-Southern Oscillation effect at periods close to 10–11 years reaches the stratospheric level rather rapidly, in the same or next month, while the effects of the Arctic Oscillation index are delayed by nine months. The estimates obtained show that a phase shift of almost 180° in the Arctic Oscillation index relative to the equatorial stratospheric wind occurred in almost all of the range of interannual periods in 1978 and 1992. For the El Nino-Southern Oscillation, an increase in local correlations on a scale of 3-to 5-year variations was observed in 1980–1990, a 180° phase shift occurred in 1992, and the correlation with stratospheric wind increased in 1992–2004. The estimates obtained are indicative of a change in the atmospheric circulation pattern that took place in the Northern Hemisphere in 1978–1991.

Potential and Limitations of Electron Holography in Silicon Research

We report on electron holography as a promising candidate for diagnostics in silicon technology and research. Electron holography determines the local phase shift of the electron wave passing through a sample. The phase is proportional to the 2D projected electrostatic potential in the sample and thus reveals p-n junctions and, indirectly, doping. We demonstrate detection of submonolayer boron layers in Si and SiGe, measurement of Ge concentration in SiGe and qualitative 2D oxygen mapping in SiO2/Si structures with 0.5 nm resolution, and comparison of doping in two bipolar transistors with different base implant. Resolution and noise limits are discussed.

Local phase shift from Acropora-dominant to Condylactis-dominant community in the Tiao-Shi Reef, Kenting National Park, southern Taiwan

Local phase shift from Acropora-dominant to Condylactis-dominant community in the Tiao-Shi Reef, Kenting National Park, southern Taiwan

Unitary-gate synthesis for continuous-variable systems

We investigate the synthesis of continuous-variable two-mode unitary gates in the setting where two modes A and B are coupled by a fixed quadratic Hamiltonian $H.$ The gate synthesis consists of a sequence of evolutions governed by Hamiltonian $H,$ which are interspaced by local phase shifts applied to A and $B.$ We concentrate on protocols that require the minimum number of necessary steps and we show how to implement the beam splitter and the two-mode squeezer in just three steps. Particular attention is paid to Hamiltonian ${x}_{A}{p}_{B}$ that describes the effective off-resonant interaction of light with the collective atomic spin.

Leading Lyapunov Vectors of a Turbulent Baroclinic Jet in a Quasigeostrophic Model

Leading Lyapunov exponents and vectors are calculated for a turbulent baroclinic jet in a quasigeostrophic model with O(105) degrees of freedom. The leading exponent is close to 0.4 day 21, and the unstable subspace has dimension between 30 and 40. The leading Lyapunov vectors exhibit a strong correlation of their potential vorticity (PV) with the PV gradients of the unperturbed flow. These perturbations do not, however, appear to be instabilities of smaller scale on the turbulent flow. Instead, they share the scales of the flow itself (at least if measured along PV contours) and often simply represent local phase shifts or displacements of existing features in the flow. Singular vectors constrained to the subspace of Lyapunov vectors are also calculated. Maximum amplification factors over 2 days are, on average, about 6, 7.5, and 9 (compared to the factor of 2 implied by the leading exponent) for subspaces of the leading 20, 35, and 60 Lyapunov vectors, respectively.

Study of C–I–C CDW phase transition in TTF–TCNQ with STM

TTF–TCNQ is a one-dimensional charge transfer compound. Charge density wave (CDW) transition occurs at 54 K in TTF–TCNQ, and CDW presents three phases: high temperature commensurate phase ( T>49 K; 2 a ×3.39 b ); inter-mediated incommensurate phase ( T=38–49 K; μ a × 3.39 b ) and low temperature commensurate phase ( T<38 K; 4 a ×3.39 b ). In this report, we present our experimental result on cleaved (0 0 1) surfaces of TTF–TCNQ with UHV–LT–STM (Omicron LTSTM). For a broad temperature range (33–100 K), molecular resolution of TTF–TCNQ has been obtained. Below 54 K an additional two-dimensional superstructure of CDW appears in our images. The ordering of CDW modulation both along a and b direction are first revealed by our STM measurement. Our result shows that, on (0 0 1) surface of TTF–TCNQ, C–I–C CDW phase transition persists in nanometer scale and C–I–C transition is homogeneous. The determination of local CDW phase shift will be presented in this report too. At high temperature (60–280 K), we observed a v-shape pseudo-gap. The pseudo-gap and Peierls-gap co-exist at low temperature.

Differential x-ray phase contrast imaging using a shearing interferometer

An x-ray interferometer has been developed that uses two transmission phase gratings to analyze wave front distortions in the hard x-ray range. The interferometer is insensitive to mechanical drift and vibrations, and it is tunable over a wide range of photon energies. This setup was used for differential phase contrast imaging of low-absorbing test objects. We obtained micrographs with moiré fringes of good visibility, which revealed the local phase shift gradient caused by the objects. A comparison with numerically simulated images indicates that quantitative analysis of unknown phase objects is possible.

Tilt-compensating algorithm for phase-shift interferometry

A self-calibrating algorithm for phase-shift interferometry is described that is able to cancel the effect of accidental relative tilts that may occur during phase stepping. The algorithm is able to retrieve both the phase steps and the tilts that accompany them. Only three phase-shifted interferograms are needed, and no other information about the intentional phase shifts or possible tilts has to be supplied. This purpose is achieved by division of the interferogram space into blocks on which a previously reported self-calibrating algorithm is applied and the actual values of the local phase shifts are calculated. The information thus obtained is used for extracting the global shift and tilt values. Further improvement in the results is achieved by means of a fitting routine.

GHZ polarization dynamics in ferroelectric thin films

We present results from experiments which measure the local dielectric response of ferroelectric thin films driven by microwave-frequency electric fields. The repetition rate of a mode-locked Ti:Sapphire laser is used to generate a microwave drive signal that is phase-locked to an optical probe pulse and applied to the ferroelectric thin film. The induced polarization change in the ferroelectric film is measured stroboscopically via the electro-optic effect. Polarization images are acquired by scanning the laser beam across the sample in a confocal geometry. Time resolution is achieved by changing the delay between the electrical pump and the optical probe. Initial results show large local phase shifts in the ferroelectric response of closely separated regions of a Ba0.5Sr0.5TiO3 thin film. This new experimental technique may help to understand the physical mechanisms of dielectric loss in these materials.

Relation between Local Composition, Chemical Environment and Phase Shift Behavior in Cr-Based Oxycarbonitride Thin Films

AbstractThe latest deep ultra-violet (DUV) photomask technology requires macroscopic properties such as optical transmission, reflectance, and chemical reactivity to be precisely controlled. Therefore, a fundamental understanding of the relationship between atomic bonding and nanometer scale property variation is required. Thin films of Cr-OC-N are compositionally graded to produce specific attenuation and phase shift of optical radiation. A combination of techniques was used to relate the local atomic bonding to macroscopic properties. Sputtered neutral mass spectroscopy was used to resolve local composition, and variable angle spectroscopic ellipsometry was used to determine local optical properties (on nm scale) that are then related to local composition. Core level shifts in X-ray photoelectron spectroscopy characterize changes in the Cr environment associated with changes in composition. A model is suggested in which bonding at the atomic level is controlled within different 10-100 nm sized regions which can be combined to produce arbitrary optical properties.

New optical probe of GHz polarization dynamics in ferroelectric thin films

We describe a method for measuring the response of ferroelectric thin films to microwave-frequency electric fields. A mode-locked Ti:sapphire laser is used to generate a microwave drive signal that is phase locked to an optical probe pulse. The induced polarization change in the ferroelectric film is measured stroboscopically via the electro-optic effect. Images are acquired by scanning the laser beam across the sample in a confocal geometry. Time resolution is achieved by changing the delay between the electrical pump and the optical probe. Initial results show large local phase shifts in the ferroelectric response of closely separated (1 μm) regions of a Ba0.5Sr0.5TiO3 thin film. This new experimental technique may help to understand the physical mechanisms of dielectric loss in these materials.

Stereoscopic ranging by matching image modulations

We apply an AM-FM surface albedo model to analyze the projection of surface patterns viewed through a binocular camera system. This is used to support the use of modulation-based stereo matching where local image phase is used to compute stereo disparities. The local image phase is an advantageous feature for image matching, since the problem of computing disparities reduces to identifying local phase shifts between the stereoscopic image data. Local phase shifts, however, are problematic at high frequencies due to phase wrapping when disparities exceed +/-pi. We meld powerful multichannel Gabor image demodulation techniques for multiscale (coarse-to-fine) computation of local image phase with a disparity channel model for depth computation. The resulting framework unifies phase-based matching approaches with AM-FM surface/image models. We demonstrate the concepts in a stereo algorithm that generates a dense, accurate disparity map without the problems associated with phase wrapping.

Phase calibration of arrays at optical and millimeter wavelengths

Aperture synthesis experiments have been performed at optical and millimeter wavelengths with an array designed for self-calibration by means of redundant spacings calibration. This calibration technique, which works at all electromagnetic wavelengths, allows the removal of phase errors caused by antenna positional errors, local oscillator phase shifts, and medium-induced transmission phase errors in a single snapshot without requiring that a model of the source be built. Results are presented that demonstrate the removal of phase errors from optical and passive millimeter-wave images by use of redundant spacings calibration with one- and two-point sources. It is shown that optical simulations provide a valuable method for determining the performance of arrays at millimeter wavelengths.

Local phase and renormalized frequency in inhomogeneous chemioscillations

Inhomogeneous evolution of a chemically reacting system capable of a homogeneous oscillation is analyzed in terms of a nonsecular perturbation method. This ’’phase diffusion’’ theory takes account of the local phase shifts and frequency renormalization that occurs due to the interaction of reaction and diffusion. The theory is used to show that oscillator like plane waves are stable to small perturbations. Boundary value problems including those for a finite volume impermeable vessel, a ring shaped vessel (periodic boundary condition) and catalytic walls and membranes are shown to lead to stable oscillatory states some of which are inhomogeneous for all times. The structure of the theory allows for clear qualitative interpretations. Several experiments are suggested for the purpose of verification of the theory and the phenomena predicted.