Showing papers on "Phase (waves) published in 1996"

Type i membranes, phase resetting curves, and synchrony

Abstract: Type I membrane oscillators such as the Connor model (Connor et al. 1977) and the Morris-Lecar model (Morris and Lecar 1981) admit very low frequency oscillations near the critical applied current. Hansel et al. (1995) have numerically shown that synchrony is difficult to achieve with these models and that the phase resetting curve is strictly positive. We use singular perturbation methods and averaging to show that this is a general property of Type I membrane models. We show in a limited sense that so called Type II resetting occurs with models that obtain rhythmicity via a Hopf bifurcation. We also show the differences between synapses that act rapidly and those that act slowly and derive a canonical form for the phase interactions.

Phase objects in synchrotron radiation hard x-ray imaging

Abstract: Phase objects are readily imaged through Fresnel diffraction in the hard x-ray beams of third-generation synchrotron radiation sources such as the ESRF, due essentially to the very small angular size of the source. Phase objects can lead to spurious contrast in x-ray diffraction images (topographs) of crystals. It is shown that this contrast can be eliminated through random phase plates, which provide an effective way of tailoring the angular size of the source. The possibilities of this very simple technique for imaging phase objects in the hard x-ray range are explored experimentally and discussed. They appear very promising, as shown in particular by the example of a piece of human vertebra, and could be extended to phase tomography.

Optical phased array technology

Abstract: Optical phased arrays represent an enabling new technology that makes possible simple affordable, lightweight, optical sensors offering very precise stabilization, random-access pointing programmable multiple simultaneous beams, a dynamic focus/defocus capability, and moderate to excellent optical power handling capability. These new arrays steer or otherwise operate on an already formed beam. A phase profile is imposed on an optical beam as it is either transmitted through or reflected from the phase shifter array. The imposed phase profile steers, focuses, fans out, or corrects phase aberrations on the beam. The array of optical phase shifters is realized through lithographic patterning of an electrical addressing network on the superstrate of a liquid crystal waveplate. Refractive index changes sufficiently large to realize full-wave differential phase shifts can be effected using low (<10 V) voltages applied to the liquid crystal phase plate electrodes. High efficiency large-angle steering with phased arrays requires phase shifter spacing on the order of a wavelength or less; consequently addressing issues make 1-D optical arrays much more practical than 2-D arrays. Orthogonal oriented 1-D phased arrays are used to deflect a beam in both dimensions. Optical phased arrays with apertures on the order of 4 cm by 4 cm have been fabricated for steering green, red, 1.06 /spl mu/m, and 10.6 /spl mu/m radiation. System concepts that include a passive acquisition sensor as well as a laser radar are presented.

Design of algorithms for phase measurements by the use of phase stepping

Abstract: If the best phase measurements are to be achieved, phase-stepping methods need algorithms that are 112 insensitive to the harmonic content of the sampled waveform and 122 insensitive to phase-shift miscalibration. A method is proposed that permits the derivation of algorithms that satisfy both requirements, up to any arbitrary order. It is based on a one-to-one correspondence between an algorithm and a polynomial. Simple rules are given to permit the generation of the polynomial that corresponds to the algorithm having the prescribed properties. These rules deal with the location and multiplicity of the roots of the polynomial. As a consequence, it can be calculated from the expansion of the products of monomials involving the roots. Novel algorithms are proposed, e.g., a six-sample one to eliminate the effects of the second harmonic and a 10-sample one to eliminate the effects of harmonics up to the fourth order. Finally, the general form of a self-calibrating algorithm that is insensitive to harmonics up to an arbitrary order is given.

The spatial variation of the refractive index in biological cells

Abstract: With a phase microscope the phase shift of cells from type L 929 fibroblast and mitochondria from liver cells was measured. Compared to the total phase shift caused by the cell relative to vacuum (approximately 1400 nm) the single phase shift of the mitochondria (approximately 180 nm) is small. Only the nucleus and the membrane of the cell give a visibly different phase shift relative to the mean value of the cell. The Fraunhofer diffraction of the measured phase object is calculated. With a simplified scattering theory, i.e. Rayleigh - Gans scattering, different phase objects are investigated and their differential cross section is discussed.

Route to phase control of ultrashort light pulses

Abstract: A feasibility study of controlling the carrier phase in ultrashort light-wave packets emitted by a sub-10-fs laser is reported. An experimental apparatus capable of exploring the phase sensitivity of nonlinear-optical interactions is presented.

Transcutaneous measurement and spectrum analysis of heart wall vibrations

Abstract: For the noninvasive diagnosis of heart disease based on the acoustic and elastic characteristics of the heart muscle, it is necessary to transcutaneously measure small vibration signals, including components with an amplitude of less than 100 /spl mu/m, from various parts of the heart wall continuously for periods of more than several heartbeats in a wide frequency range up to 1 kHz. Such measurement, however, has not been realized by any ultrasonic diagnostic methods or systems to date. By introducing the constraint least-square approach, this paper proposes a new method for accurately tracking the movement of the heart wall based on both the phase and magnitude of the demodulated signal to determine the instantaneous position of the object so that the vibration velocity of the moving object can be accurately estimated. By this method, small vibrations of the heart wall with small amplitudes less than 100 /spl mu/m on the motion resulting from a heartbeat with large amplitude of 10 mm can be successfully detected with sufficient reproducibility in the frequency range up to several hundred Hertz continuously for periods of about 10 heartbeats. The resultant small vibration is analyzed not only in the time domain, but also in the frequency domain. As confirmed by the preliminary experiments herein reported, the new method offers potential for research in acoustical diagnosis of heart disease.

X-ray holography with atomic resolution

Abstract: DIFFRACTION methods for crystallographic structure determination suffer from the so-called 'phase problem'; a diffraction pattern provides intensity but not phase information for the scattered beams, and therefore cannot be uniquely inverted to obtain the crystal structure of a sample. Holographic methods1, on the other hand, offer a means of extracting both intensity and phase information. To be useful for crystallographic applications, holography must be implemented with radiation of sufficiently small wavelength to resolve atomic-scale features2. One method, electron-emission holography3–9, uses electron waves and is a powerful tool for studying surface structure; but it cannot image the internal structure of solids because of complications arising from the highly anisotropic nature of electron scattering processes. A proposed alternative method uses X-rays2,10–13, which scatter more isotropically than electrons. Here we demonstrate the efficacy of atomic-scale X-ray holography by obtaining direct images of the three-dimensional arrangement of strontium atoms in the cubic perovskite SrTiO3. With more intense synchrotron sources for illumination, and with the development of improved X-ray detectors, X-ray holography should become a powerful general technique for unambiguous structure determination in condensed matter systems.

An experiment to observe the intensity and phase structure of Laguerre–Gaussian laser modes

Abstract: We outline an easily reproduced experiment that allows the student to investigate the intensity and phase structure of transverse laser modes. In addition to discussing the usual Hermite–Gaussian laser modes we detail how Laguerre–Gaussian laser modes can be obtained by the direct conversion of the Hermite–Gaussian output. A Mach–Zehnder interferometer allows the phase structure of the Laguerre–Gaussian modes to be compared with the phase structure of a plane wave with the same frequency. The resulting interference patterns clearly illustrate the azimuthal phase dependence of the Laguerre–Gaussian modes, which is the origin of the orbital angular momentum associated with each of them.

Random phase encoding for optical security

Abstract: A new optical encoding method for security applications is proposed. The encoded image (encrypted into the security products) is merely a random phase image statistically and randomly generated by a random number generator using a computer, which contains no information from the reference pattern (stored for verification) or the frequency plane filter (a phase‐only function for decoding). The phase function in the frequency plane is obtained using a modified phase retrieval algorithm. The proposed method uses two phase‐only functions (images) at both the input and frequency planes of the optical processor leading to maximum optical efficiency. Computer simulation shows that the proposed method is robust for optical security applications.

Method and apparatus for transmit beamformer

Abstract: A digital transmit beamformer system with multiple beam transmit capability has a plurality of multi-channel transmitters, each channel with a source of sampled, complex-valued initial waveform information representative of the ultimate desired waveform to be applied to one or more corresponding transducer elements for each beam. Each multi-channel transmitter applies beamformation delays and apodization to each channel's respective initial waveform information digitally, digitally modulates the information by a carrier frequency, and interpolates the information to the DAC sample rate for conversion to an analog signal and application to the associated transducer element(s). The beamformer transmitters can be programmed per channel and per beam with carrier frequency, delay, apodization and calibration values. For pulsed wave operation, pulse waveform parameters can be specified to the beamformer transmitters on a per firing basis, without degrading the scan frame rate to non-useful diagnostic levels. Waveform parameters can be specified to the transmitters by an external central control system which is responsible for higher level flexibility, such as scan formats, focusing depths and fields of view. The transmit pulse delay specified per-channel to each transmitter is applied in at least two components: a focusing time delay component and a focusing phase component. The carrier frequency can be specified for each transmit beam, to any desired frequency within a substantially continuous predefined range of frequencies, and a beam-interleaved signal processing path permits operation in any of several predefined processing modes, which define different parameter sets in a trade-off among (1) the number of beams produced; (2) per-beam initial waveform sample interval; and (3) transmit frequency.

Full-range, continuous, complex modulation by the use of two coupled-mode liquid-crystal televisions

Abstract: Switchable, continuous, complex-amplitude modulation is demonstrated with two cascaded, twisted nematic liquid-crystal televisions (LCTV's), both operating in phase- and amplitude-coupled modulation modes The condition for full-range complex modulation is that one of the LCTV's must provide a 2π-range phase modulation A look-up table encoding method is proposed that permits the compensation of phase-amplitude coupling and nonlinearity in the two individual LCTV modulations Experimental techniques for determining the LCTV-device parameters, for maximizing the phase-mostly modulation range and the amplitude-mostly modulation contrast, and for testing the complex-amplitude modulation are developed Optical complex-amplitude Fresnel holograms are shown

Differential ranging for a frequency-hopped remote position determination system

Abstract: A differential ranging location system is described which uses a modified time-of-arrival technique to determine the location of a frequency-hopped spread spectrum radio signal. The transmitter simultaneously transmits two radio frequency carriers having different frequencies such that a phase difference is observed between the two carriers at a distance from the transmitter. The phase difference is proportional to the range from the transmitter that the carrier signals have observed. The two carrier signals from the single transmitter are received by at least three and in special cases four base stations which calculate the differential time of arrival based on the phase differences of the received carriers. The calculated phase differences are then sent to a central location which locates the position of the transmitter based upon a planer hyperbolic location algorithm. Since a large number of narrow band frequencies across a wide spectrum are used in a frequency hopping transmission protocol, the accuracy in determining the phase differences between the two carriers is increased and the immunity to interference is also increased.

Phase error detecting method and phase tracking loop circuit

Abstract: A phase error detecting method is applied to a VSB receiver or a QAM receiver. Q-channel data is recovered by digitally filtering transmitted I-channel data, and the phases of the I-channel data and the Q-channel data are corrected according to a fed-back phase error. A decided I-channel level value is chosen approximating the phase-corrected I-channel data among predetermined reference I-channel level values. A phase error value for the received data is obtained by subtracting the decided I-channel level value from the phase-corrected I-channel data, and multiplying the sign of the difference by the difference itself, and applying a weight value from a predetermined weighting function to the phase error value weighted phase error value is fed back to be used for phase correction of received data. Thus, the reliability of phase error detection can be increased by use of the weighting function.

Phase difference plate and circularly polarizing plate

Abstract: PROBLEM TO BE SOLVED: To obtain a phase difference plate which has decreased phase differences by wavelengths and has the excellent consistency thereof by sticking a quarter-wave plate and a halfwave plate to each other in the state of intersecting their respective optical axes. SOLUTION: This phase difference plate is formed by sticking the quarter- wave plate (a double refractive film of which the phase difference of the double refractive light is a quarter wave) 13 and the halfwave plate (a double refractive film of which the phase difference of the double refractive light is a half wave) 11 to each other in the state of intersecting the respective optical axes at a preset angle. The halfwave plate 11 and the quarter-wave plate 13 are formed by subjecting high-polymer films to stretching treatments. In such a case, a polycarbonate material which is often used as a wavelength material is selected. This phase difference plate is designed to function as the quarter-wave plate improved in the wavelength dispersion characteristic when linearly polarized light of a perpendicular direction (0 deg. direction) is made incident from the halfwave plate 11 side. The phase difference plate is thus capable of converting the light to nearly perfectly circularly polarized light regardless of wavelengths in a range of visible light.

A model-based method for phase unwrapping

Abstract: Presents a model-based phase unwrapping method which represents the unwrapped phase function by a truncated Taylor series and a residual function. An efficient, noniterative computational algorithm is also proposed for calculating the model parameters from the phase derivatives. Sample experimental results are shown to demonstrate the effectiveness of the algorithm for extracting unwrapped phase images from two-dimensional (2-D) magnetic resonance imaging (MRI) data.

Wave propagation with rotating intensity distributions.

Abstract: Wave fields containing invariant features have recently stimulated the interest of the scientific community. Typical examples of such fields are Gaussian modes, Bessel beams @1#, and wave fronts containing phase dislocations @2#. Bessel beams are solutions of the wave equation that propagate with invariant intensity. Phase dislocations are discontinuities of the phase in a wave front such that the circulation of the phase around its axis is an integral multiple of 2p. Thus, they determine lines of zero intensity in space. Experimental evidences of optical dislocations can be found, for example, in Refs. @3‐5#. It was noted in Refs. @4,6# that, under certain circumstances, an array of dislocations nested in a Gaussian beam rotates by p/2 rad from the waist to the far field, expanding with the host beam. The objective of this paper is to investigate general solutions having rotating intensity distributions around and along the propagation axis. We start by demonstrating that these solutions are easily obtained in terms of the superposition of Gauss-Laguerre ~GL! modes. The rotation rate along the propagation is then derived and the set of all possible solutions presenting a specific total rotation angle is characterized. Finally, we analyze the limit of the rotation rate and present experimental results for optical beams. Let a scalar wave be represented by the function

Window function influence on phase error in phase-shifting algorithms.

Abstract: We present five different eight-point phase-shifting algorithms, each with a different window function. The window function plays a crucial role in determining the phase (wavefront) because it significantly influences phase error. We begin with a simple eight-point algorithm that uses a rectangular window function. We then present alternative algorithms with triangular and bell-shaped window functions that were derived from a new error-reducing multiple-averaging technique. The algorithms with simple (rectangular and triangular) window functions show a large phase error, whereas the algorithms with bell-shaped window functions are considerably less sensitive to different phase-error sources. We demonstrate that the shape of the window function significantly influences phase error.

Phase Frame Analysis of the Effects of Voltage Unbalance on Induction Machines

Abstract: Operating a three-phase induction motor with unbalanced voltages can lead to excessive heating. The traditional method of analyzing the operating conditions of the motor when unbalanced voltages have been applied has been to use the theory of symmetrical components. The purpose of this paper is to develop a method of analyzing the motor in the "phase frame". The method is then applied to a typical motor to demonstrate the results of operating a motor with unbalanced voltages and the reason why a motor must be derated under these conditions.

Extending the HKB model of coordinated movement to oscillators with different eigenfrequencies

Abstract: We study the dynamics of a system of coupled nonlinear oscillators that has been used to model coordinated human movement behavior. In contrast to earlier work we examine the case where the two component oscillators have different eigenfrequencies. Problems related to the decomposition of a time series (from an experiment) into amplitude and phase are discussed. We show that oscillations at multiples of the main frequency of the oscillator system may occur in the phase and amplitude due to the choice of a coordinate system and how these oscillations can be eliminated. We derive an explicit equation for the dynamics of the relative phase of the oscillator system in phase space that enables a direct comparison between theory and experiment.

Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection

Abstract: Stable phase locking of an electrically pumped vertical cavity surface-emitting semiconductor laser (VCSEL) was demonstrated experimentally by injecting light from an edge-emitting master laser into the slave laser VCSEL cavity within a large detuning range (/spl sim/80 GHz). By varying the injected power and frequency detuning, a variety of interesting nonlinear behavior was observed. A theoretical model based on two-field rate equations is presented and compared with experiment, showing good agreement.

Sagnac interferometer for gravitational-wave detection.

Abstract: We have investigated a zero-area Sagnac interferometer as a broad band gravitational-wave detector. Frequency response measurements of a laboratory-scale interferometer are in excellent agreement with theory. The measured contrast ratio, 0.996, is insensitive to induced birefringence, laser-frequency variation, arm imbalance, and dc mirror displacement. A near shot-noise-limited phase sensitivity of $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}\mathrm{rad}/\sqrt{\mathrm{Hz}}$ was measured at the interferometer's maximum sensitivity frequency, 90.9 MHz.

Phased array beam controller using integrated electro-optic circuits

Abstract: A photonic device for controlling phased array beam direction includes an electro-optic substrate; a plurality of waveguides formed in the substrate, each of which is capable of simultaneously propagating light signals with orthogonal polarizations; an input waveguide for inputting into each one of the plurality of waveguides a pair of copropagating polarized light signals having orthogonal polarizations and different frequencies; a plurality of electrodes on the substrate configured to phase shift the signals traveling through each waveguide by a different amount in response to a common applied voltage, thereby creating phase shifted polarized signals; and means for combining the phase shifted polarized signals within each one of the waveguides and propagating these combined signal to an antenna element The basic operating principle of the invention is based on the differential phase shift between optical waves of orthogonal polarizations traveling in an electro-optic optical waveguide This differential phase shift is directly proportional to the voltage applied to a control electrode and to the length of that electrode If the two optical waves are slightly offset in optical frequency, they produce a beat frequency when photodetected whose phase shift equals the optical differential phase shift An array of such phase shifters forms the basis for the photonic beam controller of the invention

Phase measurements in nonlinear optics

Abstract: Measurement of the phase, and not only the intensity, of the nonlinear optical response of a system is important in many applications which are reviewed here. We demonstrate and compare several techniques for direct measurement of the phase of the nonlinear susceptibilities through nonlinear interferometry. Different ways of imparting a controllable phase shift are discussed. Unless the coherence length is impractically large, the preferred method is to use a variable-pressure gas cell to control the phase difference between the input laser pulse and the nonlinear optical signal.

Phase and time-difference precision direction finding system

Abstract: A precision direction finding system for making precision angle of arrival estimates for a signal received through two antenna elements separated in space. Phase interferometry is used to determine a precise angle of arrival, with multiple ambiguities due to the periodic nature of the phase difference related to geometric angle. The interferometric ambiguities are resolved using the time difference of arrival (TDOA) of the signal at the two antenna elements. TDOA is measured using leading edge envelope detection for simple pulsed signals, and predetection correlation for phase and frequency modulated signals.

Phase measurement by projection synthesis.

Abstract: Experimental determination of the canonical quantum optical phase probability distribution has, until now, required sufficient measurements to determine the complete state of the field. In this Letter we present a more direct means for measuring this distribution which involves synthesising the projection onto a phase state. Projection synthesis may be applied more generally to measure the probability distribution associated with other observables. {copyright} {ital 1996 The American Physical Society.}