Showing papers on "Phase (waves) published in 1981"

The importance of phase in signals

Abstract: In the Fourier representation of signals, spectral magnitude and phase tend to play different roles and in some situations many of the important features of a signal are preserved if only the phase is retained. Furthermore, under a variety of conditions, such as when a signal is of finite length, phase information alone is sufficient to completely reconstruct a signal to within a scale factor. In this paper, we review and discuss these observations and results in a number of different contexts and applications. Specifically, the intelligibility of phase-only reconstruction for images, speech, and crystallographic structures are illustrated. Several approaches to justifying the relative importance of phase through statistical arguments are presented, along with a number of informal arguments suggesting reasons for the importance of phase. Specific conditions under which a sequence can be exactly reconstructed from phase are reviewed, both for one-dimensional and multi-dimensional sequences, and algorithms for both approximate and exact reconstruction of signals from phase information are presented. A number of applications of the observations and results in this paper are suggested.

Analysis of dispersive waves by wave field transformation

Abstract: The dispersive waves in a common‐shot wave field can be transformed into images of the dispersion curves of each mode in the data. The procedure consists of two linear transformations: a slant stack of the data produces a wave field in the phase slowness‐time intercept (p — τ) plane in which phase velocities are separated. The spectral peak of the one‐dimensional (1-D) Fourier transform of the p — τ wave field then gives the frequency associated with each phase velocity. Thus, the data wave field is linearly transformed from the time‐distance domain into the slowness‐frequency (p — ω) domain, where dispersion curves are imaged. All the data are present throughout the transformations. Dispersion curves for the mode overtones as well as the fundamental are directly observed in the transformed wave field. In the p — ω domain, each mode is separated from the others even when its presence is not visually detectable in the untransformed data. The resolution achieved in the result is indicated in the p — ω wave ...

An electrical tuning mechanism in turtle cochlear hair cells

Abstract: 1. Intracellular recordings were made from single cochlear hair cells in the isolated half-head of the turtle. The electrical responses of the cells were recorded under two conditions: (a) when the ear was stimulated with low-intensity tones of different frequencies and (b) when current steps were injected through the intracellular electrode. The aim of the experiments was to evaluate the extent to which the cochlea's frequency selectivity could be accounted for by the electrical properties of the hair cells.2. At low levels of acoustic stimulation, the amplitude of the hair cell's receptor potential was proportional to sound pressure. The linear tuning curve, which is defined as the sensitivity of the cell as a function of frequency when the cell is operating in its linear range, was measured for a number of hair cells with characteristic frequencies from 86 Hz to 425 Hz.3. A rectangular current passed into a hair cell elicited a membrane potential change consisting of a damped oscillation superimposed on a step. Small currents produced symmetrical oscillations at the beginning and end of the pulse. Larger currents increased the initial ringing frequency if depolarizing and decreased it if hyperpolarizing.4. For small currents the frequency of the oscillations and the quality factor (Q) of the electrical resonance derived from the decay of the oscillations were close to the characteristic frequency and Q of the hair-cell linear tuning curve obtained from sound presentations.5. The hair cell's membrane potential change to small-current pulses or low-intensity tone bursts could be largely described by representing the hair cell as a simple electrical resonator consisting of an inductance, resistor and capacitor.6. When step displacements of 29-250 nm were applied to a micropipette, placed just outside a hair cell in the basilar papilla, an initial periodic firing of impulses could be recorded from single fibres in the auditory nerve. Currents of up to 1 nA, injected through the same micropipette, failed to produce any change in the auditory nerve discharge. The experiment demonstrates that current injection does not produce gross movements of the electrode tip.7. The contribution of the electrical resonance to hair-cell tuning was assessed by dividing the linear tuning curve by the cell's impedance as a function of frequency. The procedure assumes that the electrical resonance is independent of other filtering stages, and on this assumption the resonance can account for the tip of the acoustical tuning curve.8. The residual filter produced by the division was broad; it exhibited a high-frequency roll-off with a corner frequency at 500-600 Hz, similar in all cells, and a low-frequency roll-off, with a corner frequency from 30 to 350 Hz which varied from cell to cell but was uncorrelated with the characteristic frequency of the cell.9. The phase of the receptor potential relative to the sound pressure at the tympanum was measured in ten cells. For low intensities the phase characteristic was independent of the sound pressure. At low frequencies the receptor potential led the sound by 270-360 degrees , and in the region of the characteristic frequency there was an abrupt phase lag of 90-180 degrees ; the abruptness of the phase change depended upon the Q of the cell.10. The calculated phase shift of the electrical resonator as a function of frequency was subtracted from the phase characteristic of the receptor potential. The subtraction removed the sharp phase transition around the characteristic frequency, and in this frequency region the residual phase after subtraction was approximately constant at +180 degrees . This is consistent with the idea that the hair cells depolarize in response to displacements of the basilar membrane towards the scala vestibuli. The high-frequency region of the residual phase characteristic was similar in all cells.11. It is concluded that each hair cell contains its own electrical resonance mechanism which accounts for most of the frequency selectivity of the receptor potential. All cells also show evidence of a broad band-pass filter, the high frequency portion of which may be produced by the action of the middle ear.

Phase relationships between adjacent simple cells in the visual cortex

Abstract: Adjacent simple cells recorded and "isolated" simultaneously from the same microelectrode placement were usually tuned to the same orientation and spatial frequency. The responses of the members of these "spatial frequency pairs" to drifting sine-wave gratings were cross-correlates. Within the middle range of the spatial frequency selectivity curves, the responses of the paired cells differed in phase by approximately 90 percent. This phase relationship suggests that adjacent simple cells tuned to the same spatial frequency and orientation represent paired sine and cosine filters in terms of their processing of afferent spatial inputs and truncated sine and cosine filters in terms of the output of simple cells.

Sampling designs for stereology.

Abstract: SUMMARY The purpose of this paper is to propose the necessary sampling techniques for estimating a global parameter defined in a solid opaque specimen (e.g. the total volume of mitochondria in a given liver, the total capillary surface area in a given lung, etc.). The geometry of the specimen often suggests a multi-level or cascade sampling design at different magnifications, whereby the object phase at one level becomes the reference phase in the next level. The final parameter is then estimated as the product of the intermediate ratios with the volume of the specimen, which is estimated independently. Each level can be regarded as an independent sampling design; a given stereological project may be planned in terms of one or more of these designs. Our development is a blend of practical experience and recent theoretical advances on sampling for stereology with well-known sampling techniques previously developed with different purposes in mind.

Optical heterodyne profilometry.

Abstract: A noncontact optical technique for the measurement of surface profile is described, which has a height sensitivity of the order of 1 A. It is based on a common path heterodyne interferometer in which two orthogonally polarized beams of slightly different frequency are focused on the surface to be measured. One focal point acts as a reference as the other point circularly scans the surface. The phase of the beat frequency of the interfering return beams is directly proportional to the surface height. The results of a surface measurement include graphical displays of the surface profile, autocovariance function, spectral density function, stability, and repeatability. Comparison with other instruments is also discussed.

Iterative techniques for minimum phase signal reconstruction from phase or magnitude

Abstract: In this paper, we develop iterative algorithms for reconstructing a minimum phase sequence from the phase or magnitude of its Fourier transform. These iterative solutions involve repeatedly imposing a causality constraint in the time domain and incorporating the known phase or magnitude function in the frequency domain. This approach is the basis of a new means of computing the Hilbert transform of the log-magnitude or phase of the Fourier transform of a minimum phase sequence which does not require phase unwrapping. Finally, we discuss the potential use of this iterative computation in determining samples of the unwrapped phase of a mixed phase sequence.

Amplified reflection, transmission, and self-oscillation in real-time holography

Abstract: A theory of phase conjugation in asymmetric materials that allow a phase shift between the grating and the light-interference pattern is developed. We find that when this phase is nonzero, maximum phase-conjugate reflectivity occurs for unequal pump intensities. The conditions for self-oscillation are studied.

Temperature-induced optical phase shifts in fibers.

Abstract: The static thermal sensitivity of the optical phase in bare and jacketed fibers has been studied both analytically and experimentally. Taking into account the exact fiber composition and geometry, the strains have been determined from the thermally induced stresses using the appropriate boundary conditions, and the resulting phase shift has been calculated. The results of this analysis are found to be in agreement with experimental results obtained from measurements employing a Mach-Zehnder fiber interferometer.

Modulated phase of an ising system with competing interactions on a Cayley tree

Abstract: A system with competing nearest-neighbour and next-nearest-neighbour interactions is considered on a Cayley tree The phase diagram contains a modulated phase, as found for similar models on periodic lattices, but the multicritical Lifshitz point is at zero temperature The variation of the wavevector with temperature in the modulated phase is studied in detail, it shows narrow commensurate steps between incommensurate regions (“incomplete devil's staircase”) The behaviour of the coherence length near the different transitions is also analyzed

The phase retrieval problem

Abstract: The phase retrieval problem arises in applications of electromagnetic theory in which wave phase is apparently lost or impractical to measure and only intensity data are available. The mathematics of the problem provides unusual insights into the nature of electromagnetic fields. The theory is reviewed and illustrated. The basic issue of the phase retrieval problem, stated for a one-dimensional field, is that although a unique Fourier transform relation exists between the field F(x) in the Fraunhofer plane and the field u(x') in the object plane, the infinite fold phase ambiguity which appears as the result of the possibilities of conjugating the zeros of F(z), z = x + jy implies that additional information or processing of the object wave must be available to obtain the phase. Among the possible solutions which are described are reference beam addition, apodization and the use of multiple intensity distributions, permitting the use of iterative computational procedures in some applications.

Low-noise fiber-optic rotation sensing

Abstract: A major source of noise in fiber-optic Sagnac interferometers was identified to be the fluctuation of the phase of Rayleigh backscattering resulting from minute temperature variations and vibration. This noise can be reduced either by introducing a phase modulation into the fiber ring or by the use of a low-coherence source. A noise-equivalent rotation rate of 8 x 10(-4) deg/sec was achieved.

Phase-shift calculation of ionized impurity scattering in semiconductors

Abstract: Partial-wave phase shifts for the scattering of electrons and holes of arbitrary degeneracy by a screened Coulomb potential have been calculated assuming isotropic, parabolic energy bands. For free particles in the effective-mass approximation, all such interactions can be characterized by two parameters. At each point in this two-dimensional space, two final results have been obtained from which the transport integrals can be evaluated. One is a sum of the phase shifts which must be employed in satisfying the Friedel sum rule, while the other corresponds to the total momentum-transfer cross section due to all partial waves. For a parametric space which includes nearly all experimental conditions of interest, these results are presented in approximate analytic form. Over a broad range of electron and hole concentrations and temperatures in Ge, Si, and GaAs, comparison is made between ionized-impurity mobilities calculated from the phase shifts and those obtained in the Born approximation.

Optical wave phase fluctuations.

Abstract: This paper presents a series of studies on the effect of low-frequency fluctuations of the atmospheric refractive index on phase fluctuations of space-limited optical beams. Theoretical calculations have been made in the approximation of a smooth perturbation method. Numerous experimental data on statistical characteristics of optical wave phase fluctuations are given. These are used to verify the theoretical conclusions and to solve an inverse problem on the determination of the atmospheric turbulence characteristics.

Detection of spatially nonuniform ultrasonic radiation with phase sensitive (piezoelectric) and phase insensitive (acoustoelectric) receivers

Abstract: An analysis is presented of the responses of a phase sensitive and a phase insensitive ultrasound receiver detecting a spatially nonuniform pressure distribution. The predicted output of each type of receiver is obtained numerically using a model of wave propagation based upon diffraction theory. Experimental verification of these predictions is obtained using a piezoelectric and an acoustoelectric receiver as a phase sensitive and a phase insensitive detector, respectively. Results are illustrated for transmission measurements of the frequency‐dependent attenuation of an irregular plastic plate and for scattering measurements of the observed angular and spatial dependence of scattering from a pair of brass rods.

Cluster and channel effect phase bunchings by whistler waves in the nonuniform geomagnetic field

Abstract: A test particle simulation has been carried out on the characteristic behavior of resonant electrons in a monochromatic whistler wave propagating along the nonuniform geomagnetic field. The geomagnetic field is approximated by a parabolic field around the equator. In addition to a phase bunching of untrapped electrons due to the inhomogeneity of the magnetic field, found by Vomvoridis zand Denavit (1979), another type of phase bunching of initially untrapped and later trapped electrons is found to take place in the parabolically nonuniform magnetic field. The former is called channel effect phase bunching, and the latter is called cluster effect phase bunching. The difference of the cluster effect phase bunching from the channel effect bunching as well as from the conventional phase bunching in a uniform magnetic field is discussed. The relative importance of these phase bunchings in forming resonant currents in the generation process of VLF-triggered emissions is also discussed.

Magnitude and phase in thermal wave imaging

Abstract: In thermal wave imaging on solids both magnitude and phase angle are used. However, a comparison between theoretical and experimental results is lacking even for the simple case of an air-backed metal plate. In the letter we present measurements and point out the difference between sinusoidal and square-wave intensity modulation.

The Transition to Turbulence in Nematic Liquid Crystals

Abstract: The article is divided in two parts. In part I we review the present state of knowledge on the problem of the transition to turbulence in isotropic liquids and we discuss analogies/differences with the case of nematics. In the well known Rayleigh-Benard case, experiments on ordinary liquids show that one must distinguish between confined and extended geometries (small or large “aspect ratios”). This difference is quite general and arises from the more or less large number of variables required to describe the structure. In confined geometry a Ruelle-Takens type of sequence seems relevant, with subharmonic bifurcation or intermittency as special cases. In extended geometry, slowly evolving imperfect structures (which may arise from an instability of the phase of rolls) result in a broad noise which can be viewed as a precursor of turbulence. In nematic liquid crystals (NLC) much less is known on the transition to turbulence. Nematic flows are verystrongly non-linear and are in large part controlle...

Phase plane description of endogenous neuronal oscillators in Aplysia

Abstract: Phase plane techniques are used to describe graphically the limit cycle behavior of identified endogenous neuronal oscillators in the isolated abdominal ganglion of Aplysia. Intracellularly recorded membrane potential from a bursting neuron and its first derivative with respect to time are used as coordinates (state variables) in phase space. The derivative is either measured electronically or calculated digitally. Each trajectory in phase space represents the entire output of the bursting neuron, i.e., both the rapid action potentials and slow pacemaker potentials. Phase plane portraits are presented for the free run limit cycle before and after a change in a system parameter (applied transmembrane current) and also for phase resetting produced by direct synaptic inhibition from an identified interneuron. The complex topology of the trajectory suggests that the bursting oscillator is a higher order system. Therefore, the second time derivative is used as another state variable. This type of phase plot can help to relate biophysical and mathematical analyses.

Photoacoustic study of layered samples

Abstract: The application of photoacoustic spectroscopy to the spectroscopy of layered samples with thicknesses of tens of microns is demonstrated both theoretically and experimentally. Theoretical expressions for the signal damping and phase delay are developed in terms of the thermal diffusion length, which is determined by the chopper frequency and the thermal properties of the sample. The theory is supported by measurements of both amplitude and phase on a color photographic film containing three light absorbing layers. The application of the method is further illustrated by a simple study of fading leaves.

Phase retrieval using two intensity measurements in the complex plane.

Abstract: A new method of using an exponential filter to generate an intensity distribution in the complex plane is presented. This intensity, with the intensity on the real axis, allows the phase of the scattered field to be determined from its zero locations. It is shown that knowledge of all zero coordinates may not be required.

Determination of phase functions for a desired one-dimensional pattern

Abstract: A method of determination of phase functions required for the generation of sector and cosecant beams using a circular aperture is determined. In the particular case of one-dimensional pattern functions, the two-dimensional form of the relation between pattern functions and aperture functions is reduced to one-dimensional form. The stationary phase method is used to obtain possible solutions for the phase functions.

Acoustic measurement of near surface property gradients

Abstract: Disclosed is a method for determining the dispersion of a surface acoustic wave in an object, including the steps of generating a broadband acoustic wave in a surface of the object, detecting the wave at first location on the surface, and detecting the wave at a second location on the surface. Fourier transforms of the first and second detected waves are calculated, then the change in phase Δφ(f) of the frequency component f of the detected wave, between the first and second locations, is computed from the phase components of the quotient of the two transforms. The dispersion of the wave in the surface is given by the formula v(f)=(2πf Δl/Δφ(f)) In a pulse-echo version of the method, the wave is generated and detected at the first location, and generated and detected at the second location, the dispersion then being according to the formula v(f)=4πf Δl/Δφ(f)).

Principles of the optimum lock-in averageing in DLTS measurement

Abstract: The advantages of the transient capacitance/current signal averageing by lock-in amplifier are emphasized: improved signal to noise ratio and better detectability of non exponential transients. The concept of rate window independent phase setting is introduced which overcomes the existing difficulties of the lock-in detection technique. Finally, details of a custom built DLTS apparatus are given.

Digital induction logging tool

Abstract: A digital induction resistivity logging tool is disclosed for digitally measuring both the in-phase (R) and quadrature (X) phase components in a receiver signal generated in response to transmitter induced currents flowing in the earth's sub-surface formations. The digital indication tool includes a digital sinewave generator for generating a highly phase stable, low distortion transmitter signal, the frequency of which is selectable from among a plurality of transmitter frequencies. One phase sensitive detector is used alternately to detect both the R and the X phase component signals. Automatic phase compensation is included to periodically compensate for both static and dynamic temperature dependent phase shift errors due to circuits of the tool involved in the component measurements. A floating point analog-to-digital converter capable of handling the wide dynamic range in the detected phase component signals is provided to convert the phase detector output into digital signals.

Emittance Growth of Beams Close to the Space Charge Limit

Abstract: In linear devices the effective phase space volume occupied by a beam can grow rapidly if the beam intensity is sufficiently close to the space charge limit and if a source of instability is available, like a periodic variation of the focusing force and/or considerable anisotropy between different phase planes. Results from analytic work and computer simulation are compared and shown to support each other. Regimes are defined in terms of tunes and tune depressions, where no emittance growth should occur; special emphasis is given to the coupling instability in case of considerably different energy content in two phase planes. The amount of transfer is found to depend critically on the strength of tune depression. The nonlinearity required for coupling is shown to arise from instability, which grows out of arbitrarily small initial fluctuations.