Showing papers on "Phase (waves) published in 1988"

Satellite radar interferometry: Two-dimensional phase unwrapping

Abstract: Interferometric synthetic aperture radar observations provide a means for obtaining high-resolution digital topographic maps from measurements of amplitude and phase of two complex radar images. The phase of the radar echoes may only be measured modulo 2 pi; however, the whole phase at each point in the image is needed to obtain elevations. An approach to 'unwrapping' the 2 pi ambiguities in the two-dimensional data set is presented. It is found that noise and geometrical radar layover corrupt measurements locally, and these local errors can propagate to form global phase errors that affect the entire image. It is shown that the local errors, or residues, can be readily identified and avoided in the global phase estimation. A rectified digital topographic map derived from the unwrapped phase values is presented.

V Phase-Measurement Interferometry Techniques

Abstract: Publisher Summary This chapter describes the phase-measurement interferometry techniques. For all techniques, a temporal phase modulation is introduced to perform the measurement. By measuring the interferogram intensity as the phase is shifted, the phase of the wavefront can be determined with the aid of electronics or a computer. Phase modulation in an interferometer can be induced by moving a mirror, tilting a glass plate, moving a grating, rotating a half-wave plate or analyzer, using an acousto-optic or electro-optic modulator, or using a Zeeman laser. Phase-measurement techniques using analytical means to determine phase all have some common denominators. There are different equations for calculating the phase of a wavefront from interference fringe intensity measurements. The precision of a phase-measuring interferometer system can be determined by taking two measurements, subtracting them, and looking at the root-meansquare of the difference wavefront. The chapter discusses the simulation results. The elimination of the errors that reduce the measurement accuracy depends on the type of measurement being performed. Phase-measurement interferometry (PMI) can be applied to any two-beam interferometer, including holographic interferometers. Applications can be divided into: surface figure, surface roughness, and metrology.

Feature Detection in Human Vision: A Phase-Dependent Energy Model

Abstract: This paper presents a simple and biologically plausible model of how mammalian visual systems could detect and identify features in an image. We suggest that the points in a waveform that have unique perceptual significance as 'lines' and 'edges' are the points where the Fourier components of the waveform come into phase with each other. At these points 'local energy' is maximal. Local energy is defined as the square root of the sum of the squared response of sets of matched filters, of identical amplitude spectrum but differing in phase spectrum by 90 degrees: one filter type has an even-symmetric line-spread function, the other an odd-symmetric line-spread function. For a line the main contribution to the local energy peak is in the output of the even-symmetric filters, whereas for edges it is in the output of the odd-symmetric filters. If both filter types respond at the peak of local energy, both edges and lines are seen, either simultaneously or alternating in time. The model was tested with a series of images, and shown to predict well the position of perceived features and the organization of the images.

Phase-aberration correction using signals from point reflectors and diffuse scatterers: basic principles

Abstract: Methods for correction of phase aberrations induced by near-field variations in the index of refraction are explored. Using signals obtained from a sampled aperture (i.e. transducer array), phase aberrations can be accurately measured with a correlation approach similar to methods used in adaptive optics and radar. However, the method presented here has no need for a beacon or an ideal point reflector to act as a source for estimating phase errors. It uses signals from random collections of scatterers to determine phase aberrations accurately. Because there is no longer a need for a beacon signal, the method is directly applicable not only to medical ultrasound imaging but also to any coherent imaging system with a sampled aperture, such as radar and sonar. >

Polymers on disordered trees, spin glasses, and traveling waves

Abstract: We show that the problem of a directed polymer on a tree with disorder can be reduced to the study of nonlinear equations of reaction-diffusion type. These equations admit traveling wave solutions that move at all possible speeds above a certain minimal speed. The speed of the wavefront is the free energy of the polymer problem and the minimal speed corresponds to a phase transition to a glassy phase similar to the spin-glass phase. Several properties of the polymer problem can be extracted from the correspondence with the traveling wave: probability distribution of the free energy, overlaps, etc.

Quantum correlations of phase in nondegenerate parametric oscillation.

Abstract: The squeezing spectrum for nondegenerate parametric oscillation above threshold is calculated, including phase diffusion. A nonclassical correlation in phase and intensity occurs which is an example of the Einstein-Podolsky-Rosen paradox, even in fields of large photon number.

Biphasic waveforms for defibrillation

Abstract: In a method and apparatus for defibrillating a heart in fibrillation, the onset of fibrillation of the heart is detected, and a biphasic waveform having only a first phase and a second phase is applied to the fibrillating heart. Each phase of the waveform is characterized by a predetermined time duration and by a predetermined polarity and magnitude of voltage, the duration of the first phase being greater than the duration of the second phase, and the initial voltage magnitude of the first phase being greater than that of the second phase. The biphasic waveform is applied by delivering it to a pair of patch electrodes affixed over and contoured to conform substantially to the surface of the right and left ventricles, respectively. The patch electrodes are affixed to either the epicardium or the pericardium. The left ventricular patch electrode is used as the cathode for the first phase of the applied biphasic waveform, and as the anode for the second phase. No further shocks are delivered to the heart pending detection of cardiac activity is response to the shocks delivered by the application of the biphasic waveform.

Eigenstructure methods for direction finding with sensor gain and phase uncertainties

Abstract: An eigenstructure-based method for direction finding in the presence of sensor gain and phase uncertainties is presented. The method provides estimates of the directions of arrival (DOA) of all the radiating sources as well as calibration of the gain and phase of each sensor in the observing array. The technique is not limited to a specific array configuration and can be implemented in any eigenstructure-based DOA system to improve its performance. >

Observation of topological phase by use of a laser interferometer.

Abstract: We report a direct experimental observation of Pancharatnam's phase, which is closely related to Berry's topological phase. The experiment involves measurement of the phase change in one beam of a laser interferometer as the polarization state of light is taken along a closed circuit on the Poincar\'e sphere. The phase change is found to be equal to half the solid angle subtended by the circuit at the center of the Poincar\'e sphere. Apart from providing a striking demonstration of the topological phase, the experiment demonstrates that unitary time evolution of a system is not essential for the appearance of the topological phase.

Invasive microwave array with destructive and coherent phase

Abstract: The hyperthermia treatment apparatus includes an invasive microwave array of applicators with destructive and coherent phase. The desired power phase shift is obtained either by (1) insertion of pre-calibrated phase shift modules or cables, (2) adjustment to the phase of an in-line electronic phase shifter, (3) adjustment of mechanically movable phase shifters such as ferrite or sliding length coaxial line stretchers. A computer provides the proper selection of radiated power for each applicator using a look up table of pre-treatment planning software calculations, and the adjustment of power levels to that determined by the pre-treatment plan. At least one applicator is centrally located with respect to applicators located peripherally. The power and phase shift applied to the central located applicator is computed and applied such as to partially cancel the in phase (coherent) power of the peripheral applicators to substantially reduce the temperature of the centrally located hot spot and provide substantially uniform temperature in the area formed by the applicators using a minimum number of applicators.

Dynamics of phase-locked semiconductor laser arrays

Abstract: Time‐dependent coupled mode theory is used to investigate the stability of phase‐locked semiconductor laser arrays. The output of individual array elements is dynamically unstable and exhibits large amplitude chaotic pulsations. The total output initially exhibits damped relaxation oscillations and then settles down to a quasi‐steady state characterized by small amplitude fluctuations. The theory predicts both the pulsation frequency and the phase lock‐in time of the array.

Least-squares phase estimation from the phase difference

Abstract: The purpose of this paper is to clarify the relationship between the isolated zero points in modulus distribution and the least-squares phase estimation from the phase difference. The concepts of phase and phase difference are reaffirmed. In addition, a necessary condition that makes the least-squares phase estimation feasible is derived by applying the concept of complete observability in estimation theory to the measurement of the phase difference. The occurrence of isolated zero points causes the conventional least-squares phase estimation to fail because the phase difference defined by this concept does not satisfy the necessary condition when isolated zero points occur. This condition also generates a new type of least-squares phase estimation that is feasible for phase retrieval even if zero points exist. One algorithm for realizing this new type of least-squares phase estimation is proposed, and its effectiveness is verified by using computer simulations. Two types of phase unwrapping are also presented: one is the exponential function type; the other results from the proposed least-squares phase-estimation algorithm.

Large‐Scale waveform inversions of surface waves for lateral heterogeneity: 2. Application to surface waves in Europe and the Mediterranean

Abstract: Linear surface wave scattering theory is used to reconstruct the lateral heterogeneity under Europe and the Mediterranean using surface wave data recorded with the Network of Autonomously Recording Seismographs (NARS). The waveform inversion of the phase and the amplitude of the direct surface wave leads to a variance reduction of approximately 40% and results in phase velocity maps in the period ranges 30–40 s, 40–60 s and 60–100 s. A resolution analysis is performed in order to establish the lateral resolution of these inversions. Using the phase velocity perturbations of the three period bands, a two-layer model for the S velocity under Europe and the Mediterranean is constructed. The S′ velocity perturbations in the deepest layer (100–200 km) are much more pronounced than in the top layer (0–100 km), which confirms that the low-velocity zone exhibits pronounced lateral variations. In both layers the S velocity is low under the western Mediterranean, while the S velocity is high under the Scandinavian shield. In the deepest layer a high S velocity region extends from Greece under the Adriatic to northern Italy. Several interesting smaller features, such as the Massif Central, are reconstructed. One of the spectacular features of the reconstructed models is a sharp transition in the layer between 100 and 200 km near the Tornquist-Tesseyre zone. This would indicate that there is a sharp transition at depth between Central Europe and the East European platform. The waveform inversion of the surface wave coda leads to good waveform fits, but the reconstructed models are chaotic. This is due both to a lack of sufficient data for a good imaging of the surface wave energy on the heterogeneities and to an appreciable noise component in the surface wave coda.

Phase modulated system with phase domain filtering

Abstract: A phase modulation system includes a phase mapping circuit (218) for mapping binary data into a plurality of discrete phase values in accordance with a predetermined phase modulation scheme. The discrete phase values are then filtered in the phase domain by a filter (220) to provide a filtered output. This filtered output is then digitized and input to a numerically controlled oscillator for phase modulating a carrier.

Ultra-high sensitivity accelerometers and gyroscopes using neutral atom matter-wave interferometry☆

Abstract: This paper shows that matter-wave interferometers employing low-velocity neutral atoms can be used as inertial sensors with sensitivities that exceed those of conventional mechanical sensors and multiple circuit optical interferometers by many powers of ten. The energy and mass dependence of the phase shifts that are due to rotation and acceleration are different. Thus a pair of interferometers with different energies and/or masses can perform simultaneous independent measurements of rotation and acceleration. A proposed configuration is one formed by a sequence of planar diffraction gratings operating in high order. Gratings consist of near-resonant standing-wave laser beams. Laser decelerated and cooled atomic beams provide a suitable source. Path curvature due to acceleration and rotation is canceled by magnetic field gradients that produce an effective magnetic levitation of the atoms in a feedback arrangement that maintains null phase shift.

The soft-mode ferroelectric effect

Abstract: In this paper a presentation is given of some of the basic physics of the soft-mode ferroelectric effect, along with its experimental background. Further, possible applications in electrooptic devices are elucidated. A fast (sub-microsecond) electrooptic switching can be achieved in the A* phase, and in similar orthogonal smectic phases made up of chiral molecules. Instead of using the phase variable Φ, it uses the tilt angle θ, which in principle is a “hard” variable, but is expected to soften on approaching the transition to a lower-lying adjacent tilted smectic phase. However, the switching is efficient in the whole range of the orthogonal phase (in fact, less efficient near the tilting transition) and is observed whether an adjacent tilted phase is present or not. As compared to the surface-stabilized (SSFLC) electrooptic mode, this soft mode (SMFLC) is based on the electro clinic, effect of essentially ferroelectric nature very closely related to the presently more investigated ferroelectric...

Measurement of the Pancharatnam phase for a light beam.

Abstract: By using a Michelson interferometer arrangement, we have measured the phase shift (the Pancharatnam phase) experienced by a light beam whose state of polarization is made to follow, by successive unitary transformations, a closed circuit on the Poincare sphere. We confirm that the phase shift equals half of the solid angle subtended by the closed circuit at the center of the sphere. This phase is closely related to the topological Berry phase.

Analysis of depletion edge translation lightwave modulators

Abstract: Presents a complete analysis of waveguide phase modulators based on the depletion-edge-translation concept. The phenomena taking place inside the depletion region which contribute to changing the refractive index there are studied. It is shown that the behavior of these modulators can be understood in terms of two electric field-related and two carrier-related effects: linear electrooptic, electrorefractive, plasma, and band filling. The sum of the refractive index variations produced by each one of these effects, taking into account the waveguide geometry, accounts quantitatively for the experimental phase shifts measured in the devices. No fitting parameters are used and a very good agreement between theory and experiment is obtained. Based on this theory, an analysis of the device is made in terms of the optimum values for the doping in the waveguide, and also in terms of the wavelength dependence of the device phase modulation properties. >

Phase retrieval based on the irradiance transport equation and the Fourier transform method: experiments

Abstract: Experimental demonstrations of deterministic phase retrieval based on the Teague-Streibl irradiance transport equation are presented. A new technique is proposed, in which the transport equation is solved by the Fourier transform method for a periodic boundary condition with high spatial carrier frequency, which is created by making a light beam with unknown phase distribution pass through a grating. Quantitative phase measurements were performed by experiments without recourse to interferometry, and the results were found to be in good agreement with theory.

Noniterative method for obtaining the exact solution for the normal equation in least-squares phase estimation from the phase difference

Abstract: We discuss how we can obtain noniteratively an exact solution for the modified normal equation in least-squares phase estimation from the measured phase difference. To achieve this, we introduce the idea of equivalent transformation of the measured phase difference into a periodic one. We perform this tranformation by using a geometric procedure based on mirror reflection. Computer simulation results indicate that the proposed noniterative algorithm works well, as was expected, and can overcome the difficulties caused by such singularities as isolated zero points.

The geometric phase

Abstract: In 1983 the author found a geometric effect exists in the quantum waves that describe matter and its interactions on the smallest scales. In this case the anholonomy appears in a system's wave function (the mathematical description of a system's physical state) after the system has been transported around a cyclic circuit on an abstract surface in parameter space. He calls this anholonomy the geometric phase, because it manifests itself specifically as a shift in the wave function's phase: a quantity that describes where the wave function is in its oscillatory cycle at any given time and place. It so happens that the geometric phase provides an elegant explanation of various quantum-mechanical phenomena in systems whose environment undergoes a cyclic change: neutrons that pass through a helical magnetic field, polarized light in a coiled optic fiber and charged particles circling an isolated magnetic field. Perhaps more surprising is the fact that the geometric phase can also be generalized to applications in classical physics. Among other things, it offers a new way to describe the behavior of such textbook objects as pendulums.

Observation of a topological phase by means of a nonplanar Mach-Zehnder interferometer.

Abstract: We report the direct observation of a topological phase, i.e., an Aharonov-Bohm-type phase, as a fringe shift in an optical interferometer, which consisted of a modified Mach-Zehnder interferometer, in which the light traveled along nonplanar paths in its two arms. These arms were arranged symmetrically so as to have nearly equal path lengths, but opposite senses of handedness. The relationship between the phase acquired by a circularly polarized light beam and the solid angle subtended by the circuit of the spin vector of a photon in this beam was found to be a linear one with a slope of unity. The sign of the fringe shift also agreed with theory.

Turbulence-induced millimeter-wave scintillation compared with micrometeorological measurements

Abstract: Scintillations of intensity and phase difference were measured at millimeter wavelengths in a horizontally homogeneous atmospheric surface layer. Simultaneous micrometeorological and optical propagation measurements characterized the clear-air turbulence. Predicted and measured propagation statistics are in good agreement. It is shown that the phase structure function showed a rolloff at large spacings as was expected because the outer scale of the turbulence and log-intensity and phase difference are Gaussian random variables. The mutual coherence function is exp(-D/2) to great accuracy, where D is the sum of phase and log-amplitude structure functions. Estimating heat and humidity fluxes from intensity variances is shown to be valid. >

Relative phases of electromagnetic waves diffracted by a perfectly conducting rectangular-grooved grating.

Abstract: A complete solution of plane-wave scattering from a groove-corrugated surface of infinite extent for arbitrary incidence is presented. The electromagnetic wave is decomposed into fast and slow modal representation, and the solution is accomplished through the use of the mode-matching method. We solved for the zero-order diffraction efficiency and the phase of each polarization component for arbitrary incident angles. Our results have verified special cases previously published by others and have illustrated the phase shift between polarizations associated with the diffraction process as a function of the incident angles.

Digital spectra of nonuniformly sampled signals. II. Digital look-up tunable sinusoidal oscillators

Abstract: For Part I see ibid., vol.37, no.2, June 1988. The author presents theories and applications of a digital spectrum analysis technique for a class of nonuniformly sampled signals. The structure of the harmonic components present in a digitally synthesized sine wave is analyzed using a table look-up method. The digital table look-up method offers several desirable features, such as high-frequency stability and precision control of both the frequency and the phase of the generated sine wave. However, undesirable spurious harmonic components are generated when one tries to tune to different frequencies by manipulating the memory-addressing mechanism rather than loading a new waveform sample into the waveform memory, which is generally time-consuming and sometimes infeasible. The frequencies, amplitudes, and phrases of all the spurious harmonic components are derived in closed form. >

Interferometer for measuring optical phase-differences

Abstract: For generating several interferograms which differ from each other in the relative phase position between the interfering partial beams, a light source is utilized having a coherence length less than the optical path difference between the two component beams in the measuring path of the interferometer. Furthermore, at least one optical delay device is provided which splits the beam into two component beams and which generates an optical path difference between these component beams which is approximately the same as the optical path difference of the partial beams in the measuring path of the interferometer. Thereafter, the delay device again unites the component beams congruently.

Third harmonic commutation control system and method

Abstract: A system for determining rotor position information from the back emf of a permanent magnet motor includes extracting the third harmonic from the back emf of the motor by summing the terminal voltages of the motor. The phase angle of the third harmonic of the back emf is a function of the position of the rotor, and a signal is produced when the phase angle of the third harmonic (measured with respect to the voltage on the neutral conductor of the motor) reaches a predetermined angle. Electronically controlled switches selectively apply power to the phase windings of the motor in response to the detection of predetermined phase angles of the third harmonic.