Showing papers on "Phase (waves) published in 1977"

Least-square fitting a wave-front distortion estimate to an array of phase-difference measurements

Abstract: The problem of fitting a wave-front distortion estimate to a (single-instant) set of phase-difference measurements has been formulated as an unweighted least-square problem. The least-square equations have been developed as a set of simultaneous equations for a square array of phase-difference sensors, with phase estimates at the corner of each measurement element. (This corresponds to the standard Hartmann configuration and to one version of a shearing interferometer of a predetection compensation wave-front sensor.) The noise dependence in the solution of the simultaneous equations is found to be expressible in terms of the solution to a particular version of the measurement inputs to the simultaneous equation, a sort of “Green’s-function” solution. The noise version of the simultaneous equations is solved using relaxation techniques for array sizes from 4 × 4 to 40 × 40 phase estimation points, and the mean-square wave-front error calculated as a function of the mean-square phase-difference measurement error. It is found that the results can be approximated within a fraction of a percent accuracy by 〈(δΦ)2〉=0.6558[1+0.2444 ln(N2)]σpd2, where 〈(δΦ)2〉 is the mean-square error (rad2) in the estimation of the wave-front distortion, for a square array consisting of N2 square subaperture elements over which two phase-difference measurements are made—one phase difference across the x dimension and the other difference across the y dimension. Here σpd2 is the mean-square error (rad2) in each phase-difference measurement.

Wave-front reconstruction for compensated imaging

Abstract: A critical component in a compensated imaging (CI) system is the wave-front sensor which measures the residual distortion of the wave front after reflecting off the active mirror. The sensor produces estimates of wave-front slopes or phase difference across the aperture. For many applications, the phase differences or slopes are not the most convenient form of data for processing or control, and they must be converted to absolute wave-front phases. This paper analyzes the conversion from phase differences to phases and derives the optimal linear estimator in terms of least noise propagation. Some remarks concerning hardware implementation are also made.

Conjugate wave‐front generation and image reconstruction by four‐wave mixing

Abstract: Operation of a new nonlinear backward‐wave optical device which produces the conjugate of an arbitrary incident wave front is demonstrated. Good‐quality reconstructed images are obtained through a phase distorting media.

Random-field instability of the ferromagnetic state

Abstract: We consider an Ising model with infinite-ranged interaction with statistically independent site fields with Gaussian distribution. The model is solved exactly and exhibits both an independent spin phase and a ferromagnetic phase, separated by a line of second-order phase transitions. We also establish that the replica technique yields exact results in the present model but not in the related random exchange system.

Optimum operation of improved wave-power converter

Abstract: An improved version of the previously proposed resonance-tuned absorber of ocean-wave power is presented. The absorber utilises a machine to control its movement in an optimum way relative to the time evolvement of the incident wave. As a result, the improved absorber becomes theoretically as efficient in non-harmonic waves as the resonance-tuned absorber is in harmonic waves. Assuming waves and oscillations of small amplitudes, mathematical expressions are derived for the maximum obtainable absorbed power and for the corresponding optimum velocity function of the oscillating heaving absorber body. Provided the wave spectrum is reasonably narrow, the optimum velocity is approximately proportional to and in phase with the excitation force due to the incident wave.

Carrier wave recovery system apparatus using synchronous detection

Abstract: A carrier wave recovery apparatus of the decision feedback type having analog multipliers of lower dynamic range. The modulated signal is phase detected by comparison with a VCO signal. The analog multipliers receive a signal derived by subtraction of the phase detected signal from the same phase detected signal compared with a reference. That signal is multiplied in an analog multiplier by the phase detected signal or by the signal produced from comparing the phase detected signal with a reference.

The Nearly Commensurate Phase and Effect of Harmonics on the Successive Phase Transition in 1T-TaS2

Abstract: The phase transitions of the charge density wave (CDW) state in 1T-TaS 2 are studied both theoretically and experimentally. The positions and intensities of the fundamental and third-order harmonic...

Correlation function dependence of the scintillation behind a deep random phase screen

Abstract: The role of the phase autocorrelation function in the generation of speckle, focusing and other scintillation effects produced when radiation is scattered by a deep random phase screen is investigated. New analytical formulae are obtained which reveal the mathematical origin of the observed physical phenomena, and these are supported by a range of numerically computed results.

Position detecting system

Abstract: The position or presence of a metallic object is detected by an electronic circuit which senses a shift in phase between a first cyclic signal and a second cyclic signal which shifts in phase in response to movement of the object. An oscillator produces the first cyclic signal which is used as the reference signal and as the excitation for a parallel resonant circuit which produces the second signal. The phase of the second signal is shifted in response to movement of a metal plate or a shorted coil in an electromagnetic field produced by an inductor in the resonant circuit. The degree of the phase shifts may be used to detect the position of an object in the electromagnetic field or rate of the phase shifts may be used to detect the velocity of an object. An exclusive-or gate senses the changes or differences in phase between the two cyclic signals and produces an output signal representative of the changes or differences in phase. The output signal of the detector may be used with a digital counter to produce a digital output or with a smoothing filter to provide an analog output.

On the theory of spatially limited light beam displacements in a randomly inhomogeneous medium

Abstract: The asymptotic theory of displacements of spatially limited light beams propagating through the turbulent atmosphere is developed as a Markovian process approximation. The asymptotic representations for variance of beam displacements corresponding to small and large values of the structure function of phase fluctuations of a spherical wave calculated for the transmitter diameter are obtained. (Phase structure function characterizes the intensity of turbulent pulsations of a medium dielectric constant along the path.) The dependence of the displacement variance on the path length is investigated. The final dimensions of the outer scale of atmospheric turbulence are taken into account. In contrast to previous papers, for the second moment of intensity the expression is used which is obtained using the Huygens-Fresnel principle for smooth inhomogeneous media. This procedure enables one to determine more accurately the field of applicability of the results previously obtained and to explain the observed disagreement of experimental data with that obtained theoretically. The saturation effect of variance of angular displacements with the path length increase was observed.

Transducer and bond phase shifts in ultrasonics, and their effects on measured pressure derivatives of elastic moduli

Abstract: Phase shifts introduced into ultrasonic signals by the presence of transducers and bonds at sample surfaces have been measured using an automated variable frequency ultrasonic interferometer. At zero pressure, phase shifts have been resolved due to transducers, bonds between transducers and samples, and bonds between buffer rods and samples. Observed transducer-bond-sample phase shifts are in good accord with theoretical estimates, and bond thicknesses of about 0.3 μ are inferred. Measurements to 7 kbar are consistent with theoretical estimates of the effect of pressure on transducer-bond-phase shifts. Providing the frequency of the ultrasonic signal is within a few percent of the resonance frequency of the transducer, and the effect of pressure on the transducer resonance frequency is accounted for (as recommended by McSkimin, [1961]), the effect of the bond phase shift on the measured pressure derivative of the elastic modulus should amount to less than about 0.02. If the frequency deviates substantially from the transducer resonance frequency, especially at zero pressure, errors of the order of 0.25 could be incurred in the pressure derivatives. The nonlinearity of transducer-bond phase shifts could cause significant errors in second-pressure derivatives, even under favorable conditions. For shear waves at zero pressure, the observed buffer-bond-sample phase shifts are consistent with those estimated theoretically for a bond of about 1 μ thickness. For compressional waves at zero pressure, phase shifts are very sensitive to the buffer-sample contact: large differences in phase are observed between dry lapped, “wetted” immersed, and resin-bonded contacts. The sources of these differences are not fully understood, but they may be due to variations in contact area produced by the ultrasonic wave. “Normal” buffer-sample bonds are estimated to be capable of affecting measured pressure derivatives by about 0.25. The behavior of the anomalous buffer-sample phase shifts under pressure is unknown, but the shifts could easily give rise to substantial errors in measured pressure derivatives.

Combination optical low pass filter capable of phase and amplitude modulation

Abstract: A combination optical low pass filter adapted for use in a single or double tube color television camera is provided with a phase retarding pattern on a transparent substrate. The pattern includes optical elements having a transmissivity which varies with the wavelength of light passing there through so that the optical low pass filter functions as both a phase diffraction and an amplitude diffraction filter. Medium indexed filler material can further supplement the pattern to eliminate any light scattering.

Optical resolution through a turbulent medium with adaptive phase compensations

Abstract: The theory of short-term average modulation transfer function developed by Fried is extended by considering the correlation between the turbulence-induced phase distortion and the residual phase aberrations after adaptive phase compensations. Calculation of the optical resolution shows that the original approximation is valid for the normalized lens diameter D/r0 less than 4.0; conversely, for D/r0 greater than 4.0 the optical resolution becomes arbitrarily large because the MTF is unrealistically overcorrected at high spatial frequencies. The extended formulation is then applied to the cases with higher-order phase compensations such as focus and astigmatism. The peak optical resolution occurs at larger values of D/r0 when the higher-order corrections are included.

Dispersion relations for complex reflectivities

Abstract: A simplified derivation of the dispersion relations connecting the phase and amplitude of the normal optical reflectivity of a vacuum-matter interface is presented. The non-Kramers-Kronig form of the expression for reflectivity in terms of phase is shown to be a consequence of the fact that amplitudes are determined only up to a multiplicative constant by the phase. The phase, however, is uniquely determined by the amplitude.

Phase fluctuations in a turbulent medium

Abstract: General relationships are shown relating the log-amplitude and the phase fluctuations to the Rytov geometric optical solution for the phase fluctuation under the assumption of normal distribution for the log-amplitude and the phase fluctuations. In the weak fluctuation region, this general relationship reduces to the Rytov solution. In the strong fluctuation region, the phase correlation function is shown to approach the Rytov geometric optical solution.

Absolute value optimization to estimate phase properties of stochastic time series (Corresp.)

Abstract: Most existing deconvolution techniques are incapable of determining phase properties of wavelets from time series data; to assure a unique solution, {\em minimum phase} is usually assumed. It is demonstrated, for moving average processes of order one, that deconvolution filtering using the absolute value norm provides an estimate of the wavelet shape that has the correct phase character when the random driving process is nonnormal. Numerical tests show that this result probably applies to more general processes.

Automatic two wavelength photoelasticimeter

Abstract: An automatic two wavelength photoelasticimeter comprising, in succession, a light source for emitting light having at least two wavelengths, λ1 and λ2 ; a polarizer rotating at constant speed, an orientable quarter-wave plate of orientation β with respect to a reference axis; a model to be analyzed exhibiting double-refraction and having a fast axis which forms an angle θ with respect to the reference axis and which provides a phase shift φ (which parameters θ and φ are to be measured) and three photodetectors 5, 6, and 7 preceded by analyzers 10, 11 and 12 respectively. The photodetectors 6 and 7 are preceded by filters 8 and 9 of wavelengths λ1 and λ2 respectively. The difference between the phases of the signals of the frequency 2ω at the outputs of the photodetectors 6 and 7 supplies the difference between the phase shifts contributed by the model from these two wavelengths, the quarter-wave plate being oriented along the bisectors of the axes of double refraction of the model at the point in question. The apparatus is applicable to photoelasticimetry on strongly photoelastic materials and materiasl under high stress.

Open-loop electric drive with corrective controller

Abstract: A controller minimizes periodic torque or force perturbations in an inductor-type synchronous motor drive by supplying current waveforms to each motor phase that contain a fundamental frequency component and selected harmonic components. The harmonic components in the phase currents heterodyne with the periodic permanent magnet flux fundamental frequency to create periodic torques or forces which subtract from the unwanted torques or forces perturbing the moving portion of the motor. The controller, which includes an interpolator, a memory, and a converter, provides for smooth incremental movement of a member such as a plot head, at substantially constant velocity, by applying selected continuous periodic waveform signals as phase currents to the windings of inductor-type synchronous motors.

Measurement of ultrasonic dispersion by phase comparison of continuous harmonic waves

Abstract: The method of phase comparison of continuous waves is applied to determine the dispersion relation, phase, and group velocities as a function of frequency of dispersive materials. A combination of the variable frequency method and the variable path‐length method is found necessary to eliminate any uncertainty in the dispersion relation determination. Experiments are performed on specimens of various thickness. A constraint equation can be derived since the dispersion relation is unique and independent of the specimen thickness. This equation provides a procedure for determining the absolute number of wavelengths in the specimen. Measurements in unidirectional, fiber‐reinforced boron–epoxy specimens show good agreement with results reported previously.

Method for classifying and measuring of timbers

Abstract: Lumber is classified in terms of knots. The method used employs high frequency radio energy and a detector responsive to phase to detect the energy passing through the lumber. The knots exhibit a different dielectric constant, the real part of which is different from normal wood, and the difference in phase of the radiation detected effects the measurement. Preferably, the frequency radiation is near 10 GHz.

Amti target/clutter discriminator

Abstract: In an AMTI radar of the type in which the difference between the phase of a current radar return signal and the phase of a radar return signal in a corresponding range bin of a preceding pulse repetition interval (PRI) is averaged over a number of range bins in the range vicinity of the current range bin, phase differences for current range bins are determined as being clutter-like or non-clutter-like by comparison with the previously-determined average phase difference by means of a rectangular distance discriminator which compares the normalized in-phase and quadrature components (cosine and sine, respectively) of the current phase difference with the normalized in-phase and quadrature components of the average phase difference in a rectangular distance discriminator. The rectangular distance discriminator sums the absolute values of the in-phase difference and the quadrature difference and compares them against a rectangular distance discriminant, which in a preferred embodiment is unity. When the summation of the absolute value of the in-phase and quadrature differences exceed the discriminant, the previously-determined phase average components are reintroduced into the phase averaging process; but when it is less than the discriminant, the current phase differences are introduced into the phase averaging process.

Circadian Rhythm of Output from Neurones in the Eye of Aplysia: IV. A Model of the Clock: Differential Sensitivity to Light and Low Temperature Pulses

Abstract: 1. 1. A relaxation oscillator, feed-back model for the circadian clock in the eye of Aplysia is proposed to account for the experimental findings described earlier. Further data on the effects of light pulses and temperature pulses are reported here to test the hypothesis that light and temperature perturb the clock oscillation at different points in the feed-back loop. 2. 2. The rising phase of the CAP frequency rhythm is postulated to be due to an energy-requiring, synthesis process, and the falling phase to a passive, diffusional process. Synthesis produces a substance, C , which controls CAP frequency, and the level of which oscillates about a reference level, R . 3. 3. The synthesis phase of the oscillation is suggested to be temperature compensated from about 9 °C to at least 22.5 °C. Cooling the eye to 6 °C for long periods therefore inhibits synthesis so that the clock eventually stops at its lowest phase point. 4. 4. 12 h cold pulses of 4 °C applied during the rising phase of the rhythm (i.e. during synthesis) cause large phase delays (9 h), while similar cold pulses applied during the falling phase (i.e. during diffusion} cause only small phase delays (2 h). 5. 5. The action of light is to lower the value of the reference level, R , so that the constant illumination damps the oscillation until the clock is stopped at its lowest phase point. 6. 6. The model predicts that light pulses applied during the rising phase will effectively accelerate the increase in level of C , thus causing phase advances, while phase delays will result from light pulses applied during the falling phase. A phase response curve for 2 h, 1100 lux light pulses confirms this. A rhythm splitting effect due to an appropriately timed light pulse is predicted and tested. 7. 7. Possibilities of clock control of the CAP generating mechanism are discussed with reference to recent findings on the regulation of membrane potential oscillations in molluscan bursting pacemaker neurones. Note: Laboratory of Sensory Sciences, University of Hawaii at Manoa, 1993 East-West Road, Honolulu, Hawaii 96822, U.S.A.

Transmission and reflection of Rayleigh wave through a step

Abstract: The transmission and reflection of a Rayleigh wave through a step on a homogeneous half-space of Poisson9s ratio σ = 0.253 have been investigated by a seismic models method. The experimental results show good agreement with numerical ones obtained by finite-difference calculations when the wave is incident onto a downward step. Phase shifts are given both for the upward and downward steps. The characteristics of the transmitted wave do not depend much on the direction of propagation but those of the reflected wave are clearly direction-dependent. In each case the transmission and reflection coefficients and phase shifts depend on the ratio of step height to wavelength. The group delays are calculated and they are positive or negative depending on the period. About 80 per cent of the incident energy is converted into body waves when the step is higher than 0.3 times the wavelength of the Rayleigh wave.

Equilibrium position of a phase boundary under horizontally varying surface loads

Abstract: Summary A two-dimensional and a three-dimensional cylindrically symmetric model are used to determine the change in equilibrium position of a phase boundary when horizontally varying loads are applied at the Earth's surface. Under the assumption that the phase boundary motion is relatively small, the problem is reduced to a linear integral equation that is solved by integral transform techniques. The results of the study show that: (1) the effects of the elastic deformations caused by the phase boundary motion are negligible as long as the surface load contains only large wavelengths (compared to the depth of the phase boundary); (2) the conclusions reached with one-dimensional models on the amplitude of the phase boundary motion are valid in the regions where the load does not vary rapidly over distances of the order of the phase boundary depth; (3) these models confirm the conclusions of one-dimensional models on the importance of phase changes in the lithosphere for explaining the subsidence of geosynclines and basins under the load of accumulating sediments when the scale of these features is larger than 200–300 km.