Showing papers on "Phase (waves) published in 1974"

Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction

Abstract: The chemical mechanism of Field, Koros, and Noyes for the oscillatory Belousov reaction has been generalized by a model composed of five steps involving three independent chemical intermediates. The behavior of the resulting differential equations has been examined numerically, and it has been shown that the system traces a stable closed trajectory in three dimensional phase space. The same trajectory is attained from other phase points and even from the point corresponding to steady state solution of the differential equations. The model appears to exhibit limit cycle behavior. By stiffly coupling the concentrations of two of the intermediates, the limit cycle model can be simplified to a system described by two independent variables; this coupled system is amenable to analysis by theoretical techniques already developed for such systems.

Spin echo of spins diffusing in a bounded medium

Abstract: The effect of reflecting boundaries on the spin echo measurement of diffusion in a geometrically bounded medium is calculated by considering the accumulation of phase shifts during the spin echo process. The distribution of phase shifts is shown to be Gaussian in the limits when the time between pulses is either long or short compared to the time required for a spin to diffuse from one boundary to another. The distribution is assumed to be Gaussian in the intermediate case, and the problem is reduced to the calculation of the mean square phase change due to diffusion. Expressions for spin echo amplitudes are derived for the cases of planar, spherical, and cylindrical boundaries, and forms are derived that are valid when the time of the measurement is very long or very short compared with the time required for diffusion between boundaries.

Geometric sources of redundancy in intensity data and their use for phase determination

Abstract: Linear equations are derived in direct space, which express the relation between the electron densities of crystals built from the same molecule, but with different lattices or several identical subunits in their asymmetric units. They are shown to be equivalent to the most general 'molecular-replacement' phase equations in reciprocal space. The solution of these phase equations by the method of successive projections is discussed. This algorithm, best implemented in direct space by averaging operations, is shown to be convergent for over-determined problems, and to be equivalent to a least-squares solution of the phase equations.

Discrete Time Analyses of Nonuniform Sampling First- and Second-Order Digital Phase Lock Loops

Abstract: The present paper considers discrete time analyses of firstand second-order digital phase lock loops. These loops are characterized by the fact that they track the zero crossings of the incoming signal; consequently, the sampling intervals are nonuniform. The firstorder loop is analyzed for phase step and frequency step inputs; mean time to skip cycle is also considered. For phase step input, approximate expressions are obtained for the steady-state phase error probability density and phase error variance, the second of which leads directly to a theoretical prediction of threshold. The second-order loop is analyzed for frequency step input. Approximate expressions for the steady-state phase error probability density, phase error variance, and a theoretical prediction of threshold are obtained. The analyses are confirmed by numerical results and simulation.

Real-time wavefront correction system

Abstract: An optical imaging system having the capability of detecting and eliminating in real-time phase distortions in a wavefront being imaged by the optical system. The resolution of ground based telescopes is severely limited by random wavefront phase changes and tilts produced by atmospheric turbulence. The disclosed invention was designed to overcome this problem. In the disclosed invention, an AC, lateral shearing interferometer measures in real-time the relative phase differences of the wavefront being imaged by the optical system. Phase differences measured by the shearing interferometer are directed to an analog data processor which, in combination with other circuitry, generates a plurality of electrical signals proportional to the required phase corrections at different areas of the wavefront. The electrical signals are applied to a phase corrector upon which the wavefront is incident to change the relative phase at various locations of the wavefront to achieve a wavefront in which the phase distortion is removed. In one embodiment the phase correction device consists of a mirror having an array of piezoelectric elements which function to selectively deform the mirror to correct phase distortions in the wavefront. In a second embodiment the phase correction device consists of a refractive device which has the capability of having its index of refraction selectively changed in different areas to correct phase distortions in the wavefront.

Phase control of the voltages applied to opposite electrodes for a cholesteric to nematic phase transition display

Abstract: An electro-optical device employing liquid crystal cell, which consists of a first electrode and a second electrode opposed to the first electrode, at least one of which being light-transparent, and a liquid crystal sandwiched between the first and second electrodes, is driven by voltage pulses with special wave form and changes in its optical transmission or reflection. The liquid crystal is cholesteric liquid crystal having positive dielectric anisotropy. A first circuit connected to the first electrode generates a.c. voltage pulse having phase phi 1 for time duration T1 and a d.c. bias voltage of the same amplitude as that of the a.c. voltage pulse. A second circuit connected to the second electrode generates a.c. voltage having the same amplitude, the same bias as that of the a.c. voltage pulse and phase phi 1 switchable to another phase phi 2 for time interval T2 which is varied with the change of a signal such as image signal. This technique is extended to an X-Y matrix display device which has plural display elements formed at intersections of plural X-electrodes and plural Y-electrodes opposing to and crossing the X-electrodes with a gap.

Digital phase detector

Abstract: OF THE DISCLOSURE A digital phase detector which periodically detects the phase angle .theta.k of a carrier signal in which data are en-coded as phase changes. A coherent or differential phase-modulated carrier signal is split into its in-phase and quadrature phase components RoSin .theta.(t) and RoCos .theta.(t). Each signal component is sampled at a predetermined modulation interval and converted into a digital word having the form RoCos .theta.k and RoSin .theta.k. In one configuration, the two signal components are applied to a digital divider network which forms the quotient ? of the two digital words such that ¦?¦ ? 1. The quotient ? is applied to a data look-up ROM, programmed for Tan-1 operation, which forms a digital reference phase angle .PHI. limited to an angle ? 45°. Phase angle .PHI. is corrected by selection logic to form the desired phase angle .theta.k. Once .theta.k is known for each modulation interval, the encoded data may be readily extracted, since .theta.k represents the encoded data.

Change of chromatin morphology during the cell cycle detected by means of automated image analysis.

Abstract: Mouse embryo fibroblasts growing asynchronously in vitro stained with Feulgen method and their nuclear chromatin was analysed by means of the image analysing computer Quantimet 720D. Cells with 2C, 3C and 4C content of DNA were considered as being in G1, middle S and G2 phase of cell cycle, respectively. It was found that the projected area of nuclei increases during the cell cycle and that the mean optical density of chromatin increases from G1 through S to G2 phase. The curves showing the areas of chromatin at different optical density thresholds are different for cells in G1, S and G2 phase. The results demonstrate cyclic changes in chromatin morphology in the interphase nuclei during the cell cycle.

The IP phase measurement and inductive coupling

Abstract: Recent work by Van Voorhis et al (1973), Zonge et al (1972), Pelton (1973), and others has begun to make available some information concerning the phase shifts that accompany the IP effects used in mineral exploration. A portable system is now available to measure phase shifts in the field in the frequency range from 0.05 hz to 1.25 hz with an accuracy of a few milliradians. Field work with this system confirms that the phase shift associated with the IP effect from metallic mineralization is relatively constant at all frequencies within this frequency range. The inductive coupling effects (for the dipole‐dipole electrode configuration) give phase shifts that increase approximately linearly with frequency for a uniform or layered earth. Theoretical solutions and scale modeling suggest that this is also a valid approximation for two‐dimensional resistivity variations of considerable extent. Therefore, it should be possible to use accurate phase measurements, at several closely spaced frequencies, to separa...

The application of dispersion relations (Hilbert transforms) to phase retrieval

Abstract: A method is given for the retrieval of phase from amplitude information using the Hilbert transform, without the need for evaluating Blaschke factors.

Phase effects in a three‐component signal

Abstract: Phase effects in a particular three‐component signal, consisting of the 9th, 10th, and 11th harmonic of 200 Hz were studied. The main interest was the effect of phase changes on the prominence of the residue pitch evoked by this signal. The prominence of residue pitch appears to be correlated to the acoustical power spectrum of the signal, modified by the internally generated combination tones. An estimate of this “internal spectrum” was obtained by means of a cancellation technique. Because of an interaction of combination tones and acoustical components, this “internal spectrum” is phase‐dependent. In this context de Boer's phase rule is reconsidered. The residue pitch seems to be most prominent if there are prominent lower harmonics in the “internal spectrum.” In general, subjective phase effects in this signal, which could be described as changes in timbre, seem to be dependent on changes in the “internal spectrum.”

Phase-bunching and other non-linear processes occurring in gyroresonant wave-particle interactions

Abstract: Consideration of the movement of individual electrons in a magnetized plasma in which a monochromatic wave is propagating in the whistler mode. Simple expressions are derived which give the displacement of the electrons as a function of time, the phase angle that their velocity vector makes with the magnetic component of the wave, their pitch angle, and energy changes. A useful formula is obtained which gives the velocity range over which particles remain trapped inside the wave, as a function of the wave intensity and of the initial phase angle of the particle. It is shown that even strictly resonant particles can escape from the wave when their initial phase angle is very small. From the derived expressions, it is possible to compute the phase-bunching effect which occurs approximately at one trapping wavelength behind the leading edge of the interaction region.

Step-Tunable Far Infrared Radiation by Phase Matched Mixing in Planar-Dielectric Waveguides

Abstract: The mixing of various pairs of CO/sub 2/ laser lines in a nonlinear material can produce thousands of step-tunable far infrared (FIR) signals in the range 70-mu m-7-mm wavelength with frequency spacings of less than 0.1 cm/sup -1/. The major problem in realizing these coherent signals is achieving phase matching in a suitable nonlinear material. In this paper, the interest is in generating tunable signals at the milliwatt level in a planar-dielectric integrated-optics waveguide configuration. Phase rnatching can be achieved with cubic materials (i.e., GaAs) by adding the waveguide dispersion to the bulk dispersion. Work on the analysis of the waveguide mixing system and its correlation with experimental data are described for a planar GaAs dielectric waveguide in the 100-1000-mu m wavelength range.

Masking of tone by tone as a function of duration

Abstract: A 500‐Hz tonal signal was masked by a continuous tone, both from the same oscillator. A two‐interval‐forced‐choice procedure was used to determine the level required for 80% correct. The masker level was 50 dB SPL, and the signal was always in phase with the masker. Signal durations from 20 msec to 2 sec were employed. The results showed a slope of approximately 3 dB per doubling over the entire range from 20 msec to 1 sec. Detection at 2 sec tended to be worse than at 1 sec. The slope of 3 dB per doubling is much steeper than has commonly been found with noise maskers, especially at the longer durations. Data from an electrical model are discussed.

Steerable antenna null combiner system

Abstract: A system employing broadband radio frequency vector multipliers in a balang process for nulling out unwanted radio frequency signals. The nulling is achieved by adjustment of both the desired and interference signals as they pass through the system. The adjustment is accomplished by using vector multipliers which shift the phase by equal amounts and vary the amplitude by proportionate amounts of one or more radio frequency signals in response to separate phase shift and amplitude control forces. To obtain a desired phase shift, an incoming radio frequency signal is split into 0° and 90° components. By multiplying the 0° component by the cosine of the desired phase shift angle, multiplying the 90° component by the sine of the desired phase shift angle, and then summing the results, the signal can be phase shifted by any amounts through all four quadrants. The phase shift and amplitude control forces may be operator initiated or may be initiated through control processing to maximize the relative strength of the desired signal with respect to the interference signal.

Phase interpolating apparatus and method

Abstract: Apparatus and method is provided by means of phase interpolation for measuring and generating time intervals with greater accuracy than that provided by the frequency of the clock utilized. A multiple phase delayed and multiple regenerated scheme is used for phase interpolation, and application of the principle for delay generation and time interval measurement is shown.

Phase‐matched second‐harmonic generation in GaAs optical waveguides by focused laser beams

Abstract: Using a tunable parametric oscillator operating near 2 μm, we have observed second‐harmonic generation in a GaAs double‐heterostructure waveguide in the region of phase matching. The harmonic intensity is strongly peaked when the guide propagation constants of the TE (m=0) fundamental and TM (m=2) harmonic are equal. Away from phase matching, the characteristic effects of strong focusing in the plane of the guide are observed. These are the one‐dimensional analogs of the harmonic generation effects observed using two‐dimensional focused laser beams.

Imagery with constant range lines

Abstract: Method and apparatus for showing the relative range from an active line scan sensor to a target, the changes in range being shown on a recording medium as an alternate series of bright and dark lines. In particular, a modulated laser beam having high frequency components is utilized to illuminate the target, the reflected energy received at the sensor having the same modulation frequency but phase modified by the transit time required to make the roundtrip from the sensor to the target and return. The phase difference between the received energy and the transmitted, or reference, energy is shown on the recording medium by directing a portion of the reference energy to a detector which is also responsive to the received energy. Points in the image formed on the recording medium where the phase angles are the same can be made to appear white while the points where the phase angles differ by 180° can be made to appear black. The difference in the range between two black lines is equal to a specific sub-interval of the wavelength of the effective laser modulation frequency, the sub-interval being l/n where n is the harmonic of the effective laser modulation frequency. The scanning laser may be a mode locked laser, thereby providing a light output having high frequency components and precise frequency and phase stability.

Low Cost Design Techniques for Semiconductor Phase Shifters

Abstract: The design and performance of two microstrip semiconductor phase shifters operating at S band and UHF are described. The S-band diode phase shifter uses thick-film metallization on a 99.5-percent alumina substrate and uses series coupled diodes for the small bits and constant phase frequency switched life bits for the three large bits. The 4-bit UHF phase shifter uses eight p-i-n diodes mounted in a low dielectric constant microstrip circuit and operates at a power level of 8 kW peak, 240 W average, and has an average insertion loss of 0.7 dB. Phase and VSWR distributions on 800 units produced are also given. The characteristics of two new microwave semiconductor switching devices, the field-effect diode (FED) and the resistive gate switch are described. These devices operate with only a voltage change. Design and performance of an SP2T switch and 3-bit phase shifter using the field-effect diode are presented.

Demodulator for amplitude-and-phase modulated signals having control means for reducing phase and amplitude errors

Abstract: Amplitude-and-phase modulated signals, as received, are represented by corresponding points on a reference signal plane of points to which results of demodulation, phase errors, and amplitude errors are preliminarily assigned. Responsive to the received signals, a detector produces position signals representative of the corresponding points. Responsive to the position signals, a demodulation and error-detection circuit produces result signals, phase error signals, and amplitude error signals representative of the results of demodulation, phase errors, and amplitude errors assigned to the corresponding points. Responsive to control signals specifying a predetermined area of the reference signal plane and to the position, phase error, and amplitude error signals, a selection circuit produces phase and amplitude control signals, which correct the reference signal plane to reduce the phase and amplitude errors of the position signals. After correction, the result signals become the demodulated signals.

Characteristics of phase-aberrated nondiffraction-limited laser beams.

Abstract: To simulate nondiffraction-limited laser beams numerically, one needs to understand their nature better. For a phase aberration the correlation length of which is much less than the width of the beam, one can show that the far-field irradiance distribution can be written as the sum of two beams. One beam is the attenuated diffraction-limited beam; the other is a much wider beam the exact shape of which is closely related to the power spectrum of the phase fluctuations. Computer simulations of random phase aberrations are shown to agree well with the analytic predictions. Attempts at simulation of nondiffraction-limited beams for nonlinear wave propagation problems are discussed.