Showing papers on "Phase (waves) published in 1987"

The Adiabatic Phase and Pancharatnam's Phase for Polarized Light

Abstract: In 1955 Pancharatnam showed that a cyclic change in the state of polarization of light is accompanied by a phase shift determined by the geometry of the cycle as represented on the Poincare sphere. The phase owes its existence to the non-transitivity of Pancharatnam's connection between different states of polarization. Using the algebra of spinors and 2 × 2 Hermitian matrices, the precise relation is established between Pancharatnam's phase and the recently discovered phase change for slowly cycled quantum systems. The polarization phase is an optical analogue of the Aharonov-Bohm effect. For slow changes of polarization, the connection leading to the phase is derived from Maxwell's equations for a twisted dielectric. Pancharatnam's phase is contrasted with the phase change of circularly polarized light whose direction is cycled (e.g. when guided in a coiled optical fibre).

Light Propagation in Singly and Doubly Periodic Planar Waveguides

Abstract: Light propagation in singly and doubly periodic planar waveguides is investigated with respect to future applications in integrated optics. The waveguides used in our experiments reveal, in the vicinity of Bragg reflection, a strong difference between the directions of phase and group velocities, the beam steering. A clear graphical representation of the observable propagation effects is given in wave-vector diagrams, showing the directional dispersion of the elementary waves in periodic structures, the Floquet-Bloch waves. The dispersion phenomena were measured with high accuracy, using selective wave excitation. In conjunction with straight tapered transitions to smooth planar waveguides, the periodic structures show a great variety of strong frequency and direction-dependent effects such as lateral beam shifting and focusing with a frequency-variant focal length. Ray optics of Floquet-Bloch waves is used to describe these phenomena. Complex interference patterns observable in the vicinity of B...

A pulse ribbon model of monaural phase perception.

Abstract: This article presents two sets of experiments concerning the ability to discriminate changes in the phase spectra of wideband periodic sounds. In the first set, a series of local phase changes is used to modify the envelopes of the waves appearing at the outputs of a range of auditory filters. The size of the local phase change required for discrimination is shown to be strongly dependent on the repetition rate, intensity, and spectral location of the signal. In the second set of experiments, a global phase change is used to produce a progressive phase shift between the outputs of successive auditory filters, without changing the envelopes of the filtered waves. Contrary to what is often assumed, listeners can discriminate between‐channel phase shifts once the total time delay across the channels containing the signal reaches 4–5 ms. In this case, however, the discrimination is largely independent of signal parameters other than bandwidth. A highly simplified model of the cochlea, consisting of an auditory filter bank and units that record the times of the larger peaks in the filter outputs, is developed to explain the two contrasting sets of results.

Phase retrieval and twin-image elimination for in-line Fresnel holograms

Abstract: Fourier phase-retrieval algorithms are modified and applied to in-line holography, where phase is lost during the hologram recording process. Retrieval of phase permits separation of real-object distributions from the twin-image interference that accompanies conventional optical reconstruction. The rate of convergence is enhanced by the availability of a good initial guess based on the digital equivalent of conventional optical reconstruction.

Steady-State Magnetizations in Rapid NMR Imaging Using Small Flip Angles and Short Repetition Intervals

Abstract: The steady-state magnetizations in three versions of rapid NMR imaging using small flip angles and short repetition intervals are studied. It is shown that in the original version, the estimation using (1 - E1) sin ?/(1 - E1 cos ?) contains errors that depend on the increment of the phase rotation angle arising from the phase encoding process. The modified version of rapid imaging, where the phase rotation due to the phase encoding process is compensated for in each time interval, can have sensitivity superior to the original version where the phase rotation is not compensated for. Here, flip angles larger than the Ernst angle must be used. In the third version, the steady-state magnetization is obtained by a rapid imaging sequence in which the phase rotations arising not only from the application of the phase encoding gradient but also from the applications of other gradients are compensated for. Analysis of this version showed a remarkable increase in sensitivity although it required the use of an extremely uniform field. It is estimated that this increase reaches 80 percent with a repetition interval of 10 ms, although a field uniformity less than 1 ?T is necessary.

Digital phase-measuring interferometry with a tunable laser diode.

Abstract: A digital phase-measuring interferometer with a laser-diode source has been developed that is based on a fringe-scanning technique with a stepwise wavelength change by variation of the laser injection current. The phase is changed to produce a relative phase difference between the beams in the two arms of the interferometer. Calibrated phase shifts used for a phase-extraction algorithm are derived from one-dimensional least-squares fits to cosine fringe functions to achieve accurate results. Experimental results are presented.

Submicrosecond electro‐optic switching in the liquid‐crystal smectic A phase: The soft‐mode ferroelectric effect

Abstract: A new liquid‐crystal electro‐optic modulating device similar to the surface‐stabilized ferroelectric liquid‐crystal device is described. It uses the same kind of ferroelectric chiral smectics and the same geometry as that device (thin sample in the ‘‘bookshelf ’’ layer arrangement) but instead of using a tilted smectic phase like the C* phase, it utilizes the above‐lying, nonferroelectric A phase, taking advantage of the electroclinic effect. The achievable optical intensity modulation that can be detected through the full range of the A phase is considerably lower than for the surface‐stabilized device, but the response is much faster. Furthermore, the response is strictly linear with respect to the applied electric field. The device concept is thus appropriate for modulator rather than for display applications. We describe the underlying physics and present measurements of induced tilt angle, of light modulation depth, and of rise time.

Effect of piezoelectric transducer nonlinearity on phase shift interferometry.

Abstract: If the nonlinearity of the motion of a piezoelectric transducer (PZT) can be described as a quadratic function, the integrated intensity of one frame in phase shift interferometry can be calculated using the Fresnel integral. For a PZT with smaller nonlinearity, the rms phase error is almost linearly proportional to the quadratic coefficient. The effects of PZT nonlinearity on the three- and the four-bucket algorithms are compared.

Optical modulation apparatus and measurement method

Abstract: In an optical micromechanical method for changing the phase of guided waves and a measurement method for measuring very small mechanical displacements and/or mechanical forces or pressures, including the pressure of sound waves and ultrasonic waves, and/or accelerations, the distance d between a section (1') of an optical waveguide (1) in an integrated optic or fibre optic circuit and a phase-shifting element (5) separated from said section (1') by a gap (4) is varied by forces (6) or by thermal expansion due to changes in temperature. The phase of the guided wave (3) is thereby modulated, and reciprocally the changes in distance d and hence small mechanical displacements and the forces (6) which produce them are determined from the measured phase changes.

Over 720 Ghz (5. 8nm) frequency tuning by a 1.5 μm DBR laser with phase and Bragg wavelength control regions

Abstract: A 15 μm distributed Bragg reflector (DBR) laser with phase and Bragg wavelength control regions was newly developed Over 720 GHz (58 nm) continuous frequency tuning with 2mW light output were achieved for the first time

A New Phase Correction Method in NMR Imaging Based on Autocorrelation and Histogram Analysis

Abstract: A new statistical approach to phase correction in NMR imaging is proposed. The proposed scheme consists of first-and zero-order phase corrections each by the inverse multiplication of estimated phase error. The first-order error is estimated by the phase of autocorrelation calculated from the complex valued phase distorted image while the zero-order correction factor is extracted from the histogram of phase distribution of the first-order corrected image. Since all the correction procedures are performed on the spatial domain after completion of data acquisition, no prior adjustments or additional measurements are required. The algorithm can be applicable to most of the phase-involved NMR imaging techniques including inversion recovery imaging, quadrature modulated imaging, spectroscopic imaging, and flow imaging, etc. Some experimental results with inversion recovery imaging as well as quadrature spectroscopic imaging are shown to demonstrate the usefulness of the algorithm.

Arrangement for generating natural resonant oscillations of a mechanical oscillating system

Abstract: An arrangement for generating natural resonant oscillations of a mechanical oscillating system includes an electromechanical oscillation exciter which on excitation by an electrical excitation signal generates a drive force setting the oscillating system in mechanical oscillations, an oscillation sensor which is formed as displacement sensor and senses the mechanical oscillations of the oscillating system and converts them to an electrical sensor signal, and an excitation circuit which receives the sensor signal and supplies to the oscillation exciter the electrical excitation signal with the frequency of the sensor signal. The excitation circuit includes a phase control circuit which controls the phase position of the excitation signal in dependence upon the phase position of the sensor signal. A phase shift circuit produces a phase displacement of 90° between the sensor signal and the excitation signal so that the phase condition for the excitation of the mechanical oscillations at the natural resonant frequency of the mechanical oscillating system is fulfilled. This makes it possible to maintain the natural resonant frequency of the mechanical oscillating system with very great accuracy and high stability with time even with oscillating systems of high quality.

Instantaneous and time-averaged energy transfer in acoustic fields

Abstract: The fundamentals of energy transfer in an acoustic field are addressed and it is shown that describing the flux of energy in an acoustic field with the active intensity alone is inaccurate. A single active intensity vector describes only the time‐average energy flux at a point in space, but not where the energy came from nor where it is going. Consequently, the instantaneous intensity must be used to properly describe energy flux as a time‐dependent process. The phenomenon of the acoustic vortex is examined and, from the perspective of active intensity, it is seen to represent a resultant wave rotating around a zero pressure line or point at which the pressure phase is discontinuous. It is shown that this resultant wave travels with a phase speed cp, which is generally different than the plane‐wave phase speed c. The instantaneous intensity, however, shows that energy is flowing through the vortex and not with the resultant waves. Although the complex intensity vector is normally separated into the active...

Optical tracking novelty filter.

Abstract: We demonstrate an optical filter that displays the time-dependent features of a scene. The heart of the device is an interferometer that is sensitive not to the difference between two optical paths lengths but to changes in the path-length difference. The interferometer arms share a phase-conjugating mirror. The phase conjugator ensures that, at steady state, the output of the interferometer is dark. The response of the interferometer to a step differential change in the optical lengths is a decaying exponential having a time constant governed by the time response of the phase conjugator. The interferometer may be used to monitor time- and space-dependent optical phase changes that are due, for example, to transparent fluid motion. With a modified liquid-crystal television used as a spatial light phase modulator in the interferometer, we detect time-dependent features of an image viewed by a video camera.

Comparison Of Phase-Measurement Algorithms

Abstract: Phase-measurement algorithms for calculating the phase of a wavefront from interference fringe data are compared. Experimental data show that different algorithms yield different phase values when using the same intensity data. A computer simulation of errors due to phase-shifter miscalibration and nonlinearity, as well as detector nonlinearity is performed to show that certain algorithms are more sensitive to some errors than others. Dependences of each of these errors is found versus percent of error over a 2ic range of phase values. These results enable the determination of what system errors are present in a phase-measurement interferometer.

An electrostatic probe technique for RF plasma

Abstract: The use of electrostatic probes in radio frequency (RF) generated plasmas is discussed. A technique is demonstrated in which the RF potential difference between probe and plasma is removed by driving the probe with synchronous RF of suitable phase and amplitude. An application of this technique is the measurement of electrical structure within a 13.56 MHz argon discharge.

Sinusoidal phase modulating interferometer using the integrating-bucket method

Abstract: We describe a sinusoidal phase modulating interferometer in which a CCD image sensor detects four values by integrating the time-varying intensity in an interference pattern for intervals of one-quarter period of the phase modulation. The optimum amplitude and phase of the sinusoidal phase modulation are determined. The measurement error caused by the additive noise and the deviation from the optimum phase modulation is analyzed. The experimental results for surface profiles of magnetic sliders show that the sinusoidal phase modulating interferometer proposed here yields a measurement accuracy of the order of 1 nm.

Lithography mask with a π-phase shifting attenuator

Abstract: The mask includes an attenuator which passes a fraction of the incident electromagnetic radiation and phase shifts the radiation relative to the radiation passing through open features of the mask by approximately an odd multiple of π radians. This phase shifting of light passing through the attenuator by π radians reduces the edge blurring that results from diffraction effects. The present invention steepens the slope of the intensity profile at the edges of features in x-ray lithographic replication relative to the slope obtained with a conventional x-ray mask. The steeper slope is a highly significant advantage because it permits improved linewidth control.

High resolution imaging doppler interferometer

Abstract: A system for simultaneously locating a plurality of targets and distinguishing the targets from noise which utilizes phase detector techniques to generate complex voltage signals and obtain phase information. Spectral analysis is performed on the complex voltage temporal functions to generate doppler frequency functions. Both spectral phase functions and spectral amplitude functions are generated from the doppler frequency functions. Spectral phase functions are analyzed using interferometry techniques to determine if a potential target has a common locational source from returns of a plurality of sensors. A zenith angle is also generated using interferometry techniques to provide locational information of the multiple targets. Range gating and two frequency range detection methods provide high resolution range information as to the location of the targets. High resolution range information and two dimensional zenith angle information are used to provide an image of the targets. The present invention uses a two-frequency pulse which can be generated simultaneously or sequenced within a pulse in a manner which is phase coherent. The two-frequency pulse eliminates problems associated with range aliasing, zenith angle aliasing, scattering point analysis and allows for range location with high resolution. An error correction factor is also generated which eliminates spectral smearing.

A new method for synthesis of low-peak-factor signals

Abstract: For a specified power spectrum, the minimum-to-maximum amplitude range of a periodic signal depends on the phase angles of the harmonics. A low value of this range, which as a fraction of the root-mean-square value is usually called the peak factor, is often desirable. A new phase angle adjusting method is proposed producing lower peak factors than the conventional method.

Measurement of optical phase with subpicosecond resolution by time-domain interferometry.

Abstract: A new and extremely general interferometric technique has been experimentally demonstrated that permits the direct measurement of optical phase on a subpicosecond time scale. The intensity is characterized by cross correlation, and thus the optical field is completely determined.

Waves in the Solar Photosphere

Abstract: Time-sequences of line profile data have been subjected to a unique analysis which produces an amplitude and phase of the velocity and intensity at several line depths for each time sample and spatial point on the Sun. The data have been filtered to pass only the frequencies and spatial wavenumbers of the 5-min band. Yet, a secondary oscillation emerges, the phase of which propagates downward. Empirical eigenfunctions for velocity and intensity are given, and the kinetic energy flux is computed.

New common-path phase shifting interferometer using a polarization technique.

Abstract: A new type of phase shifting interferometer with a common-path arrangement using a polarization technique is proposed and discussed. In the interferometer, the dc (specular) component of an object beam is separated in the Fourier transform plane and used as a reference beam for its ac component. The phase of the dc component used as the reference beam is shifted by using a polarization technique for phase shifting interferometry. The present interferometer is different from a shearing type in that the phase distribution of an object beam is directly analyzed from the acquired intensity variations obtained by a 2-D detector such as a TV camera. Some experiments were conducted to verify the validity of the present phase shifting interferometer. They showed that high stability of the phase measurements is achieved up to λ/200 with an accuracy of λ/40 for wavelength λ light. The interferometer is suitable for obtaining 2-D phase information about the surface structure of small objects.

Color-selective circular polarizer and its use

Abstract: The circular polarizer comprises a liquid crystal cell, the liquid crystal layer (8) of which is present as a so-called "blue phase" and can be exposed to a variable electric field. The blue phase is an optically isotropic chiral phase which, like the cholesteric phase, reflects circularly polarized light within a narrow frequency band and accordingly, in this spectral region, transmits only light which is circularly polarized (in the opposite sense). Under the influence of the field, the reflection band changes its position and can be shifted almost continuously from blue to red by means of relatively small voltage changes. The circular polarizer can, by means of simple additional measures, for instance by including a color-neutral circular polarizer, be developed into a color modulator and, in particular, it also makes a multi-colored display of information possible.

Phase locked loop circuit with quickly recoverable stability

Abstract: A PLL circuit for a phase comparator, a low-pass filter (LPF), a voltage-controlled oscillator (VCO) and a frequency divider. A first control circuit is responsive to a discontinuous phase change of a reference signal of the PLL circuit for inhibiting the operation of the phase comparator or disconnecting the LPF from the phase comparator during a predetermined period so that the discontinuous phase change information is not transmitted through the LPF to the VCO. At the same time, a second control circuit resets the frequency divider by a pulse of the reference signal after the discontinuous phase change or applies a voltage corresponding to the discontinuous phase change to the VCO so that the output signal of the frequency divider is locked in phase to the reference signal after the discontinuous phase change. With the cooperation of the first and second control circuits, the PLL circuit quickly recovers its stable state after the discontinuous phase change of the reference signal.

Response of a Fabry-Perot cavity to phase modulated light

Abstract: We present a solution to the lock‐in detection method which is valid for arbitrary values of the modulation frequency. Our solutions agree with the results of the quasistatic theory, in the limit of small modulation frequency compared to the resonance linewidth.

Fiber optical discrete phase modulation system

Abstract: A technique for applying selected phase delays to an optical carrier signal, the phase delays being referenced to a radio-frequency (rf) subcarrier signal. The optical signal to be phase delayed is introduced into a phase delay network comprising multiple optical paths and multiple electro-optical switches, controllable by signals generated in switching logic. The selected delays can be introduced for purposes of data modulation, or for steering an antenna beam in a phased-array antenna. As applied to the phased-array antenna system, the invention includes a data modulator, a series of star couplers for splitting the optical carrier into multiple elemental carriers, and multiple phase shifters for applying selected phase shifts to the elemental carrier signals, to effect antenna beam steering.