Showing papers on "Phase (waves) published in 1995"
TL;DR: Measurements of the birefringence of a single atom strongly coupled to a high-finesse optical resonator are reported, with nonlinear phase shifts observed for an intracavity photon number much less than one.
Abstract: Measurements of the birefringence of a single atom strongly coupled to a high-finesse optical resonator are reported, with nonlinear phase shifts observed for an intracavity photon number much less than one. A proposal to utilize the measured conditional phase shifts for implementing quantum logic via a quantum-phase gate (QPG) is considered. Within the context of a simple model for the field transformation, the parameters of the "truth table" for the QPG are determined.
1,189 citations
TL;DR: In this article, dual-quadrature spectral interferometry and Fourier transform (FT) were used to obtain a complete measurement of the complex electric field, E(ω), as a continuous function of frequency.
Abstract: Although nonlinear methods can provide only the amplitude and the phase of an isolated ultrashort pulse, linear techniques can yield such measurements with a much better sensitivity and reliability when a reference pulse is available. We demonstrate two such methods, dual-quadrature spectral interferometry and Fourier-transform spectral interferometry. These techniques are simple to implement, very sensitive, and provide a complete measurement of the complex electric field, E(ω), as a continuous function of frequency.
942 citations
TL;DR: In this paper, the influence of the tip geometry on the local magnification and atom positioning on a long-range-ordered phase was analyzed and the proposed procedure was validated by studying the effects of calculations.
406 citations
TL;DR: In this article, a scanning white-light interferometer for high-precision surface structure analysis is described, where the interferogram for each of the image points in the field of view is generated simultaneously by scanning the object in a direction perpendicular to the object surface, while recording detector data in digital memory.
Abstract: We describe a scanning white-light interferometer for high-precision surface structure analysis. Interferograms for each of the image points in the field of view of the instrument are generated simultaneously by scanning the object in a direction perpendicular to the object surface, while recording detector data in digital memory. These interferograms are then transformed into the spatial frequency domain and the surface height for each point is obtained by examination of the complex phase as a function of frequency. The final step is the creation of a complete three-dimensional image constructed from the height data and corresponding image plane coordinates. The measurement repeatability is better than 0·5 nm r.m.s. for a surface height range of 100 μm.
401 citations
TL;DR: It is found that previous results using template phasing accurate to 1.5PN order actually underestimated the errors in scrM, reduced mass, andspin parameters, and that for two inspiraling neutron stars, the measurement errors increase by less than 16%.
Abstract: The parameters of inspiraling compact binaries can be estimated using matched filtering of gravitational-waveform templates against the output of laser-interferometric gravitational-wave detectors. The estimates are most sensitive to the accuracy with which the phases of the template and signal waveforms match over the many cycles received in the detector frequency bandwidth. Using a recently calculated formula, accurate to second post-Newtonian (2PN) order [order (v/c${)}^{4}$, where v is the orbital velocity], for the frequency sweep (dF/dt) induced by gravitational radiation damping, we study the statistical errors in the determination of such source parameters as the ``chirp mass'' scrM, reduced mass \ensuremath{\mu}, and spin parameters \ensuremath{\beta} and \ensuremath{\sigma} (related to spin-orbit and spin-spin effects, respectively). We find that previous results using template phasing accurate to 1.5PN order actually underestimated the errors in scrM, \ensuremath{\mu}, and \ensuremath{\beta}. Templates with 2PN phasing yield somewhat larger measurement errors because the 2PN corrections act to suppress slightly the importance of spin-orbit contributions to the phase, thereby increasing the measurement error on \ensuremath{\beta}. This, in turn, results in larger measurement errors on scrM and \ensuremath{\mu} because of the strong correlations among the parameters. For two inspiraling neutron stars, the measurement errors increase by less than 16%.
350 citations
TL;DR: In this paper, a large data set of fundamental-mode Rayleigh and Love waveforms was used to obtain global phase-velocity maps in the period range 40-150 s.
Abstract: SUMMARY
Although much is known of the 3-D structure of the Earth, existing models do not make use of much that is known about the large structural perturbations near the surface. It has long been known, for example, that continental and oceanic crustal structures are quite different, and that these differences are evident in the dispersion of Love and Rayleigh waves sampling continental and oceanic paths. Such differences are largest at periods of less than about 100 s. Existing global models do not adequately account for such data, and make allowances for crustal structure in a very approximate way, owing to the incompleteness of information on the global distribution of crustal parameters. As a result, variations in, for example, crustal thickness translate themselves into model artefacts extending to great depth. This can be seen as one aspect of the imperfect resolution of the existing global models. In order to construct higher resolution models of the Earth's outer shell (0-200 km depth), it is necessary to gain more precise knowledge of near-surface structure by incorporating data that have sensitivity to the details of the depth distribution of heterogeneity near the surface. As a first step we analyse a large data set of fundamental-mode Rayleigh and Love waveforms to obtain global phase-velocity maps in the period range 40–150 s. Minor and major arc phase velocities have been determined from about 24 000 digital GDSN and GEOSCOPE seismograms recorded between 1980 and 1990. In order to make such measurements in an automatic way, we have developed a method, using non-linear waveform inversion, in which velocity and amplitude, as a function of frequency, are expanded in B-splines. The waveform data are inverted for the B-spline coefficients, with the application of an explicit smoothness constraint that protects against unwanted effects, such as those due to notches in the amplitude spectra, and avoids some of the problems associated with the phase ambiguity. The cost function (which is minimized in a least-squares sense) presents many local minima, and a good initial model is needed; this is derived by integration of group velocities.
The measurements made using this new technique are then used in a global inversion for phase-velocity distributions of Love and Rayleigh waves, expressed in terms of a spherical harmonic expansion. We show resulting phase-velocity maps up to degree and order 40. These maps are corrected for possible artefacts due to the truncation of the spherical harmonic expansion. We present a detailed resolution analysis which shows that global lateral resolution for surface-wave tomography is of the order of 2000 km. Love-wave phase velocities show a high correlation with known upper mantle structure at long periods and with crustal structure at shorter periods. Similarly, Rayleigh-wave phase velocities correlate well with known tectonic features, but show no clear crustal signature owing to their different sampling of the structure with depth.
293 citations
TL;DR: In this article, the direction of emission of photoexcited electrons in semiconductors is controlled by adjusting the relative phase difference between a mid-infrared radiation and its second harmonic, which is achieved by using quantum interference of electrons produced with one-and two-photon bound-to-free intersubband transitions in AlGaAs/GaAs quantum well superlattices.
Abstract: The direction of emission of photoexcited electrons in semiconductors is controlled by adjusting the relative phase difference between a midinfrared radiation and its second harmonic. This is achieved by using quantum interference of electrons produced with one- and two-photon bound-to-free intersubband transitions in AlGaAs/GaAs quantum well superlattices.
272 citations
TL;DR: In this article, a quasi-phase-matched optical parametric oscillator, using bulk periodically poled LiNbO(3), was reported, which was pumped by a 1.064-microm Q-switched Nd:YAG laser, was temperature tuned over the wavelength range 1.66-2.95 microm.
Abstract: We report a quasi-phase-matched optical parametric oscillator, using bulk periodically poled LiNbO(3). The optical parametric oscillator, pumped by a 1.064-microm Q-switched Nd:YAG laser, was temperature tuned over the wavelength range 1.66-2.95 microm. The oscillation threshold of approximately 0.1 mJ was more than a factor of 10 below the damage limit. The LiNbO(3) crystal, fabricated by application of an electric field to a sample with liquid and metal surface electrodes, was 0.5 mm thick with a 5.2-mm interaction length and a quasi-phase-matched period of 31 microm.
259 citations
TL;DR: In this paper, a general procedure for constructing phase shifting algorithms that eliminate the effects of nonsinusoidal waveform characteristics is presented. But when the phase shift calibration is inaccurate, these algorithms cannot eliminate the effect of nonsinsooidal characteristics.
Abstract: In phase measurement systems that use phase shifting techniques, phase errors that are due to nonsinusoidal waveforms can be minimized by applying synchronous phase shifting algorithms with more than four samples. However, when the phase shift calibration is inaccurate, these algorithms cannot eliminate the effects of nonsinusoidal characteristics. It is shown that, when a number of samples beyond one period of a waveform such as a fringe pattern are taken, phase errors that are due to the harmonic components of the waveform can be eliminated, even when there exists a constant error in the phase shift interval. A general procedure for constructing phase shifting algorithms that eliminate these errors is derived. It is shown that 2j + 3 samples are necessary for the elimination of the effects of higher harmonic components up to the jth order. As examples, three algorithms are derived, in which the effects of harmonic components of low orders can be eliminated in the presence of a constant error in the phase shift interval.
242 citations
TL;DR: In this article, an iterative range filtering technique was proposed to separate the differential propagation phase and differential backscatter phase under a wider variety of conditions than is possible with a simple range filter.
Abstract: Copolar differential phase is composed of two components, namely, differential propagation phase and differential backscatter phase. To estimate specific differential phase KDP, these two phase components must first be separated when significant differential backscatter phase is present. This paper presents an iterative range filtering technique that can separate these phase components under a wider variety of conditions than is possible with a simple range filter. This technique may also be used when estimating hail signals from range profiles of dual-frequency reflectivity ratios.
230 citations
TL;DR: In this article, a rigorous analysis of ultrashort pulse shaping by the spectral filtering of dispersed frequency components is presented, focusing on the case of two liquid-crystal spatial light modulators used to provide programmable manipulation of both the phase and amplitude profiles of the shaped waveform in the time domain.
Abstract: A rigorous analysis of ultrashort pulse shaping by the spectral filtering of dispersed frequency components is presented. Particular attention is directed toward the case of two liquid-crystal spatial light modulators used to provide programmable manipulation of both the phase and the amplitude profiles of the shaped waveform in the time domain. Different optical configurations are evaluated and their theoretical and practical effects determined. An important result is that, even with optimal alignment and components, the diffraction arising from spectral filtering necessarily produces a transverse spatial shift that varies linearly along the temporal profile of the shaped waveform. Despite this effect it is shown that the technique can generate arbitrary phase and amplitude temporal profiles (subject to limitations in temporal extent and temporal resolution) for the Gaussian spatial component of the shaped output waveform.
TL;DR: It is shown that adaptive phase measurements can approach optimal phase measurements for states with both low and high mean photon numbers.
Abstract: In standard single-shot measurements of the phase of an optical mode, the phase and amplitude quadratures are jointly measured, and the latter information discarded. These techniques are consequently suboptimal. Here I suggest an adaptive scheme, whereby the phase is estimated from the results so far and fed back to control the phase of the local oscillator so as to measure the (estimated) phase quadrature only. I show that adaptive phase measurements can approach optimal phase measurements for states with both low and high mean photon numbers.
TL;DR: A gross approximation of the mean relative phase for the intended coordination pattern occurred quickly, but the attainment of stability occurred much more gradually, and results were accompanied by changes in pattern stability across practice and on various transfer tests.
Abstract: The purposes of the research reported here were (a) to examine changes in relative phase during the acquisition of a new coordination pattern and (b) to determine the effect of learning this pattern on the ability to perform other coordination patterns. Ten subjects practiced an upper limb coordination task that required a 90 degrees phase offset and different amplitudes for each arm. A gross approximation of the mean relative phase for the intended coordination pattern occurred quickly, but the attainment of stability occurred much more gradually. These results were accompanied by changes in pattern stability across practice and on various transfer tests. Learning of the new coordination pattern also affected the stability of the antiphase mode, but this effect was only temporary.
TL;DR: It is shown that although the reflection characteristics can be accurately modeled with the second-order EMT, the phase difference created by form birefringence for TE- and TM-polarized waves requires the use of a more rigorous, RCWA approach.
Abstract: Diffraction characteristics of high-spatial-frequency (HSF) gratings are evaluated for application to polarization-selective computer-generated holograms by the use of two different approaches: second-order effective-medium theory (EMT) and rigorous coupled-wave analysis (RCWA). The reflectivities and the phase differences for TE- and TM-polarized waves are investigated in terms of various input parameters, and results obtained with second-order EMT and RCWA are compared. It is shown that although the reflection characteristics can be accurately modeled with the second-order EMT, the phase difference created by form birefringence for TE- and TM-polarized waves requires the use of a more rigorous, RCWA approach. The design of HSF gratings in terms of their form birefringence and reflectivity properties is discussed in conjunction with polarization-selective computer-generated holograms. A specific design optimization example furnishes a grating profile that provides a trade-off between the largest form birefringence and the lowest reflectivities.
TL;DR: The 1/n limit achieved here is independent of the interferometer phase shift; prior information about the expected phase shift is not necessary to attain this limit.
Abstract: Quantum information theory is applied to practical interferometer-based phase measurements to deduce the optimal phase measurement scheme with two optical modes Optimal phase measurements, given ideal input states, reveal an asymptotic $1/n$ decrease in phase uncertainty $\ensuremath{\Delta}\ensuremath{\theta}$ for $n$ the mean photon number of the input state In contradistinction to previous schemes for realizing the number-phase uncertainty limit, the $1/n$ limit achieved here is independent of the interferometer phase shift; prior information about the expected phase shift is not necessary to attain this limit These results apply more generally to su(2) and so(3) phase parameter estimation
TL;DR: Experimental tests confirmed that the system could identify and locate both scattering and absorbing inhomogeneities in a tissue-simulating phantom and accuracy of the initial estimates for the optical properties was confirmed.
Abstract: Diffuse optical tomography is an imaging technique whereby spatial maps of absorption and scattering coefficients are derived from the characteristics of multiply scattered light transmitted through the object. The system described here used four intensity-modulated light sources and measurements of the intensity and phase (relative to each source) at 16 or 20 detectors on the surface of a 10 cm diameter cylinder. An iterative Newton-Raphson algorithm was used to estimate the absorption and scattering coefficients at each pixel in a 17 x 17 array minimizing the difference between measured and calculated values of the intensity and phase at the measurement sites. Forward calculations of the intensity and phase were based on a multigrid finite-difference solution of the frequency domain diffusion equation. Numerical simulations were used to examine the resolution, contrast, and accuracy of the reconstructions as well as the effects of measurement noise, systematic uncertainties in source-detector location, and accuracy of the initial estimates for the optical properties. Experimental tests also confirmed that the system could identify and locate both scattering and absorbing inhomogeneities in a tissue-simulating phantom.
TL;DR: In this article, Fourier analysis of phase shift algorithms is used to predict measurement errors as a function of the frequency, the phase, and the amplitude of the vibrations in phase shift interferometry.
Abstract: Unexpected mechanical vibrations can significantly degrade the otherwise high accuracy of phase-shifting interferometry. Fourier analysis of phase-shift algorithms is shown to provide the analytical means of predicting measurement errors as a function of the frequency, the phase, and the amplitude of vibrations. The results of this analysis are concisely represented by a phase-error transfer function, which may be multiplied by the noise spectrum to predict the response of an interferometer to various forms of vibration. Analytical forms for the phase error are derived for several well-known algorithms, and the results are supported by numerical simulations and experiments with an interference microscope.
TL;DR: By starting with a distributed phase plate that is a strictly continuous surface and using only a few cycles of a phase-retrieval algorithm, good fourth-order super-Gaussian fit and lower scattering loss is obtained.
Abstract: The design of phase plates based on a phase-retrieval algorithm has been shown to be successful in achieving high order super-Gaussian distributions in the far field; however, these phase plates exhibit wide-angle scattering losses due to phase discontinuities. We report that, by starting with a distributed phase plate that is a strictly continuous surface and using only a few cycles of a phase-retrieval algorithm, we have obtained good fourth-order super-Gaussian fit and lower scattering loss.
TL;DR: The authors have developed a technique based on a solution of the Poisson equation to unwrap the phase in magnetic resonance (MR) phase images that is robust in the presence of noise and applies to the 3-point Dixon technique for water and fat separation.
Abstract: The authors have developed a technique based on a solution of the Poisson equation to unwrap the phase in magnetic resonance (MR) phase images. The method is based on the assumption that the magnitude of the inter-pixel phase change is less than /spl pi/ per pixel. Therefore, the authors obtain an estimate of the phase gradient by "wrapping" the gradient of the original phase image. The problem is then to obtain the absolute phase given the estimate of the phase gradient. The least-squares (LS) solution to this problem is shown to be a solution of the Poisson equation allowing the use of fast Poisson solvers. The absolute phase is then obtained by mapping the LS phase to the nearest multiple of 2 K from the measured phase. The proposed technique is evaluated using MR phase images and is proven to be robust in the presence of noise. An application of the proposed method to the 3-point Dixon technique for water and fat separation is demonstrated. >
TL;DR: In this paper, simple cells were measured as a function of contrast and the frequency of sine-wave grating patterns in order to explore the effect of contrast on the spatial and temporal phase transfer functions and on the spatiotemporal receptive field.
Abstract: The responses of simple cells (recorded from within the striate visual cortex) were measured as a function of the contrast and the frequency of sine-wave grating patterns in order to explore the effect of contrast on the spatial and temporal phase transfer functions and on the spatiotemporal receptive field. In general, as the contrast increased, the phase of the response advanced by approximately 45 ms (approximately one-quarter of a cycle for frequencies near 5 Hz), although the exact value varied from cell to cell. The dynamics of this phase-advance were similar to the dynamics of the amplitude: the amplitude and the phase increased in an accelerating fashion at lower contrasts and then saturated at higher contrasts. Further, the gain for both the amplitude and the phase appeared to be governed by the magnitude of the contrast rather than the magnitude of the response. For the spatial phase transfer function, variations in contrast had little or no systematic effect; all of the phase responses clustered around a single straight line, with a common slope and intercept. This implies that the phase-advance was not due to a change in the spatial properties of the neuron; it also implies that the phase-advance was not systematically related to the magnitude of the response amplitude. On the other hand, for the temporal phase transfer function, the phase responses fell on five straight lines, related to the five steps in contrast. As the contrast increased, the phase responses advanced such that both the slope and the intercept were affected. This implies that the phase-advance was a result of contrast-induced changes in both the response latency and the shape/symmetry of the temporal receptive field.
TL;DR: Numerical evaluation of the Cramer-Rao bound (CRB) provides further insight into the dependence of estimation accuracy on signal-to-noise ratio (SNR) and the frequency separation of the signal components.
Abstract: This paper considers the problem of estimating signals consisting of one or more components of the form a(t)e/sup j/spl phi/(t/), where the amplitude and phase functions are represented by a linear parametric model. The Cramer-Rao bound (CRB) on the accuracy of estimating the phase and amplitude parameters is derived. By analyzing the CRB for the single-component case, if is shown that the estimation of the amplitude and the phase are decoupled. Numerical evaluation of the CRB provides further insight into the dependence of estimation accuracy on signal-to-noise ratio (SNR) and the frequency separation of the signal components. A maximum likelihood algorithm for estimating the phase and amplitude parameters is also presented. Its performance is illustrated by Monte-Carlo simulations, and its statistical efficiency is verified. >
TL;DR: It is shown how a minimum-cost-matching graph-theory method can be used to find the set of cuts that has the global minimum of total cut length, in time approximately proportional to the square of the number of sources.
Abstract: An algorithm for unwrapping noisy phase maps by means of branch cuts has been proposed recently. These cuts join discontinuity sources that mark the beginning or end of a 2π phase discontinuity. After the placement of branch cuts, the unwrapped phase map is unique and independent of the unwrapping route. We show how a minimum-cost-matching graph-theory method can be used to find the set of cuts that has the global minimum of total cut length, in time approximately proportional to the square of the number of sources. The method enables one to unwrap unfiltered speckle-interferometry phase maps at higher source densities (0.1 sources pixel(-1)) than any previous branch-cut placement algorithm.
TL;DR: Experimental results of complex grating structures fabricated with uniform phase masks by the moving fiber-scanning beam approach, including self-apodized linearly chirped gratings, and phase shifted gratings with narrow-band transmission peaks have all been realized.
Abstract: We present experimental results of complex grating structures fabricated with uniform phase masks by the moving fiber-scanning beam approach. Pure apodized gratings with side-mode-suppression levels in excess of 40 dB, self-apodized linearly chirped gratings, and phase shifted gratings with narrow-band transmission peaks have all been realized.
TL;DR: Various methods for evaluating 2-D instantaneous frequency are presented and compared in the presence of noise and amplitude variations and phase aliasing arising in areas where spatial sampling is insufficient is made.
Abstract: The phase of complex signals is wrapped since it can only be measured modulo-2/spl pi/; unwrapping searches for the 2/spl pi/-combinations that minimize the discontinuity of the unwrapped phase, as only the unwrapped phase can be analyzed and interpreted by further processing. Given an estimate of the phase gradient (i.e., of the instantaneous frequency), the 2-D unwrapped phase can be obtained as a solution of a variational problem. The analysis of unwrapping is done quite separately from instantaneous frequency estimation so that the reliability of both steps can be assessed independently. Various methods for evaluating 2-D instantaneous frequency are presented and compared in the presence of noise and amplitude variations. A study has also been made on aliasing arising in areas where, with respect to instantaneous frequency, spatial sampling is insufficient. The presence of noise in the data further complicates phase aliasing analysis since there is no way to distinguish between the aliasing due to noise or that due to steep phase slopes. >
Patent•
19 Jun 1995TL;DR: In this article, the phase assignment for a phase shift mask is determined by a technique which determines, without assignment conflict, the intersection of the gate pattern with the active gate pattern and divides the intersection into categories of stacks where a slightly different phase assignment rules is employed for the different stacks.
Abstract: A method of performing poly level lithography in manufacturing an integrated circuit using a phase shift mask in a step and repeat optical tool where the phase assignment for said phase shift mask is determined by a technique which determines, without assignment conflict, the Intersection of the gate pattern with the active gate pattern and which divides the Intersection into categories of stacks where a slightly different phase assignment rules is employed for the different stacks.
TL;DR: In this paper, the first x-ray images of a simple phase object using a new technique of differential phase contrast imaging were reported, which was obtained by resolving phase gradients in a beam of 0.154 nm x rays using diffraction from a perfect crystal analyzer.
Abstract: We report the first x-ray images of a simple phase object using a new technique of differential phase-contrast imaging. The image contrast is obtained by resolving phase gradients in a beam of 0.154 nm x rays using diffraction from a perfect crystal analyzer. The contrast variations in the images are explained using dynamical x-ray diffraction theory.
TL;DR: By locally varying the index, using fabricated two-dimensional arrays of dielectric cylinders, this work can achieve a desired phase modulation to produce a diffractive phase element in one processing step.
Abstract: We have designed, fabricated, and tested a blazed artificial dielectric transmission grating in fused quartz for use at the 633-nm wavelength. By locally varying the index, using fabricated two-dimensional arrays of dielectric cylinders, we can achieve a desired phase modulation to produce a diffractive phase element in one processing step. The effective index depends on the fill fraction of the cylinders.
TL;DR: A direct-search scheme is used to adjust gain and phase in one amplifier branch, guided by the measured output signal in adjacent channels, and the functionality of the method has been verified by means of simulation.
Abstract: The Letter describes a new method to correct for gain and phase imbalances in LINC transmitters. A direct-search scheme is used to adjust gain and phase in one amplifier branch, guided by the measured output signal in adjacent channels. The functionality of the method has been verified by means of simulation.
TL;DR: Phase-space tomography is experimentally demonstrated for the determination of the spatially varying amplitude and phase of a quasi-monochromatic optical field by measurements of intensity only.
Abstract: Phase-space tomography is experimentally demonstrated for the determination of the spatially varying amplitude and phase of a quasi-monochromatic optical field by measurements of intensity only. Both fully and partially coherent sources are characterized. The method, which makes use of the fractional-order Fourier transform, also yields the Wigner distribution of the field and works in one or two dimensions.
TL;DR: A technique to increase the velocity‐to‐noise ratio (VNR) of phase‐contrast magnetic‐resonance velocity images based on making three measurements/flow encoding axis rather than the usual two to be a much more efficient way to increase VNR than simple averaging.
Abstract: We describe a technique to increase the velocity-to-noise ratio (VNR) of phase-contrast magnetic-resonance velocity images based on making three measurements/flow encoding axis rather than the usual two. A phase-aliased high first moment data set and a nonaliased low first moment data set are acquired, and the high-moment data are phase unwrapped using the low-moment data. The VNR of the resulting measurement is given by that of the high-moment measurement and increases linearly with the first moment. A factor of 4 gain in VNR was observed with only a 50% increase in scan time. Thus, this method is a much more efficient way to increase VNR than simple averaging.