Relative Phase Measurements Research Articles

Lower-limb inter-joint coordination during balance recovery after trips

BackgroundTrips are one of the most common external perturbations that can lead to accidental falls. Knowledge about postural control attributes of balance recovery after trips could help reveal the biomechanical causes for trip-induced falls and provide implications for fall prevention interventions. Research questionThe objective of the present study was to examine coordinated lower-limb movements during balance recovery after trips. MethodsOne hundred and twenty-three volunteers participated in an experimental study. They were tripped unexpectedly by a metal pole when walking on a linear walkway at their self-selected speed. Lower-limb inter-joint coordination quantified by continuous relative phase measures, including the mean of the absolute relative phases (MARP) and the deviation phase (DP), was analyzed during the execution of the first recovery step after unexpected trips. ResultsCompared to unsuccessful balance recovery, smaller MARPknee-ankle and DPknee-ankle of successful recovery were observed with distal inter-joint coordination on the swing side. Inter-joint coordination of the stance limb did not significantly differ between successful and unsuccessful recovery conditions. These findings indicate that the control of the swing limb’s distal joints is crucial for regaining balance after trips. SignificanceAn implication derived from this study is that greater in-phase coordination and smaller coordination variability in distal joints of the swing limb could be considered as potential targets for interventions aimed at preventing trip-induced accidental.

The Effect of Neuromuscular Fatigue on the Spatiotemporal Coordination of Rowing

Within rowing, lower back disorders (LBDs) are common, but the mechanisms underpinning LBDs are poorly understood. Considering this, it is essential to understand how coordination and motor control change under different constraints such as ergometer rowing and fatigue. This can help better inform movement features linked to LBDs. Measurement of the continuous relative phase (CRP) is a method used to quantify body segment and joint coordination, as CRP measures the spatiotemporal control of multi-joint movement. The purpose of this study was twofold: to examine the general spatiotemporal coordination aspects of ergometer rowing in an unfatigued state, and to quantify how the spatiotemporal coordination of a rowing movement changes in response to a fatigue-inducing rowing trial. Wearable IMUs monitored 20 participants’ movement during a 2000 m ergometer row. The Borg-10 Rating of Perceived Exertion (RPE) scale was used to quantify perceived fatigue. Despite significant RPE increases across all athletes, the spatiotemporal coordination of rowing revealed prevailing strategies for the lumbar spine and lower extremity but no significant effects (α = 0.05) of fatigue on CRP outcomes (MARP, DP), cross-correlation lag (RXY), or range of motion. These findings provide further insight into rowing movements and support the idea that heterogeneous responses to fatigue may exist, requiring further study.

Optical Waveform Synthesis and Its Applications

AbstractThe quest for ever‐shorter optical pulses has been ongoing for over half a century. Although few‐cycle pulses have been generated for nearly 40 years, pulse lengths below the single‐cycle limit have remained an elusive goal for a long time. For this purpose, optical waveform synthesizers, generating high‐energy, high‐average‐power pulses via coherent combination of multiple pulses covering different spectral regions, have been recently developed. They allow unprecedented control over the generated optical waveforms, spanning an extremely broad spectral range from ultraviolet to infrared. Such control allows for steering strong‐field interactions with increased degrees of freedom. When driving high‐harmonic generation, tailored waveforms can produce bright attosecond pulse trains and even isolated attosecond pulses with tunable spectra up to the soft X‐ray range. In this paper recent progress on parametric and hollow‐core fiber waveform synthesizers is discussed. Newly developed seeding schemes; absolute, relative, and spectral phase measurement; and control techniques suitable for synthesizers are described. The progress on serial and parallel waveform synthesis based on Ti:sapphire and Ytterbium laser systems and their latest applications in high‐harmonic generation in gaseous and solid media, attosecond science, and laser wakefield acceleration is discussed.

Front Cover: Measurement of relative phase for 5G NR digitally modulated signal using cumulative distribution function

The cover image is based on the Original Article Measurement of relative phase for 5G NR digitally modulated signal using cumulative distribution function by Soon-Soo Oh et al., https://doi.org/10.1049/ell2.12345.

Thomson and collisional regimes of in-phase coherent microwave scattering off gaseous microplasmas

The total number of electrons in a classical microplasma can be non-intrusively measured through elastic in-phase coherent microwave scattering (CMS). Here, we establish a theoretical basis for the CMS diagnostic technique with an emphasis on Thomson and collisional scattering in short, thin unmagnetized plasma media. Experimental validation of the diagnostic is subsequently performed via linearly polarized, variable frequency (10.5–12 GHz) microwave scattering off laser induced 1–760 Torr air-based microplasmas (287.5 nm O2 resonant photoionization by ~ 5 ns, < 3 mJ pulses) with diverse ionization and collisional features. Namely, conducted studies include a verification of short-dipole-like radiation behavior, plasma volume imaging via ICCD photography, and measurements of relative phases, total scattering cross-sections, and total number of electrons N_{e} in the generated plasma filaments following absolute calibration using a dielectric scattering sample. Findings of the paper suggest an ideality of CMS in the Thomson “free-electron” regime—where a detailed knowledge of plasma and collisional properties (which are often difficult to accurately characterize due to the potential influence of inhomogeneities, local temperatures and densities, present species, and so on) is unnecessary to extract N_{e} from the scattered signal. The Thomson scattering regime of microwaves is further experimentally verified via measurements of the relative phase between the incident electric field and electron displacement.

Measurement of relative phase for 5G NR digitally modulated signal using cumulative distribution function

This letter proposes a measurement technique for the relative phase of a 5G new radio (NR) signal. The total radiated power (TRP) is measured to evaluate wireless equipment. However, this cannot be implemented using the near-field measurement system owing to the digitally modulated signal. The relative phase detected by using a vector network analyser (VNA) changes significantly owing to the fast change in the signal in the time domain and the imperfect synchronisation of internal receivers of VNA. This study calculated the cumulative distribution function and medium value for the signal from the multi-probe measurement system. The detected phase agreed well with the exact value obtained from the continuous wave signal. The proposed technique can be used for TRP calculations using the near-to-far field transformation.

Bimanual Coordination in a Whole-Body Dynamic Balance Sport, Slacklining: A Comparison of Novice and Expert.

As previous studies have suggested that bimanual coordination is important for slacklining, the authors questioned whether this important skill plays a role in the performance of a fundamental task of slacklining. To address this question, the authors compared single-leg standing on the slackline between novices and experts in terms of bimanual coordination dynamics within a dynamical systems framework using relative phase and recurrence quantification analysis measures. Five novices and five experts participated in the experiment. Participants were required to perform single-leg standing on a slackline. To collect motion data while slacklining, the authors used a 3D motion capture system and obtained time series data on the wrist position of both hands. The authors compared bimanual coordination dynamics between novices and experts. Although this preliminary study was limited in its sample size, the results suggest that experts tend to show a more antiphase coordination pattern than novices do and that they can more sustainably coordinate their hands compared with novices in terms of temporal structure in diagonal-related recurrence measures (i.e.,maxline, mean line, and percentage determinism).

Age induced modifications in the persistency of voluntary sway when actively tracking the complex motion of a visual target

Movement persistency, reflected in systematic cycle to cycle fluctuations of a rhythmical task such as walking or voluntary sway, is compromised with increasing age, making older adults more susceptible to falls. In the present study, we tested whether it is possible to improve rhythmic voluntary sway persistency in old age by actively tracking the complex (i.e. persistent) motion of a visual target. Twenty healthy young and 20 older adults performed 132 cycles of anterior-posterior sway under two conditions: a) self-paced sway and b) sway while tracking the vertical motion of a complex visual target. The persistency of sway cycle amplitude and duration, detected from the center of pressure displacement, was quantified using the Fractal exponent α. We also recorded body kinematics in order to assess the intersegmental coordination that was quantified in the Mean Absolute Relative Phase (MARP) and the Deviation Phase (DPh) between the trunk and the lower limbs. In self-paced sway, older adults showed a lower persistency of cycle duration and a higher MARP and DPh between the trunk and the lower limbs compared to young adults. Tracking the complex visual target motion increased the persistency of cycle amplitude, in young but not in older adults, when compared to the self-paced sway while it decreased the persistency of cycle duration in both groups. The relative phase measures showed a moderate to strong relationship with the persistency of cycle amplitude and duration when older adults swayed in their self-pace. These findings suggest older adults cannot exploit active tracking of the complex visual motion cue to improve voluntary sway persistency. This could be related to the less stable and out of phase intersegmental coordination characterizing rhythmic voluntary sway in old age.

Noncontact Monitoring of Overhead Transmission Lines Using Space Potential Phasor Measurements

Power system reliability requirements necessitate the development of measurement systems to monitor the operational state of critical transmission lines. In this article, a novel noncontact method for monitoring overhead transmission lines is proposed. The method is based on measuring the amplitude and relative phase of the transmission line’s space potential at two or more strategically located points in space along with the use of passive phase shifters to enhance the sensitivity of the measurements. Applications of voltage unbalance and conductor sag measurements are demonstrated along with the results of conductor sag measurements on an operating 230-kV transmission line. It is shown that using enhanced relative phase measurements can significantly improve the sensitivity of the measurements.

Influence of driving ways on measurement of relative phase in a two-atoms cavity system**Project supported by the National Natural Science Foundation of China (Grant Nos. 11874287 and 11574229), the National Basic Research Program of China (Grant No. 2016YFA0302800), and the Fund from Shanghai Science and Technology Committee, China (Grant No. 18JC1410900).

We study the influence of driving ways on the interaction in a two-atoms cavity quantum electrodynamics system. The results show that driving ways can induce different excitation pathways. We show two kinds of significantly different excitation spectrums under two ways: driving cavity and driving atoms. We demonstrate that driving atoms can be considered as a method to obtain the position information of atoms. This research has very practical application values on obtaining the position information of atoms in a cavity.

Extracting phase information on continuum-continuum couplings

In measurements of relative phases in photoionization processes, the contribution of continuum-continuum (CC) couplings to the atomic (Wigner) phases, corresponding to attosecond time delays, is currently accounted for only by theoretical models. Here, we introduce a measurement scheme that is sensitive to phase differences of CC transitions after photoionization in the presence of an optical field. The method allows us to separate CC transitions from the ionization process and can help in testing existing theoretical models. It is based on a multicolor interferometer, similar to the RABBITT (reconstruction of attosecond beating by interference of two-photon transitions) method. The key idea involves the comparison of two measurements with different orders of CC transitions. The scheme is illustrated by an ab initio calculation on atomic hydrogen.

Relative phase measures of intersegmental coordination describe motor control impairments in children with cerebral palsy who exhibit stiff-knee gait

BackgroundThe purpose of this retrospective study was to explore lower limb intersegmental coordination as a clinically important indicator of motor control mechanisms in individuals with cerebral palsy exhibiting stiff-knee gait. We used the relative phase of thigh and foot segments around foot-off to describe motor control, given the relevance of the pre-swing phase of gait to the existence of stiff-knee gait. MethodsTraditional gait parameters and thigh/foot intersegmental coordination were calculated using pre-and postoperative kinematic data from a cohort of 54 subjects (92 legs) with spastic cerebral palsy. All participants had stiff-knee gait, walked without assistive devices, and underwent rectus femoris transfer surgery to improve swing period knee flexion. Analyses included correlations between a) preoperative intersegmental coordination and gait variables (knee flexion range, rate and gait performance) and b) pre-to-postoperative intersegmental coordination change and change in gait variables. FindingsThigh/foot intersegmental coordination significantly (P < 0.001) correlated with knee flexion range, rate and walking speed. Postoperative intersegmental coordination was significantly more uncoupled than preoperative. Pre-to-postoperative intersegmental coordination improvement also significantly correlated with improvements in knee flexion range, rate and walking speed. Pre-to-postoperative changes in intersegmental coordination accounted for 43% and 36% of variance in knee flexion range change and knee flexion rate change respectively. InterpretationIntersegmental coordination is a clinically important factor in knee flexion limitations associated with stiff-knee gait for individuals with cerebral palsy. These findings are a foundation for further study of intersegmental coordination measures as complements to traditional instrumented gait analysis.

Anomalous behavior of the ionosphere before strong earthquakes

In the recent years, the seismo-ionospheric coupling has been studied using various ionospheric parameters like Total Electron Content, Critical frequencies, Electron density and Phase and amplitude of Very Low Frequency waves. The present study deals with the behavior of the ionosphere in the pre-earthquake period of 3–4 days at various stations adopting the critical frequencies of Es and F2 layers. The relative phase measurements of 16 kHz VLF wave transmissions from Rugby (UK), received at Visakhapatnam (India) are utilized to study the D-region during the seismically active periods. The results show that, f0Es increases a few hours before the time of occurrence of the earthquake and day time values f0F2 are found to be high during the sunlit hours in the pre-earthquake period of 2–3 days. Anomalous VLF phase fluctuations are observed during the sunset hours before the earthquake event. The results are discussed in the light of the probable mechanism proposed by previous investigators.

On the Estimation Performance and Convergence Rate of the Generalized Power Method for Phase Synchronization

An estimation problem of fundamental interest is that of phase (or angular) synchronization, in which the goal is to recover a collection of phases (or angles) using noisy measurements of relative phases (or angle offsets). It is known that in the Gaussian noise setting, the maximum likelihood estimator (MLE) is an optimal solution to a nonconvex quadratic optimization problem and can be found with high probability using semidefinite programming (SDP), provided that the noise power is not too large. In this paper, we study the estimation and convergence performance of a recently proposed low-complexity alternative to the SDP-based approach, namely, the generalized power method (GPM). Our contribution is twofold. First, we show that the sequence of estimation errors associated with the GPM iterates is bounded above by a decreasing sequence. As a corollary, we show that all iterates achieve an estimation error that is on the same order as that of an MLE. Our result holds under the least restrictive assumpti...

A 2–15-GHz Accurate Built-in-Self-Test System for Wideband Phased Arrays Using Self-Correcting Eight-State $I/Q$ Mixers

A built-in-self-test (BIST) system for wideband phase arrays channels is presented. The BIST is implemented using an on-chip in-phase/quadrature ( $I/Q$ ) receiver with an integrated ring oscillator that provides both the channel test signal and the mixer local oscillator (LO). The BIST achieves wideband accuracy for relative phase and gain measurements at 2–15 GHz with a one-time self-correction algorithm with eight LO phases. The sequential algorithm determines the $I/Q$ errors, such as dc offset, gain and phase imbalances from the $I/Q$ outputs resulting from different LO phase states. An rms power detector network is also implemented for absolute gain measurements. The BIST can operate at rates >1 MHz (less than 1- $\mu \text{s}$ sampling time) with signal-to-noise ratio greater than 50 dB and provides measurements that agree well with the vector network analyzer S-parameter data over a wide frequency range. To the best of our knowledge, this is the first implementation of high accuracy wideband BIST system for phased-array channels.

Tightness of the maximum likelihood semidefinite relaxation for angular synchronization

Maximum likelihood estimation problems are, in general, intractable optimization problems. As a result, it is common to approximate the maximum likelihood estimator (MLE) using convex relaxations. In some cases, the relaxation is tight: it recovers the true MLE. Most tightness proofs only apply to situations where the MLE exactly recovers a planted solution (known to the analyst). It is then sufficient to establish that the optimality conditions hold at the planted signal. In this paper, we study an estimation problem (angular synchronization) for which the MLE is not a simple function of the planted solution, yet for which the convex relaxation is tight. To establish tightness in this context, the proof is less direct because the point at which to verify optimality conditions is not known explicitly. Angular synchronization consists in estimating a collection of $n$ phases, given noisy measurements of the pairwise relative phases. The MLE for angular synchronization is the solution of a (hard) non-bipartite Grothendieck problem over the complex numbers. We consider a stochastic model for the data: a planted signal (that is, a ground truth set of phases) is corrupted with non-adversarial random noise. Even though the MLE does not coincide with the planted signal, we show that the classical semidefinite relaxation for it is tight, with high probability. This holds even for high levels of noise.

Coherent beam combining in atmospheric channels using gated backscatter.

This paper introduces the concept of atmospheric channels and describes a possible approach for the coherent beam combining of lasers of an optical phased array (OPA) in a turbulent atmosphere. By using the recently introduced sparse spectrum harmonic augmentation method, a comprehensive simulative investigation was performed and the exceptional properties of the atmospheric channels were numerically demonstrated. Among the interesting properties are the ability to guide light in a confined manner in a refractive channel, the ability to gather different sources to the same channel, and the ability to maintain a constant relative phase within the channel between several sources. The newly introduced guiding properties combined with a suggested method for channel probing and phase measurement by aerosol backscattered radiation allows coherence improvement of the phased array's elements and energy refocusing at the location of the channel in order to increase power in the bucket without feedback from the target. The method relies on the electronic focusing, electronic scanning, and time gating of the OPA, combined with elements of the relative phase measurements.

Nonconvex Phase Synchronization

We estimate $n$ phases (angles) from noisy pairwise relative phase measurements. The task is modeled as a nonconvex least-squares optimization problem. It was recently shown that this problem can be solved in polynomial time via convex relaxation, under some conditions on the noise. In this paper, under similar but more restrictive conditions, we show that a modified version of the power method converges to the global optimum. This is simpler and (empirically) faster than convex approaches. Empirically, they both succeed in the same regime. Further analysis shows that, in the same noise regime as previously studied, second-order necessary optimality conditions for this quadratically constrained quadratic program are also sufficient, despite nonconvexity.

Quantum precision measurement based on squeezed light

According to the Heisenberg uncertainty principle, the precision of any physical quantity measurement is limited by quantum fluctuation in general, which leads to the so-called standard quantum limit (SQL). The SQL can be beaten by using squeezed light, hence enhancing the measurement accuracy. Squeezed light is a typical nonclassical light, it exhibits reduced noise in one quadrature component. Since Caves proposed the scheme of phase measurement enhancement with squeezing, squeezed light has been used to enhance measurement precision in many areas. This review focuses on the following four kinds of precision measurements based on squeezed light: the measurements of relative phase, small lateral displacement and tilt, magnetic field, and clock synchronization. For all of these measurements, vacuum squeezing has been used to enhance measurement precision, while the types of squeezing (squeezing angle, transverse mode, polarization etc.) are different. For phase measurement, quadrature squeezing is injected into the conventionally unused input port of Mach-Zehnder interferometer (MZI) or Michelson interferometer (MI). For displacement or tilt measurement, a vacuum squeezing beam of a special transverse mode is coupled into an intense coherent beam, yielding a spatial-squeezed light whose transverse position or tilt angle noise is lower than that of a classical light beam. Based on the Faraday effect of polarization rotation, the magnetic field can be detected precisely. The precision can be increased further by using the polarization squeezing. The polarization squeezing can be generated by coupling two orthogonal polarized beams together, a coherent beam and a vacuum squeezed beam. Various polarization squeezing can be illustrated on the Poincaré sphere. Finally, in the clock synchronization based on the optical frequency comb, squeezed light can be used to enhance the time measurement precision. A theoretical scheme with multimode squeezing of supermode (a kind of mode describing the frequency mode of a pulse laser beam) is introduced. The squeezing has extensively been applied into the quantum precision measurements such as gravitational wave detection as well as biological measurement and will play a more important role in the near future.

Assessing the Gold Standard: The Complex Vibrational Nonlinear Susceptibility of Metals

Sum-frequency generation techniques can offer molecular-level, structural details of surfaces and interfaces. The incorporation of a metallic layer, either exposed or buried, is frequently used to provide a nonvibrationally resonant reference to which the phase of the resonant responses may be compared. This in turn provides further structural information, such as the polarity of interfacial groups. Because the phase of the metal depends strongly on factors that alter the electronic structure of the interface, such as the wavelength of the visible beam, chemical bonding, and surface coverage, it is beneficial to characterize the phase of the nonresonant response. A direct measurement of the absolute phase of a commonly prepared model hydrophobic surface, 1-octadecanethiol bound to gold, is presented and compared with relative phase measurements. Assignment of the phase of metallic samples requires careful consideration of the effects of the local field upon phase in both the near and far fields. We have outlined an approach that is suitable for the characterization of any dielectric or metal surface.