Phase Jumps Research Articles

Random jumps in the phase-OTDR response

In the paper, we present a qualitative analysis of the dual-pulse phase optical time domain reflectometry (phase-OTDR) response to uniform and nonuniform propagating fiber strain. It is found that on average over all realizations of scattering centers the response of the dual-pulse phase-OTDR is linear with respect to an external perturbation. Meanwhile, individual responses contain random phase jumps, which are an intrinsic property of phase-OTDR. These jumps are the result of nonlinear responses of the scattering fiber segments and arise due to interference of random backscattered fields varying in time. Two types of phase jumps are considered: π jumps and 2π jumps; the first type is caused by the fading in phase-OTDR spatial channel, while the second type occurs when a nonuniform perturbation propagates along the fiber. The origin of the phase jumps is explained by considering the simulated response on the complex plane. It is shown that the distribution of 2π jumps can be well described by the Gaussian probability mass function (PMF), provided the number of 2π jumps is large. The conducted experiments on the registration of uniform and nonuniform fiber strain confirm the presence of the jumps in the phase-OTDR response.

Transition to chaos in a reduced-order model of a shear layer

The present work studies the nonlinear dynamics of a shear layer, driven by a body force and confined between parallel walls, a simplified setting to study transitional and turbulent shear layers. It was introduced by Nogueira & Cavalieri (J. Fluid Mech., vol. 907, 2021, A32), and is here studied using a reduced-order model based on a Galerkin projection of the Navier–Stokes system. By considering a confined shear layer with free-slip boundary conditions on the walls, periodic boundary conditions in streamwise and spanwise directions may be used, simplifying the system and enabling the use of methods of dynamical systems theory. A basis of eight modes is used in the Galerkin projection, representing the mean flow, Kelvin–Helmholtz vortices, rolls, streaks and oblique waves, structures observed in the cited work, and also present in shear layers and jets. A dynamical system is obtained, and its transition to chaos is studied. Increasing Reynolds number $Re$ leads to pitchfork and Hopf bifurcations, and the latter leads to a limit cycle with amplitude modulation of vortices, as in the direct numerical simulations by Nogueira & Cavalieri. Further increase of $Re$ leads to the appearance of a chaotic saddle, followed by the emergence of quasi-periodic and chaotic attractors. The chaotic attractors suffer a merging crisis for higher $Re$ , leading to a chaotic dynamics with amplitude modulation and phase jumps of vortices. This is reminiscent of observations of coherent structures in turbulent jets, suggesting that the model represents a dynamics consistent with features of shear layers and jets.

On digital phase detector

A digital phase detector for processing signals with phase modulation in a wide range of changes in the phase of the received signal is considered. A block diagram of a digital detector with minimal computational costs for the signal period is proposed. The problem of phase jumps when it changes by more than 2π is solved. An estimate is obtained for the noise immunity of a phase detector when exposed to Gaussian noise. Supposed hardware implementation of a phase detector based on field-programmable gate arrays. It can be used in devices for digital processing of the angular modulation signals, devices for controlling the phase of the reference signal and in different measurers.

Azimuthal and radial modulation of double-four-wave mixing in a coherently driven graphene ensemble.

We investigate in detail the azimuthal and radial modulation (i.e., the azimuthal order lj and radial order pj with j = 1, 2) of double-four-wave mixing (double-FWM) by use of two higher-order Laguerre-Gaussian (LG) beams in a Landau quantized graphene ensemble. A pair of weak probe pulses in the graphene ensemble interacts with two LG beams and thus two vortex FWM fields with the opposite vorticity are subsequently generated. In combination with numerical simulations, we reveal that (i) there appear l1 + l2 periods of phase jumps in the phase profiles under any conditions; (ii) p + 1 concentric rings emerge in the intensity profile and the strength is mainly concentrated on the inner ring when the two LG beams have the same radial orders (i.e., p1 = p2 = p); (iii) there are p raised narrow rings occurring in the phase profile in the case of p1 = p2 = p and l1 ≠ l2, and the raised narrow rings would disappear when p1 = p2 and l1 = l2; (iv) pmax + 1 concentric rings appear in the intensity profile, meanwhile, |p1 - p2| convex discs and pmin raised narrow rings emerge in the phase diagram in the case of p1 ≠ p2, here pmax = max(p1, p2) and pmin = min(p1, p2). Moreover, the two generated FWM fields have the same results, and the difference is that the phase jumps are completely opposite. These findings may have potential application in graphene-based nonlinear optical device by using LG beams with adjustable mode orders.

Phase Unwrapping for Time-of-Flight Sensor Based on Image Segmentation

Phase unwrapping is a fundamental problem in Time-of-Flight (ToF) imaging, especially when high modulation frequency is used to achieve precise measurement accuracy. This paper proposes a novel double-frequency based phase unwrapping method for ToF sensors. The new method incorporates the idea of image segmentation to solve phase unwrapping region-by-region instead of pixel-by-pixel. The depth image is segmented based on the constraint between depth measurements and wrap numbers at two modulation frequencies. To avoid misclassification of the pixels around phase jump edges in the presence of inevitable noise, we employ a modified distance function to classify the edge pixels into the corresponding connected area. Furthermore, a graph model is used to accurately model the phase jumping relation between different connected areas. On this basis, we propose an MRF framework to fuse the amplitude and depth information to unwrap the phase. Experimental results on both synthetic and real-world data demonstrate that, the proposed method is robust to noise and outperforms state-of-the-art methods, while being highly efficient enabling real-time running.

Phase Dislocations in Hollow Core Waveguides

This paper discusses the basic concepts of phase dislocations and vortex formation in the electric fields of fundamental air core mode of hollow core waveguides with specific types of rotational symmetry of the core-cladding boundary. Analysis of the behavior of the electric field phase in the transmission bands shows that the mechanism of light localization in the hollow core waveguides with discrete rotational symmetry of the core-cladding boundary cannot be completely described by the ARROW model. For an accurate description of the phase behavior, it is necessary to account for phase jumps of the magnitude of π when passing through the phase dislocations.

Control of single and multiple phase solitons in a ring cavity.

Phase solitons are localized structures characterized by phase jumps of 2π or multiples arising in forced ring lasers. Here, we show numerically that they can be created by superimposing to the constant driving field a suitable control beam matched in frequency with a different cavity mode for a time of the order of ten cavity round trip times. If the two beams are separated in frequency by n free spectral ranges of the cavity, a train of solitons like a perfect soliton crystal consisting of n equispaced phase solitons is generated. This may represent a simple way to produce frequency combs with flexible frequency spacing and high power per line.

Association between Change in Regional Phase Angle and Jump Performance: A Pilot Study in Serie A Soccer Players

Purpose: This observational longitudinal investigation aimed to investigate whether change in bioelectrical regional phase angle (PhA) is a predictor of change in vertical jump performance in elite soccer players. Methods: Fifteen soccer players (age: 28.7 ± 5.0 years, body weight: 82.4 ± 6.8 kg, height: 186.0 ± 0.1 cm, body mass index: 23.8 ± 1.2 kg/m2) competing in the first Italian division (Serie A) were included in this study and tested before the pre-season period and after the first half of the championship. Whole body and lower hemisoma PhA were obtained with a phase-sensitive 50 kHz bioelectrical impedance analyzer and legs lean soft tissue was estimated using specific bioimpedance-based equation developed for athletes. Vertical jump performance was assessed using the countermovement jump (CMJ). Results: The major findings of the study are that changes in lower hemisoma PhA are more strongly related with changes in jump performance (r2 = 0.617, p = 0.001) than changes in whole-body PhA (r2 = 0.270, p = 0.047), even after adjusting for legs lean soft tissue and for body mass index (β = 5.17, p = 0.004). Conclusions: These data suggest that changes in lower hemisoma PhA might be used as a tool for evaluating performance related parameters in sports where specific body segments are involved, in preference to the whole-body measured value.

On the Effect of Beating during Nonlinear Frequency Chirping

Spectral analyses of energetic particle (EP) driven bursts of MHD fluctuations in magnetically confined plasmas often exhibit multiple simultaneous chirps. While the superposition of oscillations at multiple frequencies necessarily causes beating in the signal acquired by a localized external probe, self-consistent hybrid simulations of chirping EP modes in a JT-60U tokamak plasma have demonstrated the possibility of global beating, where the electromagnetic field vanishes globally between beats and reappears with opposite phase. This implies that there can be a single field mode that oscillates at multiple frequencies simultaneously when resonantly driven by multiple density waves in EP phase space. Conversely, this means that the EP density waves are mutually coupled and interfere with each other via the jointly driven field, a mechanism ignored in some theories. In this treatise, we study the role of field pulsations in general and beating in particular using the Hamiltonian guiding center orbit-following code ORBIT with a reduced wave-particle interaction model in realistic geometry. Through amplitude pulsations and phase jumps, beating is found to drive the evolution of EP phase space structures. Observations: (1) Beating causes density wave fronts to advance radially in pulses. The resulting chirps become staircase-like. (2) The beats facilitate convective transfer of material between neighboring layers of phase space density waves. On the one hand, this may delay detachment of solitary vortices. On the other hand, it facilitates the accumulation of hole and clump fragments into larger structures. (3) Long-range chirping occurs when massive holes or clumps detach and drift away from the turbulent belt around the seed resonance. The detached vortices can remain robust and, on average, maintain their concentric nested layers while being perturbed by the field's continued beating.

Comparison of DSOGI-Based PLL for Phase Estimation in Three-Phase Weak Grids

The paper presents a summary of different double second-order generalized integrator (DSOGI)-based phase-locked loop (PLL) algorithms for synchronization with three-phase weak grids. The different methods are compared through simulation under a variety of grid conditions, such as unbalanced phase voltages, high low-order harmonics distortion, frequency steps, phase jumps, and voltage sags. Following the simulation results, the three methods that have shown the overall best results are compared through an experimental setup for further results validation under operation with a voltage-source converter. Based on the obtained results, a benchmark table is presented that allows ranking the performance of the tested methods for different expected grid conditions.

A robust Kalman filter time scale algorithm with data anomaly

Kalman filtering is utilized in many fields because of its capability to separate data from white phase noise. In time and frequency domain, employing Kalman filter is particularly important because of its use in building time scales. The studied time scale algorithms have been usually based on an ensemble of clocks without data anomaly, or the anomaly data is processed in advance to secure the reliability of the data used in Kalman filter algorithm. This increases the amount of computation and affects the real-time performance of the algorithm. In this study a robust Kalman filter is employed to present a method of time scale calculation. It extends a previously published Kalman filter algorithm that is useful for an ensemble of clocks without phase anomalies. In the algorithm, the inflation factor and the optimal adaptive factor are applied to the clock ensemble. The introduced algorithm may be useful for an ensemble of clocks with measurement outliers and phase jumps. The effectiveness of the proposed method can be verified through simulation and experimental analysis. The analysis result shows that the robust Kalman filter algorithm can resist the influence of measurement outliers and phase jumps on time scale performance. So, the accuracy and the stability of time scale can be improved.

Digital analysis of a speckle pattern of chaotic mode composition and restoration of a regular intensity pattern after a multimode fiber

A process of mode matching in a chaotic speckle pattern without a reference beam responsible for the formation of a holographic grating was studied experimentally and theoretically. Our approach was based on measuring the amplitudes and phases of the Hermite-Gauss (HG) and Laguerre-Gauss (LG) modes in a speckle pattern formed by the radiation of a multimode gradient fiber. The speckle pattern was formed in a hologram of a spatial light modulator using a multimode gradient fiber model while taking into account the mode and polarization dispersion, as well as random phase jumps of each eigenmode. We managed to match 210 modes of the speckle pattern and restore not only the original pattern, but also each structured LG mode and the entire chain of HG eigenmodes.

Enhanced nonlinear least squares for power system frequency estimation with phase jump immunity

Nonlinear least squares (NLLS) fitting is a method that can be used for estimating power system signal parameters. NLLS algorithms posit a model for the measured signal and then fit the model to the data by finding the parameters that minimize the sum of squared error between the measurements and model predictions. Here, we focus on the particular problem of frequency estimation and show that the NLLS algorithm is flexible enough to be made immune to harmonic distortion, DC offset, and phase imbalances. Tools for tuning the algorithm for desired noise/bandwidth performance are presented. Finally, a new method for estimating frequency in the presence of phase jumps is presented and tested. The new algorithm is capable of estimation in the presence of phase and amplitude jumps with near-zero error. This performance is shown to be vastly superior to two benchmark algorithms.

A Single-Phase Globally Stable Frequency-Locked Loop Based on the Second-Order Harmonic Oscillator Model

This paper presents a novel frequency-locked-loop (FLL) scheme that provides estimates of the in-phase and square-phase fundamental components of a distorted single-phase reference signal and an estimate of its fundamental angular frequency. The main feature of the proposed scheme is that its design is fully based on the dynamical model of a single-phase signal generator, namely, the second-order harmonic oscillator (SOHO), which adds originality to the scheme. In fact, the proposed scheme owns a particular structure involving a set of orthogonal signals, which can be seen as the fixed-frame representation of three-phase balanced signals. Additionally, a plug-in block is included as a mechanism to mitigate the effect of the harmonic distortion. A proof of global stability for the proposed scheme based on nonlinear argumentation is also included, which contributes to the novelty of the work and ensures convergence disregarding the initial conditions of the to-be-estimated signal components. In addition, explicit conditions are presented for the tuning of control parameters. Experimental results corroborate the performance of the proposed scheme under angular frequency variations, phase jumps, voltage sags and harmonic distortion on the reference signal. For comparison purposes, also the state-of-the-art second-order-generalized-integrator-based FLL and the single-phase synchronous-reference frame phase-locked loop are tested.

Long-term performance detection and evaluation of GLONASS onboard satellite clocks

The cesium atomic clock installed on the GLObal NAvigation Satellite System (GLONASS) is a key piece of equipment. However, its performance is easily affected by the external environment and its physical characteristics. Therefore, it is essential to evaluate the long-term performance of the clock. In this study, using eight years of continuous GLONASS precise satellite clock offset products, the long-term performance of GLONASS satellite clocks is revealed for the first time. The results showed that the mean number of phase and frequency jumps for one satellite clock in one year were 0.29 and 0.19, respectively. The fitting precision, which is the standard deviation of the fitting residuals, was 0.88 nanoseconds (ns). Except for the R06 satellite clock, the first or second period was 11.24 h in the clock offset. In terms of clock stability, the short-term clock offset prediction accuracy was 0.52 ns, the frequency stability at 1000 and 10000 s was 4.03 × 10-13 and 1.01 × 10-13, respectively. Both the short-term clock offset prediction accuracy and frequency stability were inferior to those of the rubidium atomic clock of the Global Positioning System (GPS) Block IIF satellites, the second-generation BeiDou Navigation Satellite System (BDS-2), Quasi-Zenith Satellite System (QZSS), and Galileo Passive Hydrogen Maser (PHM). The mean switching number for each GLONASS satellite clock was 0.27 per year. Furthermore, the R15 satellite clock, maybe owing to its hardware noise, delivered the poorest performance among those of all the GLONASS satellite clocks.

A New Recurrent Approach for Phase Unwrapping

True phase including phase characteristic of different complex functions and transfer functions is calculated by applying modulo 2 operation to tangent inverse function. Tangent inverse function is value limited to 2 2      x . Different artificial discontinuities or phase jumps appear in the phase function. The problem of phase unwrapping is considered here and a new phase unwrapping method for removing artificial phase jumps was described and tested. A quantitative study is made to compare modulo 2unwrapping algorithm with the proposed algorithm in this paper.

Optimization of Diverse PCFM Waveforms and Joint Mismatched Filters

Finding codes for the desired autocorrelation function (ACF) based on phase-coded modulation waveforms has always been a popular research topic, and the relevant literature is abundant. However, the optimized ACF may not be obtained in band-limited hardware due to the extended spectral sidelobes generated by instantaneous phase changes. Polyphase-coded FM (PCFM) waveforms based on continuous phase modulation (CPM), which uses a shape filter to smooth phase jumps, can provide effective spectral containment. However, for PCFM waveforms using the existing optimized phase codes, the original desired property of the ACF, e.g., a low integrated sidelobe level (ISL) or weighted ISL (WISL), will not be obtained because of the smoothness among all phases. Hence, PCFM waveforms based on CPM should be redesigned and optimized. Moreover, designing pulse-agile waveforms with different phase codes to mitigate range ambiguity has also attracted increased attention in recent years. However, different waveforms will yield range sidelobe modulation (RSM) in Doppler processing, which degrades the attendant Doppler coherency, leading to high sidelobes in the Doppler dimension. In this article, optimization algorithms for designing diverse PCFM waveforms and relevant joint mismatched filters (JMMFs) are proposed. A CPM-based cyclic algorithm (CPM-CA) using the method of alternating projection for optimizing the PCFM waveform with a desired ACF is proposed in the first step. The design of multiple diverse PCFM waveforms with similar ACFs and a small RSM effect is also considered. Then, to further optimize the ISL/WISL and reduce the RSM effect, a novel method for designing JMMFs using a cyclic algorithm (JMMF-CA) is proposed. Simulations and an experiment based on a real radar system indicate that the optimized PCFM waveforms and JMMFs using CPM-CA and JMMF-CA can yield a desired ISL/WISL while achieving a small RSM effect with a low loss of signal-to-noise ratio and satisfactory Doppler robustness.

HARP-I: A Harmonic Phase Interpolation Method for the Estimation of Motion From Tagged MR Images.

We proposed a novel method called HARP-I, which enhances the estimation of motion from tagged Magnetic Resonance Imaging (MRI). The harmonic phase of the images is unwrapped and treated as noisy measurements of reference coordinates on a deformed domain, obtaining motion with high accuracy using Radial Basis Functions interpolations. Results were compared against Shortest Path HARP Refinement (SP-HR) and Sine-wave Modeling (SinMod), two harmonic image-based techniques for motion estimation from tagged images. HARP-I showed a favorable similarity with both methods under noise-free conditions, whereas a more robust performance was found in the presence of noise. Cardiac strain was better estimated using HARP-I at almost any motion level, giving strain maps with less artifacts. Additionally, HARP-I showed better temporal consistency as a new method was developed to fix phase jumps between frames. In conclusion, HARP-I showed to be a robust method for the estimation of motion and strain under ideal and non-ideal conditions.

A Nonlocal Noise Reduction Method Based on Fringe Frequency Compensation for SAR Interferogram

Phase noise reduction is one of the key steps for synthetic aperture radar interferometry data processing. In this article, a novel phase filtering method is proposed. The main innovation and contribution of this research is to 1) incorporate local fringe frequency (LFF) compensation technique into the nonlocal phase filtering method to include more independent and identically distributed samples for filtering; 2) modify the nonlocal phase filter from three aspects: 1) executing nonlocal filtering in the complex domain of the residual phase to avoid gray jumps in phase, 2) adaptively calculating the smoothing parameter based on the LFF and the coherence coefficient, and 3) using the integral image in similarity calculation to improve the efficiency; 3) perform Goldstein filter in high coherence areas to reduce the computation expense. Experiments based on both simulated and real data have shown that the proposed method has achieved a better performance in terms of both noise reduction and edge preservation than some existing phase filtering methods.

PLL wrap function for synchronization in phase jump disturbances

Synchrony plays a major role in the interconnection process between local electric power generation systems and the electrical grid. Grid phase disturbances prevent the generation system from maintaining synchrony. Therefore, an efficient phase tracking method is necessary in order to detect phase jumps and abrupt changes in amplitude. In this paper, we propose a software-designed method to strengthen phase tracking based on the wrap process of a second-level Phase Locked Loop (PLL). The term ‘wrap’ means establishing the phase values of the reference signal in intervals of π to match it with the values obtained from the PLL output (sync pulse). To quantify phase error, a mathematical transformation of the time domain to the frequency domain is implemented. The validity of the proposed wrap function is verified using electrical disturbances.