Random Phase Shifts Research Articles

Simulation and investigations of a software implemented phase-locked loop with improved noise immunity

The improvement of noise immunity of a communication system is an effective way to increase the capacity of communication systems, which would provide more qualitative service for a larger number of users. This task can be solved by lowering the noise threshold of a phase-locked loop (PLL) in these systems if the dynamic properties of the device are preserved. The literature review indicates that such a device with improved noise immunity has already been implemented, but the effects of noise and modulation on its dynamic behavior were analyzed separately. This article is devoted to the analysis of the behavior of a digital firmware PLL under the simultaneous influence of noise and modulation of the input signal. The article depicts the structure of the classical digital PLL and its modifications and explains key differences between them. The simulation of the classical PLL with either absence or presence of noise at the device input was carried out. The simulation results show that the PLL is not able to detect all phase changes when the noise is present. Besides, the modified PLL has a wider working frequency range than the classical one under noisy conditions. The investigations of the PLL dynamic behavior with the simultaneous influence of random noise and Binary Phase Shift Keying (BPSK) modulated input signal was performed. The results of the research show that the duration of the transient processes during the processing of the BPSK modulated signal in the modified device is at least twice as low as that for the classical one. In addition, the number of errors during the signal detection increases faster for the classical PLL than for the modified one when the noise level rises. The use of the modified PLL in modern communication systems gives an opportunity to increase their capacity.

Development of two-frame shadow moiré profilometry by iterative self-tuning technique

Shadow moire fringes have a complex intensity distribution, which makes the existing arcsine function or arccosine function that is used in random phase-shift extraction algorithms unstable in applications. We propose a high-precision algorithm to determine the random phase shift in a robust way. The idea consists of constructing three consecutive fringe patterns by the addition of two background terms suppressed fringe patterns. Then, an iterative self-tuning phase-shifting algorithm is developed to extract the measurement phase in a pointwise manner. Due to the use of an iterative procedure and tangent function, the present method can evaluate the phase shift accurately and robustly and can be implemented easily in many applications. In addition, the proposed method provides a solution for the development of the two-frame random shadow moire technique. We present simulation and optical experiments to demonstrate the correctness of the proposed method. The results show that the proposed method performs better than other methods.

New matrix solution of the phase-correlation technique in a Brillouin dynamic grating sensor

In the phase-correlation measurement technique of Brillouin dynamic grating sensors, two counterpropagating pump waves are modulated by a pseudo-random bit sequence (PRBS) that applies a random phase shift of either 0 or π with a specified period. In order to define the sensing length and spatial resolution, the shape of the correlation peak has to be found. So far, many methods have been used to demonstrate the phase correlation, but they often require several lengthy and sometimes complicated mathematical assumptions and equations. One of the techniques that has the best reported spatial resolution is called the time gated phase-correlation technique. We introduce a novel method based on a matrix solution to show the phase modulation in the phase-correlation technique. It is a straightforward and intuitive pattern to visualize the phase modulation of the pumps and to attain the shape of the phase-correlation peaks. Finally, the results of the matrix method are completely consistent with the previous results.

Analysis of a dual aperture approach and standing wave suppression pulse sequences for controlled transvertebral focused ultrasound delivery in ex vivo human thoracic vertebrae

Focused ultrasound (FUS), in conjunction with microbubbles (MB), can open the blood-brain barrier to aid therapeutic delivery. Its feasibility for blood-spinal cord barrier opening (BSCBO) has been demonstrated in small animals. Controlled transvertebral delivery of FUS to the human vertebral canal requires low frequencies to penetrate thick vertebral bone. The resulting focal depth of field (DoF) is comparable to the size of the canal, promoting the formation of standing waves (SW) and potentially compromising treatment safety. Through k-Wave simulations and experimental acoustic field scans, a confocal, dual aperture approach was investigated in combination with SW suppressing pulses (linear chirp, short bursts and random phase shift keying (PSK)) to simultaneously reduce DoF and mitigate SWs. Two transducers (470/530 kHz, angle 90°) reduced the DoF by 85% compared to a single transducer (500 kHz). While all modified pulses reduced SWs relative to a 30 cycle sinusoid, short bursts performed significantly better than longer burst methods such as linear chirps (p = 0.03, (59±15) vs (34±11)% reduction). In combination with PSK, short bursts implemented in the dual aperture configuration mitigated SWs, while producing a uniform focal spot. The feasibility of using confocal, dual-aperture FUS to create a controlled focus within ex vivo vertebrae has been demonstrated. Next steps will include investigating MB emissions under short burst, PSK exposures, and characterizing spectral content associated with BSCBO and tissue damage.

OA010] A 4D Monte Carlo (MC) dose calculation framework with statistical breathing phase sampling to quantify interplay effects

Purpose The interplay between dose application by complex techniques and respiratory motion of a tumor can potentially lead to undesirable and non-intuitive deviations from the planned dose distribution. We developed a 4D dose calculation framework to precisely simulate dose distributions for moving target volumes. In this study we randomly sample the simulated application of delivered dose fragments on 4D-CT phases. Methods The workflow combines MC dose calculation with linac-log files and dose accumulation based on 4D-CT images. Treatment plan fragments of 0.2s duration are retrieved from linac-log data and calculated on ten 4D-CT phases using MCverify/Hyperion V2.4 (research version of Monaco 3.2). The resulting dose fragments allow the simulation of arbitrary respiratory curves (e.g. changes in breathing frequency and pattern) with a resolution of 0.2 s by assigning every fragment to a distinct 4D-CT phase. Using deformable image registration (plastimatch) the dose fragments are accumulated by AVID, a software system for automated processing and analysis of radiotherapy data. In addition to the patient’s recorded normalized breathing curve, three statistical approaches are implemented: (1) random phase shift of the breathing curve, (2) random phase assignment of every 0.2s dose fragment and (3) random phase assignment of 1MU dose fragments. Results An exemplary 3 Gy, VMAT, SBRT treatment of a 9 cm3 lung tumor with 1.6 cm crano-caudal movement was analyzed. 128 random treatments were simulated for the three statistical approaches. In all three cases the mean 4D-CT calculated dose (original plan calculated on ten 4D-CT phases) and the mean of the randomly simulated doses agree. The dose deviations for the 128 runs are very similar for the three methods (average dose deviations: σ D 2 % ≈ 0.41 % , σ D 50 % ≈ 0.25 % and σ D 98 % ≈ 0.68 % for the three approaches). Conclusions The described random assignments (2) and (3) have similar statistics as the random start phase approach (1) and are hence promising methods to comprehensively cover treatment plan and technique specific interplay effects without the need for daily breathing curves. The MU-based random sampling approach (3) is in addition independent of the linac-log data. The introduced framework has the potential to comprehensively include breathing motion induced interplay effects in the treatment planning and evaluation process.

Coherence as resource in scattering quantum walk search on complete graph

We investigate the behavior of coherence in scattering quantum walk search on complete graph under the condition that the total number of vertices of the graph is significantly larger than the marked number of vertices we are searching, N ≫ v. We find that the consumption of coherence represents the increase of the success probability for the searching, also it is related to the efficiency of the algorithm in oracle queries. If no coherence is consumed or an incoherent state is utilized, the algorithm will behave as the classical blind search, implying that coherence is responsible for the speed-up in this quantum algorithm over its classical counterpart. The effect of noises, in particular of photon loss and random phase shifts, on the performance of algorithm is studied. Two types of noise are considered because they arise in the optical network used for experimental realization of scattering quantum walk. It is found that photon loss will reduce the coherence and random phase shifts will hinder the interference between the edge states, both leading to lower success probability compared with the noise-free case. We then conclude that coherence plays an essential role and is responsible for the speed-up in this quantum algorithm.

Covariance Matrix Estimation for Massive MIMO

We propose a novel pilot structure for covariance matrix estimation in massive multiple-input multiple-output (MIMO) systems in which each user transmits two pilot sequences, with the second pilot sequence multiplied by a random phase-shift. The covariance matrix of a particular user is obtained by computing the sample cross-correlation of the channel estimates obtained from the two pilot sequences. This approach relaxes the requirement that all the users transmit their uplink pilots over the same set of symbols. We derive expressions for the achievable rate and the mean-squared error of the covariance matrix estimate when the proposed method is used with staggered pilots. The performance of the proposed method is compared with existing methods through simulations.

Characterization of the stochastic time evolution of short-term average intercore crosstalk in multicore fibers with multiple interfering cores.

A theoretical model for the stochastic time evolution of the intercore crosstalk (ICXT) in homogeneous weakly-coupled multicore fibers (MCF) with multiple interfering cores is proposed and validated experimentally. The model relies on the introduction of non-stationary time varying random phase shifts at every center point between the phase matching points of the MCF where the difference of the effective refractive indexes of the core of the originating signal and the core suffering from ICXT is zero. Closed form-expressions for the autocovariance of the short-term average ICXT (STAXT) with stationary and non-stationary phase shift models in MCFs with multiple excited cores are derived and validated by comparison with experimental results. These expressions enable estimating the decorrelation time of the STAXT generated by multiple interfering cores from the decorrelation times of the STAXT generated by each pair of cores. The proposed model and the ICXT measurements taken continuously over more than 150 hours show that the decorrelation time of the STAXT generated by multiple interfering cores exceeds the one obtained for the pair of cores with shorter decorrelation time. The proposed model is increasingly important to simulate and design MCF-based systems where the ICXT dynamics must be properly accounted for to develop efficient ICXT-tolerant techniques.

Secret Key Exchange and Authentication via Randomized Spatial Modulation and Phase Shifting

Advances in physical layer security techniques have increasingly demonstrated their potential to replace security functionalities that are traditionally included in the upper layers of the Open Systems Interconnection model. This has made it possible for devices with limited layer structures or/and restricted hardware components to offer security measures. In this paper, we consider spatial modulation (SM) systems and propose a unique physical layer technique that uses a random constellation mapping criterion for secret key exchange. The principle idea here is to exploit the inherent symbol-antenna mapping feature of the SM technique to encode the secret key. Specifically, a random phase shift is imposed on each of the modulated symbols using a channel driven approach to uniquely authenticate the transmitted key bits or/and the encrypted confidential data. The results demonstrate that the proposed technique is superior to benchmark techniques in terms of computational complexity and key bit error rate. It will also be shown that the proposed technique offers greater flexibility in terms of the authentication process preference, which is normally unattainable in most of the key exchange proposed techniques.

Extended depth-range dual-wavelength interferometry based on iterative two-step temporal phase-unwrapping

For dual-wavelength interferometry (DWI), we propose an extended depth-range phase-shifting interferometry technique of extracting phase distributions from randomly phase-shifted interferograms. First, the generalized phase-shifting algorithm is utilized to retrieve the single-wavelength phase from interferograms with random phase shifts. Then, the phase difference and phase-sum are calculated from the wrapped single-wavelength phases, and iterative two-step temporal phase-unwrapping is introduced to unwrap the phase-sum. Finally, the height of objects is determined. Simulations and experiments are conducted to demonstrate the excellent precision and overall performance of the proposed method. As the limitation of being exclusively applicable to interferograms with special phase shifts is broken, the proposed method will greatly facilitate the practical application of DWI. Furthermore, because the phase-sum and iterative two-step temporal phase-unwrapping is introduced to extend the depth-range, the sensitivity and precision of the retrieved phase are greatly improved.

Compact single-shot radial shearing interferometer with random phase shift.

We propose a compact phase-shifting radial shearing interferometer based on a pixelated micro-retarder array (MRA). The MRA is made of a thin birefringence plate, and is composed of identical units that have pixels of four different thicknesses. We demonstrate that pixelated phase delay between two shearing beams can be introduced by applying the fast axis of birefringence plate in the horizontal or vertical orientation. We also present an approach to extract the wavefront under test with random phase shift, which dramatically reduces the machining difficulty of the MRA. The feasibility and accuracy of the proposed method are further validated through our numerical analysis. With the advantages of vibration immunity, simultaneous phase stepping, and broad spectral range, the presented interferometer is expected to be of potential use in a variety of applications, such as the detection of moving objects and dynamic processes.

Simultaneous phase-shifting dual-wavelength interferometry based on independent component analysis.

An independent component analysis-based simultaneous phase-shifting dual-wavelength interferometry approach is proposed. By using a one-time phase-shifting procedure, the simultaneous phase-shifting operation of two illumination wavelengths can be implemented, and then the background intensity and two orthogonal independent components of each single wavelength can be separated from a sequence of simultaneous phase-shifting dual-wavelength interferograms with random phase shifts. Subsequently, the wrapped phases of single wavelength can be calculated by above two orthogonal independent components; thus the unambiguous phase of synthetic wavelength can be achieved. Both the simulation and experimental results show that the proposed approach reveals the advantages of high accuracy, rapid speed, high stability, and good adaptability for arbitrary phase shifts.

Influence of localised smooth steps on the instability of a boundary layer

We consider a smooth, spanwise-uniform forward-facing step defined by a Gauss error function of height 4 %–30 % and four times the width of the local boundary layer thickness $\unicode[STIX]{x1D6FF}_{99}$. The boundary layer flow over a smooth forward-facing stepped plate is studied with particular emphasis on stabilisation and destabilisation of the two-dimensional Tollmien–Schlichting (TS) waves and subsequently on three-dimensional disturbances at transition. The interaction between TS waves at a range of frequencies and a base flow over a single or two forward-facing smooth steps is conducted by linear analysis. The results indicate that for a TS wave with a frequency ${\mathcal{F}}\in [140,160]$ (${\mathcal{F}}=\unicode[STIX]{x1D714}\unicode[STIX]{x1D708}/U_{\infty }^{2}\times 10^{6}$, where $\unicode[STIX]{x1D714}$ and $U_{\infty }$ denote the perturbation angle frequency and free-stream velocity magnitude, respectively, and $\unicode[STIX]{x1D708}$ denotes kinematic viscosity), the amplitude of the TS wave is attenuated in the unstable regime of the neutral stability curve corresponding to a flat plate boundary layer. Furthermore, it is observed that two smooth forward-facing steps lead to a more acute reduction of the amplitude of the TS wave. When the height of a step is increased to more than 20 % of the local boundary layer thickness for a fixed width parameter, the TS wave is amplified, and thereby a destabilisation effect is introduced. Therefore, the stabilisation or destabilisation effect of a smooth step is typically dependent on its shape parameters. To validate the results of the linear stability analysis, where a TS wave is damped by the forward-facing smooth steps direct numerical simulation (DNS) is performed. The results of the DNS correlate favourably with the linear analysis and show that for the investigated frequency of the TS wave, the K-type transition process is altered whereas the onset of the H-type transition is delayed. The results of the DNS suggest that for the perturbation with the non-dimensional frequency parameter ${\mathcal{F}}=150$ and in the absence of other external perturbations, two forward-facing smooth steps of height 5 % and 12 % of the boundary layer thickness delayed the H-type transition scenario and completely suppressed for the K-type transition. By considering Gaussian white noise with both fixed and random phase shifts, it is demonstrated by DNS that transition is postponed in time and space by two forward-facing smooth steps.

All correlations must die: Assessing the significance of a stochastic gravitational-wave background in pulsar timing arrays

We present two methods for determining the significance of a stochastic gravitational-wave (GW) background affecting a pulsar-timing array, where detection is based on evidence for quadrupolar spatial correlations between pulsars. Rather than constructing noise simulations, we eliminate the GWB spatial correlations in the true datasets to assess detection significance with all real data features intact. In our first method, we perform random phase shifts in the signal-model basis functions. This phase shifting eliminates signal phase coherence between pulsars, while keeping the statistical properties of the pulsar timing residuals intact. We then explore a method to null correlations between pulsars by using a "scrambled" overlap-reduction function in the signal model for the array. This scrambled function is orthogonal to what we expect of a real GW background signal. We demonstrate the efficacy of these methods using Bayesian model selection on a set of simulated datasets that contain a stochastic GW signal, timing noise, undiagnosed glitches, and uncertainties in the Solar system ephemeris. Finally, we introduce an overarching formalism under which these two techniques are naturally linked. These methods are immediately applicable to all current pulsar-timing array datasets, and should become standard tools for future analyses.

The effect of nearby scatterers on the gain achieved by an acoustic array

The coherent processing of signals from multiple sensors in an array offers improvements in angular resolution and signal-to-noise ratio. When the array is steered in a particular direction, the signals arriving from that direction are added in phase, and any signals arriving from other directions are not. Array gain (AG) is a measure of how much the signal arriving from the steering direction is amplified relative to signals arriving from all other directions. This talk presents measurements along with supporting theory and simulation showing that as scatterer density increases and AG decreases, random phase shifts in individual sensor signals become larger and occur more often, and signal correlation among the sensor is reduced. The theory and numerical simulation linking scatterer density to the AG are in good agreement with the measurements up to the point where multiple scattering becomes important.

Random phase-shifting interferometry based on independent component analysis

In random phase-shifting interferometry, a novel phase retrieval algorithm is proposed based on the independent component analysis (ICA). By performing the recombination of pixel position, a sequence of phase-shifting interferograms with random phase shifts are decomposed into a group of mutual independent components, and then the background and the measured phase of interferogram can obtained with a simple arctangent operation. Compared with the conventional advanced iterative algorithm (AIA) with high accuracy, both the simulation and the experimental results demonstrate that the proposed ICA algorithm reveals high accuracy, rapid convergence, and good noise-tolerance in random phase-shifting interferometry.

Demodulation of two-shot fringe patterns with random phase shifts by use of orthogonal polynomials and global optimization.

We propose a simple and robust phase demodulation algorithm for two-shot fringe patterns with random phase shifts. Based on a smoothness assumption, the phase to be recovered is decomposed into a linear combination of finite terms of orthogonal polynomials, and the expansion coefficients and the phase shift are exhaustively searched through global optimization. The technique is insensitive to noise or defects, and is capable of retrieving phase from low fringe-number (less than one) or low-frequency interferograms. It can also cope with interferograms with very small phase shifts. The retrieved phase is continuous and no further phase unwrapping process is required. The method is expected to be promising to process interferograms with regular fringes, which are common in optical shop testing. Computer simulation and experimental results are presented to demonstrate the performance of the algorithm.

Optical Fiber Voltage Sensor Based on Michelson Interferometer Using Phase Generated Carrier Demodulation Algorithm

We present an optical fiber voltage sensor by Michelson interferometer (MI) employing a Fabry–Perot (F–P) tunable optical filter and the phase generated carrier demodulation algorithm. By mounting an MI fabricated by an optical fiber coupler on a piezoelectric transducer, a dynamic strain would be generated to change the phase difference of the interferometer when the measured voltage is applied on the piezoelectric. The phase generated carrier demodulation method was used to obtain the phase variation of the interferometer by applying demodulate signal on an F–P tunable optical filter. The measured voltage can be obtained by the variation of the phase; the random phase shift in the interferometer and the intensity fluctuation of the light source of the sensor can be eliminated. The experiment results show that the relation between the phase variation and the voltage applied on the piezoelectric is approximately linear. The dielectric reliability of the sensor has been verified according to the IEC standard.

High performance frame synchronization for continuous variable quantum key distribution systems.

Considering a practical continuous variable quantum key distribution(CVQKD) system, synchronization is of significant importance as it is hardly possible to extract secret keys from unsynchronized strings. In this paper, we proposed a high performance frame synchronization method for CVQKD systems which is capable to operate under low signal-to-noise(SNR) ratios and is compatible with random phase shift induced by quantum channel. A practical implementation of this method with low complexity is presented and its performance is analysed. By adjusting the length of synchronization frame, this method can work well with large range of SNR values which paves the way for longer distance CVQKD.

Extracting an entangled photon pair from collectively decohered pairs at a telecommunication wavelength.

We experimentally demonstrated entanglement extraction scheme by using photons at the telecommunication band for optical-fiber-based quantum communications. We generated two pairs of non-degenerate polarization entangled photons at 780 nm and 1551 nm by spontaneous parametric down-conversion and distributed the two photons at 1551 nm through a collective phase damping channel which gives the same amount of random phase shift on the two photons. Through local operation and classical communication, we extracted an entangled photon pair from two phase-disturbed photon pairs. An observed fidelity of the extracted photon pair to a maximally entangled photon pair was 0.73 ± 0.07 which clearly shows the recovery of entanglement.