Phase Tracking Algorithm Research Articles

Ultra-miniature dual-wavelength spatial frequency domain imaging for micro-endoscopy.

There is a need for a cost-effective, quantitative imaging tool that can be deployed endoscopically to better detect early stage gastrointestinal cancers. Spatial frequency domain imaging (SFDI) is a low-cost imaging technique that produces near-real time, quantitative maps of absorption and reduced scattering coefficients, but most implementations are bulky and suitable only for use outside the body. We aim to develop an ultra-miniature SFDI system comprising an optical fiber array (diameter 0.125mm) and a micro camera ( package) to displace conventionally bulky components, in particular, the projector. First, we fabricated a prototype with an outer diameter of 3mm, although the individual component dimensions could permit future packaging to a diameter. We developed a phase-tracking algorithm to rapidly extract images with fringe projections at three equispaced phase shifts to perform SFDI demodulation. To validate the performance, we first demonstrate comparable recovery of quantitative optical properties between our ultra-miniature system and a conventional bench-top SFDI system with an agreement of 15% and 6% for absorption and reduced scattering, respectively. Next, we demonstrate imaging of absorption and reduced scattering of tissue-mimicking phantoms providing enhanced contrast between simulated tissue types (healthy and tumour), done simultaneously at wavelengths of 515 and 660nm. Using a support vector machine classifier, we estimate that sensitivity and specificity values of are feasible for detecting simulated squamous cell carcinoma. This device shows promise as a cost-effective, quantitative imaging tool to detect variations in optical absorption and scattering as indicators of cancer.

Benchmarking Real-Time Algorithms for In-Phase Auditory Stimulation of Low Amplitude Slow Waves With Wearable EEG Devices During Sleep.

In-phase stimulation of EEG slow waves (SW) during deep sleep has shown to improve cognitive function. SW enhancement is particularly desirable in subjects with low-amplitude SW such as older adults or patients suffering from neurodegeneration. However, existing algorithms to estimate the up-phase of EEG suffer from a poor phase accuracy at low amplitudes and when SW frequencies are not constant. We introduce two novel algorithms for real-time EEG phase estimation on autonomous wearable devices, a phase-locked loop (PLL) and, for the first time, a phase vocoder (PV). We compared these phase tracking algorithms with a simple amplitude threshold approach. The optimized algorithms were benchmarked for phase accuracy, the capacity to estimate phase at SW amplitudes between 20 and 60 μV, and SW frequencies above 1 Hz on 324 home-based recordings from healthy older adults and Parkinson disease (PD) patients. Furthermore, the algorithms were implemented on a wearable device and the computational efficiency and the performance was evaluated in simulation and with a PD patient. All three algorithms delivered more than 70% of the stimulation triggers during the SW up-phase. The PV showed the highest capacity on targeting low-amplitude SW and SW with frequencies above 1 Hz. The hardware testing revealed that both PV and PLL have marginal impact on microcontroller load, while the efficiency of the PV was 4% lower. Active stimulation did not influence the phase tracking. This work demonstrated that phase-accurate auditory stimulation can also be delivered during fully remote sleep interventions in populations with low-amplitude SW.

Joint parameter estimation and decoding in a distributed receiver

SummaryThis paper presents an algorithm for iterative joint channel parameter (carrier phase, Doppler shift, and Doppler rate) estimation and decoding of transmission over channels affected by Doppler shift and Doppler rate using a distributed receiver. This algorithm is derived by applying the sum‐product algorithm (SPA) to a factor graph representing the joint a posteriori distribution of the information symbols and channel parameters given the channel output. In this paper, we present two methods for dealing with intractable messages of the SPA. In the first approach, we use particle filtering with sequential importance sampling for the estimation of the unknown parameters. We also propose a method for fine‐tuning of particles for improved convergence. In the second approach, we approximate our model with a random walk phase model, followed by a phase tracking algorithm and polynomial regression algorithm to estimate the unknown parameters. We derive the Weighted Bayesian Cramer‐Rao Bounds for joint carrier phase, Doppler shift, and Doppler rate estimation, which take into account the prior distribution of the estimation parameters and are accurate lower bounds for all considered signal‐to‐noise ratio values. Numerical results (of bit error rate and the mean‐square error of parameter estimation) suggest that phase tracking with the random walk model slightly outperforms particle filtering. However, particle filtering has a lower computational cost than the random walk model‐based method.

Michelson interferometer based phase demodulation for stable time transfer over 1556km fiber links.

Time transfer based on phase modulation schemes has attracted extensive attention in recent years. We propose and experimentally demonstrate an adjustable and stable Michelson interferometer (MI) with a DC phase tracking algorithm for two-way time transfer. Time signal with one pulse per second (1 PPS) is loaded on an optical carrier modulated in phase and demodulated by a Michelson interferometer. The whole compact and cost-effective demodulator is symmetrical with a single coupler to split and recombine optical waves, flexible with one photodetector and a bias tee to separate the DC signal and recovery pulses and stable with a phase modulator to compensate for the drift-phase noise. We show the implementation of modulation and demodulation of the time signal and obtain the stability of 2.31 × 10-11 at 1000 s averaging time. We then demonstrate two-way time transfer over 1556 km lab fibers. The experimental result shows time interval stability of 1 PPS with 5.62 × 10-11 at 1000 s averaging time. It has the potential to transfer time signals in long-distance fiber optic links.

Comb-based WDM transmission at 10 Tbit/s using a DC-driven quantum-dash mode-locked laser diode.

Chip-scale frequency comb generators have the potential to become key building blocks of compact wavelength-division multiplexing (WDM) transceivers in future metropolitan or campus-area networks. Among the various comb generator concepts, quantum-dash (QD) mode-locked laser diodes (MLLD) stand out as a particularly promising option, combining small footprint with simple operation by a DC current and offering flat broadband comb spectra. However, the data transmission performance achieved with QD-MLLD was so far limited by strong phase noise of the individual comb tones, restricting experiments to rather simple modulation formats such as quadrature phase shift keying (QPSK) or requiring hardware-based compensation schemes. Here we demonstrate that these limitations can be overcome by digital symbol-wise blind phase search (BPS) techniques, avoiding any hardware-based phase-noise compensation. We demonstrate 16QAM dual-polarization WDM transmission on 38 channels at an aggregate net data rate of 10.68 Tbit/s over 75 km of standard single-mode fiber. To the best of our knowledge, this corresponds to the highest data rate achieved through a DC-driven chip-scale comb generator without any hardware-based phase-noise reduction schemes.

Polarization coherent optical communications with adaptive polarization control over atmospheric turbulence.

In wireless optical communication systems, the coherent detection scheme suffers severe performance degradation due to the phase fluctuation and polarization offset. To deal with such challenges, we propose a polarization coherent optical communication scheme with adaptive polarization control (PCPC), where the transmitted continuous-wave light is split into two paths-the binary phase shift keying modulated signal light and the reference light-which are orthogonally polarized and combined before being sent to free space. In the receiving site, the interference between the two lights can effectively suppress the atmospheric turbulence-induced phase fluctuation. Furthermore, we propose an adaptive polarization control scheme for eliminating the polarization offset caused by the transceiver misalignment and the atmospheric turbulence. Performance evaluation of the PCPC scheme with analytical expressions and numerical simulations shows that the PCPC scheme can effectively suppress the phase fluctuation without phase-locked loop and phase tracking algorithm; thus, the PCPC scheme outperforms the traditional coherent modulation in the turbulence channel. An elaborate designed indoor experiment was implemented to verify the scheme performance, where the measured residual phase fluctuation and measured residual polarization offset are both very small, and the experimental bit error rate performance can conform closely to the theory.

Coastal Sea-Level Measurements Based on GNSS-R Phase Altimetry: A Case Study at the Onsala Space Observatory, Sweden

The characterization of global mean sea level is important to predict floods and to quantify water resources for human use and irrigation, especially in coastal regions. Recently, the application of global navigation satellite system reflectometry (GNSS-R) for water level monitoring has been successfully demonstrated. This paper focuses on the retrieval of sea surface height within a field experiment that was conducted at the Onsala Space Observatory (OSO) using the phase-based altimetry method. A continuous phase tracking algorithm, which relies on the GNSS amplitude and phase observations is proposed and works even under rough sea conditions at OSO’s coast. Factors impacting the phase-based altimetry model, i.e., atmospheric propagation effects of the GNSS signals and influence of the GNSS-R observation instrument, are discussed. The relationship between the yield of coherent GNSS-R compared to the overall recorded events and the wind speed is investigated in detail. Ground-based sea-level measurements from June 10 to July 3, 2015 demonstrate that altimetric information about the reflecting water surface can be obtained with a root mean square error of 4.37 cm with respect to a reference tide gauge (TG) data set. The sea surface changes, derived from our field experiment and the reference TG, are highly correlated with a correlation coefficient of 0.93. The altimetric information can be retrieved even when the sea surface is very rough, corresponding to wind speeds up to 13 m/s. Moreover, the use of inexpensive conventional GNSS antennas shows that the system is useful for future large-scale sea level monitoring applications including numerous low-cost coastal ground stations.

A derivative based simplified phase tracker for a single fringe pattern demodulation

In this paper, a novel fringe demodulation method for the estimation of phase and its first-order derivative from a closed-fringe interferogram is proposed. The proposed method determines the phase derivatives in both x&y directions from fringe orientation and density. The phase derivatives are subsequently used to determine phase values using a novel simplified phase tracker. In the phase tracking model, the complexity of the cost function is reduced using predetermined derivatives so computation time required for phase tracking is reduced considerably. The proposed model is more robust while dealing with saddle points in fringes than the conventional phase tracker model. Hence it does not require any specialized scanning strategy. The proposed method is validated with simulated and experimental fringe patterns (obtained using electronic speckle pattern interferometry and optical holographic interferometry) and a comparison study is carried out with conventional regularized phase tracker. The simulation results show that the proposed method has good accuracy and requires less computation time than existing phase-tracking algorithms. The experimental results demonstrate the robustness of the proposed method against speckle noise and its practical applicability for static and dynamic applications.

Standard B-Mode Ultrasound Measures Local Carotid Artery Characteristics as Reliably as Radiofrequency Phase Tracking in Symptomatic Carotid Artery Patients

Local arterial stiffness can be assessed with high accuracy and precision by measuring arterial distension on the basis of phase tracking of radiofrequency ultrasound signals acquired at a high frame rate. However, in clinical practice, B-mode ultrasound registrations are made at a low frame rate (20–50 Hz). We compared the accuracy and intra-subject precision of edge tracking and phase tracking distension in symptomatic carotid artery patients. B-mode ultrasound recordings (40 mm, 37 fps) and radiofrequency recordings (31 lines covering 29 mm, 300 fps) were acquired from the left common carotid artery of 30 patients (aged 45–88 y) with recent cerebrovascular events. To extract the distension, semi-automatic echo edge and phase tracking algorithms were applied to B-mode and radiofrequency recordings, respectively. Both methods exhibited a similar intra-subject precision for distension (standard deviation = 44 μm and 47 μm, p = 0.66) and mean distension (difference: −6 ± 69 μm, p = 0.67). Intra-subject distension inhomogeneity tends to be larger for edge tracking (difference: 15 ± 35 μm, p = 0.04). Standard B-mode scanners are suitable for measuring local artery characteristics in symptomatic carotid artery patients with good precision and accuracy.

Improved Sensitivity of Fiber Fabry-Perot Interferometer Based on Phase-Tracking Algorithm

A novel signal-processing algorithm based on phase tracking in frequency domain of optical fiber Fabry-Perot interferometric spectrum is described. The concept was demonstrated with three fiber Fabry-Perot interferometers for relative humidity measurement. Experimental results show that the proposed method can yield optical path difference measurement with high resolution, especially in the lower range of absolute humidity under 2000 ppm.

Analysis of Signal Processing Algorithms of Coriolis Mass Flowmeters

For fast and precise flow measurement using coriolis flowmeters it is necessary to accurately determinate the phase difference between two noisy position signals. These signals are digitized and filtered before being processed by phase tracking algorithms. This work investigates the influence of discretization and noise shaping on different phase tracking methods and their estimation efficiency, computational complexity, real-time performance and memory requirements.

An Adaptive Phase Tracking Scheme of OFDM Wireless Communication System

This paper proposes a new phase tracking algorithm for the 802.11a system. Since this system illuminates the basic structure of 802.11a system, and introduces the OFDM frame generation principle based the transmitter, phase error estimation and channel estimation. On the basis of this, this paper presents a phase tracking scheme based on adaptive Kalman filter, and then simulates the process based on 802.11a system. The result indicates that the BER has been improved because of this adaptive phase tracking scheme.

INS Assisted Fuzzy Tracking Loop for GPS-Guided Missiles and Vehicular Applications

Autonomous Navigation Systems used in missiles and other high dynamic platforms are mostly dependent on the Global Positioning System (GPS). GPS users face limitations in terms of missile high dynamics and signal interference. Receiver’s tracking loops bandwidth requirements to avoid these problems are conflicting. The paper presents a novel signal frequency and phase tracking algorithm for very high dynamic conditions, which mitigates the conflicting choice of bandwidths and reduces tracking loop measurement noise. It exploits the flexibility of fuzzy control systems for directly generating the required Numerically Controlled Oscillator (NCO) tuning frequency using phase and frequency discriminators information and is labeled Fuzzy Frequency Phase Lock Loop (FFPLL). Because Fuzzy Systems can be computationally demanding and an Inertial Navigation System (INS) is often onboard the vehicle, an assisted INS Doppler version has been designed and is also proposed. Assessment of the new GPS tracking method is performed with both simulated and experimental data under jamming conditions. The main enhancements of the proposed system consist in reduced processing time, improved tracking continuity and faster reacquisition time.

Three-dimensional shape measurement for an underwater object based on two-dimensional grating pattern projection

In this paper, a practical method using phase tracking and ray tracing algorithms is proposed for measuring the three-dimensional (3D) shape of an underwater object. A 2D projected sinusoidal fringe goes through the water and illuminates the tested object. Firstly, the phase tracking algorithm is employed to identify homologous points in phase distributions of the deformed fringe captured by the camera and these of the fringe pattern projected by the projector. The projector is regarded as a special camera as regards the stereovision principle. In the calibrated system, both ray directions of the homologous points can be easily figured out. Secondly, the ray tracing algorithm is used to trace the propagation path of each ray and to calculate the 3D coordinates of each point on the tested object's surface. Finally, the whole shape of the tested object can be reconstructed.

Phase-coherent communications without explicit phase tracking

Phase-coherent communications typically requires a reliable phase-tracking algorithm. An initial phase estimate with training symbols allows a receiver to compensate for a motion-induced Doppler shift. Following the training period, however, explicit phase tracking can be avoided in time reversal communications that has been implemented on a block-by-block basis to accommodate time-varying channels. This is accomplished by a smaller block size and adaptive channel estimation using previously detected symbols on a symbol-by-symbol basis. The proposed time reversal approach without explicit phase tracking is demonstrated using experimental data (12-20 kHz) in shallow water.

Digital signal processing for coherent multi-level modulation formats (Invited Paper)

This paper presents a review on the recent progress of digital signal processing (DSP) in the high-speed optical transmission system using single-carrier based multi-level modulation formats. The principle of several digital phase and polarization tracking algorithms recently proposed and demonstrated for future spectrally-efficient optical transmission system are discussed in detail. A novel DSP-based interference mitigation algorithm for the single-ended coherent receiver has been included. Recent technology advance on transmitter-side DSP such as digital pulse-shaping, pre-equalization and digital nonlinear compensation has also been discussed.

A novel digital phase tracking algorithm for a high resolution fibre Bragg grating based sensor system

The development of a high-resolution, optical fibre Bragg grating sensor system is described that incorporates a novel digital, condition-based, phase-tracking algorithm for unwrapping the 2π phase ambiguity and permits the continuous up/down phase-tracking of multiple fringe changes. An all-fibre, Michelson interferometric phase-measurement approach is utilised for the determination of strain and temperature induced Bragg wavelength shifts. The system incorporates orthoconjugate mirrors and a stabilised reference channel to compensate for polarisation and random thermal induced drifts and has the potential for resolving sub-μstrain and mK temperature changes with a resolutions of <100nϵ/√Hz (at 1Hz) and <10mK respectively.

Fast algorithm for estimation of the orientation term of a general quadrature transform with application to demodulation of an n-dimensional fringe pattern

The spatial orientation of fringes has been demonstrated to be a key point in reliable phase demodulation from a single n-dimensional fringe pattern, regardless of the frequency spectrum of the signal. Recent publications have shown a general method for determination of the orientation factor by use of a regularized phase-tracking (RPT) algorithm. We propose a generalization of a RPT algorithm for estimation of the spatial orientation in a general n-dimensional case. The proposed algorithm makes use of a simplified cost function that remains one dimensional regardless of the dimension of the problem. This makes the calculation faster than with a standard RPT algorithm, with which it is necessary to minimize an n + 1-dimensional cost function for each point of the sample space. We have applied the method to the three-dimensional demodulation of a time-evolving fringe pattern, with good results.

Modulo 2pi fringe orientation angle estimation by phase unwrapping with a regularized phase tracking algorithm.

The fringe orientation angle provides useful information for many fringe-pattern-processing techniques. From a single normalized fringe pattern (background suppressed and modulation normalized), the fringe orientation angle can be obtained by computing the irradiance gradient and performing a further arctangent computation. Because of the 180 degrees ambiguity of the fringe direction, the orientation angle computed from the gradient of a single fringe pattern can be determined only modulo pi. Recently, several studies have shown that a reliable determination of the fringe orientation angle modulo 2pi is a key point for a robust demodulation of the phase from a single fringe pattern. We present an algorithm for the computation of the modulo 2pi fringe orientation angle by unwrapping the orientation angle obtained from the gradient computation with a regularized phase tracking method. Simulated as well as experimental results are presented.

Regularized phasetracking technique for demodulation of isochromatics from asingle tricolour image

In this work we propose a robust fringe demodulation techniqueapplied to the analysis of tricolour isochromatic fringepatterns produced in photoelasticity. The method used is aregularized phase tracking (RPT) algorithm, which takes intoaccount the different information contained in the three bandsof the colour image obtained with an RGB-CCD camera.Automatic determination of the zero-order isochromatic and thearea of interest, the use of a discrete fluorescentillumination and the use of the RPT configures a robust methodfor automatic demodulation of isochromatic fringe patterns. Theperformance of the method is discussed and experimental resultsare presented.