Phase Tracking System Research Articles

Influence of Medial Patellofemoral Ligament Reconstruction on Patellofemoral Contact in Patients With Low-Flexion Patellar Instability: An MRI Study.

Medial patellofemoral ligament (MPFL) reconstruction is a well-established procedure for the treatment of patients with patellofemoral instability (PFI) at low flexion angles (0°-30°). Little is known about the effect of MPFL surgery on patellofemoral cartilage contact area (CCA) during the first 30° of knee flexion. The purpose of this study was to investigate the effect of MPFL reconstruction on CCA using magnetic resonance imaging (MRI). We hypothesized that patients with PFI would have a lower CCA than patients with healthy knees and that CCA would increase after MPFL reconstruction over the course of low knee flexion. Cohort study; Level of evidence, 2. In a prospective matched-paired cohort study, the CCA of 13 patients with low-flexion PFI was determined before and after MPFL reconstruction, and the data were compared with those of 13 healthy volunteers (controls). MRI was performed with the knee at 0°, 15°, and 30° of flexion in a custom-designed knee-positioning device. To suppress motion artifacts, motion correction was performed using a Moiré Phase Tracking system via a tracking marker attached to the patella. The CCA was calculated on the basis of semiautomatic cartilage and bone segmentation and registration. The CCA (mean ± SD) at 0°, 15°, and 30° of flexion for the control participants was 1.38 ± 0.62, 1.91 ± 0.98, and 3.68 ± 0.92 cm2, respectively. In patients with PFI, the CCA at 0°, 15°, and 30° of flexion was 0.77 ± 0.49, 1.26 ± 0.60, and 2.89 ± 0.89 cm2 preoperatively and 1.65 ± 0.55, 1.97 ± 0.68, and 3.52 ± 0.57 cm2 postoperatively. Patients with PFI exhibited a significantly reduced preoperative CCA at all 3 flexion angles when compared with controls (P ≤ .045 for all). Postoperatively, there was a significant increase in CCA at 0° of flexion (P = .001), 15° of flexion (P = .019) and 30° of flexion (P = .026). There were no significant postoperative differences in CCA between patients with PFI and controls at any flexion angle. Patients with low-flexion patellar instability showed a significant reduction in patellofemoral CCA at 0°, 15°, and 30° of flexion. MPFL reconstruction increased the contact area significantly at all angles.

Change in Descriptive Kinematic Parameters of Patients with Patellofemoral Instability When Compared to Individuals with Healthy Knees—A 3D MRI In Vivo Analysis

Patellofemoral instability (PFI) leads to chronic knee pain, reduced performance and chondromalacia patellae with consecutive osteoarthritis. Therefore, determining the exact patellofemoral contact mechanism, as well as the factors leading to PFI, is of great importance. The present study compares in vivo patellofemoral kinematic parameters and the contact mechanism of volunteers with healthy knees and patients with low flexion patellofemoral instability (PFI). The study was performed with a high-resolution dynamic MRI. In a prospective cohort study, the patellar shift, patella rotation and the patellofemoral cartilage contact areas (CCA) of 17 patients with low flexion PFI were analyzed and compared with 17 healthy volunteers, matched via the TEA distance and sex, in unloaded and loaded conditions. MRI scans were carried out for 0°, 15° and 30° knee flexion in a custom-designed knee loading device. To suppress motion artifacts, motion correction was performed using a moiré phase tracking system with a tracking marker attached to the patella. The patellofemoral kinematic parameters and the CCA was calculated on the basis of semi-automated cartilage and bone segmentation and registrations. Patients with low flexion PFI showed a significant reduction in patellofemoral CCA for 0° (unloaded: p = 0.002, loaded: p = 0.004), 15° (unloaded: p = 0.014, loaded: p = 0.001) and 30° (unloaded: p = 0.008; loaded: p = 0.001) flexion compared to healthy subjects. Additionally, patients with PFI revealed a significantly increased patellar shift when compared to volunteers with healthy knees at 0° (unloaded: p = 0.033; loaded: p = 0.031), 15° (unloaded: p = 0.025; loaded: p = 0.014) and 30° flexion (unloaded: p = 0.030; loaded: p = 0.034) There were no significant differences for patella rotation between patients with PFI and the volunteers, except when, under load at 0° flexion, PFI patients showed increased patellar rotation (p = 0.005. The influence of quadriceps activation on the patellofemoral CCA is reduced in patients with low flexion PFI. Patients with PFI showed different patellofemoral kinematics at low flexion angles in both unloaded and loaded conditions compared to volunteers with healthy knees. Increased patellar shifts and decreased patellofemoral CCAs were observed in low flexion angles. The influence of the quadriceps muscle is diminished in patients with low flexion PFI. Therefore, the goal of patellofemoral stabilizing therapy should be to restore a physiologic contact mechanism and improve patellofemoral congruity for low flexion angles.

Remotely controllable phantom rotation system for ultra-high field MRI to improve Cross Calibration

Abstract Optical tracking systems, such as the Moiré Phase Tracking system (MPT), can be used to correct motion prospectively especially during magnetic resonance imaging (MRI, MR) in neurologic application. For that an MRI safe camera is mounted in the MRI bore to detect motion by tracking a specific MPT marker, which is rigidly attached on the subject’s head. To enable prospective updates of the imaging volume´s position and orientation, and therefore to correct motion from the subject, the motion information captured from the camera need to be transformed from the camera into the MR coordinate system. The process of finding the transformation between both coordinate systems is called cross calibration and is essential for the overall motion correction performance. For the procedure of the cross calibration, an MR visible phantom with an attached MPT-marker is measured simultaneously with MRI and the MPT camera in multiple specific alignment positions. To reduce cross calibration errors, it is essential to move the phantom precisely into specified alignment positions. Due to the long and narrow bore design of ultra-high field systems (tunnel length > 3 m), the phantom can not be moved simply from a person leaning inside the scanner bore. Thus, to rotate it after each measurement step, either a technician must work inside the tunnel during the complete period of the cross calibration or the table must be moved in and out of the bore multiple times. To improve this currently established cross calibration procedure, we have developed an MRI safe phantom rotation system, which can be controlled remotely and precisely from outside the MRI bore. Even for ultra-high field imaging, the rotation system is fully MRI compatible. Initial tests were performed at a 7T whole-body MRI system and have proven the benefit of our rotation system.

Quantum-limited fiber-optic phase tracking beyond 𝜋 range.

We experimentally demonstrate a fiber-based phase tracking system through an adaptive homodyne detection technique. In the experiment, we use a random phase signal as an example. The system works well when the random phase varies between -2.4 and + 2.4 radians. Such tracking range is much larger than previous work due to the improved performance of phase-locked loop. The minimum mean square error reaches theoretical value at a photon flux of ~106, which proves a quantum-limited fiber phase tracking. Such system has potential applications in high-precision real-time fiber sensing of temperature, strain, and so on.

IMPROVED PERFORMANCE PHASE DETECTOR FOR MULTIPLICATIVE SECOND-ORDER PLL SYSTEMS USING DEFORMED ALGEBRA

Phase-locked loops (PLL) is a phase and/or frequency tracking system, widely used in communication and control systems. The sinusoidal multiplicative type PLL still remains a recurrent model, due the fact that its derivation is originated from the maximum likelihood approach. In this note, it is showed as a generalized product, called q-product, which can be used to implement the phase detector and improve some important parameters of the PLL system, as the block linearity and pull-in characteristics. Numerical examples are presented in order to illustrate the proposal.

Knee cartilage MRI with in situ mechanical loading using prospective motion correction

To assess the feasibility of high resolution knee cartilage MRI with in situ mechanical loading using optical tracking to compensate for motion. In vivo cartilage MRI with in situ mechanical loading is demonstrated on a clinical 3T system for the patellofemoral as well as for the tibiofemoral knee joint using a T1-weighted spoiled three-dimensional gradient-echo sequence. Prospective motion correction is performed with a moiré phase tracking system consisting of an in-bore camera and a single tracking marker attached to the skin. Rigid-body approximation required for prospective correction with optical motion tracking is fulfilled well enough for the patellofemoral as well as for the tibiofemoral joint when the tracking marker is attached to the knee cap and the shin, respectively. Presaturation proves to be efficient in suppressing pulsation artifacts from the popliteal artery and residual motion artifacts primarily arising from nonrigid motion of the posterior knee compartment. The proposed technique enables knee cartilage imaging under in situ mechanical loading with submillimeter spatial resolution devoid of significant motion artifacts and thus appropriate for cartilage volumetry. It has the potential to provide new insight into the biomechanics of the knee and might complement the panoply of diagnostic MR methods for osteoarthritis.

Bias-Free Phase Tracking with Linear and Nonlinear Systems

The arctan function is a well-known Maximum Likelihood (ML) estimator of the phase angle α ∈ [-π,π) of a complex signal in additive white Gaussian noise. In this paper we revisit the arctan-based ML phase estimator and identify the bias problem for phase tracking. We show that the posteriori probability density function of α becomes a bi-modal distribution for small values of signal to noise ratio ρ and larger values of α. In such cases the mean and the mode differ from each other, and as a result when such ML phase estimates are used as an input to a linear system (LS), example for phase tracking, the resulting output (which is essentially the mean value of the phase) differs from its true value which is the mode. In such situations there exist a mean (tracking) error at the output of the LS from its true value α, and in (non-Bayesian) statistical terms there exist a bias in the estimates. In this paper, we provide some statistical analysis to explain the above problem, and also provide solutions for bias correction when a LS is used for tracking phase. Furthermore, we also provide two nonlinear phase tracking systems, 1) a Monte-Carlo based sequential phase tracking technique and 2) a second-order digital-phase locked loop based method, for bias-free phase tracking which eliminate the bias problem that occurs in the case of linear phase tracking with ML estimates.

Cascaded Nine-Level Inverter for Hybrid-Series Active Power Filter, Using Industrial Controller

An industrial controller, specifically designed for two- and three-level converters, was adapted to work on an asymmetrical nine-level active power filter (APF). The controller is now able to make all required tasks for the correct operation of the APF, such as current-harmonic elimination and removal of high-frequency noise. The low switching-frequency operation of the nine-level converter was an important advantage in the application of the industrial controller. In addition, with the nine-level filter, switching losses were significantly reduced. The filter was designed to work as voltage source and operates as harmonic isolator, improving the filtering characteristics of the passive filter. The control strategy for detecting current harmonics is based on the “ p-q theory ” and the phase-tracking system in a synchronous reference frame phase-locked loop. The dc-link voltage control is analyzed together with the effect of controller gain and delay time in the system's stability. Simulations for this application are displayed and experiments in a 1-kVA prototype, using the aforementioned industrial controller, were tested, validating the effectiveness of this new application.

Improving the performance of quantum key distribution apparatus

Results of active phase tracking system deployment for quantum communication are presented. The system allows high-visibility single photon interferometry over 100 km of standard optical fibre. Single photon detector optimization is performed and the estimates for long-distance quantum key distribution with heralded single photon source are presented.

The Exit Problem in a Nonlinear System Driven by 1/f Noise: The Delay Locked Loop

The frequency generated by high frequency oscillators contains a small but significant noise component known as phase noise, also known as oscillator noise or phase jitter. The phase noise belongs to the family of stochastic processes with spectra $1/f^\alpha$, which exhibits scaleinvariance (or self-similarity) and a long-term correlation structure that decays polynomially in time. Both the phase and thermal noises cause errors in receivers that contain the oscillators. In particular, they cause losses of lock in phase tracking systems such as the phase locked loop in coherent systems, which include cellular phones, global positioning systems (GPS), and radar (e.g., synthetic aperture radar (SAR)), and in the delay locked loop (DLL), which is an important component of code division multiple access receivers and interface to modern memory modules, such as double data rate synchronous dynamic random access memory. The mean time to lose lock (MTLL) is well known to be an important design objective for various tracking loops. The evaluation of the MTLL is known in the mathematical literature as the exit problem for a dynamical system driven by noise, which is the problem of calculating the mean time for the noisy trajectories to reach the boundary of the domain of attraction of a stable point of the noiseless dynamics. In this paper we develop an analytic approach to the evaluation of the leading order term for MTLL of a second order DLL, due to both the non-Markovian $1/f^\alpha$ noise and to thermal white noise. The method is applicable to more general systems driven by a wide class of phase noises. The keys to the solution of this exit problem are the construction of a series of higher order Markovian processes that converge to the non-Markovian $1/f^\alpha$ noise and the asymptotic solution to a multidimensional elliptic boundary value problem that the mean first passage time (MFPT) satisfies.

Vibration Measurement and Flutter Suppression Using Patch-type EFPI Sensor System

An optical phase tracking technique for an extrinsic Fabry-Perot interferometer (EFPI) is proposed in order to overcome interferometric non-linearity. Basic idea is utilizing strain-rate information, which cannot be easily obtained from an EFPI sensor itself. The proposed phase tracking system consists of a patch-type EFPI sensor and a simple on-line phase tracking logic. The patch-type EFPI sensor comprises an EFPI and a piezoelectric patch. An EFPI sensor itself has non-linear behavior due to the interferometric characteristics, and a piezoelectric material has hysteresis. However, the composed patch-type EFPI sensor system overcomes the problems that can arise when they are used individually. The dynamic characteristics of the proposed phase tracking system were investigated, and then the patch-type EFPI sensor system was applied to the active suppression of flutter, dynamic aeroelastic instability, of a swept-back composite plate structure. The proposed system has effectively reduced the amplitude of the flutter mode, and increased flutter speed.

Optical phase estimation for a patch-type extrinsic Fabry–Perot interferometer sensorsystem and its application to flutter suppression

An optical phase tracking technique for an extrinsic Fabry–Perot interferometer (EFPI)is proposed in order to overcome interferometric non-linearity. The basic ideais utilizing strain rate information, which cannot be easily obtained from theEFPI sensor itself. The proposed phase tracking system consists of a patch-typeEFPI sensor and a simple on-line phase tracking logic. The patch-type EFPIsensor comprises an EFPI and a piezoelectric patch. An EFPI sensor itself hasnon-linear behavior due to the interferometric characteristics, and a piezoelectricmaterial has hysteresis. However, the composed patch-type EFPI sensor systemovercomes the problems that can arise when they are used individually. The proposedsystem can extract vibration information from severely distorted EFPI sensorsignals. The dynamic characteristics of the proposed phase tracking system wereinvestigated, and then the patch-type EFPI sensor system was applied to the activesuppression of flutter, dynamic aeroelastic instability, of a swept-back composite platestructure. The real time neural predictive control algorithm effectively reduces theamplitude of the flutter mode, and 6.5% flutter speed enhancement for the aeroelasticsystem was obtained by integrating smart materials into advanced structures.

Membrane capacitance measurement using patch clamp with integrated self-balancing lock-in amplifier.

A lock-in amplifier was incorporated directly into the resistance and capacitance compensation circuitry of a patch clamp set-up, to allow exocytosis to be monitored in the whole-cell mode by measuring changes in cell membrane capacitance. The integration of these two systems enabled us to provide a novel operating mode, which we term the "track-in" mode, where the output signals from the lock-in amplifier are used to make compensating electronic adjustments of the resistance and capacitance control settings. The lock-in amplifier outputs remain near zero, and the control voltages generated by the feedback circuits provide linear and calibrated resistance and capacitance measurements. Results obtained from model cells and mouse inner hair cells show that this is achieved without loss of sensitivity or of significant time resolution compared with the conventional lock-in amplifier technique, whereas the sensitivity to switching phase errors is effectively eliminated. An automatic phase tracking system using a low-frequency dithering of the resistance control setting can nevertheless be used to preserve the correct switching phase if required. The track-in approach has considerable advantages over software implementations in terms of economy and convenience, since the resistance and capacitance signals can be recorded directly on any general-purpose data-acquisition system.

A phase tracking system for three phase utility interface inverters

The analysis and design of the phase-locked loop (PLL) system is presented for the phase tracking system of the three phase utility interface inverters. The dynamic behavior of the closed loop PLL system is investigated in both continuous and discrete-time domains, and the optimization method is considered for the second order PLL system. In particular, the performance of the three phase PLL system is analyzed in the distorted utility conditions such as the phase unbalancing, harmonics, and offset caused by the nonlinear load conditions and measurement errors. The tracking errors under these distorted utility conditions are also derived. The phase tracking system is implemented in a digital manner using a digital signal processor (DSP) to verify the analytic results. The design considerations for the phase tracking system are deduced from the analytic and experimental results.

Direct ray aberration estimation in Hartmanngrams by use of a regularized phase-tracking system

The Hartmann test is a well-known technique for testing large telescope mirrors. The Hartmann technique samples the wave front under analysis by use of a screen of uniformly spaced array of holes located at the pupil plane. The traditional technique used to gather quantitative data requires the measurement of the centroid of these holes as imaged near the paraxial focus. The deviation from its unaberrated uniform position is proportional to the slope of the wave-front asphericity. The centroid estimation is normally done manually with the aid of a microscope or a densitometer; however, newer automatic fringe-processing techniques that use the synchronous detection technique or the Fourier phase-estimation method may also be used. Here we propose a new technique based on a regularized phase-tracking (RPT) system to detect the transverse aberration in Hartmanngrams in a direct way. That is, it takes the dotted pattern of the Hartmanngram as input, and as output the RPT system gives the unwrapped transverse ray aberration in just one step. Our RPT is compared with the synchronous and the Fourier methods, which may be regarded as its closest competitors.

Phase unwrapping through demodulation by use of the regularized phase-tracking technique

Most interferogram demodulation techniques give the detected phase wrapped owing to the arctangent function involved in the final step of the demodulation process. To obtain a continuous detected phase, an unwrapping process must be performed. Here we propose a phase-unwrapping technique based on a regularized phase-tracking (RPT) system. Phase unwrapping is achieved in two steps. First, we obtain two phase-shifted fringe patterns from the demodulated wrapped phase (the sine and the cosine), then demodulate them by using the RPT technique. In the RPT technique the unwrapping process is achieved simultaneously with the demodulation process so that the final goal of unwrapping is therefore achieved. The RPT method for unwrapping the phase is compared with the technique of least-squares integration of wrapped phase differences to outline the substantial noise robustness of the RPT technique.

Phase unwrapping with a regularized phase-tracking system

We develop a regularized phase-tracking (RPT) technique tounwrap phase maps. The phase maps that can be unwrapped with thisnew method may be bounded by arbitrarily shaped boundaries. Moreover, the RPT unwrapper has a higher noise robustness than previously reported phase-unwrapping schemes.

Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique

We present a two-dimensional regularized phase-tracking technique that is capable of demodulating a single fringe pattern with either open or closed fringes. The proposed regularized phase-tracking system gives the detected phase continuously so that no further unwrapping is needed over the detected phase.

Two-wavelength infrared heterodyne transceiver with a continuous phase tracking system

We describe the performance of an optical heterodyne sensor with a two-wavelength coherent infrared beam, which is used to detect the motion of remote targets in a real environment with an unambiguous sensing of the instantaneous direction along the line-of-sight propagation path. The initial phase condition of maximum sensitivity of the transceiver is stabilized and held by an active feedback system which drives the phase of the optical field of the local oscillator. The experimental results show that this feedback is particularly useful in reducing the noise generated by low-frequency environmental disturbances, leaving the signal unaffected when the respective frequency ranges are separated. Under certain circumstances, the signal can be recovered from the noise by the linearizing properties of the phase tracking on the interferometer response. The measurements reported show that the two-wavelength infrared heterodyne transceiver generates signals which replicate the target vibration exactly up to amplitudes at a multiwavelength level. This allows measurements of displacements on targets with submicron accuracy at distances of several meters.

Adaptive carrier recovery systems for digital data communications receivers

Adaptive or predictive carrier recovery systems, which are essential in high-performance quadrature-amplitude-modulated (QAM) data communications systems to correct for phase jitter and frequency offset, are considered. Analytical and experimental results are presented for two structures that implement a predictive carrier recovery system. These systems, which adapt their structure to match the spectral properties of the impairments, avoid the conflict between a wide bandwidth (to track fast jitter) and a narrow bandwidth (to minimize output noise) inherent in most carrier recovery loops. Such a system increases the likelihood that very bandwidth-efficient modems (e.g., 7 b/s/Hz for 19.2 kb/s voiceband modem applications) can provide reliable transmission in the presence of severe phase jitter and frequency offset. In particular, the predictive carrier recovery systems can track sinusoidal jitter present at more than one frequency as well as generalized time-varying phase jitter processes. Both finite-impulse-response (FIR) and infinite-impulse-response (IIR) adaptive phase tracking systems are considered. Prior limitations on adaptive IIR filters are overcome by designing a structure that is guaranteed to be stable and to possess only a global minimum as the filter coefficients converge to their desired values. >