Differential Phase Measurements Research Articles

A novel resonator cavity microwave sensor for high-temperature blade tip clearance measurement

The blade tip clearance is the key to efficiency and safety of rotating engines with accurate and real-time measurement. Existing microwave sensors can only withstand 900 °C. This paper introduces a novel resonant cavity sensor, withstanding up to 1300 °C. Using a high-impedance compensation method, the high-temperature section for the sensor has been designed. The sensor’s structure is designed based on the principle of electromagnetic field superposition and optimized by electromagnetic field simulation. A phase compensation method of transmission path based on dual-frequency technology has been proposed. Prototypes are developed and the performance tests are completed. Results show a monotonic relationship between the phase difference measurements and actual blade tip clearance values. The novel sensor is suitable for dynamic measurement of blade tip clearance. Additionally, the sensor operates reliably at high temperatures up to 1300 °C. The measurement deviation of blade tip clearance between high-temperature and room-temperature is always within ±10 %.

Modelling, optimization and application on C-shaped focusing magnetic field excitation device of electromagnetic torque sensor

To enhance accuracy and sensitivity of electromagnetic torque sensor, a highly focusing magnetic field is essential. This paper proposes a C-shaped excitation device designed to focus the magnetic field. The device is enclosed by dual layers of ferromagnetic metal shields. The C-shaped structure directs most of the magnetic field lines through its magnetic core, enhancing the focusing performance. Theoretical analysis of the device’s focusing magnetic field distribution was conducted under three conditions: unshielded, with a single-layer shield, and with a dual-layer shield, using magnetic path analysis techniques. Using COMSOL 6.1 to examine various configurations, we identified the optimal structure for the device. Subsequently, a physical prototype was fabricated, and the magnetic field distribution was measured. Furthermore, an analysis was conducted on the phase differences of the induced voltage generated under its influence. The nonlinearity of the measured phase differences was4.37%.

Carrier frequency phase calibration method for global navigation satellite systems signal simulators

Measurements of carrier frequency phase differences of global navigation satellite system signals between multiple antennas are used in many coordinate and navigation applications. Global navigation satellite systems signal simulators are used for controlling global navigation satellite systems receiver’s instrumental errors. Therefore, it is necessary to determine the systematic error of the carrier frequency phase of generated signals for signal simulators. For this purpose a new calibration method of global navigation satellite systems simulators was developed. Method is based on refined errors model of generated phase differences of two radio frequency channels of the simulator. The proposed method was implemented using a wideband oscilloscope as an analog-to-digital converter. Approbation of the calibration method was carried out by comparison with the measurement results obtained using the State secondary standard of units of complex transmission coefficients in the range of 0...–60 dB and complex reflection coefficients in the range of 0.002–1 in the frequency range of 0.05–65 GHz (registration No. 2.1.ZZT.0210.2015). The calibration method allows one to determine carrier frequencies phase offsets of navigation signals for global navigation satellite systems simulators with expanded uncertainty (with a coverage factor of 3) of 1°. The proposed method provides the required accuracy of generating phase differences of the carrier frequencies of global navigation satellite systems signals is ensured for modern types of global navigation satellite systems simulators.

Novel Approach to Phase-Sensitive Optical Time-Domain Reflectometry Response Analysis with Machine Learning Methods.

This paper is dedicated to the investigation of the metrological properties of phase-sensitive reflectometric measurement systems, with a particular focus on addressing the non-uniformity of responses along optical fibers. The authors highlight challenges associated with the stochastic distribution of Rayleigh reflectors in fiber optic systems and propose a methodology for assessing response non-uniformity using both cross-correlation algorithms and machine learning approaches, using chirped-reflectometry as an example. The experimental process involves simulating deformation impact by altering the light source's wavelength and utilizing a chirped-reflectometer to estimate response non-uniformity. This paper also includes a comparison of results obtained from cross-correlation and neural network-based algorithms, revealing that the latter offers more than 34% improvement in accuracy when measuring phase differences. In conclusion, the study demonstrates how this methodology effectively evaluates response non-uniformity along different sections of optical fibers.

Real-time high-precision baseline measurement of satellite formation flying based on GNSS

With the establishment of the Chinese space station, a series of space science missions will be conducted in its vicinity. One of the extended tasks for the in-orbit service of space station is the formation flying of small satellites centered around the space station. Satellite formations can perform simultaneous three-dimensional observations of the space station, generating three-dimensional images and monitoring and assessing the status of critical components of the space station. The real-time and accurate relative position measurement is one of the key issues in formation flying. It is a fundamental prerequisite for maintaining and reconfiguring formation configurations, collision avoidance and safety assurance. GNSS-based relative positioning is a low-cost and high-precision measurement method, which is not constrained by light, weather, or relative attitude of satellites. This study introduces a novel approach to determine the relative position of satellites based on single-epoch Global Navigation Satellite System (GNSS) carrier phase difference measurements. Unlike traditional methods, the proposed technique eliminates the need for precise ephemeris and clock bias files and does not require historical observation data. The algorithm avoids the complexity associated with full cycle ambiguity jumps, facilitating real-time, high-precision calculations of relative position baseline vectors. Special attention is given to the influence of Geostationary Earth Orbit (GEO) satellites in the BeiDou Navigation Satellite System (BDS), and measures are taken to mitigate their impact on measurement accuracy by adjusting their observation weights. Our newly developed GNSS-based real-time measurement module, designed for high-quality GNSS signal reception and data communication, was tested on terrestrial and simulated low-orbit platforms. Remarkably, over baselines ranging from 10 m to 9.3 km, while traditional pseudorange differential measurements showed errors up to 1.5571 m, our proposed method consistently held errors under 5 cm and ensured computational speeds within 0.1 s per epoch. High-dynamic zero-baseline tests further validated its potential, with errors less than 1 cm. The innovations encapsulated in this work, resonating with the evolving trends of miniaturized and scalable satellites, present a cost-efficient and real-time solution for inter-satellite relative position measurement. This promises a new horizon in satellite formation technology, with future endeavors focusing on on-orbit experiments.

Updates on the measurement of the speed of gravity using LDVs and MEMS resonators

Five years ago, at the XIII AIVELA conference, a project was presented by the author for the laboratory determination of the speed of propagation of the gravitational interaction using a vibrating tungsten disc as source of a local gravitational perturbation and a high-Q silicon resonator as gravitational antenna. Using laser Doppler vibrometers to track the vibrations of the transmitter and of the receivers, the speed of propagation of gravity would have been calculated from their measured phase difference. Numerous developments happened in the project since then, from the construction and acquirement of important components of the generator of dynamic Newtonian fields, to the experimental measurement of the speed of VHF radio waves in the near-field region as a preparatory technical test for handling and elaboration of the corresponding gravitational data. This latter experiment produced unexpected superluminal results, making it worthy of further study. The results of the test also broadened the scope of expectations and possible interpretations of the results of the gravitational experiment, including the additional role of an indirect assessment of the existence of gravitons.

GMM-based GNSS spoofing detector using double differential phase measurement

GNSS spoofing is an intentional interference wherein a GNSS receiver tracks counterfeit signals, resulting in incorrect outcome positions. This is the most dangerous type of intervention in the GNSS technology. In this study, we introduce a novel method for detecting spoofing signals using a Gaussian mixture model (GMM) on the double-carrier phase difference (DD) created by two independent receivers. The DD can completely eliminate errors caused by the satellite clock, receiver clock, and atmospheric layers; hence, the signal angle of arrival (AoA) is clearly expressed in the DD measurement. We utilized the GMM to model the probability density function of the DD measurement computed from the phase measurement of the receivers. Theoretically, AoA values of an authentic signal change over time owing to the nature of the signal broadcast from an orbiting satellite. However, fake signals are often transmitted from the generator, resulting in a central distribution of the corresponding AoA values. Existing studies deal with the spoofing detection problem using the above theoretical assumptions. However, it is practical to broadcast spoofing signals from several sources, and random noise can be mixed into the generated phase to render the DD measurement noisy. In such complicated scenarios, existing approaches are not sufficiently robust to detect non-authentic signals. Another observation is that because real satellites are moving in fixed orbits, there should be a correlation among the AoA values of the signals coming from these satellites. In contrast, counterfeit signals (with the main purpose of causing the wrong position or noisy phase) do not follow the pattern of the real signals. Therefore, instead of using the above hard assumption about the signal AoA, we propose a statistical model GMM to learn the hidden relationship of the AoA values among real signals from different real satellites, which are then used to detect spoofing signals.

Global Navigation Satellite System Spoofing Detection in Inertial Satellite Navigation Systems

The susceptibility of global navigation satellite systems (GNSSs) to interference significantly limits the possibility of their use. From the standpoint of possible consequences, the most dangerous interference is the so-called spoofing. Simultaneously, in most cases of GNSS use, an inertial navigation system (INS) or an attitude and heading reference system (AHRS) is also present on the board of mobile objects. In this regard, the research goal is to assess the possibility of detecting GNSS spoofing in inertial satellite navigation systems. This paper examines the method for detecting GNSS spoofing by combining a pair of commercially available GNSS receivers and antennas with an INS or AHRS. The method is based on a comparison of the double differences of GNSS carrier phase measurements performed by receivers under conditions of resolved integer ambiguity and the values of the range double differences predicted using an INS. GNSS carrier phase integer ambiguity can be resolved using a strapdown inertial navigation system (SINS) or AHRS data. The mathematical model of GNSS phase difference measurements and the SINS-predicted satellite range differences model are given. The proposed algorithm calculates the moving average of the residuals between the SINS-predicted satellite range double differences and the measured GNSS carrier phase double differences. The primary criterion for spoofing detection is the specified threshold excess of the moving average of the double difference residuals. Experimental studies are performed using simulation and hardware-in-the-loop simulation. The experimental results allow us to evaluate the efficiency of the proposed approach and estimate the potential characteristics of the spoofing detection algorithm based on it.

A U-Net Approach for InSAR Phase Unwrapping and Denoising

The interferometric synthetic aperture radar (InSAR) imaging technique computes relative distances or surface maps by measuring the absolute phase differences of returned radar signals. The measured phase difference is wrapped in a 2π cycle due to the wave nature of light. Hence, the proper multiple of 2π must be added back during restoration and this process is known as phase unwrapping. The noise and discontinuity present in the wrapped signals pose challenges for error-free unwrapping procedures. Separate denoising and unwrapping algorithms lead to the introduction of additional errors from excessive filtering and changes in the statistical nature of the signal. This can be avoided by joint unwrapping and denoising procedures. In recent years, research efforts have been made using deep-learning-based frameworks, which can learn the complex relationship between the wrapped phase, coherence, and amplitude images to perform better unwrapping than traditional signal processing methods. This research falls predominantly into segmentation- and regression-based unwrapping procedures. The regression-based methods have poor performance while segmentation-based frameworks, like the conventional U-Net, rely on a wrap count estimation strategy with very poor noise immunity. In this paper, we present a two-stage phase unwrapping deep neural network framework based on U-Net, which can jointly unwrap and denoise InSAR phase images. The experimental results demonstrate that our approach outperforms related work in the presence of phase noise and discontinuities with a root mean square error (RMSE) of an order of magnitude lower than the others. Our framework exhibits better noise immunity, with a low average RMSE of 0.11.

Investigation of internal electric fields in graphene/6H-SiC under illumination by the Pockels effect.

In this paper, we introduce a method for mapping profiles of internal electric fields in birefringent crystals based on the electro-optic Pockels effect and measuring phase differences of low-intensity polarized light. In the case of the studied 6H-SiC crystal with graphene electrodes, the experiment is significantly affected by birefringence at zero bias voltage applied to the crystal and a strong thermo-optical effect. We dealt with these phenomena by adding a Soleil-Babinet compensator and using considerations based on measurements of crystal heating under laser illumination. The method can be generalized and adapted to any Pockels crystal that can withstand sufficiently high voltages. We demonstrate the significant formation of space charge in semi-insulating 6H-SiC under illumination by above-bandgap light.

The Ability to Detect Sound Scattering Layers by Interferometric Side-Scan Sonar

A method and algorithm for remote detection of sound-scattering layers in the seas and oceans using strip survey data of the bottom topography by interferometric side-scan sonar (ISSS) is considered. Based on mathematical modeling of phase-difference measurements of ISSS for multilayer scattering planes in seawater, we demonstrate the possibility of detecting sound-scattering layers and measuring their depths using the proposed algorithm. The accuracy of calculating the depths of sound-dispersing layers at a constant value of the sound velocity has been evaluated and the requirements to the ISSS have been determined to ensure the necessary accuracy of detection of individual layers located at different depths. The efficiency of the proposed method is demonstrated based on the example of processing by the developed algorithm of the experimental data obtained during bottom relief studies with an 85 kHz range ISSS.

Analysis of Electrical Machines’ State by Measuring the Interturn Resistance in Its Windings

Diagnostic methods applied in the industry do not allow to control the state of electrical machines windings in working condition and to fix the defect formation in them at the early stages of development. The aim of the work was to develop a method and construct a device that allows measuring interturn resistances in the electrical machines’ windings without the need to remove it from the technological process, and thereby assess its current and future performance.A block diagram of a device for measuring of interturn resistances in the electrical machines’ windings has been developed, a method has been described, and an algorithm for carrying out diagnostic procedures has been developed. Also, as a result of the study, mathematical dependencies were determined that characterize the main operations performed by the device and a mathematical model was developed for obtaining of the interturn resistance value in the diagnosed windings from the value of the measured phase difference for the AIR63V4U3 asynchronous motor.The developed method and a device based on it allow measuring interturn resistances in the electrical machines’ windings without the need to remove it from the technological process and fix the beginning of defect formation, and, thereby, evaluate its current and future performance in real time.

K‐band CMOS low‐noise amplifier with 180° phase shift function using cascode structure

AbstractIn this study, a K‐band CMOS low‐noise amplifier (LNA) with a 180° phase shift function is presented to reduce the chip area of the beamforming system. The proposed LNA is composed of three stages, and the last stage is designed with a differential cascode structure for 180° phase shift function. The 180° phase shift function was implemented by dividing one cascode transistor into two transistors. As a result, it is possible to equip the 180° phase shift function without an additional chip area. The LNA was designed with a 65‐nm CMOS process to verify the feasibility of the proposed technique. The core size was 0.66 × 0.41 mm2. The measured phase difference between 0° and 180° phase shift modes was approximately 178° in the operating frequency of 22.0 GHz. The measured noise figure and gain were 3.8 and 12.7 dB, respectively.

Measurement of Phase Difference and Direction of Arrival Using Time-Modulated Array With General Modulation Parameters

An extraction method and formulas are proposed for phase difference and direction of arrival (DOA) using a two-element time modulated array with the general modulation parameters. The relevant spectral components are described with the help of a phasor diagram and equations for phase difference and the DOA are derived from the measured magnitude and complex quantities of these spectral components. Issues involving measurement with frequency down-conversion are addressed. Simulations and experiments are performed to evaluate the proposed method and the related theory.

Antenna Phase Center Determination Using a Six-Port-Based Direction-of-Arrival Detector

This article presents a novel technique to determine the antenna phase center. It relies on measuring the direction of arrival of the radiated field. Therefore, no access of the measurement equipment to the antenna under test is required. A direction-of-arrival detector is implemented that performs phase difference measurements in two orthogonal planes. Six-port interferometers are used for this purpose. By considering phase differences, the proposed method is robust against phase disturbances, which may occur at the feed of the antenna under test, e.g., due to flexible cables or rotary joints. Besides, impairments stemming from reflections in the measurement environment are addressed. Measurements of a K-band horn and a patch antenna in an anechoic chamber validate the approach. A single phase center is determined for each principle plane as well as for the three-dimensional main beam. In addition, the phase center locus is retrieved.

Design and Implementation of Precision Phase Measurement Module Base on Digital Dual Mixer Time Difference

Precise phase difference measurement is critical for distributed time synchronization systems. Aiming at the problem of how to realize the sub-nanosecond phase difference measurement of the time signal, the digital dual mixer time difference (DDMTD) measurement technology is used to measure the fine transmission delay and the two digital clock phase difference. Given the problem that it is difficult to generate a common clock source with fine frequency changes inside the FPGA chip, the Si5338 chip is used to generate 4 differential clocks, and the communication with the FPGA is completed through the I2C protocol, and the differential signal is converted into a single-ended clock source inside the FPGA as two The common standard frequency of clock signals with the same frequency and different phases, realize the amplification of the phase difference measurement range, making the measurement accuracy reach sub-nanosecond level.

A Phase Difference Measurement Method for Integrated Optical Interferometric Imagers

Interferometric imagers based on integrated optics have the advantages of miniaturization and low cost compared with traditional telescope imaging systems and are expected to be applied in the field of space target detection. Phase measurement of the complex coherence factor is crucial for the image reconstruction of interferometric imaging technology. This study discovers the effect of the phase of the complex coherence factor on the extrema of the interference fringes in the interferometric imager and proposes a method for calculating the phase difference of the complex coherence factor of two interference signals by comparing the extrema of the interferometric fringes in the area of approximate linear change in the envelope shape to obtain the phase information required for imaging. Experiments using two interferometric signals with a phase difference of π were conducted to verify the validity and feasibility of the phase difference measurement method. Compared with the existing phase measurement methods, this method does not need to calibrate the position of the zero optical path difference and can be applied to the integrated optical interferometric imager using a single-mode fiber, which also allows the imager to work in a more flexible way. The theoretical phase measurement accuracy of this method is higher than 0.05 π, which meets the image reconstruction requirements.

Phase analysis of signals using frequency-dependent attenuation for measurements of seismic waves

Attenuation refers to any decrease in the power of a propagated signal through a medium. Attenuation measurement techniques include ultrasonic, resonance bar, and stress-strain methods. The stress-strain method measures elastic and viscoelastic properties in the seismic frequency range. The signals received via attenuation measurement systems using the stress-strain method can be considerably weak. Moreover, the noise in these signals causes errors when estimating the signal phase-angle difference between the sample signal and probe signal, thereby reducing system precision and measurement accuracy. Accurate measurements of such phase differences are essential to the measurement of attenuation. A seismic-wave attenuation with frequency-dependent measurement based on the stress-strain method and digital signal processing techniques has been performed. The system estimates the attenuation of a rock by measuring the phase shift in the stress-strain cycle. As a preprocessing method, the finite impulse response band-pass filters are designed to eliminate the influence of noise and direct current offset while ensuring that the phase difference of the measured signal remains unchanged. Three methods for phase difference estimation, i.e., crosscorrelation, fast Fourier transform (FFT), and Hilbert transform are compared, for different signal-to-noise ratios, sampling frequencies, data sample lengths, and true phase differences. The results find that the phase difference estimation based on FFT is the best among all three methods and can effectively improve the precision of the experimental results. Simulation and measurement results further indicate that the attenuation measurement system achieves stable and reliable attenuation measurements in the range of 3–2000 Hz.

Polarization Diversity-Enabled LOS/NLOS Identification via Carrier Phase Measurements

The provision of accurate localization is an increasingly important feature of wireless networks. To this end, a reliable distinction between line-of-sight (LOS) and non-LOS (NLOS) radio links is necessary to avoid degenerative localization estimation biases. Interestingly, LOS and NLOS transmissions affect the polarization of the received signals differently. In this work, we leverage this phenomenon to propose a threshold-based LOS/NLOS classifier exploiting weighted differential carrier phase measurements over a single link with different polarization configurations. Operation in either full or limited polarization diversity systems is possible. We develop a framework for assessing the performance of the proposed classifier, and show through simulations the performance impact of the reflecting materials in NLOS scenarios. For instance, the classifier is far more efficient in NLOS scenarios with wooden reflectors than in those with metallic reflectors. Numerical results evince the potential performance gains from exploiting full polarization diversity, properly weighting the differential carrier phase measurements, and using multi-carrier/tone transmissions. Finally, we show that the optimum decision threshold is inversely proportional to the path power gain in dB, while it does not depend significantly on the material of potential NLOS reflectors.

Design of K-Band Power Amplifier with 180-Degree Phase- Shift Function Using Low-Power CMOS Process

In this study, a K-band complementary metal oxide semiconductor (CMOS) power amplifier was designed using a low-power (LP) process to improve the integration of the beamforming system. In order to reduce the overall system size, a 180° phase-shift function was mounted. It was designed in a four-stage structure to secure sufficient gain. In addition, we propose a way to secure wideband characteristics by utilizing the gains of each of the four stages. The power amplifier was designed with a 40-nm LP CMOS process to verify the feasibility of the proposed technique. The measured P1dB for 0° and 180° phase-shift modes were 15.25 dBm and 14.30 dBm, respectively, at the operating frequency of 25.0 GHz. The measured phase difference between the two modes was 217° at the 25.0 GHz.