Differential Phase Measurements Research Articles

Carrier phase difference measurement method for GNSS-simulator navigation signal

A method for measuring phase difference of carrier frequency of GNSS-simulator navigation signal, based on the use of a multichannel analogue-to-digital converter and phase processing at intervals of its linear change is proposed. The developed method makes it possible to measure the phase difference of carrier frequency of radio navigation signal with a non-excluded systematic error 1.5°.

Determining the angle-of-arrival of a radio-frequency source with a Rydberg atom-based sensor

In this work, we demonstrate the use of a Rydberg atom-based sensor for determining the angle of arrival of an incident radio frequency (RF) wave or signal. The technique uses electromagnetically induced transparency in Rydberg atomic vapor in conjunction with a heterodyne Rydberg atom-based mixer. The Rydberg atom mixer measures the phase of the incident RF wave at two different locations inside an atomic vapor cell. The phase difference at these two locations is related to the direction of arrival of the incident RF wave. To demonstrate this approach, we measure phase differences of an incident 19.18 GHz wave at two locations inside a vapor cell filled with cesium atoms for various incident angles. Comparisons of these measurements with both the full-wave simulation and the plane wave theoretical model show that these atom-based sub-wavelength phase measurements can be used to determine the angle of arrival of an RF field.

Software-Defined Radio Implemented GPS Spoofing and Its Computationally Efficient Detection and Suppression

This article demonstrates global positioning system (GPS) spoofing with a commercial, off-the-shelf software-defined radio (SDR) emitter fitted with a local oscillator exhibiting a stability consistent with the medium-term (0.01-1 000 s) stability of atomic clocks on GPS satellite systems. Computationally efficient means of detecting spoofing is then addressed, namely codeless spoofing detection by phase-difference measurement of the signals received from a two-antenna array. We conclude by using a simple and effective method to suppress spoofing to restore positioning and time-transfer capabilities, and extend the demonstration to jamming cancellation. Experiment results demonstrate the performance of the proposed methods with an emphasis on computational efficiency for real-time execution on embedded single-board computers.

Improved Interoperability Evaluation Method for Wireless Charging Systems Based on Interface Impedance

The interoperability between the vehicle assembly and ground assembly of wireless charging systems has been specified in international standards. SAE J2954 first proposed an interoperability evaluation method based on interface impedance. However, the impedance measurement is challenging at high frequency since the phase difference between the voltage and current is not easy to measure accurately, especially when it is close to 90°. Small errors in phase angle measurement are amplified in impedance calculation due to the sine/cosine function. This letter proposes an impedance measurement method using the power decomposition algorithm. By decomposing the input power into two orthogonal components, the impedance angle can be calculated without directly measuring the phase difference between the voltage and current. Thus, the measurement results of the impedance angle do not introduce errors. With the proposal, the high-cost probe or complex high-precision phase difference measurement circuit is not needed. The experimental results show that the conventional method's maximum relative error reaches 80%, making interoperability hard to determine. Reversely, with the proposed method, the relative error of impedance measurement is reduced to less than 10%.

A Method of Full-Range Gas Concentration Detection Based on Multi-Frequency Ultrasonic Cross-Cycle Phase Difference Measurement

Ultrasonic technology is widely used in the field of gas detection due to its advantages of low power consumption, high speed and strong adaptability to the environment. The current ultrasonic time-of-flight (TOF) measurement method has the large measurement error caused by ringing effect, and the phase detection method can only detect the phase change within 2π of a single cycle. These problems cannot meet the requirements of certain high concentration gas detection. This paper proposes a method of multi-frequency ultrasonic phase difference measurement to solve the problem that the phase difference across multiple cycles cannot be detected, hereby realizing full range gas concentration detection, and the continuous wave detection of this method also eliminates ringing effect in TOF. The phase difference within 2π of a single period is obtained by loading a single frequency driving signal on two channels, and the phase difference of low-frequency envelope of the modulated signal is obtained by loading multi-frequency modulated signals. The total cross-cycle phase difference can be obtained by combining the two results, and the measured gas concentration can be obtained by the relationship model between gas concentration and phase difference. The experimental results show that the average absolute error of 4% hydrogen concentration measurement is 0.12%, and the relative error of 99% hydrogen measurement is less than 5%. This method also provides a solution for extracting cross-cycle phase difference in other fields.

A Systematic Design of a Compact Wideband Hybrid Directional Coupler Based on Printed RGW Technology

Printed ridge gap waveguide (PRGW) is considered among the state of art guiding technologies due to its low signal distortion and low loss at Millimeter Wave (mmWave) spectrum, which motivates the research community to use this guiding structure as a host technology for various passive microwave and mmWave components. One of the most important passive components used in antenna beam-switching networks is the quadrature hybrid directional coupler providing signal power division with 90° phase shift. A featured design of a broadband and compact PRGW hybrid coupler is propose in this paper. A novel design methodology, based on mode analysis, is introduced to design the objective coupler. The proposed design is suitable for mmWave applications with small electrical dimensions ( $1.2\,\,\lambda _{o} \times 1.2\,\,\lambda _{o}$ ), low loss, and wide bandwidth. The proposed hybrid coupler is fabricated on Roger/RT 6002 substrate material of thickness 0.762 mm. The measured results highlight that the coupler can provide a good return loss with a bandwidth of 26.5% at 30 GHz and isolation beyond 15 dB. The measured phase difference between the coupler output ports is equal $90^\circ \pm ~5^\circ $ through the interested operating bandwidth. A clear agreement between the simulated and the measured results over the assigned operating bandwidth has been illustrated.

ОЦІНЮВАННЯ ТОЧНОСТІ ВИМІРЮВАННЯ МИТТЄВИХ ЧАСТОТ ТА ФАЗ КОМПОНЕНТ БАГАТОКОМПОНЕНТНОГО НЕСТАЦІОНАРНОГО СИГНАЛУ

Measurements of instantaneous frequencies and phases of non-stationary components of the multicomponent signals are actual in processing medical, radar, sonar, seismic, vibration, and speech signals. When we measure the parameters of multi-component non-stationary signals, it is a need to measure the instantaneous frequency and current phase of several non-stationary frequency-modulated signal components. In this article, estimates of the measurement accuracy of the specified parameters of the non-stationary signal components were obtained using the method of simulation modeling. Measurement methods based on the short-time Fourier transform and the proposed method with local adaptive matching filtering of signal components in the frequency domain in the time-sliding observation window were studied. Adjustment of matched filters is performed separately for each component of the signal, returning to the time domain and taking into account the filter settings in the previous time window. The simulation method is used for the signal model consisting of three components. The first two components are the frequency modulated harmonic ones and the last is harmonic with constant frequency. The amplitudes of components and additive Gaussian noise variance were variated to study the influence of signal-to-noise ratio on the accuracy of measurements. Estimates of the experimental standard deviation of instantaneous frequencies and current phase measurements were obtained by comparing them with their known dependencies. The frequency laws of non-stationary signal components were chosen to be harmonic, which also allowed us to evaluate the influence of the nonlinearity of the instantaneous frequency change on the measurement accuracy. The results of differential phase measurements between two measurement channels are obtained to illustrate the quality of such ones for multi-component non-stationary signals situations. The results of this study may be useful for the development of imaging methods in inverse synthetic aperture radars (ISAR) and interferometric ISAR.

Quasi-Coherent Phase-Based Localization and Tracking of Incoherently Transmitting Radio Beacons

The direct measurement of distance-dependent information between wireless units represents a challenge for wireless locating systems, because it requires the exact time synchronization of separate wireless units. To avoid these synchronization efforts, many wireless locating systems only evaluate phase difference of arrival (PDOA) measurements. While simple PDOA localization techniques rely on multiangulation, advanced PDOA concepts like the holographic extended Kalman filter (HEKF) directly evaluate the measured phases without non-linear preprocessing. However, these differential phase measurement approaches are less sensitive than systems that can measure absolute phase variations, which allow the tracking of much smaller position changes than the signal’s carrier wavelength. This paper proposes to extend the HEKF by the evaluation of absolute phases in an incoherent measurement setup, which consists of a continuous wave (CW) beacon and several receivers. The developed quasi-coherent holographic extended Kalman filter (QCHEKF) uses the overdetermined PDOA measurements to estimate the phase–frequency relation between each beacon–receiver pair. Then, the established phase–frequency relations allow the evaluation of absolute phase measurements and, thus, the accurate localization and tracking of a simple, unsynchronized, narrowband CW beacon, even under severe multipath conditions. This novel concept is experimentally validated via 3D localization results in a challenging indoor scenario using a 24 GHz CW measurement setup. Here, the QCHEKF improves the achieved localization accuracy in comparison to the HEKF by 35 % from 0.78 cm to 0.51 cm, while the maximum deviation from the trajectory reduces by 68 % from 5 cm to 1.6 cm. Furthermore, the QCHEKF enables the exact tracking of fast changes in direction, which is usually a significant challenge for standard wireless target tracking systems.

Synthetic Aperture Radar Interferometry: Utilizing Radar Principles

One of the most important applications of synthetic aperture radar interferometry (SARIF) is making a geometrical plot of observed points on the ground surface. For that purpose, we derive the two points' distances using a radar principle. Mathematically, this problem is a two-unknown-variables problem. To solve, it we need only two equations. Due to limitations of the measured distances by radar, we require one more equation. The availability of the data is carefully investigated. Then, we obtain a very clear expression for the parallel and perpendicular components of the distance. The perpendicular component is expressed by the difference of the measured phase differences with an extremely large amplifier. We discuss the conversion of the measured phase differences, the plot of which is an interferogram, to distance. We present a numerical example that verifies the likelihood of obtaining the difference of the phase differences. We also show the phase differences and calculate the perpendicular component for the Advanced Land Observing Satellite-Phased Array-Type L-Band Synthetic Aperture Radar (ALOSPALSAR). The plot of ground points is very noisy; therefore, we must improve our calculation by reconsidering the coregistration calculation.

Polarimetric Radar Variables in Snowfall at Ka- and W-Band Frequency Bands: A Comparative Analysis

AbstractDual-frequency millimeter-wavelength radar observations in snowfall are analyzed in order to evaluate differences in conventional polarimetric radar variables such as differential reflectivity (ZDR) specific differential phase shift (KDP) and linear depolarization ratio (LDR) at traditional cloud radar frequencies at Ka and W bands (~35 and ~94 GHz, correspondingly). Low radar beam elevation (~5°) measurements were performed at Oliktok Point, Alaska, with a scanning fully polarimetric radar operating in the horizontal–vertical polarization basis. This radar has the same gate spacing and very close beam widths at both frequencies, which largely alleviates uncertainties associated with spatial and temporal data matching. It is shown that observed Ka- and W-band ZDR differences are, on average, less than about 0.5 dB and do not have a pronounced trend as a function of snowfall reflectivity. The observed ZDR differences agree well with modeling results obtained using integration over nonspherical ice particle size distributions. For higher signal-to-noise ratios, KDP data derived from differential phase measurements are approximately scaled as reciprocals of corresponding radar frequencies indicating that the influence of non-Rayleigh scattering effects on this variable is rather limited. This result is also in satisfactory agreement with data obtained by modeling using realistic particle size distributions. Observed Ka- and W-band LDR differences are strongly affected by the radar hardware system polarization “leak” and are generally less than 4 dB. Smaller differences are observed for higher depolarizations, where the polarization “leak” is less pronounced. Realistic assumptions about particle canting and the system polarization isolation lead to modeling results that satisfactorily agree with observational dual-frequency LDR data.

CPLD-Based Displacement Measurement System for Nanoscale Grating Ruler

With the continuous development of science and technology, industrial production has higher and higher requirements for precision. Many high-precision measurement technologies emerge as the times require, and nanoscale grating ruler displacement measurement technology is one of them. As a kind of precision sensor, nanoscale grating ruler has important application in displacement measurement system. CPLD has the advantages of high integration and fast programming speed, which is often used to control the displacement measurement system of nanoscale grating ruler. The purpose of this paper is to deeply explore the measurement effect and related application principle of nanoscale grating ruler displacement measurement system based on CPLD technology. A set of nanoscale grating ruler displacement measurement system is designed based on CPLD technology. The output signal of grating ruler is programmed by CPLD. The x-axis displacement of the experimental platform controlled by stepping motor is measured, and the measured data are recorded by carrying out analysis and research. The results show that compared with the traditional phase difference measurement system, the measurement accuracy of the system based on CPLD is improved by 24.7%, the robustness of the measurement system is improved by 18.6%, and the measurement speed is increased by 27.3%. Therefore, this kind of nanoscale measurement precision grating ruler displacement measurement control system based on CPLD has three characteristics: high measurement accuracy, strong anti-interference ability, and high measurement motion efficiency, which can effectively meet the requirements of grating ruler displacement measurement system for high-precision manufacturing technology.

Simultaneous Measurement and Simulation of Angular Position and Angular Speed for Time Grating

A method is presented in order to realize the measurement of angular position and angular speed simultaneously based on the theory of time grating and the measurement of angular position and angular speed is transformed into the measurement of phase difference. Four orthogonal excitation signals are generated by the internal phase-locked loop module of FPGA. The excitation signals are superposed and input to the stator sensor. At this time, the rotation of the motor causes the rotation of the rotor sensor to generate the induction signal. The phase difference of the two signals will be obtained by the input comparison circuit of the induction signal and the excitation signal. The phase difference will be processed in FPGA, and finally the angular position and angular speed values will be obtained. The simulation results show that the method is feasible. The experimental results show that the accuracy error of angular position measurement can reach ±3", and the measurement speed stability can reach 3rpm(3%o) when the angular speed is 1000rpm.

A Portable Cost-Effective Amplitude and Phase Antenna Measurement System

This article presents a simple, cost-effective system for complex measurements of the field radiated by an antenna. In particular, the proposed architecture is based on an array of antenna probes connected to a set of phase difference detectors and a power detector. Phase difference measurements are processed to recover the phase of the antenna under test. The main novelty of the proposed system is that it does not require regular sampling, making it suitable for in situ antenna measurements. The influence of parameters, such as the number of antennas composing the array (and hence the number of phase difference detectors) and the positioning errors, is analyzed. The proposed architecture, implemented with off-the-shelf hardware, has been assessed for antenna measurement and diagnostics. A discussion of the issues related to the implementation of the system has been included, as well as the proposed solutions to improve its accuracy. Finally, diagnostics and radiation pattern measurement results are compared with those calculated with other phaseless techniques.

Self-compensating quantitative differential interference contrast microscopy imaging system using liquid crystal shearing assembly

A quantitative differential interference contrast microscopy (DICM) using a liquid crystal shearing assembly (LCSA) is proposed and demonstrated experimentally. Differential interference contrast (DIC) imaging with arbitrary shearing amount and different shearing direction can be implemented by changing the driving voltage applied to the liquid crystal without mechanical devices. Moreover, by combining a quarter-wave plate and a mirror, not only the shearing amount is enlarged, but also the aberration and the additional phase shift induced by the refractive index difference between ordinary and extraordinary light can be compensated. Using the proposed LCSA/DICM system, we implement DIC imaging of a polystyrene microsphere crown and the quantitative differential phase measurement of an oral epithelial cell.

Employment of Fizeau fringe disintegration to magnify small phase variations

When an object produces a small phase variation not less than the minimum phase variation detectable by the used system and more than the system’s noise, the object is considered as a tiny (or small) object. The measurement of interferometric phase differences evolved from a tiny optical phase object has gained attention in recent years due to its usefulness in accurate detection of nanometric dimensions. In the current work, a Fizeau wedge interferometer is used as an aberrationless method to amplify phase variations of a tiny object. The phase object is inserted between the two semi-reflecting/partially transmitting plates making a small wedge angle in between. The fast Fourier transformation (FFT) spectrum of the obtained interferograms is characterized by some frequency equidistant peaks. The number of these peaks is related to the number of the interfered rays and each peak represents a set of two-beam interferences. We applied a mask to select one of these peaks and reproduced its corresponding optical phase map via employing inverse fast Fourier transformation. The produced map contains the magnified phase variation with a magnification factor equal to 2 times the selected peak’s order. Experimental verification of two different phase object samples to amplify their phase variations with different amplification factors is performed. An integrated magnified phase by the object is calculated to test the validity of the proposed method. It is found that the magnification according to the selection of different FFT peaks is a little bit deviated from the expected magnification factors which is referred to ignoring refraction of the optical rays by the object. In spite of these deviations, good results are obtained.

Algorithm for Eliminating of the Limiting Disambiguation of Measurement Made by Phase Radio Direction Finders by Sorting Out the Abnormally Large Errors

The aim of the article is to find the upper probability limit of the measurement results to correct disambiguation in case of multi-base phase direction finders, where all bases are ambiguous. Direction finding is done using the maximum likelihood method based on a set of measured phase differences and an algorithm of rejecting (erasing) abnormally large measurement errors. The theoretical background of the article is the maximum likelihood method applied to disambiguate results of the phase measurements in multi-base measuring systems. The physical meaning of the method is that if the disambiguation process is correct, the results of angular measurements for each base are grouped around the true value of bearing. The mathematical background of the article are methods of linear algebra based on the geometric interpretation of disambiguation measurement results. We obtained formulas for calculating upper bounds for the probability correct disambiguation of measurement results, which are applicable to direction finders with linear, planar and conformal antenna arrays. The obtained theoretical relations are exemplified by a numerical calculation of error probability including the upper bounds for a specific three-base direction finder 'bad' measurement results. The calculations proved effectiveness of the proposed algorithm, which depends on the accuracy of phase measurements. The proposed algorithm is applicable not only in case of the direction finders, but also for other multi-base phase measurements. The work may be interesting for designers of direction finders in terms of achievable accuracy of measurement results even if some of the results are rejected.

Direction-of-Arrival Estimation Methods in Interferometric Echo Sounding.

Nowadays, there are two leading sea sounding technologies: the multibeam echo sounder and the multiphase echo sounder (also known as phase-difference side scan sonar or bathymetric side scan sonar). Both solutions have their advantages and disadvantages, and they can be perceived as complementary to each other. The article reviews the development of interferometric echo sounding array configurations and the various methods applied to determine the direction-of-arrival. “Interferometric echo sounder” is a broad term, applied to various devices that primarily utilize phase difference measurements to estimate the direction-of-arrival. The article focuses on modifications to the interferometric sonar array that have led to the state-of-the-art multiphase echo sounder. The main algorithms for classical and modern interferometric echo sounder direction-of-arrival estimation are also outlined. The accuracy of direction-of-arrival estimation methods is dependent on the configuration of the array and external and internal noise sources. The main sources of errors, which influence the accuracy of the phase difference measurements, are also briefly characterized. The article ends with a review of the current research into improvements in the accuracy of interferometric echo sounding and the application of the principle of interferometric in other devices.

PR3: A system For radio-interferometry and radiation measurement on sounding rockets

The PR3 (Payload for Radio-interferometry and Radiation measurement on Rockets) payload was designed for, and flown on, the REXUS 25 rocket and performed two experiments inside a single module.11Part of this work has been presented at the ESA PAC symposium in 2019The first experiment uses radio-interferometry to precisely localize the sounding rocket during flight. An accuracy in the range of 10 cm was expected with an update rate of 1 kHz. In order to achieve this, three antennas mounted on the outside of the module transmit unmodulated carrier signals at three distinct wavelengths around 70 cm. These carrier signals are received by six ground stations placed around the Esrange launch site. Each ground station uses three antennas to perform phase-difference measurements to compute a vector pointing in the direction of the rocket. All six vectors are combined to find a solution of the rocket’s position. Since three different frequencies are transmitted, three sources can be identified. This should allow for attitude and accuracy estimation of the system.The second experiment was designed to evaluate whether ionizing radiation can be detected with three types of commercial off-the-shelf camera sensors. A scintillator-based radiation sensor designed for cubesats was also onboard to serve as a reference radiation sensor. Furthermore, three types of commercial off-the-shelf cameras are evaluated. The cameras have different properties with respect to the technique (CCD versus CMOS) as well as different resolutions. Particle interactions are processed on-board and are made available via a telemetry link. Raw data is stored for post-flight processing. The scintillator sensor is used as a reference sensor to compare the camera results against. We present the technical aspects of the experiment design and the obtained results.

Absolute interferometric testing of a flat surface based on the Laplacian method.

In the present study, a method is introduced for absolute interferometric testing. An interferometer is used to measure the phase difference distributions at five positions of the reference surface with respect to the test surface. The Laplacian of the phase distribution is calculated from the measured phase difference distributions. Then, the reference phase distribution is reconstructed by solving the Laplacian equation by the Fourier method. The accuracy of the method with respect to the amount of the displacement and noise is investigated by simulation and compared with the conjugate differential method. It is shown that the spatial frequencies of the phase distributions reconstructed by the Laplacian method are less filtered out with respect to the conjugate differential methods. Finally, the experimental result is presented.

Flow properties of surfactant solutions of rod-like micelles passing through a small slit

Pressure drops in flows through a small slit were experimentally measured at constant flow rates to investigate flows with an abrupt contraction and expansion. The flow properties of water, 50 wt% glycerol solution, and two types of surfactant solutions (Lipoquad and Lipothoquad) with a counterion (NaSal) were examined. The slit heights used were 480 µm, 222 µm, and 129 µm, with estimated hydraulic diameters of 938 µm, 439 µm, and 256 µm, respectively. Viscosity was measured using a capillary-type viscosity meter. Water and the 50 wt% glycerol solution exhibited Newtonian viscosity, with the viscosity of the glycerol solution being 10 times that of water. By contrast, the surfactant solutions, which contained rod-like micelles, exhibited non-Newtonian viscosity. A power law model was therefore applied for the relationship between shear viscosity and shear rate on the wall. The observed flow properties of water (and the 50 wt% glycerol solution) and the numerical predictions of the Navier–Stokes equations were found to agree to within the experimental errors. In plots of the dimensionless pressure drop against the generalized Reynolds number, however, anomalous flow properties of the surfactant solutions were observed. The pressure drops of Lipoquad/NaSal agreed with those of water (and the 50 wt% glycerol solution) at low apparent strain rate (Reynolds number) but were larger at high apparent strain rate (Reynolds number). Furthermore, the pressure drops of Lipothoquad/NaSal were greater than those of water in the investigated range of the generalized Reynolds number. To examine these experimental results further, flows in a planar channel with an abrupt contraction and expansion were observed using a polarization measurement system based on a high-speed polarization camera. In contrast to polymer solutions (in which polymer chains were oriented along the flow direction), the phase difference for Lipoquad/NaSal before and in the slit region was high in regions with a strong elongational component. In addition, it was high along the centerline after the slit region. These results also differ from those of simple shear flows. Furthermore, the phase difference of Lipothoquad/NaSal was very unstable. In addition, the relationship between the resultant pressure drop and the measured phase differences was investigated, and a dependence was found on the apparent strain rate (Weissenberg number).