Measured Phase Error Research Articles

Instability Compensation of Recording Interferometer in Phase-Sensitive OTDR.

In the paper, a new method of phase measurement error suppression in a phase-sensitive optical time domain reflectometer is proposed and experimentally proved. The main causes of phase measurement errors are identified and considered, such as the influence of the recording interferometer instabilities and laser wavelength instability, which can cause inaccuracies in phase unwrapping. The use of a Mach-Zender interferometer made by 3 × 3 fiber couplers is proposed and tested to provide insensitivity to the recording interferometer and laser source instabilities. It is shown that using all three available photodetectors of the interferometer, instead of just one pair, achieves significantly better accuracy in the phase unwrapping. A novel compensation scheme for accurate phase measurements in a phase-sensitive optical time domain reflectometer is proposed, and a comparison of the measurement signals with or without such compensation is shown and discussed. The proposed method, using three photodetectors, allows for very good compensation of the phase measurement errors arising from common-mode noise from the interferometer and laser source, providing a significant improvement in signal detection. In addition, the method allows the tracking of slow temperature changes in the monitored fiber/object, which is not obtainable when using a simple low-pass filter for phase unwrapping error reduction, as is customary in several systems of this kind.

The application of neural networks in the problem of radio monitoring with the use of a two-coordinate radio direction finder and the estimation of their efficiency

Problem statement. Measuring bases of two-coordinate phase direction finders (PDF), as a rule, are located along the same line, while bearing occurs in two planes independently. The procedure for determining the bearing in this case consists in restoring the true wave front and is quite computationally expensive. The study of PDF using a neural network with simultaneous use of information from all possible combinations of measurement bases is of particular interest from the point of view of evaluating the possibility of increasing the probability of correctly eliminating the ambiguity of bearing and increasing the accuracy of bearing, reducing computational costs and reducing the time to determine the bearing. Goal. Evaluation of the effectiveness of the use of artificial neural networks (NN) for direction finding of radio emission sources (RES) in solving radio monitoring problems using two-coordinate PDF, evaluation of the possibility of increasing the probability of correct elimination of ambiguity of bearing and increasing the accuracy of bearing when using all measuring bases of PDF. Results. A model of two-coordinate PDF based on NN has been developed, which makes it possible to evaluate the effectiveness of RES bearing in two planes with variations in model parameters and initial data. The obtained modeling results allow us to conclude that it is possible to create a two-coordinate PDF based on NN. The evaluation of the effectiveness of bearing shows that PDF based on NN has a commensurate accuracy of bearing and a high probability of eliminating ambiguity compared with PDF using classical methods and is somewhat inferior to them at high values of the phase measurement error in the receiving channels. Practical significance. The use of artificial neural networks (NN) for direction finding of radio emission sources (RES) in solving radio monitoring problems and further research on their development will improve the accuracy and reliability of measurements while reducing computational costs.

Adaptive chessboard-like high-frequency projection method for three-dimensional measurement of shiny surfaces

Abstract Shiny surface is challenging for the structured light fringe projection three-dimensional measurement technique, since the image saturation caused by highlight results in incorrect intensities in captured images of fringe patterns, and leads to serious phase errors and measurement errors. To address the issue, an adaptive chessboard-like high-frequency projection intensity adjustment technique is proposed. The proposed method alleviates image saturation by adaptively adjusting the intensity of the high-frequency chessboard-like projection pattern. And the complementary patterns are projected to suppress reflections and enhance the robustness of decoding. The experimental results demonstrate that the proposed method achieve high measurement accuracy for shiny surfaces.

Phase space analysis of two-wavelength interferometry.

Multiple wavelength phase shifting interferometry is widely used to extend the unambiguous range (UR) beyond that of a single wavelength. Towards this end, many algorithms have been developed to calculate the optical path difference (OPD) from the phase measurements of multiple wavelengths. These algorithms fail when phase error exceeds a specific threshold. In this paper, we examine this failure condition. We introduce a "phase-space" view of multi-wavelength algorithms and demonstrate how this view may be used to understand an algorithm's robustness to phase measurement error. In particular, we show that the robustness of the synthetic wavelength algorithm deteriorates near the edges of its UR. We show that the robustness of de Groot's extended range algorithm [Appl. Opt.33, 5948 (1994)APOPAI0003-693510.1364/AO.33.005948] depends on both wavelength and OPD in a non-trivial manner. Further, we demonstrate that the algorithm developed by Houairi and Cassaing (HC) [J. Opt. Soc. Am. A26, 2503 (2009)JOAOD60740-323210.1364/JOSAA.26.002503] results in uniform robustness across the entire UR. Finally, we explore the effect that wavelength error has on the robustness of the HC algorithm.

Localization of GNSS Spoofing Interference Source Based on a Moving Array Antenna

GNSS spoofing interference utilizes falsified navigation signals to launch attacks on GNSS systems, posing a significant threat to applications that rely on GNSS signals for positioning, navigation, and time services. Therefore, achieving effective localization of the sources causing spoofing interference is crucial in ensuring the secure operation of GNSS. This article proposes a method for locating GNSS spoofing interference sources using a moving array antenna. Firstly, the proposed method utilizes the inherent characteristics of the double-differenced carrier phase from the deception signals received by the array antenna to effectively extract the spoofing signals. Subsequently, by moving the antenna array, the original carrier phase single-difference data of multiple observation points for deception signals are fused to provide a cost function for direct localization of spoofing interference, and a solution method for the cost function is designed. The proposed method addresses the challenge of extracting and localizing GNSS spoofing interference weak signals, effectively avoiding the data correlation of traditional two-step methods for DOA estimation parameters and ensuring the location accuracy of spoofing interference and the robustness of the method. The effectiveness of the proposed method has been validated through simulation experiments, and its adaptability to factors such as errors in carrier phase measurements has been examined. The method exhibits strong applicability and is well-suited for the hardware platform of the GNSS nulling antenna, thereby enabling it to possess simultaneous capabilities in both anti-interference and spoofing interference localization.

A novel method for obtaining gamma precoding values

AbstractThe grating projection‐based three‐dimensional (3D) measurement technique has been widely used in various fields, such as industrial inspection, cultural relic protection, and reverse engineering. However, due to the nonlinear response between the input and output of the measurement system, phase measurement errors occur, which reduces the accuracy of 3D reconstruction, which is known as the gamma effect. To address this issue, a novel method has been proposed to reduce the nonlinear response of the system. Ultimately, this method reduces the impact of the gamma value on the phase accuracy in subsequent measurements. Experimental results have shown that this method can quickly calibrate the correct precoding gamma value, effectively reduce the gamma nonlinear response during the measurement process, and improve measurement accuracy.

An 8-18 GHz 90° Switched T-Type Phase Shifter.

This paper proposes a novel 8-18 GHz 90° switched T-type phase shifter (TPS). In contrast to the conventional TPS, the proposed TPS adds a compensation capacitance to greatly enhance the phase shifting capacity. Moreover, the designed structure also integrates a filtering compensation network, which can effectively achieve a flat relative phase shift in a wide band. The proposed 90° TPS is fabricated using 0.15 μm GaAs pHEMT technology. The TPS achieves homogeneous phase shift at 8-18 GHz, with the measured phase error of less than ±1.5°. The insertion loss of the proposed phase shifter is 1.3-2.6 dB, and the chip size is merely 0.53 × 0.86 mm2. Thanks to these excellent performance characteristics, the designed phase shifter is well-suited for ultra-wideband wireless communication and radar systems.

Low-dose measurement of electric potential distribution in organic light-emitting diode by phase-shifting electron holography with 3D tensor decomposition.

To improve the performance of organic light-emitting diodes (OLEDs), it is essential to understand and control the electric potential in the organic semiconductor layers. Electron holography (EH) is a powerful technique for visualizing the potential distribution with a transmission electron microscope. However, it has a serious issue that high-energy electrons may damage the organic layers, meaning that a low-dose EH is required. Here, we used a machine learning technique, three-dimensional (3D) tensor decomposition, to denoise electron interference patterns (holograms) of bilayer OLEDs composed of N,N'-di-[(1-naphthyl)-N,N'-diphenyl]-(1,1'-biphenyl)-4,4'-diamine (α-NPD) and tris-(8-hydroxyquinoline)aluminum (Alq3), acquired under a low-dose rate of 130 e- nm-2 s-1. The effect of denoising on the phase images reconstructed from the holograms was evaluated in terms of both the phase measurement error and the peak signal-to-noise ratio. We achieved a precision equivalent to that of a conventional measurement that had an exposure time 60 times longer. The electric field within the Alq3 layer decreased as the cumulative dose increased, which indicates that the Alq3 layer was degraded by the electron irradiation. On the basis of the degradation of the electric field, we concluded that the tolerance dose without damaging the OLED sample is about 1.7 × 105 e- nm-2, which is about 0.6 times that of the conventional EH. The combination of EH and 3D tensor decomposition denoising is capable of making a time series measurement of an OLED sample without any effect from the electron irradiation.

Polarization-insensitive 90° optical hybrid using silica-based PLC.

A 90° optical hybrid (OH) based on a 4×4 multimode interference (MMI) coupler is characterized and analyzed using the silica-based planar light circuit. The OH is designed to be polarization-insensitive with an extremely low polarization-dependent loss (<0.18d B) and phase error (w i t h i n±1.3∘). The fabricated chip exhibits an excess loss of 3.4dB and 3.8dB for TE and TM polarizations at 1550nm. The measured phase error is w i t h i n±7.2∘ over 50nm in the C+L band with a polarization-dependent error w i t h i n±3.5∘. The fabrication tolerance of the MMI width and waveguide sidewall angle is analyzed, which can well explain the deviation from the theoretical calculation.

Determination of optimal binary defocusing based on digital correlation for fringe projection profilometry

In fringe projection profilometry (FPP), non-sinusoidal projected fringes due to the gamma effect of a projector will cause phase measurement errors. To solve this problem, a binary defocusing technique has been introduced in recent years, while it is difficult to determine an appropriate amount of defocus quantitatively with high sensitivity and high accuracy. In this paper, a novel approach based on digital correlation is proposed to determine an optimal amount of defocus, aiming to get sinusoidal fringes from a binary-structured fringe pattern with projector defocusing. Firstly, a window containing multiple fringes is selected from the captured binary defocusing fringe pattern projected onto a calibration plate or a flat part of the surface of the object being measured. Then calculate the correlation coefficient between the selected window and its second-order differential in the direction perpendicular to the fringe. Since the second-order differential of a sinusoidal wave remains still sinusoidal, the maximum correlation coefficient should correspond to the optimal sinusoidality of the binary defocusing fringe. Therefore, by finding the maximum correlation coefficient while defocusing the projector, the optimal binary defocusing level can be determined accordingly. One of the characteristics of the proposed method is that only one fringe window is required to judge the defocus level in practical measurement, which may speed up 3D measurement. In addition, the proposed method has no requirements for fringe pitch and is applicable to fringes of any spatial frequency. Both numerical simulations and experimental results have been demonstrated to exhibit the validity and high accuracy of the proposed method.

Influence of measurement errors of the complex coherence factor on reconstructed image quality of integrated optical interferometric imagers

Interferometric imagers need to measure the phase, modulus, and spatial frequency coordinates of the complex coherence factor to reconstruct images. However, these three measurement parameters are accompanied by certain measurement errors in the actual imaging process, thereby affecting the quality of the reconstructed image. Based on the checkerboard integrated optical imaging system, we simulate the influence of measurement errors of the complex coherence factor on the imaging performance of the integrated optical interferometric imager. The simulation results show that, on the premise that measurement errors follow the normal distribution, the modulus measurement error does not significantly reduce the quality of the reconstructed image, whereas the phase and spatial frequency coordinate measurement errors have a great impact. When the mean value of the phase measurement error is 0, the standard deviation must be <0.18π to ensure the high quality of the reconstructed image. For the measurement error of the spatial frequency coordinates, when the standard deviation of the lenslet position errors is <0.075 times the shortest baseline length, its influence on the quality of the reconstructed image is acceptable. The simulation results are of great help to the engineering, manufacturing, and application of integrated optical interferometric imaging technology.

Active projection nonlinear γ correction method for fringe projection profilometry.

In fringe projection profilometry (FPP), the luminance nonlinearity generated by the superimposed γ effect of the projector and camera can lead to distortion of the intensity of the sinusoidal phase-shift fringe, resulting in a reduction of measurement precision and resolution. Traditional phase error compensation and γ-correction methods need to focus on the projector's optimal performance. However, commercial projectors often have huge apertures and are, therefore, unable to project a perfectly focused sinusoidal fringe image. This paper proposes an easy-to-implement active projection error correction method with high precision that is insensitive to projector defocus. After calibrating the projector to establish the nonlinear γ-response model of the optical measurement system, inverse γ compensation is performed. By generating and projecting a set of precorrected sinusoidal fringes, the camera can capture the high-quality sinusoidal fringe image and decrease the phase measurement error caused by the nonlinear γ effect of the FPP system. Computer simulations and experiments verify the effectiveness and feasibility of the proposed method for estimating and correcting the nonlinear γ distortion of the FPP system. The experimental results show that using the proposed active projection method to compensate for the error of the three-step phase-shift algorithm can achieve a high-precision measurement, and the influence of the system's nonlinear γ effect on the measurement accuracy is significantly suppressed.

Inertia alignment of phase-shifting algorithms for high-numerical-aperture spherical testing in Fizeau interferometry.

In Fizeau interferometry for high-numerical-aperture spherical surface tests, the mechanical phase shift becomes spatially nonuniform within the observation aperture. We divided the aperture into annular regions and calculated the object phase using several algorithms designed for different phase shifts. The division substantially decreased the nonuniformity; however, it caused bias errors at the regional boundaries in the measured phase. The error is due to the different error coefficients of the algorithms for the phase-shift nonlinearity. A convolution technique that modifies a sampling window to align the error coefficients of a set of algorithms is proposed. The technique is experimentally shown to minimize phase measurement errors.

Improved Current Shunt Characterization Method for Core Loss Measurement

With the increasing switching frequencies and power densities in modern power converters, magnetic core losses are becoming more essential for efficiency and thermal optimization. Traditionally, the two-winding method suffers from sensitivity to phase error in practical measurements; this is mainly created by the unknown phase shift of a current-sensing resistor. Several methods have been developed to characterize the phase shift of a current shunt resistor; however, the load effects of oscilloscopes are ignored. As a result, the corresponding phase shift can be significantly underestimated. This article proposes an improved method for phase shift extraction of a current shunt to solve the problem. The effectiveness of the shunt characterization method is experimentally verified up to 50 MHz. Benefits from the proposed method, the time-consuming component tuning process is not required for core loss measurement. A measurement verification at 10 MHz shows its validity. Finally, a current shunt implemented with a coaxial resistor array is designed with a phase shift of 0.05 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^\circ$</tex-math></inline-formula> at 10 MHz and a parasitic inductance as low as 42 pH.

Multiplication sampling moire method for full-field deformation measurement of composite materials.

A multiplication sampling moire (MSM) method was proposed for robust deformation distribution measurement by performing phase analysis of the second harmonic (second-order frequency) of a single grating pattern. The MSM method has a very strong noise immunity because the second harmonic spectrum is far from the low-frequency region of the background noise in the frequency domain. Phase analysis of an experimental grid image on a carbon fiber-reinforced plastic (CFRP) specimen indicated that the MSM method effectively solved the problem of non-negligible phase measurement errors of conventional methods that extract the fundamental frequency of the grating, in the case of severe local noise. The displacement and strain distributions of CFRP in a tensile test were successfully measured. This method is suitable for deformation measurement of various composite materials.

Verification of phase measurement error sources in phase-shifting interferometry with four step phase-shifting algorithms.

The phase-shifting technique is one of the most important techniques in interferometry. The measurement accuracy of this technique is affected by several kinds of systematic and random errors like miscalibration, nonlinear response and tilt shift of the phase shifter, nonlinear recording, speckles, fringe fluctuation, etc. In this paper, a method for verification of all of these phase measurement error sources is proposed by introducing a grayscale image. This image is composed from the lattice-site representation determined by a four step phase-shifting algorithm, which represents the distribution of phase-shift angle values. The shape of the grayscale image is definitely more expressive and demonstrative for the kinds of measurement error sources than the black dot distribution in lattice-site representation. So, with this technique, we can recognize the existence of various measurement error sources and roughly estimate their magnitudes before proceeding with experiments. Our method is to be rather qualitative than quantitative. The availability of this method is discussed in a phase-shifting Fizeau interferometer and a fringe projection profilometry. This method is useful in all kinds of interferometric measurements based on the phase-shifting technique.

Flexible millimeter‐wave Butler matrix based on the low‐loss substrate integrated suspended line patch hybrid coupler with arbitrary phase difference and coupling coefficient

In this paper, a millimeter-wave Butler matrix with flexible phase differences is proposed using the substrate integrated suspended line technology. To begin with, a low-loss substrate integrated suspended line (SISL) circular patch coupler consisting of four circular sectors is presented, achieving arbitrary phase difference and coupling coefficient by adjusting the angle and radii of the sectors. Based on the proposed coupler, two prototypes of the SISL Butler matrix are designed, fabricated and measured for the demonstration. In prototype I, the crossovers are removed and a flexible phase difference is obtained with an area size of 2.5 λg × 2.8 λg. In prototype II, both the crossovers and 45° phase shifters are removed and the phase differences of ±45° and ±135° are obtained with an area size of 1.86 λg × 2.24 λg. Low crosstalk between components and minimal radiation loss can be achieved by the SISL self-packaged characteristic and electromagnetic shielding. For both prototypes, the measured insertion losses are less than 2 dB at 26 GHz, including the loss of transitions and connectors, and the measured phase errors are less than ±10° within a bandwidth of more than 10%. The proposed Butler matrix shows the advantages of compact size, low loss and high integration.

Phase error compensation based on Tree-Net using deep learning

The nonlinear effect in phase shifting profilometry (PSP) is an essential source of phase error in 3D measurement. In this paper, we propose a universal phase error compensation method with a three-to-three deep learning framework (Tree-Net). Perfectly meeting the phase error compensation requirements, Tree-Net can construct six-step phase-shifting patterns from three-step. As a result, this compact network of fringe-to-fringe transformation has excellent performance when coping with different PSP systems after only one training. Experimental results demonstrate that the phase error can be reduced by about 90% in three-step PSP, which verified the effectiveness, universality, and robustness of the proposed method.

Performance Analysis of Interferometer Algorithm under Phase Measurement Error

Direction finding has been extensively studied over the past decades and a number of algorithms have been developed. In direction finding, theoretic performance prediction is a fundamental problem. This paper addresses the performance analysis issue of interferometer-based 2D angle of arrival estimation using uniform circular array (UCA). We propose an analytic method for performance analysis of interferometer in the presence of Gaussian or uniform error in phase measurement of incident signal on each sensor. The analytic mean square error (MSE), which is approximately equal to the MSE of actual interferometer-based DOA estimation, is derived via Taylor expansion and approximation. The derived analytic MSE is useful for predicting how the MSE of the interferometer-based DOA estimation algorithm is dependent on the phase measurement error.

Waveform Difference Feature-Based Protection Scheme for Islanded Microgrids

Unlike conventional synchronous generators, the fault characteristics of inverter-based distributed generators (IBDGs) are mainly determined by the inverter control strategies. Their limited fault current contributions make the protection design of islanded microgrids (MGs) become a major challenge. This article focuses on the fault characteristics and protection scheme design of islanded MGs. First, the phase differences between the positive-sequence current fault components (PSC-FCs) at both terminals of fault line are analyzed under different network topologies and fault severities. It points out the phase characteristic differences between internal and external faults. Then, on basis of this to overcome the problems of the phase measurement error and protection setting, a waveform difference feature-based protection scheme is proposed. The protection criteria are formulated using the first peak sign and time information of PSC-FCs between both terminals of line, which are extracted by the mathematical morphology (MM) technology. Only relatively low bandwidth communication is required to achieve accurate fault identification. Finally, the simulation results on a 10-kV islanded MG model demonstrate that the proposed scheme can identify internal faults reliably in both looped and radial islanded MGs under different fault resistances and measurement noises.