Phase Error Research Articles

Exact surface measurement based on phase error insensitive method for white-light scanning interferometer

Phase error induced by the scanning error of piezoelectric transducer and vibration in white-light interference signal (WLIS) impose limitations on measurement accuracy. In this paper, two techniques are investigated to eliminate phase error cooperatively. A monochromatic interferometer owning the same optical path as the white-light scanning interferometer (WLSI) is employed to detect and compensate the phase error. Due to the incomplete consistency between the detected phase error and its actual distribution, an algorithm is introduced to further enhance the measurement accuracy. The simulation is given to prove the proposed method is available in different magnitude of noise. In the experiment, the front surface of wedged window is measured, whose maximum fluctuations are reduced to 28.8 nm and 3.0 nm from 62.7 nm with the gradual application of two technologies, and the repeatability reach 5.0 nm and 0.4 nm from 16.8 nm, respectively. The root mean square height S q and maximum height S z ultimately decrease to 1.3 nm and 1.6 nm. The measurement of step with height of about 3.0 μm also has the good accuracy and repeatability after phase error elimination. Since the different reflectivity of measured surfaces in the wavelength range of light source will also bring the measurement error, its influences are analyzed by simulation. The proposed techniques provide a phase error insensitive method for WLSI that has potential on measurement in the complex environment.

Improving the Feasibility of Mitigating Phase Errors in 4DCT caused by a Random Reference Breathing Pattern in the Quasar Phantom and the Role of Slice Thickness.

The study aimed to validate a method for minimizing phase errors by combining full-length lung 4DCT (f4DCT) scans with shorter tumor-restricted 4DCT (s4DCT) scans. It assessed the feasibility of integrating two scans one covering the entire phantom length and the other focused on the tumor area. The study also evaluated the impact of Maximum Intensity Projection (MIP) volume and imaging dose for different slice thicknesses (2.5mm and 1.25mm) in both full-length and short target-restricted 4DCT scans. The study utilized the Quasar Programmable Respiratory Motion Phantom, simulating tumor motion with a variable lung insert. The setup included a tumor replica and a six-dot IR reflector marker on the breathing platform. The objective was to analyze volume differences in fMIP_2.5mm compared to sMIP_1.25mm within their respective 4D_MIP CT series. This involved varying breathing periods (2.5s, 3.0s, 4.0s, and 5.0s) and longitudinal tumor sizes (6mm, 8mm, and 10mm). The study also assessed exposure time and expected CTDIvol of s4D_2.5mm and s4D_1.25mm for different breathing periods (5.0s to 2.0s) in the sinusoidal wave motion of the six-dot marker on the breathing platform. Conducting two consecutive 4DCT scans is viable for patients with challenging breathing patterns or when the initial lung tumor scan is in close proximity to the tumor location, eliminating the need for an additional full-length 4DCT. The analysis involves assessing MIP volume, imaging dose (CTDIvol), and exposure time. Longitudinal tumor shifts for 6mm are [16.6-17.2] in fMIP_2.5mm and [16.8-17.5] in sMIP_1.25mm, for 8mm [17.2-18.3] in fMIP_2.5mm and [17.8-18.4] in sMIP_1.25mm, and for 10mm [19-19.9] in fMIP_2.5mm and [19.4-20] in sMIP_1.25mm (p≥ 0.005), respectively. The Quasar Programmable Respiratory Motion Phantom accurately replicated varied breathing patterns and tumor motions. Comprehensive analysis was facilitated through detailed manual segmentation of Internal Target Volumes and Internal Gross Target Volumes.

Study on the influence of gap dependent error on the cryogenic permanent magnet undulator performance

The mass production of the first stage of HEPS (High Energy Photon Source) is approaching its final stage. 6 CPMUs (cryogenic permanent magnet undulators) have been manufactured, with four successfully finalizing the tuning of the magnetic field. To ensure radiation performance, HEPS's CPMUs enforce stringent phase error protocols. Moreover, the contraction properties at cryogenic temperature lead to a decrease in phase error after cooling. In the process of CPMU commissioning, a technique for forecasting the change of magnetic errors from room to cryogenic temperature was discovered and studied, as will be demonstrated in this paper.

Design of A 12-phase Clock Generator Based on DLL

Abstract This article proposes a 12-phase clock generator for DC-DC power supply chips, which can be used for external clock synchronization of DC-DC and serves as the foundation for multiple parallel connections of DC-DC. This article is based on the NTC 0.35 um BCD process and verified through simulation by using Cadence software. In typical environments of 3.3 V and 27°, the clock input range is 832 K-49.6 MHz, the time to reach stability is less than 5 us, the clock jitter is less than 1%, the duty cycle error is less than 3.5%, and the phase error generated is less than 1%.

Improved Representation of Vegetation Soil Moisture Coupling Enhances Soil Moisture Data Assimilation in Water‐Limited Regimes: A Case Study Over Texas

AbstractAssimilating remotely sensed surface soil moisture (SSM) into land surface models (LSM) is widely used to improve model representations of soil moisture (SM). However, the efficacy of SSM data assimilation (DA) has been found to be limited, particularly in resolving root‐zone soil moisture (RZSM). This study investigates how the representation of vegetation phenology, modulates the efficacy of SSM DA in enhancing the realism of RZSM simulations. To this end, two sets of climatological leaf area index (LAI) are implemented in Noah‐MP LSM over the state of Texas: (a) Noah‐MP default based on long‐term MODIS observations, (b) an alternative LAI adapted from AVHRR products. The former are found to exhibit conspicuous phase errors whereas the latter are more consistent with observed seasonal cycle. Two sets of DA experiments were performed accordingly, wherein SMAP L3 SSM is assimilated into Noah‐MP equipped with each LAI product from 2015 to 2019, Validation of the resulting products against in‐situ data reveals that (a) using the AVHRR‐based LAI, the Noah‐MP outperforms the baseline in reproducing the dynamics of RZSM, and the outperformance is particularly evident over the warm season and water‐stressed western Texas; (b) using the alternative LAI enhances the ability of DA to improve the accuracy of Noah‐MP RZSM, and to a lesser extent, SSM; and (c) gains in SM attained through improvement of LAI and application of DA is most pronounced over regions featuring tight vertical SM coupling. Additional model mechanistic limitations that need to be overcome to improve efficacy of DA are discussed.

Relationship between the shape of cross‐inductive loop coils and the induced voltage for position detection system

AbstractMaglev trains require precise position data to control their propulsion systems. Specifically, sensing accurate phase based on position is necessary, for which cross‐inductive loop coils are used. To minimize phase errors, the envelope of the received voltage must be a sinusoidal wave depending on the position. This letter proposes the shapes of transmitting and receiving coils and presents, through simulation and experimentation, that the shapes of the transmitting and receiving coils and the induced voltage are in a convolution.

An efficient sub-aperture millimeter-wave imaging technique based on boundary-type MIMO array

Millimeter-wave (MMW) 3-D imaging based on multiple-input-multiple-output (MIMO) radar has been widely studied due to its unique advantages in human security screening. However, more research has been done on the use of scanning 1-D MIMO array and the fast imaging methods that match them. This limits the rate of data acquisition and imaging speed to some extent. It is necessary to study frame rate imaging system as well as efficient imaging methods. In this article, a boundary-type MIMO array is designed, based on which an efficient frequency-domain imaging algorithm with sub-aperture is proposed. The proposed algorithm solves the target reflectivity function by dividing the uniform array into two sub-apertures and solving the echo signals of each sub-aperture separately. The final target reflectivity function is obtained by superposing all the solutions. Compared with the advanced RMA, FSA and FωK algorithms, the proposed sub-aperture frequency-domain imaging algorithm (SFA) does not require a large amount of zero-padding to satisfy the requirements of fast Fourier transform (FFT) in all dimensions. It greatly improves the speed of imaging and saves the space required for computation. We derive the theoretical formulation of SFA applied to MIMO array and analyze its computational complexity and phase error. Simulation and experiment verify the efficiency of the proposed SFA.

Intensity patterns of a focused electromagnetic spherical wave with aberration

The laser pulse focused by a relativistic flying parabolic mirror can exceed the laser intensity focused by conventional physical focusing optics. Depending on the Lorentz γ-factor, the focal length of the relativistic flying mirror in the boosted frame of reference becomes much shorter than the incident beam size. The 4π-spherical focusing scheme is applied to describe such a focused field configuration. In this paper, a theoretical formalism has been developed to describe the field configuration focused by the 4π-spherical focusing scheme with an arbitrary phase error of an incident electromagnetic wave. The focused field configuration is described by the linear combination of the product of the spherical Bessel function and the spherical harmonics, resulting in the same expression as the multipole radiation. The mathematical expression showing the focused field for the femtosecond laser pulse, as well as the continuous wave, has been derived for the application to the femtosecond high-power laser. We show the three-dimensional intensity distribution near focus for the 4π-spherically focused electromagnetic field with phase error.

Interspectral Error Tracking and Compensation of DSDT in Satellite Internet of Things

With the rapid growth of satellite Internet of Things (SIoT) services, existing frequency band resources are insufficient to meet future business demands. To effectively address this issue, it is necessary to enhance the utilization of existing frequency resources. However, idle frequency resources are typically scattered across multiple bands and vary in bandwidth size. Direct Spectrum Division Transmission (DSDT), dividing a complete signal into sub-spectrum signals for transmission in idle frequency bands, can take the use of fragmented spectrum resources for satellite communication. Nevertheless, the performance of DSDT depends heavily on accurate synchronization toward multiple sub-spectrums. In this paper, an algorithm for error synchronization tracking and compensation is proposed by utilizing the focusing nature of constellation. All sub-spectrums are weighed by the minimum Euclidean distance of the constellation to compensate for amplitude–frequency–phase errors simultaneously. Simulations and experimental verification demonstrate synchronization performance and feasibility of proposed method in a multi-radio frequency channels environment.

Coherent beam combining of two all-PM thulium-doped fiber chirped pulse amplifiers

In this paper, we report a coherent beam combining (CBC) system that involves two thulium-doped all-polarization maintaining (PM) fiber chirped pulse amplifiers. Through phase-locking the two channels via a fiber stretcher by using the stochastic parallel gradient descent (SPGD) algorithm, a maximum average power of 265 W is obtained, with a CBC efficiency of 81% and a residual phase error of λ/17. After de-chirping by a pair of diffraction gratings, the duration of the combined laser pulse is compressed to 690 fs. Taking into account the compression efficiency of 90% and the main peak energy proportion of 91%, the corresponding peak power is calculated to be 4 MW. The laser noise characteristics before and after CBC are examined, and the results indicate that the CBC would degrade the low frequency relative intensity noise (RIN), of which the integration is 1.74% in [100 Hz, 2 MHz] at the maximum combined output power. In addition, the effects of the nonlinear spectrum broadening during chirped pulse amplification on the CBC efficiency are also investigated, showing that a higher extent of pulse stretching is effective in alleviating the spectrum broadening and realizing a higher output power with decent combining efficiency.Graphical

Diagnostics of Mixed-State Topological Order and Breakdown of Quantum Memory

Topological quantum memory can protect information against local errors up to finite error thresholds. Such thresholds are usually determined based on the success of decoding algorithms rather than the intrinsic properties of the mixed states describing corrupted memories. Here we provide an intrinsic characterization of the breakdown of topological quantum memory, which both gives a bound on the performance of decoding algorithms and provides examples of topologically distinct mixed states. We employ three information-theoretical quantities that can be regarded as generalizations of the diagnostics of ground-state topological order, and serve as a definition for topological order in error-corrupted mixed states. We consider the topological contribution to entanglement negativity and two other metrics based on quantum relative entropy and coherent information. In the concrete example of the two-dimensional (2D) Toric code with local bit-flip and phase errors, we map three quantities to observables in 2D classical spin models and analytically show they all undergo a transition at the same error threshold. This threshold is an upper bound on that achieved in any decoding algorithm and is indeed saturated by that in the optimal decoding algorithm for the Toric code. Published by the American Physical Society 2024

Design of a Millimeter-Wave Broadband Linearizer Based on an Extended Design Space

In this study, a broadband linearizer design method based on an extended design space is proposed to optimize the design complexity and linearization performance of conventional linearizers for broadband operation. The gain characteristics of the power amplifier (PA) and linearizer are fitted to simplify the analyses and to quickly derive the ideal objective function of the linearizer design. Then, the 1 dB compression point of a nonlinear system is redefined and used to further extend the design space of the linearizer. To verify the proposed design method, a millimeter-wave linearizer prototype based on the extended design space was designed and fabricated. The linearizer was tested with continuous-wave and 100 MHz two-tone signals from 40 GHz to 43 GHz. The measurement results of the linearized PA showed that the output 1 dB power point (OP1dB) was improved by more than 1.7 dB, the phase error was reduced by more than 15°, and the third-order intermodulation distortion (IMD3) was suppressed by 8.6 dB–13.1 dB over the working frequencies. The proposed linearizer achieved good linearization performance, low power consumption, and simple design implementation, and it was not necessary to tune the bias during broadband operation, making it applicable in complex communication scenarios.

Range-Dependent Channel Calibration for High-Resolution Wide-Swath Synthetic Aperture Radar Imagery.

High-resolution and wide-swath (HRWS) synthetic aperture radar (SAR) imaging with azimuth multi-channel always suffers from channel phase and amplitude errors. Compared with spatial-invariant error, the range-dependent channel phase error is intractable due to its spatial dependency characteristic. This paper proposes a novel parameterized channel equalization approach to reconstruct the unambiguous SAR imagery. First, a linear model is established for the range-dependent channel phase error, and the sharpness of the reconstructed Doppler spectrum is used to measure the unambiguity quality. Furthermore, the intrinsic relationship between the channel phase errors and the sharpness is revealed, which allows us to estimate the optimal parameters by maximizing the sharpness of the reconstructed Doppler spectrum. Finally, the results from real-measured data show that the suggested method performs exceptionally for ambiguity suppression in HRWS SAR imaging.

Reconstructing phase space of injection beam based on the measurement of accumulated beam: A novel tomography algorithm and its applications

The measurement of phase space has always been an important topic in the field of accelerator physics, playing an indispensable role in understanding the beam dynamics. The phase space distribution of the injected beam is crucial for optimizing the multiturn accumulation injection process in synchrotrons. However, directly and accurately measuring the phase space distribution is a challenging task. In this study, we propose an innovative tomographic algorithm based on the measurement data of the accumulated beam profile obtained from the wall current monitor (WCM) in a synchrotron, to reconstruct the longitudinal phase space of the injected beam. Simulations were conducted for various initial distribution scenarios, and the results showed that this algorithm can achieve a difference of about 4% in the rms momentum spread between the initial and reconstructed phase space distribution of the injected beam. This algorithm has been applied to the China Spallation Neutron Source and successfully measured the momentum spread of the injected beam. Machine studies considering the phase error of the injected beam showed a high consistency between the reconstructed beam profiles and the measurement results from the WCM on Rapid Cycling Synchrotron. The research results demonstrate that this algorithm can be an effective approach for measuring the momentum distribution of the injected beam in a synchrotron. Furthermore, this method also has the potential to be extended to reconstruct the transverse phase space of the injected beam. Published by the American Physical Society 2024

Phase tracking using a Kalman filter based on probability density distribution in frequency-scanning interferometry

Frequency-scanning interferometry (FSI) utilizing external cavity diode lasers (ECDL) stands out as a potent technique for absolute distance measurement. Nevertheless, the inherent scanning nonlinearity of ECDL and phase noise pose a challenge, as it can compromise the accuracy of phase extraction from interference signals, thereby reducing the measurement accuracy of FSI. In this study, we propose a composite algorithm aimed at mitigating non-orthogonal errors by integrating the least-squares and Heydemann correction technique. Furthermore, we employ Kalman filtering for precise phase tracking. We introduce a parameter selection strategy based on the statistical distribution of instantaneous frequency to achieve the fusion estimation of phase observation values and theoretical models, which starts a new perspective for the application of multi-dimensional data fusion in FSI measurement. Through simulation and experimental validation, the efficacy of this approach is confirmed. The experimental results show promising outcomes: with an average phase error of 0.12%, a standard deviation of less than 1.7 µm in absolute distance measurement, and an average positioning accuracy error of 0.29 µm.

Design of a comprehensive sounding system for observing underdense meteors and ionospheric irregularities

Radar detection technology has been used to observe meteors since the last century. According to the echoes of electromagnetic waves scattered by meteor trails, the drift velocity of meteors is calculated to research the atmospheric dynamics characteristics in their distribution height. In this paper, complementary code sequences are applied to a Very High Frequency (VHF) ionospheric sounding system. Unlike the common VHF meteor radar, the system parameters can be set with a pulse duty cycle, allowing for flexible adjustment of detection range. At the same time, the detection frequency can also be adjusted within a certain range, breaking through the traditional fixed frequency detection mode. Moreover, by employing a miniaturized antenna array composed of an orthogonal dipole antenna for the VHF receiving, the system takes account of the requirements of the inversion algorithms of meteor radar and the detection need for the irregularities sounding concurrently, achieving the function of detecting multiple targets. Therefore, the system is called the Wuhan VHF Comprehensive Sounding (WHCS) system. This system has the function of integrating transmission and reception, which can be directly detected by a single station or synchronously detected through the separation of transmission and reception. This system has the function of internal channel calibration to compensate for the phase error of meteor echoes. Through further analysis of the detection data, the height distribution of meteors, as well as typical echoes of ionospheric irregularities, were obtained. The experiments verified the availability of the system scheme and its engineering application significance.

A phase-error immune approach for measuring transport AC loss by determination of minimum compensated voltage

Alternating current (AC) loss measurement is crucial for the theoretical evaluation and optimization in the fabrication of superconducting AC devices. Lock-in amplifier based on the lock-in phase is commonly adopted and inevitably involves with phase error. In this work, a novel approach for measuring transport AC loss by determining the minimum compensated voltage (MCV) was developed, in which the lock-in amplifier was removed. Since it just uses the voltage signal from an AC voltmeter, it is phase-error immune. Experimental results demonstrated that when using the lock-in amplifier, there existed a system error as the initial phase difference between the sampled (reference) and real current phases, which required careful compensation. In contrast, the phase error no longer needed to be considered by the MCV method, and the AC loss results were obtained much more conveniently with the relative error between the theoretical and the experimental of less than 5%. Finally, the AC loss of a coated conductor spiral wound on an epoxy bar was obtained using the presented approach, demonstrating its low cost, ease of operation, and high accuracy.

Receiver in-phase and quadrature skew tolerant baud-rate timing recovery scheme for short-reach coherent optical interconnection.

A baud-rate sampling timing recovery (TR) scheme with receiver IQ skew tolerance is proposed and experimentally demonstrated. The proposed scheme performs independent TR for the in-phase and quadrature (IQ) tributary signals, thereby tracking the sampling phase error while naturally compensating for receiver IQ skew. The robustness of the IQ-independent TR to frequency offset (FO) and phase noise is theoretically analyzed. To address IQ misalignment caused by the IQ-independent TR, the use of pseudo-noise (PN) sequences for IQ frame synchronization is proposed. The proposed scheme achieves accurate timing recovery with hardware-efficient baud-rate sampling in the presence of receiver IQ skew, laying the foundation for stable performance of subsequent baud-rate equalization. The performance of the scheme is validated in a 56 GBaud polarization division multiplexed (PDM) 16QAM coherent experimental system. Experimental results demonstrate that the proposed scheme achieves similar BER performance to the modified Gardner + real-valued multiple-input multiple-output (RVMIMO) (@2 SPS) scheme. Moreover, the proposed scheme exhibits robustness to arbitrary IQ skew compared to the ABSPD + RVMIMO (@1 SPS) scheme.

Review on Phase Synchronization Methods for Spaceborne Multistatic Synthetic Aperture Radar.

Multistatic synthetic aperture radar (SAR) is a special mode of SAR system. The radar transmitter and receiver are located on different satellites, which brings many advantages, such as flexible baseline configuration, diverse receiving modes, and more detailed ground object classification information. The multistatic SAR has been widely used in interferometry, moving target detection, three-dimensional imaging, and other fields. The frequency offset between different oscillators will cause a modulation phase error in the signal. Therefore, phase synchronization is one of the most critical problems to be addressed in distributed SAR systems. This article reviews phase synchronization techniques, which are mainly divided into two methods: synchronization by direct microwave link and synchronization by a data-based estimation algorithm. Furthermore, the future development of synchronization technology is anticipated.

Measurement analysis of three phase intelligent electricity meter based on nonlinear load

In order to improve the accuracy of non-linear load measurement in three-phase smart meters, the author proposes a measurement analysis of three-phase smart meters based on non-linear loads. The author analyzed the nonlinearity of most differential amplifiers in metering chips, theoretically analyzed the reasons for low metering accuracy under non-linear loads, and analyzed and designed the reasons for phase errors in electric energy meters. The results indicate that: At 5 %, 20 %, 100 %, and 120 % of the rated current, the phase error limits of the current transformer are ±15 ', ±8', ±5 ', and ±5', respectively. At 5 % of the rated current, the phase error generated by the transformer reaches 100 % of the rated current and 3 times that of 120 %. This is also the reason for the large error in measuring small current signals in electric energy meters. ConclusionThe author provides a precise analysis and design method for nonlinear load measurement of three-phase smart meters to improve the performance of measurement chips and improve the accuracy of nonlinear load measurement.