Phase Error Research Articles

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.

Heimdallr, Baldr, and Solarstein: designing the next generation of VLTI instruments in the Asgard suite

High angular resolution imaging is an increasingly important capability in contemporary astrophysics. Of particular relevance to emerging fields such as the characterization of exoplanetary systems, imaging at the required spatial scales and contrast levels results in forbidding challenges in the correction of atmospheric phase errors, which in turn drives demanding requirements for precise wavefront sensing. Asgard is the next-generation instrument suite at the European Southern Observatory’s Very Large Telescope Interferometer (VLTI), targeting advances in sensitivity, spectral resolution, and nulling interferometry. In this paper, we describe the requirements and designs of three core modules: Heimdallr, a beam combiner for fringe tracking, low order wavefront correction, and visibility science; Baldr, a Zernike wavefront sensor to correct high order atmospheric aberrations; and Solarstein, an alignment and calibration unit. In addition, we draw generalizable insights for designing such system and discuss integration plans.

Weakly Supervised Depth Estimation for 3D Imaging with Single Camera Fringe Projection Profilometry.

Fringe projection profilometry (FPP) is widely used for high-accuracy 3D imaging. However, employing multiple sets of fringe patterns ensures 3D reconstruction accuracy while inevitably constraining the measurement speed. Conventional dual-frequency FPP reduces the number of fringe patterns for one reconstruction to six or fewer, but the highest period-number of fringe patterns generally is limited because of phase errors. Deep learning makes depth estimation from fringe images possible. Inspired by unsupervised monocular depth estimation, this paper proposes a novel, weakly supervised method of depth estimation for single-camera FPP. The trained network can estimate the depth from three frames of 64-period fringe images. The proposed method is more efficient in terms of fringe pattern efficiency by at least 50% compared to conventional FPP. The experimental results show that the method achieves competitive accuracy compared to the supervised method and is significantly superior to the conventional dual-frequency methods.

Study on the effect of inter-channel phase error in coherent beam combining of laser

Study on the effect of inter-channel phase error in coherent beam combining of laser

Analysing the impact of SWOT observation errors on marine gravity recovery

SUMMARY The wide-swath altimeter satellite Surface Water and Ocean Topography (SWOT) will provide high spatiotemporal resolution sea surface heights (SSHs), which is crucial for studying the impact of observation errors on marine gravity recovery. This study uses simulated SWOT data to derive deflection of the vertical (DOV) and gravity anomalies in the northern South China Sea. We quantified the impact of SWOT errors on DOV and gravity anomalies, and analysed the contributions from different directions of geoid gradient. The results show that the geoid gradient in the cross-track direction significantly improves gravity field recovery by enhancing the precision of east component of DOV. For one-cycle SWOT observations, phase errors emerge as the most impactful error affecting both DOV and gravity anomalies, followed by random errors. 2-D Gaussian filtering and the tilt correction proposed in this study could effectively mitigate their impact. Using the corrected data for DOV computation, the precision in the east and north components improves by 75.32 and 46.80 per cent, respectively, while enhancing the accuracy of the gravity field by 70.23 per cent. For 17-cycle data, phase errors and random errors remain the predominant factors affecting DOV and gravity anomalies, but their impact diminishes with an increase in SWOT observations. Our results indicate that marine gravity accuracy improves by approximately 70 per cent compared to a single cycle. Whether for single-cycle or multicycle data, the impact of phase errors is roughly twice that of random errors. These data processing strategies can serve as valuable references for wide-swath altimeter data processing, aiming to advance the precision and resolution of marine gravity field recovery.

Dead-time compensation and single-loop control strategy for ground power unit

Instead of the auxiliary power system, the ground power unit supplies to airplanes during stopovers in airports, which is an important means of reducing carbon emissions of airport. However, under the restraint of switching frequency and high dynamic response speed, a single control loop is usually implemented in 400 Hz voltage-source inverter, the sampling and control of the inductor current in the LC filter are avoided, result in the design of the control system being more difficult, and the direction of the dead-time compensation can not be obtained due to the lack of the current polarity. In view of the above problem, this paper firstly analyzes the influence on the output voltage of inverter due to the dead-time, including the errors of fundamental amplitude and phase, and the low-order harmonic distortion. Then, according to the state equation of the inductor current, a current observation model without zero drift is proposed to obtain the polarity of the inductor current. On this basis, feedforward compensation is carried out for the voltage error generated by the dead-time. Combined with the amplitude-frequency characteristic curve, the parameter optimization design method of the single closed-loop proportional-resonant controller is presented. Finally, a simulation model and an experimental platform are established to verify the feasibility and effectiveness of the current observation model, dead-time compensation method and controller parameter optimization design method proposed in this paper.

An Extended Polar Format Algorithm for Joint Envelope and Phase Error Correction in Widefield Staring SAR with Maneuvering Trajectory

Polar format algorithm (PFA) is a widely used high-resolution SAR imaging algorithm that can be implemented in advanced widefield staring synthetic aperture radar (WFS-SAR). However, existing algorithms have limited analysis in wavefront curvature error (WCE) and are challenging to apply to WFS-SAR with high-resolution and large-swath scenes. This paper proposes an extended polar format algorithm for joint envelope and phase error correction in WFS-SAR imaging with maneuvering trajectory. The impact of the WCE and residual acceleration error (RAE) are analyzed in detail by deriving the specific wavenumber domain signal based on the mapping relationship between the geometry space and wavenumber space. Subsequently, this paper improves the traditional WCE compensation function and introduces a new range cell migration (RCM) recalibration function for joint envelope and phase error correction. The 2D precisely focused SAR image is acquired based on the spatially variant inverse filtering in the final. Simulation experiments validate the effectiveness of the proposed method.

Collaborative strategy research of target tracking based on natural intelligence by UAV swarm

Regarding the regional area target collaborative tracking problem widely existing in intelligent scenarios, this paper built a distributed UAV swarm framework inspired by natural intelligence to heighten intricate missions’ efficiency. Also, a standoff collaboratively continuous tracking strategy was proposed based on a lateral guidance law with an improved Reference Point Guidance (RPG) and a longitudinal guidance law with an improved phase collaboration. Under an uncertain environment, this framework used an improved bat algorithm (IBA) to optimize the speed allocation of the UAV swarm’s online control strategy with information consensus estimation. Compared with a case without the designed transformation, statistically, the results demonstrate that the framework operates efficiently and robustly in phase error convergence, swarm flight distance, and fuel consumption, where a dynamic target exists.

A Phase Correction Model for Fourier Transform Spectroscopy

In Fourier transform spectroscopy (FTS), the conventional Mertz method is commonly used to correct phase errors of recovered spectra, but it performs poorly in correcting nonlinear phase errors. This paper proposes a phase correlation method–all-pass filter (PCM-APF) model to correct phase errors. In this model, the proposed improved phase correlation method can correct linear phase errors, and all-pass filters are applied to correct the residual nonlinear phase errors. The optimization algorithm for the digital all-pass filters employs an improved algorithm which combines the subtraction-average-based optimizer (SABO) and the golden sine algorithm (Gold-SA). The proposed PCM-APF model demonstrates high correction precision, and the optimization algorithm for the filters converges faster than traditional intelligent optimization algorithms.

Error analysis of calibration for horizontal tensor rotating accelerometer gravity gradiometer

The rotating accelerometer gravity gradiometer (RAGG) is regarded as a significant tool in geophysics applications such as resource exploration and gravity-assisted navigation research. Here we develop a prototype of the horizontal tensor RAGG and build a dedicated calibration platform for evaluating its performance. The error of calibration is theoretically computed and experimentally verified. The errors considered include higher-order terms of the gravity gradient error, positioning error, demodulation phase error, as well as the dimensions and density error of the gravitational mass. It has witnessed a high-accuracy gravity gradient calibration platform based on a motorized translation stage, with error values of 0.49 E (1 E = 10−9 s2) in channel Γsin and 0.24 E in channel Γcos . At an averaging time of 32 s, the RAGG demonstrates optimal stability, featuring a minimum Allan deviation value of 6.6 E in channel Γsin and 5.5 E in channel Γcos . And the RAGG has achieved a measurement noise floor of about 40 E/√Hz @ 0.001–0.1 Hz in both channels. For simulating engineering applications, the experimental results demonstrate a standard deviation error of only 3.2 E by employing a gravity gradient excitation step signal of 10 E. It shows that this RAGG has the potential for a wide range of applications.

Design and fabrication of waveguide‐based graded refractive index Rotman lens with an improved insertion loss at Ka‐band

AbstractThe design and optimisation of a five‐cascade layer Rotman Lens based on waveguide with a graded refractive index at Ka‐band frequency are presented. The proposed lens incorporates 5 layers within the cavity, utilises a modified three focal Rotman lens design methodology to achieve perfect phasing for true time delay beam steering, and optimises each layer's parameters such as refractive index, vertex location, and contour angle to improve insertion loss between input ports and output array elements. This approach enhances energy concentration between input and output ports, reducing spillover to dummy ports. The graded layers are formed using periodic cubic metallic posts with varying heights within a parallel plate waveguide. The results show an average improvement in the insertion loss of 16% and a peak improvement of 48% across the bandwidth when compared to conventional Rotman lenses. The normalised average phase error across the array elements for all beam ports excitation is 4 × 10−3 and the peak degradation of the main beam during beam scanning from 0° to ±22° varies from 0.7 to 1 dB at different frequencies operating in the Ka‐band (24–30 GHz) with potential applications for 5G communications. The simulation results demonstrate good agreement with the measurement results.

Comparative study of variant shifting-phase coding method based on noise error model

Phase shifting algorithm, which is well-known for its high-accuracy and high-resolution, plays a crucial role in fringe projection profilometry. A class of variant shifting-phase coding method (VSPCM) has been proposed for high-speed 3D measurement. The three kinds of VSPCM include the inner shifting-phase method (ISPM), the intensity-coded method (ICM) and the modified Carré algorithm (MCA). These methods project only four patterns avoiding the need for extra images, yet achieve accuracy comparable to the classical three-frequency heterodyne method. In VSPCM, the shifting-phase, as a key code-word for phase unwrapping, is encoded as a variable value. In practice, the noise and the encoding of shifting-phase have varying degrees of impact on the performance of these methods. But the coded ranges of the shifting-phase were previouly empirical values. Besides, there are no studies related to these factors, and also a lack of comparative researches on such methods. This paper compares three kinds of VSPCM for the first time. We derive the noise error models for shifting-phase and wrapped phase in three methods and examine the impact of variant shifting-phase on fringe orders and wrapped phase in these methods. We find that the abnormal shifting-phase errors predominantly cause fringe orders errors. Fortunately, median filtering can effectively handle shifting-phase errors to ensure successful phase unwrapping. To improve their accuracy, we also deduce that the optimal shifting-phase encoding range is [−77°, 77°] for ISPM, and is [−61°, 61°] for ICM, and is [34°, 74°] for MCA. For wrapped phase errors, the distributions of ICM and MCA exhibit a U-shaped distribution, while ISPM demonstrates a uniform distribution. Based on theoretical analysis and experiment results, this paper gives recommendations for better use of these methods to boost their accuracy and offers valuable guidance for selecting an appropriate VSPCM under the specific measurement requirements.

Phasing segmented telescopes via deep learning methods: application to a deployable CubeSat.

Capturing high-resolution imagery of the Earth's surface often calls for a telescope of considerable size, even from low Earth orbits (LEOs). A large aperture often requires large and expensive platforms. For instance, achieving a resolution of 1m at visible wavelengths from LEO typically requires an aperture diameter of at least 30cm. Additionally, ensuring high revisit times often prompts the use of multiple satellites. In light of these challenges, a small, segmented, deployable CubeSat telescope was recently proposed creating the additional need of phasing the telescope's mirrors. Phasing methods on compact platforms are constrained by the limited volume and power available, excluding solutions that rely on dedicated hardware or demand substantial computational resources. Neural networks (NNs) are known for their computationally efficient inference and reduced onboard requirements. Therefore, we developed a NN-based method to measure co-phasing errors inherent to a deployable telescope. The proposed technique demonstrates its ability to detect phasing errors at the targeted performance level [typically a wavefront error (WFE) below 15nm RMS for a visible imager operating at the diffraction limit] using a point source. The robustness of the NN method is verified in presence of high-order aberrations or noise and the results are compared against existing state-of-the-art techniques. The developed NN model ensures its feasibility and provides a realistic pathway towards achieving diffraction-limited images.

Parasitic Reflection Eliminating for Planar Elements Based on Multi-Frequency Phase-Shifting in Phase Measuring Deflectometry.

Phase measuring deflectometry (PMD) stands as an extremely important technique for specular surface measurement. However, the parasitic reflection from the rear surface poses a challenge for PMD. To solve this problem, this paper proposes an effective method based on multi-frequency and phase-shifting to search for the correct phase. Firstly, the relationship between the phase error and fringe frequency is adequately investigated. Subsequently, an auxiliary function is established to find the special frequency at which the phase error is zero theoretically and the unwrapped phase is the phase of the top surface exactly. Then, the shape of the top surface can be reconstructed correctly. A standard plane element with a thickness of 40 mm and a flat glass with 19 mm were measured. The experimental results verify the feasibility of the proposed method. Considering the result of the interferometer as a reference, the RMSE of the error map is up to 20 nm for the standard plane element. The experimental results demonstrate that the proposed method can successfully untangle the superposed reflections and reliably reconstruct the top surface of the object under test.

A 28 GHz GaN 6-Bit Phase Shifter MMIC with Continuous Tuning Calibration Technique.

A 28 GHz digitally controlled 6-bit phase shifter with a precision calibration technique in GaN high-electron mobility transistor (HEMT) technology is presented for Ka-band phased-array systems and applications. It comprises six stages, in which stages 1 and 2 for 5.625° and 11.25° are designed in the form of a switched-line circuit, and stages 3, 4, and 5 for 22.5°, 45°, and 90° are designed in the form of a switched-filter circuit. The final stage 6 for 180° is designed in a single-to-differential balun followed by a single-pole double-throw (SPDT) switch for achieving an efficient phase inversion. A novel continuous tuning calibration technique is proposed to improve the phase accuracy. It controls the gate bias voltage of off-state HEMTs at the stage 6 SPDT switch for fine calibration of the output phase. Fabricated in a 0.15 μm GaN HEMT process using a die size of 1.75 mm2, the circuit produces 64 phase states at 28 GHz with a 5.625° step. The experimental results show that the Root-Mean-Square (RMS) phase error is significantly improved from 8.56° before calibration to 1.08° after calibration. It is also found that the calibration does not induce significant changes for other performances such as the insertion loss, RMS amplitude error, and input-referred P1dB. This work successfully demonstrates that the GaN technology can be applied to millimeter-wave high-power phased-array transceiver systems.

A Robust Track Estimation Method for Airborne SAR Based on Weak Navigation Information and Additional Envelope Errors

As miniaturization technology has progressed, Synthetic Aperture Radar (SAR) can now be mounted on Unmanned Aerial Vehicles (UAVs) to carry out observational tasks. Influenced by airflow, UAVs inevitably experience deviations or vibrations during flight. In the context of cost constraints, the precision of the measurement equipment onboard UAVs may be relatively low. Nonetheless, high-resolution imaging demands more accurate track information. It is therefore of great importance to estimate high-precision tracks in the presence of both motion and measurement errors. This paper presents a robust track estimation method for airborne SAR that makes use of both envelope and phase errors. Firstly, weak navigation information is employed for motion compensation, which reduces a significant portion of the motion error. Subsequently, the track is initially estimated using additional envelope errors introduced by the Extended Omega-K (EOK) algorithm. The track is then refined using a phase-based approach. Furthermore, this paper presents the calculation method of the compensated component for each target and provides an analysis of accuracy from both theoretical and simulation perspectives. The track estimation and imaging results in the simulations and real data experiments validate the effectiveness of the proposed method, with an estimation accuracy of real data experiments within 5 cm.

Observational Study on Adherence to modified Clinical and Laboratory Standard Institute H3-A6 Guidelines on Blood Sampling Procedures

Background: The accuracy of clinical laboratory results is paramount for effective patient diagnosis and treatment. However, errors in the pre-analytical phase, particularly during phlebotomy, significantly impact the reliability of laboratory data. With the Clinical and Laboratory Standards Institute (CLSI) guidelines serving as a benchmark for best practices in blood collection, adherence to these standards is crucial for minimizing errors. Objective: This study aimed to assess compliance with modified CLSI guidelines in phlebotomy procedures within a healthcare setting and identify the most prevalent errors in the pre-analytical phase that could compromise patient safety and the integrity of laboratory results. Methods: Conducted at the Combined Military Hospital Lahore from January to March 2023, this observational study scrutinized phlebotomy practices across three distinct healthcare settings: emergency department, outpatient department, and clinical wards. A structured checklist, adapted from the European Federation for Clinical Chemistry and Laboratory Medicine (EFLM) guidelines and aligned with local modifications, was employed to evaluate compliance in 20 specific areas of phlebotomy practice. A total of 285 phlebotomies were observed by specialized staff, with data analyzed using SPSS version 25 to compare error frequencies and compliance rates across different settings and among various healthcare professionals. Results: The study revealed an overall compliance rate of 88% for identified request forms, 76% for patient identification according to local guidelines, and 66% for proper hand sanitization. However, significant errors were identified in checking for potential complications of venipuncture (34% compliance), with tubes being clearly under or overfilled (46% compliance), and in verifying that patients were prepared for phlebotomy (46% compliance). The error frequency varied across settings, with the highest discrepancies observed in the emergency department. Differences in compliance rates between laboratory staff and nurses were statistically significant in key areas, including patient identification (p<0.001) and tube labeling (p=0.081). Conclusion: The study highlights a critical need for improving adherence to CLSI guidelines within phlebotomy practices to enhance patient safety and the accuracy of laboratory results. Targeted educational and training interventions are essential for addressing the identified gaps in compliance, particularly in patient identification, sample volume control, and verification of patient preparation for phlebotomy.

Color crosstalk compensation method for color phase-shifting fringe projection profilometry based on the phase correction matrix.

Color phase-shifting fringe projection profilometry is one of the single-shot three-dimensional shape measurement techniques. The color crosstalk of the projector-camera system yields undesired phase errors when using phase-shifting method. In this paper, a color crosstalk compensation method based on phase correction matrix is proposed. In this method, the phase correction matrix is established to compensate the deviations between the actual phase-shift values in the acquired fringes and the standard ones in the ideal fringes. Only two fringe patterns are utilized to obtain the phase correction matrix. The quadratic equations for calculating the actual phase-shift values of the fringes in the three color channels are derived. The actual phase-shift values and the corresponding standard ones are employed to form the equilibrium equations for computing the phase correction coefficients in the matrix. Experimental results demonstrate the feasibility of the proposed method and it can effectively reduce the induced overall phase error caused by the color crosstalk.

Expected Precision of Gravity Gradient Recovered from Ka-Band Radar Interferometer Observations and Impact of Instrument Errors

Full tensor of gravity gradients contains extremely large amounts of information, which is one of the most important sources for research on recovery seafloor topography and underwater matching navigation. The calculation and accuracy of the full tensor of gravity gradients are worth studying. The Ka-band interferometric radar altimeter (KaRIn) of surface water and ocean topography (SWOT) mission enables high spatial resolution of sea surface height (SSH), which would be beneficial for the calculation of gravity gradients. However, there are no clear accuracy results for the gravity gradients (the gravity gradient tensor represents the second-order derivative of the gravity potential) recovered based on SWOT data. This study evaluated the possible precision of gravity gradients using the discretization method based on simulated SWOT wide-swath data and investigated the impact of instrument errors. The data are simulated based on the sea level anomaly data provided by the European Space Agency. The instrument errors are simulated based on the power spectrum data provided in the SWOT error budget document. Firstly, the full tensor of gravity gradients (SWOT_GGT) is calculated based on deflections of the vertical and gravity anomaly. The distinctions of instrument errors on the ascending and descending orbits are also taken into account in the calculation. The precision of the Tzz component is evaluated by the vertical gravity gradient model provided by the Scripps Institution of Oceanography. All components of SWOT_GGT are validated by the gravity gradients model, which is calculated by the open-source software GrafLab based on spherical harmonic. The Tzz component has the poorest precision among all the components. The reason for the worst accuracy of the Tzz component may be that it is derived by Txx and Tyy, Tzz would have a larger error than Txx and Tyy. The precision of all components is better than 6 E. Among the various errors, the effect of phase error and KaRIn error (random error caused by interferometric radar) on the results is greater than 2 E. The effect of the other four errors on the results is about 0.5 E. Utilizing multi-cycle data for the full tensor of gravity gradients recovery can suppress the effect of errors.

Reflecting Elements Analysis for Secure and Energy-Efficient UAV-RIS System With Phase Errors

Reflecting Elements Analysis for Secure and Energy-Efficient UAV-RIS System With Phase Errors