Azimuth Axis Research Articles

Cyclic pitch control for aerodynamic load reductions of floating offshore wind turbines under pitch motions

Floating offshore wind turbines suffer severe aerodynamics under platform motions. Novel control methods are urgently needed to improve power and load performances. A mechanical cyclic pitch control strategy is introduced in this paper, and the load reduction effect on the NREL 5-MW wind turbine is investigated under dominant pitch motions. The simulation is performed by the standalone Aerodyn_Driver code. Results show that the relative airflow under pitch motions can be equated to a linear sheared flow and is only related to wind velocity and pitch angular velocity. Cyclic pitch control hardly affects power and thrust but significantly changes aerodynamic moments. The resultant moment and moment axis azimuth are defined, and they are controlled respectively by pitch amplitude and phase. The optimal pitch parameter equations to minimize pitching and yawing moments are derived from fitting and derivation, and the standard deviations of aerodynamic moments are reduced by over 70 % under the sinusoidal pitch motion and steady inflow below rated operation. This paper provides a new idea for the individual pitch control structure, and the mechanism study for aerodynamic control is important and instructive to fill the technological gap in mature pitch control strategies for floating offshore wind turbines.

Direct Closed-Loop Control Structure for the Three-Axis Satcom-on-the-Move Antenna

The traditional Satcom-on-the-Move (SOTM) mechanical structure consists of a dual-axis configuration with an azimuth axis and a pitch axis. In this structure, when the pitch angle is 90 degrees, the rotation of the azimuth axis cannot change the antenna’s direction. To solve this issue, a three-axis SOTM mechanical structure has been developed. The traditional three-axis SOTM servo control system adopts a closed-loop control scheme. In this scheme, due to the difficulty in directly obtaining the antenna’s rotation angle, the angles of rotation for each axis are typically selected to represent the antenna’s rotation angle. The closed-loop feedback includes the angles and angular velocities of the axes, which cannot completely capture the antenna’s motion state, essentially constituting an indirect closed-loop control. Addressing the shortcomings of this indirect closed-loop control, this paper first establishes the kinematic relations between the axes of the three-axis SOTM antenna using the Denavit–Hartenberg (DH) method. Subsequently, the relationship between antenna pointing and the rotational states of the three axes was derived using the Jacobian operator. Building upon this foundation, a direct closed-loop control structure for a three-axis SOTM antenna was designed. To enable the control system to achieve rapid convergence with minimal overshoot, an Active Disturbance Rejection Control (ADRC) algorithm based on smooth continuous functions is introduced as the inner and outer loop controller algorithms within the direct closed-loop control structure. To address the nonlinearity in the design scheme, a piecewise linearization method is proposed to reduce the demands on the microprocessor’s performance and enhance the engineering feasibility of the solution. Finally, the effectiveness of the proposed approach is validated through experiments. The experimental results demonstrate that compared to traditional indirect closed-loop control methods, utilizing the direct closed-loop control method for the three-axis SOTM antenna presented in this paper can lead to higher precision in pointing the antenna towards satellites and enhance communication effectiveness.

Comparative analysis of geometric transformation-based sorting systems for fractional vector beams with polarization mutation angle indeterminacy

The Polarization Topological Charge (PTC) is a crucial parameter of a Cylindrical Vector Beam (CVB). Defined as the repetition number of polarization state changes along the azimuth axis, its sign indicates the polarization’s rotation direction. This paper delves into the effects of polarization mutation within Fractional Vector Beams (FVB) with angular uncertainty on PTC sorting systems. We compare three optical geometric coordinate transformation methods: Log-Polar (LP), Beam-Copying (BC), and Spiral Transformation (ST), focusing on their robustness and suitability. Our findings show that the azimuth angle of polarization mutation markedly influences the PTC sorting system’s output, leading to measurable uncertainties. Importantly, these uncertainties are not intrinsic to the FVB, but rather stem from the sorting system itself. Our study concludes that the BC method is optimal for PTC spectra analysis, whereas the ST method with carefully selected parameters is preferable for average PTC analysis.

Solar Tracking Methods: A Comprehensive Survey

Abstract: In the pursuit of maximizing solar energy utilization, solar tracking systems have emerged as indispensable tools for enhancing the efficiency of photovoltaic (PV) systems. This comprehensive survey delves into the multifaceted landscape of solar tracking methods, elucidating the diverse techniques and strategies employed in optimizing solar panel orientation relative to the sun's position Solar tracking systems are classified into two primary categories: single-axis and dual-axis tracking. Single-axis tracking systems adjust solar panels along one axis, typically the azimuth axis, while dual-axis tracking systems dynamically alter both azimuth and elevation angles to accurately follow the sun's apparent motion across the sky.Within the realm of solar tracking, passive and active tracking methods are explored. Passive tracking mechanisms rely on natural phenomena such as gravity or thermal expansion to adjust panel orientation, whereas active tracking systems employ mechanical, electrical, or hydraulic actuators driven by motors or other means to actively adjust panel angles based on real-time tracking algorithms.A pivotal aspect of solar tracking systems is the selection and implementation of tracking algorithms. Various algorithms, including sun position algorithms, maximum power point tracking (MPPT) algorithms, and predictive algorithms, are analyzed for their effectiveness in accurately predicting and optimizing solar panel orientation.Furthermore, this survey scrutinizes the role of sensor technologies in solar tracking, encompassing GPS-based tracking, light-intensity-based tracking, weather-based tracking utilizing meteorological sensors, and horizon tracking techniques. These sensor-based methodologies offer different advantages and trade-offs in terms of accuracy, cost, and reliability. To provide a comprehensive understanding, comparative analyses are conducted, evaluating the efficiency, cost-effectiveness, and energy yield of different tracking methods. These comparative assessments offer valuable insights into the performance characteristics and suitability of various tracking methodologies across diverse applications and environmental conditions.In conclusion, this survey serves as an invaluable resource for researchers, engineers, and policymakers involved in the design, development, and optimization of solar tracking systems for renewable energy applications. By synthesizing the latest advancements and comparative analyses, this survey facilitates informed decision-making and fosters the advancement of sustainable solar energy technologies.

Rapid Tracking Satellite Servo Control for Three-Axis Satcom-on-the-Move Antenna

To overcome the possible gimbal lock problem of the dual-axis satcom-on-the-move (SOTM) antenna, a three-axis tracking satellite SOTM antenna structure appears. The three-axis SOTM antenna is realized by adding a roll axis to the azimuth axis and pitch axis in the dual-axis SOTM structure. There is coupling among the azimuth axis, pitch axis and roll axis in the mechanical structure of the three-axis SOTM antenna, which makes the kinematic modeling of the antenna difficult. This paper introduces a three-axis SOTM antenna kinematic modeling method based on the modified Denavit–Hartenberg (MDH) method, named the new modified Denavit–Hartenberg (NMDH) method. In order to meet the modeling requirements of the MDH method, the NMDH method adds virtual coordinate systems and auxiliary coordinate systems to the three-axis SOTM antenna and obtains the kinematic model of the three-axis SOTM antenna. During the motion of the carrier, the SOTM antenna needs to adjust the antenna pointing in real time according to the changes of the location and attitude of the moving carrier. Therefore, this paper designs a servo control system based on the active disturbance rejection controller (ADRC), introducing a smooth and continuous ADRC fal function to enhance the tracking speed of the servo control system and reduce the overshoot of the output response. Finally, system experiments were carried out with a 60 cm caliber three-axis SOTM antenna. The experiment results show that the proposed servo control method achieves higher antenna tracking satellite accuracy and better communication effects.

Seamount detection using SWOT-derived vertical gravity gradient: advancements and challenges

SUMMARY Launched on 2022 December 16, the Surface Water and Ocean Topography (SWOT) satellite, using synthetic aperture radar interferometric techniques, measures sea surface heights (SSHs) across two 50-km-wide swaths, offering high-resolution and accurate 2-D SSH observations. This study explores the efficiency of SWOT in seamount detection employing the vertical gravity gradient (VGG) derived from simulated SWOT SSH data. Simulated circular and elliptical seamounts (height: 900–1500 m) are integrated within the South China Sea's 4000 m background depths. Geoid perturbations induced by these seamounts are extracted through the residual depth model principle, subsequently merged with the DTU21MSS model for simulating SWOT SSH observations. For comparative assessment, SSH data from Jason-2 and Cryosat-2 are included. An automatic algorithm (AIFS) is presented to identify seamount centres and base polygons using VGG derived from simulated altimeter SSH data. The analysis reveals SWOT-derived VGGs precisely locate all seamount centres, base polygons and elliptical seamount azimuths. The merged Jason-2 and Cryosat-2 data face challenges with identifying small circular and elliptical seamounts. Detecting long narrow elliptical seamounts remains arduous; however, SWOT-derived VGGs successfully elucidate the approximate shapes and major axis azimuths of the elliptical seamounts. Validated against ‘true values’ of VGG, the root-mean-squared deviation (RMSD) of SWOT-derived VGG stands at 1.33 Eötvös, whereas the merged Jason-2 and Cryosat-2 data exhibit an RMSD of 1.93 Eötvös. This study shows the enhanced capability of SWOT from its high-resolution 2-D SSH observations in advancing seamount detection via satellite-derived VGG. We identify challenges and recommend improved detections using data integration and machine learning.

Using the traditional microscope for mineral grain orientation determination: A prototype image analysis pipeline for optic-axis mapping (POAM).

This paper reports on the development of an open-source image analysis software 'pipeline' dedicated to petrographic microscopy. Using conventional rock thin sections and images from a standard polarising microscope, the pipeline can classify minerals and subgrains into objects and obtain information about optic-axis orientation. Five metamorphic rocks were chosen to test and illustrate the method. Thin sections were imaged using reflected and cross- and plane-polarised transmitted light. Images were taken at different angles of the polariser and analyser (360° with 10° steps), both with and without the full-lambda plate. The resulting image stacks were analysed with a modular pipeline for optic-axis mapping (POAM). POAM consists of external and internal software packages that register, segment, classify, and interpret the visible light spectra using object-based image analysis (OBIAS). The mapped fields-of-view and grain orientation stereonets of interest are presented in the context of whole-slide images. Two innovations are reported. First, we used hierarchical tree region merging on blended multimodal images to classify individual grains of rock-forming minerals into objects. Second, we assembled a new optical mineralogy algorithm chain that identifies the mineral slow axis orientation. The c-axis orientation results were verified with scanning electron microscopy electron backscattered diffraction (SEM-EBSD) data. For quartz (uniaxial) in a granite mylonite the test yielded excellent correspondence of c-axis azimuth and good agreement for inclination. For orthorhombic orthopyroxene in a deformed garnet harzburgite, POAM produced acceptable results for slow axis azimuth. In addition, the method identified slight anisotropy in garnet that would not be appreciated by traditional microscopy. We propose that our method is ideally suited for two commonly performed tasks in mineralogy. First, for mineral grain classification of entire thin sections scans on blended images to provide automated modal abundance estimates and grain size distribution. Second, for prospective fields of view of interest, POAM can rapidly generate slow axis crystal orientation maps from multiangle image stacks on conventionally prepared thin sections for targeting detailed SEM-EBSD studies.

Analysis and design of PI-based controllers for the axes of European Solar Telescope

European Solar Telescope (EST) represents the largest European research infrastructure projected in the field of solar astrophysics. It is a 4-meter class solar telescope currently in the design phase. Within this phase, an essential objective is to analyze the control strategy of the telescope axes to achieve an accurate sun trajectory tracking. This paper presents a cascade control scheme based on proportional-integral (PI) controllers specifically designed for the elevation and azimuth axes of EST. The control strategy, which employs nested position-velocity loops, is devised to adeptly track the sun’s trajectory while mitigating wind impact. The controller tuning adheres to criteria of relative stability margins and bandwidth constraints using the state-space representation derived from Finite Element Model of the EST structure. An end-to-end dynamics model has been proposed to evaluate the performance of the control strategy during a ten-minute simulation. Results evidenced the convenience of the proposed controllers, highlighting wind as the main source of the control error (0.78 arcsec and 0.14 arcsec in azimuth and elevation axes, respectively) compared to the sun tracking error. Future control strategy enhancements should target the reduction of wind-induced effects to meet stringent image stability requirements.

Characterization of Polarimetric Properties in Various Brain Tumor Types Using Wide-Field Imaging Mueller Polarimetry.

Neuro-oncological surgery is the primary brain cancer treatment, yet it faces challenges with gliomas due to their invasiveness and the need to preserve neurological function. Hence, radical resection is often unfeasible, highlighting the importance of precise tumor margin delineation to prevent neurological deficits and improve prognosis. Imaging Mueller polarimetry, an effective modality in various organ tissues, seems a promising approach for tumor delineation in neurosurgery. To further assess its use, we characterized the polarimetric properties by analysing 45 polarimetric measurements of 27 fresh brain tumor samples, including different tumor types with a strong focus on gliomas. Our study integrates a wide-field imaging Mueller polarimetric system and a novel neuropathology protocol, correlating polarimetric and histological data for accurate tissue identification. An image processing pipeline facilitated the alignment and overlay of polarimetric images and histological masks. Variations in depolarization values were observed for grey and white matter of brain tumor tissue, while differences in linear retardance were seen only within white matter of brain tumor tissue. Notably, we identified pronounced optical axis azimuth randomization within tumor regions. This study lays the foundation for machine learning-based brain tumor segmentation algorithms using polarimetric data, facilitating intraoperative diagnosis and decision making.

2–Bit Programmable Metasurface for Low Radar Cross Section Antenna and Beam Steering Applications

AbstractIn this paper, a 2‐bit water‐based programmable digital metasurface for beam steering and backscatter field reduction applications is presented, a reflective and transmissive type water based programmable metasurface (WPMS) for RCS reduction and the antenna's beam steering is suggested, respectively. It has been demonstrated that a 2‐bit water‐based programmable unit cell can reduce RCS by changing its state (0/1). If the unit cell channel is empty, the state is “0,” if the channel is filled, the state is “1.” So at different resonance frequencies, the four phase and reflection coefficient responses are achieved as "00"01"10"11". This functionality enables beam steering in both the elevation and azimuth axis and also backscattering reduction of the antenna. Furthermore, the impacts of the number of unit cells and reflection phase states on the far‐field pattern are examined. Beam steering of ±45° in the elevation is attained with 10‐dB impedance bandwidth of 4.25–4.40 GHz, radiation gain of more than 7.1 dBi is maintained. With the present antenna, it is possible to achieve volumetric beamsteering performance directly. The patterns of far‐field radiation that are predicted theoretically coincide well with full waves simulations. As such, the proposed prototype can be a good option for applications that require a low RCS platform including beam steering in radars, 5G/6G, etc.

A Simplified Pointing Model for Alt-Az Telescopes

The telescope pointing model plays a crucial role in characterizing and explaining the inaccuracies in the telescope’s pointing. It uses mathematical models to express these errors and suggests methods to calibrate and rectify them. By employing the pointing model, one can gain a deeper understanding of the discrepancies in the telescope’s pointing accuracy at various positions and orientations. This article introduces the establishment and validation of a simplified pointing model for correcting the pointing errors of an alt-az telescope. The traditional telescope pointing model, with its complex formulas, makes it difficult to quickly apply for the calibration of the telescope’s pointing. This method utilizes two-dimensional surface fitting to obtain the telescope’s pointing error function, enabling a rapid determination of the telescope’s pointing model, which is then validated on the Planetary Atmospheric Spectroscopic Telescope (PAST). Using this method, the azimuth axis and altitude axis errors (root mean square error—RMSE) of the PAST telescope are 6.8 arcs and 3.8 arcs, respectively.

An Intelligent Dual-Axis Solar Tracking System for Remote Weather Monitoring in the Agricultural Field

Agriculture is a critical domain, where technology can have a significant impact on increasing yields, improving crop quality, and reducing environmental impact. The use of renewable energy sources such as solar power in agriculture has gained momentum in recent years due to the potential to reduce the carbon footprint of farming operations. In addition to providing a source of clean energy, solar tracking systems can also be used for remote weather monitoring in the agricultural field. The ability to collect real-time data on weather parameters such as temperature, humidity, and rainfall can help farmers make informed decisions on irrigation, pest control, and other crop management practices. The main idea of this study is to present a system that can improve the efficiency of solar panels to provide constant power to the sensor in the agricultural field and transfer real-time data to the app. This research presents a mechanism to improve the arrangement of a photovoltaic (PV) array with solar power and to produce maximum energy. The proposed system changes its direction in two axes (azimuth and elevation) by detecting the difference between the position of the sun and the panel to track the sun using a light-dependent resistor. A testbed with a hardware experimental setup is designed to test the system’s capability to track according to the position of the sun effectively. In the end, real-time data are displayed using the Android app, and the weather data are transferred to the app using a GSM/WiFi module. This research improves the existing system, and results showed that the relative increase in power generation was up to 52%. Using intelligent artificial intelligence techniques with the QoS algorithm, the quality of service produced by the existing system is improved.

Frequency splitting of hemispherical resonators trimmed with focused ion beams

This paper studies a high-precision etching process based on focused ion beam static trimming of the defective mass of fused silica hemispherical resonators to eliminate frequency splitting. This trimming method effectively overcomes the shortcomings of inefficiency and poor robustness, and the accuracy is seriously dependent on the stability of the trimming equipment in the traditional approach based on the harmonic form of trimming. The vibration model of an imperfect hemispherical resonator is firstly established by equating structural defects into point mass defective units, revealing that the frequency splitting is a function of the size of the equivalent defect mass and that the angular position of the stiffness axis is determined by the spatial distribution of the defect mass, which further elucidates that the frequency splitting of the resonator is the equivalent form of the defect mass on its low-frequency axis. To validate the accuracy of the present method, a simulation model of the imperfect resonator is established, and the results show that the theoretical model is in good agreement with the finite element method. Then, a high-precision nonlinear parameter identification model containing frequency splitting and low-frequency axis azimuth parameters is established based on the standing wave oscillation effect and spectral analysis, and the frequency splitting and low-frequency axis azimuth are identified by analyzing the vibration function of the hemispherical resonator. Finally, based on the parameter identification results and the ion beam removal function analysis, an ion beam trimming process is designed to eliminate frequency splitting by trimming the defective mass on the low-frequency axis. The results show that the frequency splitting after mass trimming is better than 0.001 Hz, significantly improving the hemispherical resonator's performance.

An Improved Rotational Modulation Scheme for Tri-Axis Rotational Inertial Navigation System (RINS) with Fiber Optic Gyro (FOG)

An optimized scheme can improve the navigation accuracy of RINS without changing the inertial devices. In the multi-position stop scheme, the IMU remains stationary for most of the time, which makes motor control easier. However, the installation errors and the scale factor errors of FOG can cause platform misalignment after a certain angle of rotation around the horizontal axis, resulting in a velocity error. Continuous rotation can suppress time-varying errors better, which is of particular importance for FOG, but it can also increase the sawtooth error of the navigation output, and the error in the direction of rotation cannot be offset. To integrate the advantages of both rotation schemes, we propose an improved rotational modulation scheme for tri-axis RINS. In this scheme, the inner gimbal rotates in a two-position and four-order manner, while the middle and outer gimbals rotate continuously in the order of forward-reverse-reverse-forward. Simulation and navigation test results demonstrate that this improved rotational modulation scheme can effectively improve navigation accuracy by 50% and 25% compared with continuous rotation around the azimuth axis and a 16-position scheme with the same inertial devices, which is of great importance for RINS with FOG.

Calibration method of spatial transformations between the non-orthogonal two-axis turntable and its mounted camera.

In order to expand the field of view and measuremenst range, the camera is often mounted on a two-axis turntable to perform various visual tasks. And the calibration of the position and attitude relationship between the mounted camera and the two-axis turntable is a prerequisite for visual measurement. The turntable is considered an ideal orthogonal two-axis turntable in conventional methods. However, the rotation axes of the actual two-axis turntable may be neither vertical nor intersecting, and the optical center of the mounted camera is not always located in the rotation center of the turntable even for orthogonal two-axis turntables. The quite difference between the actual physical model of the two-axis turntable and the ideal model can cause large errors. Therefore, what we believe to be a novel position and attitude calibration method between a non-orthogonal two-axis turntable and the mounted camera is proposed. This method describes the spatial hetero-planar lines relationship between the azimuth axis and pitch axis of the turntable accurately. By the geometric invariant characteristics of the mounted camera in motion, the axes of turntable are recovered and the base coordinate system is established, and the position and attitude of the camera are calibrated. Simulation and experiments verify the correctness and effectiveness of our proposed method.

How do fault systems and seafloor bathymetry influence the structure and distribution characteristics of gas chimneys?

AbstractGas chimneys are key pathways for geofluid vertical migration; therefore, deciphering their formation and evolution is crucial for hydrocarbon exploration and geohazard risk assessment. However, the influences of ambient conditions (e.g. bathymetry, tectonics, sediment supply flux) on gas chimney development have not been thoroughly investigated. Using high‐resolution 3D seismic data, we have identified 59 gas chimneys beneath the Shenhu Slope (a gas hydrate test production area on the northern South China Sea margin), 35 of which intersect faults. Above fault interfaces, internal seismic structures are dominated by chaotic discontinuous reflections. Internal structures below interfaces display more continuous reflections, which are also apparent in gas chimneys, not intersecting faults. A higher degree of chaotic or discontinuous seismic reflections may indicate more fragmented networks. This may occur due to increased fluid flow along faults and concomitant fluid overpressure. The present‐day undulating seafloor comprises the inter‐canyon (IT) region, intra‐canyon (IN) region and flat slope (FD) region downstream of canyons. Gas chimneys beneath IT and IN regions exhibit elongated elliptical shapes in the plane, with the long axis azimuth (sub‐) parallel to the main strike of canyons. Chimneys beneath the IT region have larger heights than those beneath the IN and FD regions. Thicker sediment in the IT region corresponds to a higher overburden pressure, which may induce stronger overpressure in the subsurface reservoir region. This overpressure may promote chimneys gathering in the IT region. Canyons' main directions are likely to limit hydraulic fracturing due to maximum gradient boundaries between overlying sediment stress fields. This study provides insights into gas chimney distribution, morphology and structure evolution in relation to bathymetry and fault conditions. It contributes to an improved understanding of how geofluids migrate in marginal ocean basins.

ANFIS and ANN models to predict heliostat tracking errors

The efficiency and performance of solar tower power are greatly influenced by the heliostats field. To ensure accurate tracking of reflectors often requires an evaluation of the beam reflected positions. This operation is costly time-consuming due to the number of heliostats. It is also necessary to set up a fast and less expensive method able to evaluate tracking heliostat. In this paper, prediction models based on the Adaptive Neuro-Fuzzy Inference System (ANFIS) and Artificial Neural Network (ANN) were applied to estimate rapidly and accurately heliostat error tracking. The modeling is based on the experimental data of seven different days. The input parameters are time and day number and the output is the beam reflected position following the altitude and azimuth axes. Both techniques have been able to predict the beam reflected position. A comparison of results showed that intelligent methods recorded better performance than conventional model based on geometric errors. For ANFIS model, coefficients of correlation (R2) of 0.97 is obtained compared to that of the ANN, 0.96 and 0.92 for altitude and azimuth axes respectively. The intelligent methods may be a promising alternative for predicting heliostat beam reflected the position.

Study on the tracking error and focused spot trajectory characteristics of the dish concentrator under the azimuth axis tilt error

The dish concentrator is an indispensable optical device for solar dish/stirling power system, which requires accurate tracking sun’s position. However, both the foundation settlement caused by long-term service and installation error can cause the support column tilt, thus destroying the vertical relationship between the column axis (i.e. azimuth axis) and ground plane resulting tracking errors. In this paper, a tracking error model of dish concentrator with elevation–azimuth dual-axis tracking considering column tilt is developed, the radial error angle θ1 and circumferential error angle φ1 are used to describe column tilt angle and tilt direction. The concentrator tracking error and focused spot position under column tilt error are analyzed using several dimensional evaluation indexes for the whole year, every day and every moment, and are verified by a novel virtual experiment of the concentrator tracking and optical simulation. When θ1 is constant, the tracking performance is worst throughout the year at φ1 of 90° and 270°, while the influence of column tilt can be effectively reduced at φ1 of 0° or 180°. The maximum daily tracking error can reach 1.91∼3.49 mrad in whole year at θ1=0.1° and φ1 in 0°∼360°, so θ1 should be controlled within 0.1°.

Simultaneous measurement of phase retardation and fast axis azimuth of wave plate based on equivalent component and phase detection

Wave plates (WPs) are key components in optical polarization systems whose phase retardations and fast axis azimuths should be determined accurately. At present many measurement methods are based on light intensity detection which is inevitably affected by light intensity fluctuations so that the measurement accuracy is limited. What’s more, quite a few methods cannot measure WPs’ fast axis azimuths simultaneously. In this paper a method of simultaneously measuring the phase retardation and fast axis azimuth of arbitrary WP is proposed, which is based on equivalent component and phase detection. A rotatable half wave plate (HWP) and a retroreflector are used and its effect is equivalent to measuring an equivalent WP whose phase retardation is twice that of the measured wave plate, which is equivalent to doubling the measurement resolution. Phase detection is used to process the signals which means the measurement accuracy is better than that by usual light intensity detection. What’s more, the presented method eliminates the angle positioning errors of birefringent components in principle which exists in many present WP measurement methods. Finally, the measurement system setup is simple as well as the measurement process. The measurement formulae are deduced and corresponding WP measuring system is established. The error analysis shows that the system measurement uncertainty is about 3.9′ for the phase retardation and 5” for the fast axis azimuth. Experiment results and comparisons of quarter WPs and HWPs show that the presented method is in good agreement with other method. The phase retardation measurement repeatability is also good with a standard deviation about 2′.

Effect of the Azimuth Axis Tilt Error on the Tracking Performance of a Solar Dish Concentrator System

A solar dish concentrator system has a large windward area and heavy structural mass, and under the action of wind loads and self-weight loads, foundation settlement can easily occur and cause the column (the azimuth axis) to tilt. Upon tilting, the azimuth axis is no longer perpendicular to the horizontal plane, causing a tracking error in the service of the solar dish concentrator system. In this paper, a tracking error model of a solar dish concentrator system is established based on the rigid body motion theory, which considers the azimuth axis tilt error. In this model, a radial angle and tangential angle parameters are used to describe the azimuth axis’s tilt angle and tilt direction. Under the tilt error of the azimuth axis, we analyze, in detail, the initial tracking position of a solar dish concentrator system, the system operation area, and the variation rule of tracking performance in long-term operation. The results show that under the azimuth axis tilt error of the solar dish concentrator system, the deviation of the initial tracking position of the solar dish concentrator system in the horizontal or vertical plane will reduce its tracking performance and the stability of tracking performance compared with the initial tracking position being due east. The tracking performance of a solar dish concentrator system and its stability are better in areas with a relatively low latitude. In different areas with close latitude, the tracking performance of the solar dish concentrator system and its stability are better, particularly with lower longitudes. During a whole year operation period, the tracking performance of an solar dish concentrator system in the first quarter and the fourth quarter is relatively better, and its stability in June and July is relatively better. This work can provide a theoretical basis for the installation, debugging, and error control of solar dish concentrator systems.