Spot Centroid Research Articles

Enlarge the dynamic range of Shack-Hartmann wavefront sensor based on biplanar image acquisition and segmentation method

In present paper, a simple and robust method to expand the SHWS dynamic range is proposed. The intensity patterns are obtained with biplanar image acquisition and segmentation. The process involves calculating the spot centroids of two images and then matching the centroid of the spots of light with the center of a micro-lens array. This also resolves the issue of mandating the determination of centroids exclusively within the corresponding detection area. It is performed a comparative analysis between our proposed method and the conventional method for measuring large wavefronts, utilizing both numerical simulations and experiments. Additionally, a statistical analysis of the dynamic range of the method for wavefront measurement was conducted. This study demonstrates that the biplanar image acquisition and segmentation method provided a larger dynamic range while ensuring accuracy relative to the single image acquisition of conventional algorithm

Neural network assisted high flexibility and high resolution Shack-Hartmann wavefront sensing for astronomical observation in darker sky areas.

Shack-Hartmann (SH) wavefront sensing is widely applied to astronomical observations with its fast and accurate measurement. However, due to the computational nature of SH that the input beam is segmented to provide local wavefront slopes, the sampling density of the sub-apertures and the calculation accuracy of each sub-focal spot's centroid have great influence on the wavefront reconstruction accuracy. Therefore, it is usually difficult to achieve high resolution wavefront reconstruction for dark stars in the astronomical observations with insufficient light intensity. We present a neural-network assisted high resolution SH wavefront sensing method to overcome the shortages and obtain results with enhanced resolution from the separated information inside each sub-aperture. With this method, high resolution wavefront sensing in darker sky area could be realized.

Convolutional neural network for improved event-based Shack-Hartmann wavefront reconstruction

Shack-Hartmann wavefront sensing is a technique for measuring wavefront aberrations, whose use in adaptive optics relies on fast position tracking of an array of spots. These sensors conventionally use frame-based cameras operating at a fixed sampling rate to report pixel intensities, even though only a fraction of the pixels have signal. Prior in-lab experiments have shown feasibility of event-based cameras for Shack-Hartmann wavefront sensing (SHWFS), asynchronously reporting the spot locations as log intensity changes at a microsecond time scale. In our work, we propose a convolutional neural network (CNN) called event-based wavefront network (EBWFNet) that achieves highly accurate estimation of the spot centroid position in real time. We developed a custom Shack-Hartmann wavefront sensing hardware with a common aperture for the synchronized frame- and event-based cameras so that spot centroid locations computed from the frame-based camera may be used to train/test the event-CNN-based centroid position estimation method in an unsupervised manner. Field testing with this hardware allows us to conclude that the proposed EBWFNet achieves sub-pixel accuracy in real-world scenarios with substantial improvement over the state-of-the-art event-based SHWFS. An ablation study reveals the impact of data processing, CNN components, and training cost function; and an unoptimized MATLAB implementation is shown to run faster than 800 Hz on a single GPU.

Extraction of Laser Spot Centroid of Turbulent Disturbance Based on Ellipse Fitting Method

Extraction of Laser Spot Centroid of Turbulent Disturbance Based on Ellipse Fitting Method

Laser Spot Centroid Extraction Method and Stability Analysis of "Gou Mang"

Laser Spot Centroid Extraction Method and Stability Analysis of "Gou Mang"

Accurate piecewise centroid calculation algorithm for wavefront measurement in adaptive optics.

Adaptive optics using direct wavefront sensing (direct AO) is widely used in two-photon microscopy to correct sample-induced aberrations and restore diffraction-limited performance at high speeds. In general, the direct AO method employs a Sharked-Hartman wavefront sensor (SHWS) to directly measure the aberrations through a spot array. However, the signal-to-noise ratio (SNR) of spots in SHWS varies significantly within deep tissues, presenting challenges for accurately locating spot centroids over a large SNR range, particularly under extremely low SNR conditions. To address this issue, we propose a piecewise centroid calculation algorithm called GCP, which integrates three optimal algorithms for accurate spot centroid calculations under high-, medium-, and low-SNR conditions. Simulations and experiments demonstrate that the GCP can accurately measure aberrations over a large SNR range and exhibits robustness under extremely low-SNR conditions. Importantly, GCP improves the AO working depth by 150 µm compared to the conventional algorithm.

Design of a real-time automatic resonator alignment method for unstable resonators

The auto-alignment method for unstable resonators proposed in this paper innovatively replaces the secondary mirror of traditional unstable resonators with a double-convex lens coated with a high reflective film on one side, and installs the primary mirror on a designed electrically adjustable bracket. During the laser emission process, the computer calculates the relative displacement of the centroid of the far-field spot on the camera detection surface to determine the magnitude of the resonator misalignment, and simultaneously controls the electrically adjustable bracket to complete the compensation for the resonator misalignment. Finally, the experimental results show that when using the real-time automatic resonator alignment method, the output power of the laser remains very stable with a relative standard deviation of the normalized power less than 1.1% (if the auto-alignment method is not adopted, the output power will decay to 89.8% of the peak value). Therefore, this method can effectively solve the resonator misalignment problem of unstable resonator lasers. In addition, this method has the advantages of simple optical path structure and high detection speed while ensuring high accuracy.

High-speed modal analysis of dynamic modal coupling in fiber laser oscillator

Up till now, the spatial and temporal dynamics of transverse mode instability (TMI) in fiber laser oscillator have increasingly attracted a worldwide attention. Here, we develop a high-speed modal decomposition (MD) system to analyze the modal coupling for fiber laser oscillator above the TMI threshold. A set of angular-multiplexing transmission functions (TFs) are designed for simultaneous MD and monitoring the far-field beam profile. The TMI threshold of the deployed fiber laser oscillator is 181 W at a co-pumping power (CPP) of 279 W. As the CPP increases from 318 W to 397 W, the power fluctuations of the output laser become more drastic. The changes of the far-field beam profile and the centroid of far-field spot (COFFS) indicate an increased velocity of energy transfer between modes. The high-speed MD verifies above process and analyzes the modal components, indicating that the single cycle of modal coupling decreases from 11 ms to 4 ms. Otherwise, the strong mode coupling occurs between modes with relatively large weights. The high-speed MD provides a powerful tool to research the TMI effect.

Centroid Extraction of Laser Spots Captured by Infrared Detectors Combining Laser Footprint Images and Detector Observation Data

On-orbit geometric calibration of satellite-borne laser based on infrared detectors is the key tool to ensure the elevation measurement accuracy, and the accuracy of on-orbit geometric calibration is directly determined by laser spots captured by detectors. Mathematical methods, such as gray-scale barycenter, are widely applied for centroid extraction of spots captured by infrared detectors and completely depend on the energy values at points measured by detectors, which have low precision and are greatly affected by the consistency of the detectors and other factors at present. Based on the above question, considering the consistency between the real laser footprint shape and spot captured by detectors, a centroid extraction method of laser spots captured by infrared detectors combining laser footprint images and detector observation data is proposed for making up this defect to some extent. First, the self-adaptive “two-step method” is used to denoise footprint images hierarchically to obtain the real shape of footprints for constraining the spots captured by detectors, and then the centroids of spots are extracted by using the energy-weighted barycenter method based on regional blocks. In the experiment, Gaofen-7 (GF-7) satellite is taken as the research object, and the proposed method, as well as the other six methods, are used for the centroid extraction of laser spots captured by detectors, the calculation of calibration parameters based on the single-beam and dual-beam laser calibration models, the positioning of laser footprints, and cross verification. According to the results, the plane accuracy of centroid extraction using the proposed method is as follows: 0.34 grids for Beam 1 and 0.33 grids for Beam 2. In addition, on flat terrain, the elevation accuracy of Beam 1 and Beam 2 in 2021 is 5.2 cm and 5.0 cm, respectively, 0.6 cm and 4.2 cm higher than those in the most accurate one among other methods; the elevation accuracy in 2020 is 23.3 cm and 7.1 cm, respectively, 7.7 cm and 2.7 cm higher than those in the most accurate one among other methods. On slopes and gentle slopes, the method proposed is also superior to other methods. Since the change of pointing angle caused by satellite jitter, atmosphere, etc., between different years, the accuracy drops when laser footprints of 2020 are located using the parameters of 2021. In summary, under different terrains and years, the results fully demonstrate the effectiveness and accuracy of the proposed method, which has more significant advantages than other traditional methods.

Inertial information based star detection for airborne star sensor

Star sensors are among the most promising attitude measurement devices owing to their high accuracy. Insufficient star detection ability during daytime is a major issue in airborne applications because of the highly dynamic and strong sky background present. A star detection algorithm for a medium field-of-view star sensor combined with a zero-lock laser goniometer is proposed in this paper. The star sensor employs a high-frame-rate detector that shortens the exposure time to obtain an undistorted star spot under dynamic conditions. To improve the low signal-to-noise ratio of the star image influenced by the strong sky background, a technique for multi-frame image accumulation was introduced, prior to which attitude compensation for each star image frame was carried out by using the inertial information related to the reference frame measured by zero-lock laser gyro goniometers. Both simulations and laboratory experiments were conducted. The simulation results show that the proposed algorithm effectively enhances the stability of the star spot and signal-to-noise ratio of the star image. The experimental results demonstrate a fine star spot centroid extraction performance for the medium field of view star sensor with an extraction error of less than 0.2 pixels or 2 arc-second under four different types of one-dimensional angular motion after compensation. Based on this, the multi-frame accumulation of star images demonstrates little star spot dispersion compared with no compensation and exhibits a higher signal-to-noise ratio than a single-frame star image. In the real situation experiments, a K0 spectrum star with magnitude +3.0 was successfully observed under dynamic condition during daytime. The signal-to-noise ratio is up to 20, which is more than 5 times than that by the traditional method.

Research on achromatic Risley prism in normal tracing angle measurement system

The normal tracing angle measurement system based on Risley prisms can eliminate the influence of aberrations other than the dispersion of Risley prisms on the angle measurement accuracy. Although the traditional dispersion optimization method based on the extreme point can make the beam directions of different wavelengths more consistent after passing through the Risley prisms, the light intensity distribution that deviates from the extreme point wavelength causes the spot centroid to deviate from the target position, thus introducing the angle measurement error. In this paper, we propose a highly symmetry-glued achromatic Risley prisms optimization method for the needs of a normal tracing angle measurement system. Our method not only realizes the beam direction as closely as possible after the deflection of the Risley prisms but also compensates for the centroid error caused by the beam deviating from the central wavelength. ZEMAX simulation shows that, in the normal tracing angle measurement system, within the angle measurement range of ±700 ″ and the light source wavelength range of 600 to 700 nm, the angle measurement error introduced by the dispersion of the optimized Risley prisms is not >0.01 ″ .

Determining the Centroid of a Laser Spot in the Plane of a Multimedia Shooting Gallery Sensor Based on the Methods of Interpolation and Filtering of the Image Fragment

Determining the Centroid of a Laser Spot in the Plane of a Multimedia Shooting Gallery Sensor Based on the Methods of Interpolation and Filtering of the Image Fragment

Про підхід до визначення відповідності між пікселями камери і проєктора у мультимедійному тирі

Предметом вивчення в статті є геометричні перетворення у системі«проєктор–екран–камера» для визначення відповідності між пікселямикамери і проєктора у мультимедійному тирі. Метою є розробка математичної моделі та алгоритму визначення відповідності між пікселямикамери і проєктора. Це потрібно для співставлення положення центроїдалазерної плями від пострілу в матриці камери і мішені, що генеруєтьсяу матриці проєктора. Завдання: формалізувати задачу виникнення геометричних спотворень у системі «проєктор–екран–камера»; розробитиматематичну модель визначення відповідності між пікселями камериі проєктора; вибрати ефективний алгоритм її вирішення. Використовуваними методами є: математична модель вирівнювання зображення наоснові гомографії, метод бінаризації з вибором значення порога методом Оцу; метод Дугласа–Пекера, який зменшує кількість точок, що апроксимують криву. Отримано такі результати. Згідно аналізу геометричних спотворень у системі «проєктор–екран–камера» сформульовано задачу розробки моделі для вирівнювання зображення з метоювизначення відповідності між пікселями камери і проєктора. Розроблено математичну модель і алгоритм вирівнювання точок зображення мішені у матриці камери з точками зображення мішені у матриці проєктора. Розроблено і програмно реалізовано алгоритм визначення відповідності між пікселями камери і проєктора. Математичнізалежності для визначення відповідності між пікселями камери і проєктора встановлено на основі матриці гомографії. Коефіцієнти матриціобчислюються за відповідними кутовими точками прямокутника матриці проєктора і його спотвореного трапецеїдального зображення наматриці камери. Розроблено алгоритм автоматичного визначення вершин трапеції та встановлення відповідності між пікселями камериі проєктора. Проведено аналіз та експериментальні дослідження факторів, що впливають на точність алгоритму: точність визначення вершин трапеції, за якими знаходяться коефіцієнти матриці гомографії; ступіньзаповнення області огляду камери зображенням із проєктора; відповідність роздільної здатності камери і проєктора. Дано рекомендації щодозменшення їхнього впливу. Зроблено такі висновки. Наукова новизнаотриманих результатів полягає в наступному: розроблено і експериментально досліджено математичну модель визначення відповідності міжпікселями камери і проєктора у мультимедійному тирі через вирівнюваннязображення, що відображається з екрана проєктора у камері, на основігомографії. До цього для вирівнювання зображень у мультимедійному тирі використовувалась модель на основі 2D-перетворень, у якій взаємнеположення у просторі проєктора, екрана і камери не враховується.Оскільки у гомографії враховуються тільки лінійні перетворення, у подальшому планується удосконалити модель — врахувати нелінійніспотворення, що виникають у об’єктивах камери і проєктора.

Study on dip error compensation model of laser displacement sensor and its application in measurement of spiral curved surface profile

Featuring high resolution, excellent stability, great rapidity, and small size, the laser displacement sensor (LDS) has been extensively utilized in multiple domains. However, its accuracy is severely constrained by data acquisition (DAQ) errors. To solve this problem, we concentrate on the problem that DAQ errors seriously deteriorate the LDS measuring accuracy. Based on laser triangulation, we analyze the impact of laser beams and convergent spot centroid on the system measuring accuracy and establish mathematical models for quantitatively calculating LDS measured surface dip errors and charge-coupled device (CCD) dip errors. Further, these models can be used to compensate for the data collected by the LDS in real-time. Finally, experimental results show that after these two compensation models are used to correct measuring results, the accuracy of LDS-based DAQ is greatly improved, the measurement error is well controlled within 0.008 mm, and the LDS measuring accuracy on spiral curved surfaces is effectively boosted.

Kalman filter spot centroid detection algorithm in optical wireless communication

Atmospheric turbulence creates a light spot on the focal plane of the receiving end scintillation and angle of arrival fluctuation in optical wireless communication. The combination of a spot centroid detection algorithm and Kalman filter (KF) is proposed for spot tracking. The theoretical calculated value of the spot circle fit is filtered to obtain an optimal estimate of the spot center. The root mean square error of the detected spot centroids is used as an evaluation metric to verify the conventional algorithm and KF algorithm for the real-time tracking of the laser spot at transmission distances of 1.3, 4.1, and 10.3 km. The results show that the root mean square error of the spot in the pitch direction decreases from 0.740, 2.537, and 7.256 pixels to 0.683, 1.792, and 4.756 pixels, respectively, whereas the root mean square error of the spot in the horizontal direction decreases from 0.481, 2.131, and 5.932 pixels to 0.463, 1.471, and 4.362 pixels, respectively, compared with the conventional algorithm at three transmission distances. The envelope fluctuation of the baseband signal at the receiving end is significantly improved using KF algorithm compared with the conventional algorithm, which improves the stability of the optical wireless communication link.

Star spot centroid extraction method in high dynamic condition based on difference hash algorithm

In high dynamic conditions, star spot exhibits a tailing phenomenon, which makes it impossible to accurately extract the star centroid. Adjusting the exposure time can shorten the tail length but it will reduce the energy received by the detector, which also makes it difficult to extract the star target. Aiming at the above two problems, this paper proposes a star spot centroid extraction method under high dynamic conditions based on different hash algorithm. The method is divided into three steps. Firstly, establish a mathematical model of dynamic star spots. Then using difference hash algorithm and Hamming distance to realize coarse positioning of star targets in star tracking window. Finally, adopt threshold segmentation and connected domain method to extract star spot centroid in the coarse location area. The experimental results show that the proposed method can adapt to various exposure time, making the star sensor realize the stable tracking at the angular velocity of 3°/s. When the exposure time is 50ms and the angular velocity is 3°/s, the angular distance error is 13 arcseconds, the average extraction rate is 96%, which is 29.6% and 29.7% better than the traditional method.

Stable propagation of Ince–Gaussian vector beams through atmospheric turbulence

In this paper, we investigate the propagation properties of the Ince–Gaussian​ vector beams through atmospheric turbulence. For this type of generalized fundamental vector beams, the spatial structures of intensity and polarization are demonstrated to have the stability of transmission over kilometers. Analysis of scintillation index and spot centroid drift also supports this view. The von Kármán type index power spectrum and the resulting random phase screens are used to simulate the atmospheric turbulence model. Owing to the strong quantum-like correlation between polarization and the spatial components, the Ince–Gaussian vector beams exhibit stable photon entanglement and high inseparability. In particular, the increasing complexity of light field structure will enhance this stability of structure transmission. Higher-order Ince–Gaussian vector beams have the longer decoherence time and longer identified distance. The fourth-order Ince–Gaussian vector beams have stronger transmission stability than the third-order Ince–Gaussian vector beams. Our work contributes to the understanding of the stable propagation of the vectorial structured light and improves imaging and free-space optical communication in perturbing media.

Three-dimensional echo distribution analysis of multi-band and oblique Gaussian beams propagating through cat-eye optical system

The cat-eye effect in optical systems enables active laser detection at long distances and high orientation precision. However, few studies focus on the influence of a multi-band laser with a large incident angle on the echo distribution. This study proposes a three-dimensional echo distribution calculation model of an obliquely incident multi-band laser based on the Collins diffraction integral formula and aperture function expansion as the sum of complex Gaussian functions. The echo distributions for different detection ranges are calculated by coupling the size of the detector in a cat-eye optical system into the model. In the numerical simulation, the influences of laser wavelength, incident angle, and target detector parameter are quantitatively analysed by introducing a target-missing quantity of echo spot and peak light intensity. The results show that the peak light intensity decreases with an increase in incident laser wavelength. When the incident angle increases to a particular value, the peak light intensity decreases sharply, and the target-missing quantity of the echo spot centroid is positively correlated with the incident angle. We can effectively extract important information, such as the working band and detector size, from the cat-eye target echo using this model and provide a trajectory prediction theory for the active detection of a cat-eye target moving at high speed.

Evaluation of the Emissions State of a Satellite Laser Altimeter Based on Laser Footprint Imaging

The GaoFen-7(GF-7) satellite is equipped with China’s first laser altimeter for Earth observation; it has the capability of full waveform recording, which can obtain global high-precision three-dimensional coordinates over a wide range. The laser is inevitably affected by platform tremors, random errors in the laser pointing angle, laser state, and other factors, which further affect the measurement accuracy of the laser footprint. Therefore, evaluation of the satellite laser launch state is an important process. This study contributes to laser emission state evaluations based on the laser footprint image in terms of two main two aspects: (1) Monitoring changes in the laser pointing angle—laser pointing is closely related to positioning accuracy, which mainly results from monitoring the change in the laser spot centroid. We propose a threshold constraint algorithm that extracts the centroid of an ellipse-fitting spot. (2) Analysis of the energy distribution state—directly obtaining the parameters used in the traditional evaluation method is a challenge for the satellite. Therefore, an index suitable for evaluating the laser emissions state of the GF-7 satellite was constructed according to the data characteristics. Based on these methods, long time-series data were evaluated and analyzed. The experimental results show that the proposed method can effectively evaluate the emissions state of the laser altimeter, during which the laser pointing angle changes monthly by 0.434″. During each continuous operation of the laser, the energy state decreased gradually, with a small variation range; however, both were generally in a stable state.

Calculation of spot entroid based on physical informed neural networks

To determine the centroid of far-field laser beam spot with high precision and accuracy under intense noise contamination, a positioning algorithm named centroid-PINN is proposed, which is based on physical information neural network. A U-Net neural network is utilized to optimize the centroid estimation error. In order to demonstrate this new method, Gaussian spots polluted by two kinds of noises, i.e. ramp noise and white noise, are generated by simulation to train the neural network. The neural network is tested by two kinds of spots, i.e. Gaussian spot and Sinc-like spot. Both are predicted with high accuracy. Compared with traditional centroid method, the centroid-PINN needs no parameter tuning, especially can cope with ramp noise interference with high accuracy. This work will be conducive to developing the far-field laser beam spot measurement device, and can also serve as a reference for developing the Shack-Hartmann wavefront sensor.