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Three-dimensional (3D) reconstruction technology has found widespread applications across various domains, including intelligent driving and underwater exploration. But the existing imaging systems and methods still have deficiencies in terms of reconstruction accuracy, detection distance and system volume. Herein, this paper presents a three-dimensional detection and reconstruction method based on a compact Risley-prism 3D imaging system that achieves multi-viewpoint imaging by rotating the Risley prism to adjust the camera’s optical axis. A refractive camera model that integrates the pinhole camera model with the vector form of Snell’s law is established to precisely describe beam trajectory. A forward projection method suitable for refractive interfaces is developed based on Fermat’s principle, and the influence of systematic errors on the reconstruction is analyzed in detail through simulation. Furthermore, a new 3D reconstruction method combining error calibration based on the optimization iteration is introduced to avoid the influence of error and improve reconstruction quality. Experimental results demonstrate that the proposed approach markedly enhances 3D reconstruction accuracy, reducing the Normalized Root Mean Square Error (NRMSE) from 0.9076 to 0.0207.

The use of optically pumped magnetometers (OPMs) has provided a feasible, moveable and wearable alternative to superconducting detectors for magnetoencephalography (MEG) measurements. Recently, the widely used beamformer imaging technique has greatly improved spatial accuracy of MEG in the field of source reconstruction of neuroimaging. The spatial resolution of the source reconstruction using beamformer imaging technique was explored in the present study. The spatial accuracy of a beamformer reconstruction depends on accurate estimation of the data covariance matrix and lead field. In practical measurements, many sensor calibration errors including the gain error, crosstalk and angular error of the sensitive axis of OPMs due to for example, the low frequency magnetic field drift will distort the measured data as well as the forward model and thus reduce spatial resolution. The theory of OPM calibration errors was first provided based on the Bloch equations. The calibration errors are then quantified using the self-developed OPM array. And an analytical relationship between the Frobenius norm of the covariance matrix error and gain error, crosstalk was derived. The relationship between point-spread function (PSF) and the forward model error caused by the angular error of sensitive axis was analyzed. Finally, the effects of calibration errors on spatial resolution of OPM-MEG were investigated using simulations of two dipoles with orthogonal signals at the source level based on realistic head models. We find the presence of calibration errors will decrease the spatial resolution of beamformer reconstruction. And this decrease will become more severe as the signal-to-noise ratio increases. •An analytical relationship between calibration errors of OPMs and point-spread function was developed.•The OPM calibration errors are analysed theoretically and quantified experimentally.•Effects of calibration errors related to uniaxial and biaxial OPMs on spatial resolution were investigated.

A laser tracker is an essential tool in the field of precise geometric measurement. Its fundamental operating idea is a dual-axis rotating device that propels the laser beam to continuously align and measure the attitude of a collaborating target. Such systems provide numerous benefits, including a broad measuring range, high precision, outstanding real-time performance, and ease of use. To solve the issue of low beam recovery efficiency in typical laser trackers, this research offers a two-dimensional laser tracking system that incorporates a machine vision module. The system uses a unique off-axis optical design in which the distance measuring and laser tracking paths are independent, decreasing the system’s dependency on optical coaxiality and mechanical processing precision. A tracking head error calibration method based on singular value decomposition (SVD) is introduced, using optical axis point cloud data obtained from experiments on various components for geometric fitting. A complete prototype system was constructed and subjected to accuracy testing. Experimental results show that the proposed system achieves a relative positioning accuracy of less than 0.2 mm (spatial root mean square error (RMSE) = 0.189 mm) at the maximum working distance of 1.5 m, providing an effective solution for the design of high-precision laser tracking systems.

Factory-calibrated continuous glucose monitoring (FC-CGM) sensors are new devices used in type 1 diabetes (T1D) therapy to measure the glucose concentration almost continuously for 10–14 days without requiring any in vivo calibration. Understanding and modelling CGM errors is important when designing new tools for T1D therapy. Available literature CGM error models are not suitable to describe the FC-CGM sensor error, since their domain of validity is limited to 12-h time windows, i.e., the time between two consecutive in vivo calibrations. The aim of this paper is to develop a model of the error of FC-CGM sensors. The dataset used contains 79 FC-CGM traces collected by the Dexcom G6 sensor. The model is designed to dissect the error into its three main components: effect of plasma-interstitium kinetics, calibration error, and random measurement noise. The main novelties are the model extension to cover the entire sensor lifetime and the use of a new single-step identification procedure. The final error model, which combines a first-order linear dynamic model to describe plasma-interstitium kinetics, a second-order polynomial model to describe calibration error, and an autoregressive model to describe measurement noise, proved to be suitable to describe FC-CGM sensor errors, in particular improving the estimation of the physiological time-delay.

In computerized adaptive testing (CAT), item parameter estimates derived from calibration studies are considered to be known and are used as fixed values for adaptive item selection and ability estimation. This is not completely accurate because these item parameter estimates contain a certain degree of error. If this error is random, the typical CAT procedure leads to standard errors of the final ability estimates that are too small. If the calibration error is large, it has been shown that the accuracy of the ability estimates is negatively affected due to the capitalization on chance problem, especially for extreme ability levels. In order to find a solution for this fundamental problem of CAT, we conducted a Monte Carlo simulation study to examine three approaches that can be used to consider the uncertainty of item parameter estimates in CAT. The first two approaches used a measurement error modeling approach in which item parameters were treated as covariates that contained errors. The third approach was fully Bayesian. Each of the approaches was compared with regard to the quality of the resulting ability estimates. The results indicate that each of the three approaches is capable of reducing bias and the mean squared error (MSE) of the ability estimates, especially for high item calibration errors. The Bayesian approach clearly outperformed the other approaches. We recommend the Bayesian approach, especially for application areas in which the recruitment of a large calibration sample is infeasible.

Magnetoencephalography (MEG) systems based on optically pumped magnetometers (OPMs) have rapidly developed in the fields of brain function, health, and disease. Functional connectivity analysis related to the resting-state has gained popularity as a field of research in recent years. Several studies have attempted to use OPM-based MEG (OPM-MEG) for brain network estimation research; however, the choice of source connectivity analysis pipeline may lead to outcome variability. Several methods and related parameters must be selected carefully at each step of the analysis. Therefore, this study assessed the effect of such analytical variability on the OPM-MEG connectivity analysis by conducting simulations. Synthetic MEG data corresponding to two default mode networks (DMN) with six or ten DMN regions were generated using the Gaussian Graphical Spectral (GGS) model. Six intersensor spacings were constructed, and six inverse algorithms and six functional connectivity measures were selected to assess their impact on the network reconstruction accuracy. Three potential sources of error – errors in the sensor gain, crosstalk, and angular errors of the sensitive axis of the OPM – were also assessed. Analytical variability with regard to the tested intersensor spacings, inverse solutions, and functional connectivity measures led to high result variability. Crosstalk exerted a significant impact on the accuracy, which may lead to network reconstruction failure. The accuracy improvement caused by an increase in the sensor density may be reduced by gain and angular errors. The minimum norm estimate (MNE) and weighted minimum norm estimate (wMNE) exhibited low robustness to sensor noise and calibration errors. Hence, a calibration workflow for accurate sensor parameters, such as the gain and direction of the sensitive axis, before commencing OPM-MEG measurement and a careful choice of different method combinations play crucial roles in ensuring that OPMs yield optimal results for functional connectivity analysis. A thorough framework for analyzing brain connectivity networks was provided herein. •We designed a resting-state networks (DMN) simulation and analysis protocol.•Effect of channel density, inverse solutions and connectivity metrics on OPM-MEG connectivity reconstruction accuracy was assessed.•Effect of OPM calibration errors on results variability of connectivity reconstruction was investigated.

Efficient, precise and automated in-process calibration schemes are essential to improve the accuracy and productivity of five-axis machine tools. This paper presents a new calibration approach, which combines an on-machine measurement cycle and self-calibration techniques, to evaluate the position errors and the error motions of a rotary axis using a touch trigger probe and an uncalibrated cylindrical artefact. This significantly reduces the downtime of machine tools required for the calibration process. In contrast to many common calibration strategies for rotary axes of five-axis machine tools, the presented self-calibration concept does not neglect the positioning errors of the linear axes when identifying the position errors and the error motions of the rotary axis. The self-calibration procedure is able to separate the positioning errors of the linear axes in radial direction, and the radial error motions and the position errors of a rotary axis, as well as the errors related to the uncalibrated artefact. This error separation is realized by a test cycle consisting of four tests in which the measurements are conducted by particular axis movements. Furthermore, an uncertainty analysis of the self-calibration concept is conducted to visualize the uncertainty propagation within the mathematical model. The self-calibration procedure is analyzed by an experimental evaluation, which includes a comparison between the results of the self-calibration approach and an R-Test. This comparison shows that the results of both measurement procedures are consistent.

The paper introduces a new automatic drilling and riveting system for aircraft panel assembly which is composed of two five-axis machines in coordination. Kinematic modeling and base frame calibration are fundamental problems for the dual-machine system to improve its positioning accuracy. In this paper, a comprehensive kinematic model for the dual-machine system is established based on the modularization concept, and a new base frame calibration method is proposed which consists of the direct calibration based on laser tracker and calibration error compensation based on a specially designed instrument. In the kinematic modeling stage, the kinematic model of the dual-machine system is divided into three parts and three corresponding sub-models are established. With the pose constraints of coordinated machines, a comprehensive kinematic model of the dual-machine system is built. In the base frame calibration stage, the base frames of dual machines are firstly established by laser tracker. Due to many error sources in the calibration process, the relative pose errors of dual machines exist with the relationship between the base frames of coordinated machines. Then, the calibration error is measured by a specially designed instrument and used to modify the primary base frame calibration results. To verify the validity of the proposed method, experiments have been performed and the results have shown great improvement in base frame calibration accuracy. With the advantage of easy operation and high accuracy, this method can be extended to other multi-machine and multi-robot systems.

Digital Beamforming SAR (DBF-SAR) provides high-resolution wide-swath imaging capability, yet it is affected by inter-channel amplitude, phase and time-delay errors induced by temperature variations and random error factors. Since all elevation channel data are weighted and summed by the DBF module in real time, conventional record-then-compensate approaches cannot meet real-time processing requirements. To resolve the problem, a real-time calibration architecture for Intermediate Frequency DBF (IFDBF) is presented in this paper. The Field-Programmable Gate Array (FPGA) implementation estimates amplitude errors through simple summation, time-delay errors via a simple counter, and phase errors via single-bin Discrete-Time Fourier Transform (DTFT). The time-delay and phase error information are converted into single-tone frequency components through Dechirp processing. The proposed method deliberately employs a reduced-length DTFT implementation to achieve enhanced delay estimation range adaptability. The method completes calibration within tens of PRIs (under 1 s). The proposed method is analyzed and validated through a spaceborne simulation and X-band 16-channel DBF-SAR experiments.

In this paper, we consider the gain-phase error calibration problem for uniform linear arrays (ULAs). Based on the adaptive antenna nulling technique, a new gain-phase error pre-calibration method is proposed, requiring only one calibration source with known direction of arrival (DOA). In the proposed method, a ULA with M array elements is divided into M−1 sub-arrays, and the gain-phase error of each sub-array can be uniquely extracted one by one. Furthermore, in order to obtain the accurate gain-phase error in each sub-array, we formulate an errors-in-variables (EIV) model and present a weighted total least-squares (WTLS) algorithm by exploiting the structure of the received data on sub-arrays. In addition, the solution to the proposed WTLS algorithm is exactly analyzed in the statistical sense, and the spatial location of the calibration source is also discussed. Simulation results demonstrate the efficiency and feasibility of our proposed method in both large-scale and small-scale ULAs and the superiority to some state-of-the-art gain-phase error calibration approaches.