Structured light system calibration with unidirectional fringe patterns

Purpose This paper aims to propose a measurement principle and a calibration method of measurement system integrated with serial robot and 3D camera to identify its parameters conveniently and achieve high measurement accuracy. Design/methodology/approach A stiffness and kinematic measurement principle of the integrated system is proposed, which considers the influence of robot weight and load weight on measurement accuracy. Then an error model is derived based on the principle that the coordinate of sphere center is invariant, which can simultaneously identify the parameters of joint stiffness, kinematic and hand-eye relationship. Further, considering the errors of the parameters to be calibrated and the measurement error of 3D camera, a method to generate calibration observation data is proposed to validate both calibration accuracy and parameter identification accuracy of calibration method. Findings Comparative simulations and experiments of conventional kinematic calibration method and the stiffness and kinematic calibration method proposed in this paper are conducted. The results of the simulations show that the proposed method is more accurate, and the identified values of angle parameters in modified Denavit and Hartenberg model are closer to their real values. Compared with the conventional calibration method in experiments, the proposed method decreases the maximum and mean errors by 19.9% and 13.4%, respectively. Originality/value A new measurement principle and a novel calibration method are proposed. The proposed method can simultaneously identify joint stiffness, kinematic and hand-eye parameters and obtain not only higher measurement accuracy but also higher parameter identification accuracy, which is suitable for on-site calibration.

The intensity distribution of fringe patterns becomes nonsinusoidal in real testing environments. Thus, the performance of existing phase shift extraction algorithms, which usually compute the desired phase shift by arccosine function or arcsine function, may be affected. In the presented paper, we report an arctangent-function-based technique to solve this disturbance. First, two orthogonal fringe patterns are constructed through subtraction and addition of two background-removed images. Second, the unequal amplitude between two new fringe patterns is eliminated using a normalization process. Third, the phase shift is determined by computing the norms of the two new images. The proposed method is fast and can be implemented easily in many applications. We verify the algorithm performance and robustness using both simulated and experimental data, indicating the high accuracy of the presented method.

Channel reciprocity is regarded as one of the most important advantages of TDD systems. However, the uplink (UL) and downlink (DL) channels are not actually reciprocal because of different characteristics of transmitters (TXs) and receivers (RXs). When the antenna elements are placed with large distance, the Radio Frequency (RF) gain mismatch of TXs and RXs is the dominant un-reciprocal factor, but if the antenna elements are placed close, such as compact antenna array, mutual coupling (MC) should be considered. In general, the MC effects for a transmitting and receiving array are different, even if the physical geometry of the array remains unchanged. Conventional reciprocity calibration methods mainly target at compensating RF gain mismatch and regard reciprocity error as diagonal matrix. However, the reciprocity error is no longer diagonal for compact antenna array due to the un-reciprocal MC of TXs and RXs, and thus the conventional calibration methods do not work in this scenario. In this paper, a comprehensive reciprocity error model is proposed firstly, and a combined MMSE and dot-division calibration scheme is then presented for calibrating MC and RF mismatch at the same time. Link level simulation results demonstrate the efficiency of the proposed scheme. The calibration method can well calibrate the UL and DL channel reciprocity, and the performance can be boosted up to around 1dB~2dB less than the ideal reciprocal case.

Deflectometry is a well-known method to characterize pure phase objects by measuring the deformation of fringes. In principle, the retrieved magnitude is the partial derivative of the phase along the coordinate orthogonal to the fringes. In order to recover the phase it is necessary to know the derivatives in two orthogonal directions, which is usually achieved by rotating 90° the original fringes and acquiring a new deformed pattern. This "time-multiplexed" two-dimensional deflectometry is a time-consuming operation if the goal is to characterize phase objects in real time. In the present paper we propose a kind of two-dimensional deflectometry that allows acquisition of fringe patterns in two orthogonal directions in a single frame. The proposed procedure utilizes a two-dimensional ("additive") fringe pattern that allows the application of Takeda's method to each coordinate independently. The advantage of the method (with respect to the traditional one) is that it simplifies the setup and reduces the acquisition time. Validation experiments are presented.

In fringe projection profilometry, system calibration serves as a critical prerequisite for ensuring measurement precision. During calibration procedures, the elimination of specular reflection-induced saturated image poses significant challenges due to inherent surface reflectance variations. Therefore, a calibration technique utilizing adaptive polarization fringe projection is proposed in this paper. The proposed method analyzes gray-level information model from the polarization camera and employs a dichotomizing search strategy to determine optimal polarization projection intensity for saturated pixels. Furthermore, precise correspondence between image pixels and projection pixels is established. Then, adaptive polarization projection fringe patterns are generated. The proposed method enables the acquisition of high-quality calibration images, effectively enhancing system calibration accuracy. Compared with conventional calibration methods under natural conditions, the proposed method improves calibration accuracy while achieving a 9.6% improvement in measurement precision.

The erosion produced by cavitation is a serious problem in hydraulic machinery. During investigations of the dynamic loading generated by collapsing cavitation on a surface, a dynamic pressure transducer was developed. The piezoelectric polymer PVDF (Polyvinylidene fluoride) was used as the pressure sensitive material. A novel method of dynamic calibration has also been developed. The transducer is loaded through pencil lead by a beam supported at its other end on a knife edge and loaded at the center by weights. As the static load is increased, the pencil lead breaks and the load is released suddenly. The unloading time is faster than for any other conventional calibration method and is of the same order as cavitation loading. Descriptions of the developments of both the calibration method and the transducer are given. The principal advantages of the new method are the short pulse duration and the simplicity of the test procedure. The paper is an extension of the previously reported work by Momma and Lichtarowicz (1994), giving further information on the operating characteristics of the transducer in comparison with the traditional ball-dropping method.

Monitoring the static and dynamic displacements of large engineering structures, such as buildings and bridges, can provide quantitative information for evaluating structural safety and maintenance purposes. Camera calibration is a key process in vision-based sensor systems for remote displacement measurement. Due to the large field of view of engineering structures, conventional camera calibration methods using precise calibration boards are difficult to apply. A modified calibration method for a binocular stereo vision system based on the epipolar constraint relationship is proposed to simplify the calibration process. Due to the absence of reference points in outdoor applications, an unmanned aerial vehicle that carries a reference marker is adopted. During its flight in the field, sequential images are captured simultaneously with the left and right imaging stations. An alternative to determine the scale factor is also proposed, which provides adequate precision for camera calibration. Two important issues are discussed, including the number of reference points and their selection with regards to the depth of view. The experimental results show that the proposed method is convenient to apply in outdoor situations and can achieve high accuracy in displacement measurement.

Structured light systems are a simple and efficient tool in the field of 3D reconstruction. Existing calibration methods of structured light systems are either not precise or elastic. In this paper, an easy to use method is proposed. The calibration of a structured light system can accomplished with a good accuracy. The projector projects a checkerboard pattern rendered by OpenGL functions onto a planar board, and the coordinates of corner points in the projector image plane are adjusted to the target position with an iterative algorithm. Thus, the projector can view the printed chessboard pattern. The calibration of a projector becomes essentially the same as that of a monocular camera. Meanwhile, the projector calibration doesn't depend on a pre-calibrated camera, which makes errors of the camera calibration cannot effect the projector calibration. Experimental results show that the mean re-projection error of the projector is less than 1 pixel.

As dense sensor networks for air quality monitoring become increasingly prevalent, effective calibration remains a critical yet challenging component of their operation, particularly for large-scale networks. Conventional calibration methods, which rely heavily on co-locating sensors with reference monitors for learning and training, often face significant scalability challenges, rendering them impractical for post-deployment recalibration. To address this limitation, we propose an in-situ baseline calibration method (b-SBS) that calibrates sensors remotely without the need for direct co-location. This approach is grounded in the physical characteristics of electrochemical sensors and is informed by statistical analyses of calibration coefficients across a large group of similar sensors. Through preliminary field tests conducted on a batch of sensors for NO2, NO, CO, and O3, two key linear calibration coefficients, sensitivity and baseline, were systematically investigated. Sensitivity analysis of over 100 short-term calibration samples for each gas revealed coefficients clustered within 20% variation, enabling universal parameterization. Long-term baseline drift remained stable within ±5 ppb for NO2, NO, and O3, and ±100 ppb for CO over 6 months, supporting semi-annual recalibration. Applying the b-SBS calibration approach to 73 NO2 sensors in a large-scale Shanghai network yielded pronounced data quality improvements compared to their original measurements (initially calibrated before deployment): the median R2 increased by 45.8% (from 0.48 to 0.70), and RMSE decreased by 52.6% (from 16.02 to 7.59 ppb), as validated against nearby reference stations. The Shanghai application, while showing the method’s potential for large-scale deployments, awaits further real-time validation to confirm its robustness under diverse operational conditions. This study is a valuable advancement in calibration strategies, offering a cost-effective solution that reduces operational costs while ensuring accurate measurements across numerous sensors and long-term network deployments.

A novel online antenna array calibration method is presented in this paper for estimating direction-of-arrival (DOA) in the case of uncorrelated and coherent signals with unknown gain-phase errors. Conventional calibration methods mainly consider incoherent signals for uniform linear arrays with gain-phase errors. The proposed method has better performance not only for uncorrelated signals but also for coherent signals. First, an on-grid sparse technique based on the covariance fitting criteria is reformulated aiming at gain-phase errors to obtain DOA and the corresponding source power, which is robust to coherent sources. Second, the gain-phase errors are estimated in the case of uncorrelated and coherent signals via introducing an exchange matrix as the pre-processing of a covariance matrix and then decomposing the eigenvalues of the covariance matrix. Those parameters estimate values converge to the real values by an alternate iteration process. The proposed method does not require the presence of calibration sources and previous calibration information unlike offline ways. Simulation results verify the effectiveness of the proposed method which outperforms the traditional approaches.

Improving the transferability of the crash prediction model using the TrAdaBoost.R2 algorithm

Radar calibration has always been essential for compensating unavoidable manufacturing inaccuracies, component variations, or aging effects in multichannel radar systems. The demand for high-resolution radars, particularly in automotive applications, necessitates increasing carrier frequencies, bandwidths, synthetic apertures, and channel counts, imposing exceptionally high calibration requirements. Conventional calibration methods often rely on expensive positioning systems and large-scale anechoic chambers, yet offer only limited calibration accuracy. This publication presents a novel calibration method that achieves exceptionally high accuracy for single-input multiple-output (SIMO) radars with uniform linear arrays (ULAs) by estimating amplitude and phase deviations as well as mutual coupling between the channels. The proposed method leverages the established theory of accumulating channel imbalances in synthetic aperture radar (SAR) processing, enabling the isolation of error power from the desired signal and noise within the image. The applied optimization minimizes only at deterministic artifact locations, which enhances the optimization sensitivity and improves calibration precision, while reducing the computational complexity. The proposed approach demonstrates high performance by calibrating an antenna array with eight elements in a 77 GHz frequency-modulated continuous wave SIMO radar. The resulting calibration quality is validated in a test scene, demonstrating significantly reduced artifacts within the generated image compared to the uncalibrated array.

An improved geometrical calibration method for stereo deflectometry by using speckle pattern

In the phase measuring deflectometry, two groups of fringe patterns in orthogonal directions are usually applied to establish the correspondences between the pixel pairs on the screen and camera. Usually, 16 phase-shifting fringe patterns with different spatial frequencies are required in order to calculate the absolute phases in the conventional temporal phase unwrapping algorithms. This requirement makes the measurement inefficient and not robust against environmental noise. In this paper, an efficient phase retrieval strategy is developed, which requires only six fringe patterns. The modulating information in one-direction is obtained by first using four fringe patterns, and then it is applied to assist the phase calculation in the other direction, so that only two extra fringe patterns are needed. Subsequently the phases are unwrapped by using the geometric constraints of the software configurable optical test system without additional image acquisition. The measurement time is saved by 5/8, compared to the conventional methods. In this way, the influence of the low-frequency disturbances can be suppressed in the workshop condition. Experiments demonstrate that the proposed method can reliably retrieve the absolute phases, and it is of significance to improve the measuring efficiency and stability of in situ deflectometry.

A structured-light system with a binary defocusing technique has the potential to have more extensive application due to its high speeds, gamma-calibration-free nature, and lack of rigid synchronization requirements between the camera and projector. However, the existing calibration methods fail to achieve high accuracy for a structured-light system with an out-of-focus projector. This paper proposes a method that can accurately calibrate a structured-light system even when the projector is not in focus, making it possible for high-accuracy and high-speed measurement with the binary defocusing method. Experiments demonstrate that our calibration approach performs consistently under different defocusing degrees, and a root-mean-square error of about 73 μm can be achieved with a calibration volume of 150(H) mm×250(W) mm×200(D)mm.