Calibration Plate Research Articles

On-site calibration of underwater stereo vision based on light field

In underwater stereo vision calibration, the refractive index of water varies with the depth, temperature and salinity, and the position relationship between the two cameras varies with the deformation of the equipment in the water, so these two parameters need to be calibrated according to the scene. In this paper, an on-site calibration of underwater stereo vision is proposed to adapt to the changes of refractive index of water and the relative position between the two cameras. A method based on coplanar constraint in view of light field is proposed to determine the initial value of the underwater refractive index. After obtaining the initial value, an optimal objective function is constructed to optimize the whole underwater stereo vision system, which can reduce the error caused by the change of relative position between two cameras due to deformation of the device. The proposed method is easy to operate and the calibration can be completed by taking a calibration plate only once in the measured water area.

A novel circular points-based self-calibration method for a camera’s intrinsic parameters using RANSAC

Intrinsic parameters in camera calibration are commonly solved with high precision using the homography matrix of space coordinates and image coordinates of a template. However, in practice the accuracy in the extraction of corner points of the calibration plate is usually affected by the lighting environment, leading to obvious fluctuation in the calibration results. This study proposes a novel self-calibration method to improve the calibration accuracy and reduce the instability of calibration results by using circular points and the RANdom SAmple consensus (RANSAC) method. The circular points for the intrinsic parameters are calculated using the cross-ratio method with a calibration plate containing nine corner points. The distance between the circular points and image of the absolute conic is defined. The threshold value of the RANSAC model is simulated by a computer. The intrinsic parameters are initially estimated using the unreliable calibrating images excluded by the RANSAC method. The definition of the threshold is based on the Sampson estimation. The maximum likelihood estimation method is performed to reestimate the intrinsic parameters and optimize the calibration result. The findings of the numerical simulations and experiments on wing-fuselage docking based on monocular vision demonstrate that the proposed method is more robust and efficient at improving the calibration accuracy than the traditional methods. The measurement error is reduced to less than 0.013 mm when the calibration algorithm is applied to actual applications such as wing-fuselage docking.

Differential astrometric framework for the Jupiter relativistic experiment with Gaia

Abstract We employ differential astrometric methods to establish a small field reference frame stable at the microarcsecond (μas) level on short time-scales using high-cadence simulated observations taken by Gaia in 2017 February of a bright star close to the limb of Jupiter, as part of the relativistic experiment on Jupiter’s quadrupole. We achieve subμas-level precision along scan through a suitable transformation of the field angles into a small-field tangent plane and a least-squares fit over several overlapping frames for estimating the plate and geometric calibration parameters with tens of reference stars that lie within ∼0.5 deg from the target star, assuming perfect knowledge of stellar proper motions and parallaxes. Furthermore, we study the effects of unmodelled astrometric parameters on the residuals and find that proper motions have a stronger effect than unmodelled parallaxes, e.g. unmodelled Gaia DR2 proper motions introduce extra residuals of ∼23 μas (AL) and 69 μas (AC) versus the ∼5 μas (AL) and 17 μas (AC) due to unmodelled parallaxes. On the other hand, assuming catalogue errors in the proper motions and parallaxes such as those from Gaia DR2 has a minimal impact on the stability introducing subμas and μas level residuals in the along and across scanning direction, respectively. Finally, the effect of a coarse knowledge in the satellite velocity components (with time-dependent errors of 10 μas s−1) is capable of enlarging the size of the residuals to roughly 0.2 mas.

Robust calibration method for microscopic vision systems

In order to improve the stability of the calibration method based on a single parallel plane, we propose a robust calibration method based on the calculation of traditional homography matrix and Gaussian imaging model. This method first uses a convenient and accurate method to calculate the physical focal length of the entire microscope optical system, and then uses the Gaussian imaging model to calculate the effective focal length and intrinsic matrix of the camera. Then, the camera’s extrinsic parameters can be easily calculated from the homography matrix. Finally, all camera parameters can be optimized along with the lens distortion through a nonlinear optimization process. In this method, only two images of the parallel calibration plate need to be captured to complete the calibration. The proposed method overcomes the problem of instability of the existing microscope calibration methods and significantly improves the robustness and accuracy of the whole calibration process.

High-Precision Measurement of Binocular Telecentric Vision System With Novel Calibration and Matching Methods

In stereo vision-based three-dimensional measurements, calibration, and stereo matching are the most challenging tasks for accurate three-dimensional reconstruction. The traditional binocular vision algorithm has low precision, and we propose a binocular vision system using a telecentric lens. In this paper, we propose a calibration and matching algorithm for the telecentric binocular vision system, which collects only two pictures of the calibration plate to complete the system calibration. The algorithm is a special application of 3D reconstruction. In this paper, if the measurement points are selected as points on the grid, the appropriate extension can be used for high-precision 3D reconstruction, which will be explained in detail in the experiments. In order to reduce the calibration error and obtain high maneuverability, the binocular vision system is only calibrated once with a two-dimensional calibration board, and the depth information is obtained through the parallax of the detection process, so as to effectively simplify the calibration process and reduce the errors introduced in the calibration process. For the matching of images in the right and left cameras, the polar theory of telecentric binocular vision system is constructed according to the characteristics of telecentric lens imaging model based on the traditional binocular vision system theory. The matching algorithm only needs to apply the two-dimensional calibration information and then calculates the results according to the parallax combined with the polar line matching algorithm, which simplifies the algorithm flow and reduces the error. In this paper, experiments show that the algorithm proposed is simple and has high precision, good stability, and high-practical value.

Flexible calibration method of an FPP system based on a geometrical model and NLSM with fewer parameters.

Fringe projection profilometry (FPP) technology is an important method for 3D reconstruction. In this paper, we proposed a flexible calibration method of an FPP system based on the imaging principle and geometrical structure of the system. The target coordinates are only related to its pixel coordinates and phase. First, the fringe images are projected onto the calibration plate, and the phase can be calculated through the four-step phase-shifting method. Then, the pixel coordinates of the feature points can be located with the binarized fringe images and the centroid method. Finally, the calibration parameters are calculated by the nonlinear least-squares method (NLSM). The reconstructed experiment of 162 testing points was carried out, and the result shows that the maximum relative errors on coordinates X, Y, and h are 0.27%, 0.42%, and 0.59%, respectively. The other two surface reconstruction experiments also verify the feasibility of the calibration method.

Multi-camera calibration for accurate geometric measurements in industrial environments

Accurate camera calibration is a challenging task required for 3D reconstruction sensors. In structured light sensors based on laser line projection, it is necessary to determine the position and orientation of the camera relative to the laser plane. The standard approach based on laser plane fitting requires a difficult setup, particularly in multi-camera configurations. This work proposes a calibration method based on a calibration plate with protruding cylinders. The projection of the laser line on the calibration plate produces a set of partial contours of ellipses, resulting from the projection of the cross section of the cylinders. These contours are used to calculate the position and orientation of the camera accurately. The proposed procedure is divided in two steps: a coarse calibration based on a robust estimator, which provides a rough approximation, and a fine calibration that iteratively optimizes the solution. The result is an accurate and robust procedure that can be applied to multiple cameras simultaneously on devices with limited computational power. Extended tests are used to validate the procedure with test pieces. Results indicate the calibration can be performed in 30 ms, producing a calibration error of only 0.027 mm.

Camera calibration method based on optimal polarization angle

The accurate estimation of camera internal and external parameters is one of the keys to high-precision camera calibration. At present, the mainstream Zhang's calibration method requires the use of a checkerboard to achieve high-precision calibration result. Therefore, the precise extraction of the pixel coordinates at the corner points on the checkerboard is one of the key technologies. The traditional methods are to improve the corner extraction algorithm, but ignore the imaging process of the calibration images. It is difficult to detect and eliminate the high-light regions in the process of calibrating image, and the existence of high-light regions will cause low accuracy of camera calibration. Therefore, a camera calibration method based on optimal polarization information is proposed in this paper. The method first uses a Stokes variable linear feedback through a CCD camera equipped with a polarizer to obtain a checkerboard calibration image at an optimal polarization angle in different spatial positions. Then use the sub-pixel level detection algorithm and Gaussian fitting method to locate the corner points in the image and to solve the sub-pixel coordinates of the corner points precisely. At last, the two-dimensional pixel coordinates of the corner points in each checkerboard image are extracted to perform camera calibration. The experimental results show that the coordinates of corner points of calibration plate image based on the optimal polarization angle have about 1 pixel difference compared with the coordinates of the calibration plate corner points under natural illumination, and the slopes between the parallel lines of the fitted are closer, meet the high precision calibration requirement of camera.

Camera calibration method based on phase encoding for out-of-focus condition

The state-of-art camera calibration method requires the user to provide accurate pixel coordinates of calibration plate feature points. For some cameras with special sensing range, general calibration objects' (such as calibration plates with a centimeter-long dimension) using range is outside their clear sensing range. Using these cameras to take a picture for general calibration objects, you can only get out-of-focused blurred images that can not accurately extract feature points' pixel coordinates. This paper analyzes the influence on the phase of the structured light based on sine grating (abbreviated as sinusoidal structured light) when optical system is in defocus state. Based on the fact that the state of focus is independent of the phase of sinusoidal structured light, a method of phase-shifted sinusoidal structured light encoding by phase shift is proposed to encode the feature points on the calibration object and this method realizes the calibration of the camera under out-of-focus condition. The experimental results show that the maximal deviation of focal length from the real value is 0.47% and the maximal pixel reprojection error is 0.17 pixels. This paper provides a solution to camera calibration with a special sensing range.

The Design and Characteristics of a 630-mm Phase-Shifting Interferometer

A large-aperture Fizeau interferometer has been developed for measuring the characteristics of optical elements with flat surfaces. The interferometer has two fields of view with dimensions of 630 and 100 mm and with transverse resolutions of 0.63 and 0.1 mm/pixel, respectively. Due to the calibration of the reference plates, the absolute measurement accuracy of the interferometer is λ/1000 RMS (λ = 632.8 nm) on a 630-mm field of view.

The Requirements for the Calibration Conditions in Large-Aperture Fizeau Interferometers

The problems that arise during the calibration of the reference plates of large-aperture interferometers are discussed and the methods for solving them are presented. It is shown that the repeatability of shapes of the reference plates after their rearrangements can be provided by selecting the mechanism of their fixing in place. It is demonstrated that the temperature deformations of the reference-plate surfaces can be determined from a numerical model. These measures have made it possible to calibrate the reference plates of the 630-mm interferometer with an accuracy of λ/1000 RMS (λ = 632.8 nm).

Real-Time Inspection of Long Steel Products Using 3-D Sensors: Calibration and Registration

Calibration and registration are two challenging tasks required by a real-time inspection system for long steel products based on multiple three-dimensional sensors. Spatial calibration is required to transform the information acquired by each sensor into a common reference system. Registration is used to align the calculated shape with the model of the product being inspected, which enables the calculation of quality control parameters. This paper proposes efficient solutions for these two problems. Calibration is performed using a specially designed calibration plate that can be used to detect the position and orientation of each sensor. Registration is applied using an analytic alignment between the data and the model. The proposed methods are specially designed to perform accurately in industrial environments where inspection systems are exposed to adverse conditions, such as dust, oil, or water, which provoke noise in the signals. Moreover, vibrations affect the position of the inspected product randomly, which makes accurate measurements much more difficult to achieve. The proposed procedures are validated with extensive tests using real and simulated data showing excellent performance.

К вопросу о реконструкции остаточных напряжений и деформаций пластины после дробеструйной обработки

Предметом исследования является математическое описание формы и напряженно-деформированного состояния стальной пластины, подвергнутой односторонней дробеструйной обработке, его экспериментальное подтверждение и применение результатов для верификации методов реконструкции полей остаточных напряжений и деформаций по экспериментальным данным. Подобная пластина используются на производстве в качестве калибровочного образца для определения времени пневмодробеструйной обработки, необходимого для формирования в поверхностном слое обрабатываемого изделия сжимающих тангенциальных остаточных напряжений заданной величины, а сам метод калибровки оказывается удобным и довольно широко распространенным для различных способов поверхностно упрочняющей обработки. Источником остаточных напряжений в данном случае является пограничный слой пластических деформаций, наводимый рассматриваемым технологическим процессом. Для постановки задачи задается структура поля тензора пластических деформаций. Форма и напряженно-деформированное состояние упругой пластины с пограничным слоем пластических деформаций были рассчитаны численно, в результате чего были выявлены качественные особенности данных полей, ослаблены граничные условия задачи и сформулированы гипотезы о структуре решения соответствующей пространственной задачи теории упругости, которое далее было найдено аналитически. Показано, что в рамках приближения плоского напряженного состояния в поперечных направлениях результат точно соответствует формуле Давиденкова - Биргера, связывающей зависимость тангенциальной компоненты остаточных напряжений от координаты по толщине пластины с функцией прогибов. Получена явная формула для зависимости остаточной (пластической) деформации от координаты по толщине. Проанализированы источники погрешностей полученных выражений и способы их коррекции. Проведен эксперимент по односторонней дробеструйной обработке калибровочной пластины, изготовленной из закаленной стали 65Г, для которой выполнено травление обработанной поверхности с измерением изменения стрелы прогиба (метод Н. Н. Давиденкова). С помощью полученных экспериментальных данных были численно реконструированы профили остаточных напряжений и деформаций с разумной точностью. Результат применим к широкому классу задач для упругих тел с упрочняющими покрытиями, а также имеет определенную методическую ценность для усовершенствования основ экспериментального исследования таких задач, позволяет формулировать и подтверждать экспериментом гипотезы о структуре решения, изучать связь рассматриваемых полей в предельных случаях, верифицировать применение различных способов учета остаточных напряжений и деформаций в численных расчетах. Найденное решение может быть использовано для верификации полей напряжений и перемещений при выборе различных вариантов предварительно напряженных или деформированных поверхностных оболочечных конечных элементов в рамках пакетов прикладных программ для расчета усталостной долговечности деталей машин с поверхностными упрочняющими покрытиями и также представляется опорным для исследования поверхностно упрочненных тел с криволинейной свободной границей, к которым сводится большинство практически важных задач.

Concurrent prediction of ground reaction forces and moments and tibiofemoral contact forces during walking using musculoskeletal modelling

Ground reaction forces and moments (GRFs and GRMs) measured from force plates in a gait laboratory are usually used as the input conditions to predict the knee joint forces and moments via musculoskeletal (MSK) multibody dynamics (MBD) model. However, the measurements of the GRFs and GRMs data rely on force plates and sometimes are limited by the difficulty in some patient's gait patterns (e.g. treadmill gait). In addition, the force plate calibration error may influence the prediction accuracy of the MSK model. In this study, a prediction method of the GRFs and GRMs based on elastic contact element was integrated into a subject-specific MSK MBD modelling framework of total knee arthroplasty (TKA), and the GRFs and GRMs and knee contact forces (KCFs) during walking were predicted simultaneously with reasonable accuracy. The ground reaction forces and moments were predicted with an average root mean square errors (RMSEs) of 0.021 body weight (BW), 0.014 BW and 0.089 BW in the antero–posterior, medio–lateral and vertical directions and 0.005 BW•body height (BH), 0.011 BW•BH, 0.004 BW•BH in the sagittal, frontal and transverse planes, respectively. Meanwhile, the medial, lateral and total tibiofemoral (TF) contact forces were predicted by the developed MSK model with RMSEs of 0.025–0.032 BW, 0.018–0.022 BW, and 0.089–0.132 BW, respectively. The accuracy of the predicted medial TF contact force was improved by 12% using the present method. The proposed method can extend the application of the MSK model of TKA and is valuable for understanding the in vivo knee biomechanics and tribological conditions without the force plate data.

Development of a contact-type probe for measurements of ultra-fine-pitch gears and application to pseudo roughness evaluation

Gears used in actuators for robot articulations are showing a trend toward having smaller modules. Thus, profile measurements of small module gears are strongly desired. Our aim was to develop a probe artifact that enables ultra-fine-pitch cylindrical gears to be measured, by minimizing the size of the probe head. The configurations of the contact-type probe and holder were designed under consideration of interference with an adjacent tooth during profile measurements of an objective tooth. After manufacturing the artifact, a 0.1-module spur gear was measured as a trial, and reasonable results were obtained. In addition, a calibration plate for roughness was measured using the developed probe artifact. The evaluated roughness showed a strong correlation with the “true roughness”. Therefore, the developed probe can be expected to enable “pseudo” roughness to be evaluated.

Laboratory Calibration of Impact Plates for Measuring Gravel Bed Load Size and Mass

AbstractContinuous monitoring of gravel transport in rivers is necessary for understanding the effect of dam removal on river systems. Impact plates, such as those deployed on the Elwha River in th...

A novel dual-camera calibration method for 3D optical measurement

A novel dual-camera calibration method is presented. In the classic methods, the camera parameters are usually calculated and optimized by the reprojection error. However, for a system designed for 3D optical measurement, this error does not denote the result of 3D reconstruction. In the presented method, a planar calibration plate is used. In the beginning, images of calibration plate are snapped from several orientations in the measurement range. The initial parameters of the two cameras are obtained by the images. Then, the rotation and translation matrix that link the frames of two cameras are calculated by using method of Centroid Distance Increment Matrix. The degree of coupling between the parameters is reduced. Then, 3D coordinates of the calibration points are reconstructed by space intersection method. At last, the reconstruction error is calculated. It is minimized to optimize the calibration parameters. This error directly indicates the efficiency of 3D reconstruction, thus it is more suitable for assessing the quality of dual-camera calibration. In the experiments, it can be seen that the proposed method is convenient and accurate. There is no strict requirement on the calibration plate position in the calibration process. The accuracy is improved significantly by the proposed method.

Wearable inertial sensor based parametric calibration of lower-limb kinematics

In this study, the calibrations of the lower-limb kinematics based on the five wearable IMU sensors were performed to reduce the inherent kinematic errors due to the both incorrect measurements of the kinematic parameters and the uncertainties of the geometric modeling of the lower-limb joints. Unlike the actual body structure, the ankle and knee joint of the lower-limb part are generally modeled as pure revolute joints of two or three degrees of freedom with some assumptions. However, it is obvious that these mismatches in the simplified geometrical modeling of the joint in the lower-limb kinematics lead to uncertainties in the model-based 3D motion tracking of human body such as walking velocity estimation, gait analysis, etc. As main research contributions, we intended to examine exactly which error factors are responsible for the kinematic uncertainties that arises from the 3D motion tracking based on the lower-limb kinematics and wearable IMU sensors. The lower-limb kinematics model in this research assumes that the ankle, knee, and hip joints are all three degrees of freedom, and that the three principle axes at each joint may not intersect at a common point. That is, the kinematic uncertainties included in the joint model will be confirmed by performing a kinematic calibration taking into account the orientation of joint axes and joint offsets as kinematic error parameters as well as the case of only calibrating the link lengths. This study also uses a new calibration plate with seven sole-shaped jigs and five wearable IMU sensors to measure the actual pose of the right foot, which is the distal end of the lower-limb kinematics with respect to the left foot. In order to secure an in-depth insight into the wearable IMU sensor based calibrations of the lower-limb kinematics, the seven sole-shaped jigs were designed to independently allow the right foot on those jigs to have predefined 3-dof poses. Finally, an iterative least square method is adopted to minimize the error between the nominal kinematic model-based pose and the actual poses of the right foot with respect to the left foot on the calibration plate. In an experiment with one subject, the reduction rate of the position error depends on the measurement of the initial kinematic parameters, but the RMS position error of the right foot relative to the left foot was improved by 336.1% from 36.5mm to 11.3mm.

In-situ force plate calibration: 12 years’ experience with an approach for correcting the point of force application

Force plates are common assessment tools used in biomechanics to measure ground reaction forces during motion capture or strength exercises. While the accuracy of the resulting kinetic data is critical for accurate gait analysis, factors such as plate mounting are thought to influence the measured point of force application (PFA) of the ground reaction forces. The aim of this study was therefore to present an accurate in-situ PFA calibration method. In addition, the approach was evaluated by examining the required PFA corrections over a period of ten years, which included plate remounting and a change of foundation.The in-situ PFA calibration was performed on six plates by assessing the locations of up to 98 points of force application per plate using an instrumented pole. Application of the in-situ PFA calibration approach reduced the root mean square errors by up to approximately 60% compared to the manufacturers calculation. Correction coefficients were strongly dependent on the individual platform as well as the location of the applied force on the plate. Remounting of the plates altered the plate coefficient corrections considerably, while changes over time were notable but not as extensive. We therefore recommend that plates should be recalibrated after remounting, but also at least every 5 years, in order to ensure the preservation of an accurate PFA.

Fabrication of calibration plate for total internal reflection fluorescence microscopy using roll-type liquid transfer imprint lithography

A strong demand exists for the visualization of the fluid flow in microchannels, such as those in labs-on-a-chip. Multilayer nanoparticle image velocimetry (MnPIV) is a promising technique for this purpose, wherein the x- and y-positions of a nanoparticle are measured using a camera and its z-position is estimated via its fluorescence intensity. To accurately estimate the z-position, however, MnPIV requires a fluorescence intensity calibration process. Water is typically used in the microfluidic devices and a nanoscale level with a refractive index matching method is conventionally used for the calibration of MnPIV. Therefore, a calibration plate with nanoscale levels whose refractive index is matched to water is necessary to calibrate the z-position of fluorescent particles in water. In this study, a fabrication technique of the calibration plate was performed using ultraviolet (UV) nanoimprint with a UV-curable resin, whose refractive index is matched to water and which possesses a high viscosity of 2900cps. Although the residual layer thickness (RLT) of the level must be less than 100nm to perform MnPIV, it is challenging to reduce the RLT with such a high viscosity of the resin using conventional UV nanoimprint lithography. To reduce the RLT, therefore, in this study roll-type liquid-transfer imprint lithography (LTIL) was used with the high-viscosity UV-curable resin, where a two-fold repetition of the roll-type LTIL process demonstrated a calibration pattern RLT of 40nm or less. As a result, calibration of the MnPIV system was achieved with the calibration plate developed herein and fabricated by UV nanoimprint lithography.