Calibration Plate Research Articles

Research on the Hand–Eye Calibration Method of Variable Height and Analysis of Experimental Results Based on Rigid Transformation

In view of the phenomenon that camera imaging will appear large up close and small from afar in the eye-to-hand hand-calibration system, one hand–eye calibration is carried out. The manipulator is only suitable for grasping objects of the same height, and the calibration results cannot be applied to grasping products with variable height. Based on the study of the pinhole camera model and the rigid transformation model between coordinate systems, the introduction of the calibration height parameters, the relationship between parameters of the rigid transformation matrix between image the coordinate system and the robot coordinate system, and sampling height are established. In the experiment, firstly, through the calibration of camera parameters, the influence of camera distortion on imaging quality is eliminated, and the influence of calibration height is ignored. Then, the machine coordinate system and image coordinate system of the calibration plate at different heights are calibrated using the four-point calibration method. The parameters of the rigid transformation matrix at different heights (H) are calculated. Finally, through experimental analysis, the high linear relationship between the parameters of the rigid transformation matrix from the image coordinate system to the robot coordinate system and the calibration height is fitted. By analyzing the random error of the experiment, the linear relationship between calibration height and pixel density is further established, and the systematic error of the experimental process is deeply analyzed. The experimental results show that the hand–eye calibration system based on this linear relationship is precise and suitable for grabbing products of any height, and the positioning error is less than 0.08%.

Research on the global calibration of the multi-vision line structured light measurement system based on auxiliary camera

<p indent="0mm">To solve the problem of the absence of a common field of view between the cameras in the existing multi-vision line structured light measurement system, which leads to high requirements for calibration tools and complicated global-calibration process, a global-calibration method for the multi-vision line structured light measurement system based on an auxiliary camera is introduced to achieve a large-field-of-view measurement. First, an auxiliary camera is used as an intermediary to acquire an approximately one-half overlapped field of view with the line structured light sensor, which can constitute a binocular subsystem. Then, the spatial geometric relationship between the auxiliary camera and two adjacent line structured light sensors is established based on the different pose images of the calibration plate. Second, the position relationship between the two adjacent line structured light sensors without a common field of view is solved using coordinate transformation. Finally, the transformation matrix from a local to a global coordinate system is solved one at a time to complete the global calibration process. The requirement in terms of calibration tools of the proposed calibration method is low. Further, it does require the use of high-precision measuring equipment and complex targets but only requires a simple chessboard target to complete the global calibration of a multi-vision line structured light measurement system. Meanwhile, the calibration process can achieve high calibration accuracy. Meanwhile, the measurement experiment demonstrates that the global calibration error of this method is <sc>0.067 mm,</sc> which effectively improves the measurement accuracy and can guarantee the required accuracy for the integration of “measurement and machining” of large components using robots.

A Stereo Calibration Method of Multi-Camera Based on Circular Calibration Board

In the application of 3D reconstruction of multi-cameras, it is necessary to calibrate the camera used separately, and at the same time carry out multi-stereo calibration, and the calibration accuracy directly affects the effect of the 3D reconstruction of the system. Many researchers focus on the optimization of the calibration algorithm and the improvement of calibration accuracy after obtaining the calibration plate pattern coordinates, ignoring the impact of calibration on the accuracy of the calibration board pattern coordinate extraction. Therefore, this paper proposes a multi-camera stereo calibration method based on circular calibration plate focusing on the extraction of pattern features during the calibration process. This method preforms the acquisition of the subpixel edge acquisition based on Franklin matrix and circular feature extraction of the circular calibration plate pattern collected by the camera, and then combines the Zhang’s calibration method to calibrate the camera. Experimental results show that compared with the traditional calibration method, the method has better calibration effect and calibration accuracy, and the average reprojection error of the multi-camera is reduced by more than 0.006 pixels.

Binocular camera calibration based on timing correction.

Camera calibration is crucial to the application of binocular measurement. However, many of the calibrations are carried out manually, so shaking of the calibration plate cannot be avoided. When the cameras are not synchronized or the exposure time is inconsistent, the image acquisition time of different cameras does not correspond strictly, which will introduce inevitable calibration errors. In this paper, two consecutive frames are collected instead of one frame, and the calibration data are corrected by the image acquisition time value returned by the camera. Experiments show that the proposed method can greatly reduce the re-projection error of calibration, and achieve higher calibration accuracy and less image quantity dependence.

Research on the calibration method of a new multifunctional calibrator based on AACMM

Calibrators can effectively improve the calibration accuracy of articulated coordinate measuring machine (AACMM). However, the traditional calibration method of a calibrator is usually cumbersome. To study the influence of sampling strategies of various calibration methods on the calibration effect of AACMM, we design a new multifunctional calibrator for AACMM kinematics parameters, and propose three calibration methods with high accuracy and high efficiency. In the multifunctional calibrator, 84 different calibration points are provided by changing the rotation angle of calibration bar and the inclination angle of calibration plate. Compared with previous calibrators, the calibrator can obtain more positions and directions. The length calibration, multi-point calibration and virtual center distance calibration methods are proposed to calibrate kinematic parameter of AACMM. In addition, the sampling strategy for the three calibration methods is explored. Finally, the consistency of single-axis coordinate measurement is verified based on the three calibration methods. The results show that the three calibration methods can effectively improve the measurement accuracy of AACMM. Especially, the length calibration method has the highest accuracy of the three methods. The multi-point calibration method can significantly improve the calibration efficiency.

A Simple Calibration Method for a Fringe Projection System Embedded within an Additive Manufacturing Machine

In additive manufacturing (AM), especially for advanced powder fusion machines, it is of high importance to develop an in situ inspection system to monitor the printed surface and pre-print powder bed as the build cycle proceeds. Consequently, high resolution, high precision and fast detection measurement systems need to be investigated, as such optically based measurement systems can provide feedback for manufacturing process optimisation. Fringe projection technology has a great advantage in the measurement of topography in such environments. The implementation of a fringe projection system requires that the system is pre-calibrated in order to obtain high measurement resolution and repeatability. This paper presents a simple calibration method for an AM-based in situ fringe projection system using a phase-depth calibration model. If a calibration plate with certificated marks is used, however, the texture of the plate will affect the measured phase accuracy. A simple calibration method to reduce the calibration plate texture effect in the process of calibration is outlined. Experimental results show that the proposed method can eliminated these effects and improve measurement resolution and repeatability. The proposed in situ/in process inspection technique has been implemented within a commercial electron beam powder bed fusion additive manufacturing machine (EBAM), to demonstrate the capability for effective feedback during the manufacturing process.

Calibration correction of arbitrary optical distortions by non-parametric 3D disparity field for planar and volumetric PIV/LPT

In this study, a new image calibration approach is presented that corrects arbitrary optical distortions by utilizing non-parametric, 3D disparity fields. A calibration plate with a high spatial resolution (i.e., high density of calibration marks) was used to identify optical distortions that remain after the initial calibration, which were then used to create a correction field for the pinhole or polynomial mapping functions. Results from a pipe flow experiment with four cameras using volume self-calibration (VSC) and Shake-the-Box Lagrangian particle tracking (STB LPT) are presented and the impact of the improved calibration is discussed. Using the calibration marks with the correction field, distortions of initially more than 20 pixels are reduced below 1 pixel. Using VSC with the correction field allows further reduction of average calibration disparities below 0.02 pixels (maximum 0.5 pixels), whereas without a correction field the remaining average disparity is much higher at 1 pixel (maximum 5 pixels). STB analysis of the data shows a considerable higher spatial resolution at the pipe wall and a consistent spatial distribution of the number of detected particles in the measurement volume.

Point-to-point coupling and imbalance correction in color fringe projection profilometry based on multi-confusion matrix

Fringe projection profilometry (FPP) has been widely used in three-dimensional (3D) profile measurements for its efficiency and high accuracy. As an offshoot of FPP, color fringe projection profilometry (CFPP) has the advantage of being dynamic, non-contact, and full-field, which makes it one of the most valuable 3D profile measurement techniques. However, phase errors may arise in CFPP when the phase is retrieved by phase-shifting algorithms. This is due to the gamma nonlinear response, color coupling, and color imbalance of electro-optical devices. In this paper, a multi-confusion matrices (MCM) correction technique is proposed to reduce the phase error by compensating the captured color fringe pattern intensity. This can be accomplished in three steps. Firstly, project 30 ~ 220 (with the step of ten gray levels) uniform intensity patterns on a calibration plate, and then extract the intensity information to construct multi-confusion matrices (MCM) and LUTs (look up tables). Secondly, search optimal confusion matrix (OCM) from MCM to correct the fringe pattern. Finally, retrive the unwrapping phase using the corrected fringe pattern. The simulation and experimental results indicate that the proposed approach can reduce phase errors and use one color fringe pattern to reconstruct 3D topography.

Investigation of pixel scale calibration on the Elekta iView electronic portal imager.

This study investigated the variation in electronic portal imager pixel scale at the isocenter plane for Elekta Agility linear accelerators. An in‐house MATLAB script was written to process and calculate the pixel scale based on a metal calibration plate supplied by Elekta. Eight pixel plates were compared and found to have manufacturing tolerances within 0.1 mm of nominal dimensions. The impact of these variations on pixel scale factor was negligible, and plates could be used interchangeably. Uncertainties from other parameters such as source‐to‐surface distance and user variability summed to a combined uncertainty of 0.0003 mm/pixel, compared to a pixel scale range of 0.003 mm/pixel measured across 10 machines. Most of the inter‐machine variation was shown to be attributable to differences in source‐to‐panel distance. Other factors such as focal spot size and shape, electronic portal imager manufacturing consistency, panel sag, and setup errors may account for the residual variation. Individual characterization of machine and imaging panel pixel scale factors is important to ensure accurate geometric information is derived from electronic portal images, which is critical where the portal imager is used for multi‐leaf collimator calibration or other clinical tasks.

Angular Calibration of Visible and Infrared Binocular All-Sky-View Cameras Using Sun Positions

Visible and infrared binocular all-sky-view cameras can provide continuous and complementary ground-based cloud observations. Accurate angular calibration for every pixel is an essential premise to further cloud analysis and georeferencing. However, most current calibration methods mainly rely on calibration plates, which still remains difficult for simultaneously calibrating visible and infrared binocular cameras, especially with different imaging resolutions. Thus, in this study, we present a simple and convenient angular calibration method for wide field-of-view visible and infrared binocular cameras. Without any extra instruments, the proposed method only utilizes the relation between the angular information of direct sun lights and the projected sun pixel coordinates to compute the geometric imaging parameters of the two cameras. According to the obtained parameters, the pixel-view-angle for the visible and infrared all-sky images is efficiently computed via back projection. Meanwhile, the projected pixel coordinates for the incident lights at any angle can also be computed via reprojection. Experimental results show the effectiveness and accuracy of the proposed angular calibration through the error estimation of reprojection and back projection. As a novel application, we successfully achieve visible and infrared binocular image registration at the pixel level after finishing angular calibration, which not only verifies the accuracy of calibration results, but also contributes to further cloud parameter analysis under these two different imaging features. The registration results, to our knowledge, also provide a reference for the current blank in visible and infrared binocular cloud image registration.

Algorithm optimization of cross-interfaces computed tomography into full field.

Tomographic approaches in confined space require advanced imaging algorithms that can properly consider the refractive distortion as the imaging rays pass through the optical wall. Our previous work established an algorithm (cross-interfaces computed tomography, CICT) and practically solved tomographic problems in confined space. However, critical restriction was found in CICT, which is that images simulated at small azimuth angles are contaminated with noticeable signal loss and become unusable. Based on this recognition, this work has developed an improved tomography approach, namely, full-field cross-interfaces computed tomography (FCICT), to extend the available view angles to all perspectives. The key to this approach involves the 3D domain discretization using voxel parallelepipeds instead of traditional voxel layers to establish the ray-tracing relationship between imaging planes and the measurement domain. The imaging process of FCICT is first validated by quantitatively comparing the grid imaging locations in measured and simulated projections of a calibration plate. By evenly distributing the view angles in the whole azimuth angle range, the FCICT reconstruction is then numerically validated by reconstructing a simulated double-cone flame phantom. The reconstruction presents a high correlation coefficient of ${\sim}{98}\%$ with the original phantom. Finally, the FCICT is employed to reconstruct an ethylene-air premixed flame. Comparisons show that re-projections generated by the FCICT reconstruction are in accordance with measured flame images, with the mean correlation coefficients of more than 95%.

Commissioning of optical surface imaging systems for cranial frameless stereotactic radiosurgery.

PurposeThis study aimed to evaluate and compare different system calibration methods from a large cohort of systems to establish a commissioning procedure for surface‐guided frameless cranial stereotactic radiosurgery (SRS) with intrafractional motion monitoring and gating. Using optical surface imaging (OSI) to guide non‐coplanar SRS treatments, the determination of OSI couch‐angle dependency, baseline drift, and gated‐delivered‐dose equivalency are essential.MethodsEleven trained physicists evaluated 17 OSI systems at nine clinical centers within our institution. Three calibration methods were examined, including 1‐level (2D), 2‐level plate (3D) calibration for both surface image reconstruction and isocenter determination, and cube phantom calibration to assess OSI‐megavoltage (MV) isocenter concordance. After each calibration, a couch‐angle dependency error was measured as the maximum registration error within the couch rotation range. A head phantom was immobilized on the treatment couch and the isocenter was set in the middle of the brain, marked with the room lasers. An on‐site reference image was acquired at couch zero, the facial region of interest (ROI) was defined, and static verification images were captured every 10° for 0°–90° and 360°–270°. The baseline drift was assessed with real‐time monitoring of the motionless phantom over 20 min. The gated‐delivered‐dose equivalency was assessed using the electron portal imaging device and gamma test (1%/1mm) in reference to non‐gated delivery.ResultsThe maximum couch‐angle dependency error occurs in longitudinal and lateral directions and is reduced significantly (P < 0.05) from 1‐level (1.3 ± 0.4 mm) to 2‐level (0.8 ± 0.3 mm) calibration. The MV cube calibration does not further reduce the couch‐angle dependency error (0.8 ± 0.2 mm) on average. The baseline drift error plateaus at 0.3 ± 0.1 mm after 10 min. The gated‐delivered‐dose equivalency has a >98% gamma‐test passing rate.ConclusionA commissioning method is recommended using the 3D plate calibration, which is verified by radiation isocenter and validated with couch‐angle dependency, baseline drift, and gated‐delivered‐dose equivalency tests. This method characterizes OSI uncertainties, ensuring motion‐monitoring accuracy for SRS treatments.

High-precision and Arbitrary Arranged Projection Moiré System Based on an Iterative Calculation Model and the Self-calibration Method

Background As a full-field optical metrology, projection moire approach has been widely used in many engineering applications. The modeling of moire system and the calibration, including the calibration of relationship between the moire phase and object’s height, and the calibration of optical system parameters, are the key points in this method as they directly determine the measurement accuracy and complexity of operations. Objective In this paper, a projection moire system is established and the axes of the projector and the camera are arbitrary. Methods The moire model is modified based on the idea of iteration to reach a higher precision in describing the topography of the surface. A system calibration method is implemented by adopting a self-calibration approach. Both the projection system and reception system can be parameterized accurately and conveniently, as the error caused by the misalignment of the reference plane and the calibration plate is eliminated. Results The feasibility and accuracy are validated through simulations and experiments. Results show that the proposed methods can reduce the systematic error and simplify the complex of operation effectively. Conclusions By adopting the two methods, the precision and applicability of the established system are greatly improved.

Method of simultaneous calibration of dual view 3D measurement system

In view of the limitations of the existing methods when the camera has no common field of view, this paper proposes a method of using two plane calibration plates to calibrate two cameras at the same time. By deriving the coordinate transformation between the two cameras and two calibration plates, the solution of the relative pose relationship between any camera and the reference camera is transformed into a more mature hand-eye calibration equation. The experimental results show that this method can achieve simultaneous calibration of two cameras, and the absolute error is less than 0.089 mm. In the dual vision 3D measurement system, the cumulative error with phase height is less than 0.116 mm, which can provide a reliable initial value for the next step of data fusion.

Measurement of the beam diameter at the polarimeter for quartz control plate calibration

The Knife Edge method was used to measure the diameter of a HeNe laser beam in the sample position of the high resolution polarimeter at Diopt. The acquired data profile was fitted to an equation and from the fitting parameters the diameter was calculated. The resulting laser beam diameter value obtained is a part of the polarimeter full characterization.

Calibration of imaging plates sensitivity to high energy photons and ions for laser-plasma interaction sources

Imaging plates are widely used in laser-plasma interaction experiments for detection of electrons, x-ray, gamma-ray, ions, and neutrons, therefore, the calibration of imaging plates to different types of ionizing and non-ionizing radiation is vital. In this paper, a universal response function of FUJI BAS-TR imaging plate is presented using experiment and Monte-Carlo simulation with respect to high-energy photons and ions. The sensitivity of imaging plate sensitivity to x-ray radiation was examined using radioactive Co-60 isotope. Furthermore, the fading and decay mechanism affected by phosphor stimulated process were also investigated by employing the high energy gamma-rays produced in laser-plasma experiment. Finally, an ion spectrometer was designed to examine the IP response to different ion energies during a laser-driven plasma experiment. The universal relation given, can be used to evaluate the response of the imaging plate against any other types of radiation.

Binocular vision calibration method for a long-wavelength infrared camera and a visible spectrum camera with different resolutions.

We present a calibration plate for the binocular vision system, which is composed of a long-wavelength infrared camera and a visible spectrum camera with different resolutions. The calibration plate mainly consists of a white low-temperature aluminum plate with 7×7 round through-holes, a black high-temperature stainless steel plate, and a heating plate. It can be captured by the long-wavelength infrared camera and visible spectrum camera simultaneously. In order to reduce the influence of thermal crosstalk on the edge and angle sharpness of the thermal image of the chessboard calibration plate, we use the round through-holes to replace the black-white squares in the chessboard calibration plate. Based on the fabricated calibration plate, we also propose a related calibration method. The proposed method can quickly detect the calibration plate by using the YOLO-V4 neural network. The affine transformation is performed to get the front view of the calibration plate, and a novel circular detection strategy based on arc level instead of pixel-level is adopted to detect the edges of the round through-holes in the calibration plate. The centers of round through-holes are detected, and the parameters of the cameras are calculated according to the coordinates of the centers in the image coordinate system. The simulation experiments and error analysis have been done to verify the centers detection method. The simulation results show that the error of center detection is always less than 1.4 (pixel). In order to further verify the performance of the calibration plate and the proposed calibration method, a binocular vision system based on long-wavelength infrared camera and visible spectrum camera is fabricated, and the verification experiments have been done. In experiments, our calibration plate and the proposed method are compared with the famous Zhang's method. The calibration's average overall mean errors of the visible spectrum camera and long-wavelength infrared camera are about 0.0126 (pixel) and 0.0238 (pixel), and they are respectively decreased by 78.13% and 81.93% compared with Zhang's method. The re-projection error of the binocular vision system is about 0.548 (pixel), which is decreased by 24.52% compared with Zhang's method. The average calibration time of the proposed method is about 0.26s.

A Model of Diameter Measurement Based on the Machine Vision

If the shaft diameter can be measured in-situ during the finishing process, the closed-loop control of the shaft diameter processing process can be realized and the machining accuracy can be improved. Present work studies the measurement of shaft diameter with the structured light system composed of a laser linear light source and a camera. The shaft is a kind of part with rotationally symmetric structure. When the linear structured light irradiates the surface of the shaft, a light stripe will be formed, and the light stripe is a part of the ellipse. Therefore, the in-situ measurement of the shaft diameter can be realized by the light stripe and the rotational symmetry of the shaft. The measurement model of shaft diameter is established by the ellipse formed by the intersection of the light plane and the measured shaft surface. Firstly, in the camera coordinate system, normal vector of the light plane and the coordinates of the ellipse center are obtained by the calibration; then, the equation of oblique elliptic cone is established by taking the ellipse as the bottom and the optical center of the camera as the top. Next, the measurement model of shaft diameter is obtained by the established oblique elliptic cone equation and theoretical image plane equation. Finally, the accuracy of the measurement model of shaft diameter is tested by the checkerboard calibration plate and a lathe. The test results show that the measurement model of shaft diameter is correct, and when the shaft diameter is 36.162mm, the speed is 1250r/min, the maximum average measurement error is 0.019mm. The measurement accuracy meets the engineering requirement.

Research and evaluation of the measurement uncertainty with the two-dimensional optical calibration plate

As a portable standard, two-dimensional optical calibration plate is playing an increasingly important role in precision industry measurement. Therefore, it is of great scientific significance and obvious socioeconomic benefits to carry out the research of comparator. This paper was based on rich experience with the institute in the field of the geometric measurement technology for a long time, the measurement uncertainty of the optical calibration plate was studied, and the measurement uncertainty of the instrument has been researched. The measurement uncertainty of the error of the calibration plate’s setting and marking value was U= (0.14+ 0.015L) m k=2 L: mm.

Calibration of Structured Light Scanning System

Abstract On the basis of studying the calibration method of the camera and the rotating platform, we designed an automatic camera calibration scheme based on four azimuth circles, which can realize the automatic sorting of the mark points. In order to improve the efficiency of identifying the center of the calibration plate, this paper uses RANSAC to improve the RED ellipse center detection algorithm. Experimental verification shows that the improved RED algorithm has increased 29.34% in anti-noise interference ability and 30.10% in center detection accuracy, which effectively guarantees the measurement stability and accuracy of the measurement system. Then, with the aid of the designed calibration board, we fit the rotation center of the turntable using the principle of three points in a circle, which provides a basis for the subsequent point cloud splicing. Experiments show that the back-projection error of the calibration method in this paper is less than 1 pixel, and the calibration accuracy is better than Zhang’s algorithm.