Three-dimensional Calibration Research Articles

Refraction correction for deep-water three-dimensional visual measurement based on multi-objective optimization.

Refraction-induced errors affect the accuracy of three-dimensional visual measurements in deepwater environments. In this study, a binocular camera refractive imaging model was established, and a calibration method for the refraction parameters was proposed for high-accuracy shape and deformation measurements in deep-water environments. First, an initial estimate of the refractive axis was obtained using a three-dimensional calibration target. Then, the errors in the distance between the spatial point pairs and the reprojection errors are taken as the dual optimization objectives, and the Non-dominated Sorting Genetic Algorithm II is applied to optimize the refraction parameters. To efficiently calculate the reprojection error, an improved numerical computation method is proposed to accelerate the calculation of the analytical forward projection. Underwater experiments were conducted to verify the method's effectiveness. The results showed that the average error of the absolute position of the reconstructed points was less than 1.1 mm and the average error of the displacement was less than 0.04 mm. This study provides a sound solution for accurate three-dimensional visual measurement in deep-water environments.

Development and application of automatic monitoring equipment for differential deformation of element joint in immersed tunnel

The reliability of the immersed tunnel element joint is the key to determine whether the immersed tunnel can operate safely. At present, the immersed tunnel monitoring mostly pays attention to the joint opening and closing amount and neglects the differential deformation of the joint. Based on the immersed tunnel of Hong Kong-Zhuhai-Macao Bridge, combined with the operating environment and structural characteristics of the immersed tunnel, this paper introduces a close-range photogrammetry method to monitor the differential deformation of the immersed tunnel element joint. Through theoretical analysis, software and hardware development, laboratory test and field test, the paper puts forward puts forward a comprehensive multi-parameter evaluation and screening algorithm of boundary fitting ellipse based on fitting rate, ellipticity and area difference and a micro-displacement correction algorithm for camera based on three-dimensional calibration object, and develops an automatic monitoring system equipment for differential deformation of immersed tunnel element joint. Upon tests in tunnels, the monitoring equipment is proven in automatic monitoring on differential deformation of immersed tunnel element joints. This equipment has been successfully applied to the E31~E32 element joint of Hong Kong-Zhuhai-Macao Bridge immersed tunnel, which verifies the effectiveness of the equipment from the perspective of practical engineering application.

A Three-Dimensional Calibration and Reconstruction Method Using Omnidirectional Cameras with Control Points of Unknown Coordinates

A Three-Dimensional Calibration and Reconstruction Method Using Omnidirectional Cameras with Control Points of Unknown Coordinates

Time resolved trace element calibration strategies for LA-ICP-MS

Three-dimensional calibration surfaces, along with downhole fractionation corrections, can provide improved accuracy for trace element concentration analysis by LA-ICP-MS.

Fast and precise laser beam scanning by nonperiodic grating on a binary micromirror array

We report a precise and stable laser beam positioning method with a high scanning speed by a pixelated binary grating (PBG) realized by a compact on-off state digital micromirror device (DMD). The overall procedure for PBG pattern generation is proposed, analyzed, and experimentally verified. The resulting performances correspond to an angular resolution of 0.01 deg and angular repeatability of ± 2.54 × 10 − 4 deg over a beam steering range of ± 7.5 deg. The scanning speed of 40 deg/s is achieved in continuous scanning with a resolution of 0.01 deg. Arbitrary positions can be targeted in the scanning range with DMD’s frame rate of 4000 Hz. To verify its applicability in precision metrology, absolute distances to multiple off-axial targets were determined in parallel with a high speed. This method will open a wider application of DMD in precision LIDARs, three-dimensional calibration of precision machines, and high-resolution laser patterning.

Stereoscopic PIV measurements in a two-stage axial turbine

In the present work, the three-dimensional flow field in the interstage region of a twostage axial turbine has been measured by a stereoscopic PIV system. The stereoscopic method is used to compensate for perspective as well as to observe the highly threedimensional flows. The digital images are recorded with a set of two cameras positioned perpendicularly to the measurement plane and inclined by an angle varying between 22° and 30° to allow stereoscopic measurements. The laser beam is delivered to a laser endoscope able to access the measurement areas. By traversing radially, several blade-to-blade planes can be illuminated with the laser endoscope from 66 to 96% blade span. To compensate for the perspective distortion of the field of view due to the tilt angle of camera B as well as the optical distortion through the double-curvature windows, a threedimensional calibration method is used. In the current investigation, a Monte Carlo simulation has been conducted to evaluate measurement errors of PIV. Results of these measurements are compared with velocities derived from time resolved pressure measurements using fast aerodynamic response probe (FRAP). A good agreement is found at the exit of the second rotor. The present work present a unique set of steady and unsteady data measured in a two-stage axial turbine. Measured data in a volume can be used for numerical tool validation as well as improve existing kinematic model of vortex transport and dissipation.

Three-dimensional videography using omnidirectional cameras: An approach inspired by the direct linear transformation method

Direct linear transformation (DLT) is one of the most frequently used methods in motion analysis. This method was developed in 1971 and has subsequently been used in numerous studies. However, owing to the structure of the camera, unfavorable challenges are associated with this method. Because the DLT method is based on the structure of ordinary optical cameras in which the perspective projection is used, the camera’s angle of view is limited. In this study, we propose a three-dimensional (3-D) calibration and reconstruction method using omnidirectional cameras, which have significantly wider angles of view than conventional cameras. For the interest points, the longitude and latitude of the celestial sphere are obtained from the image captured with an omnidirectional camera. The direction of the interest points relative to the camera’s reference frame is determined via the longitude and latitude. In the calibration phase, the position and orientation of the omnidirectional camera relative to the global reference frame are determined from the image of the control points with known 3-D coordinates. In the reconstruction phase, the intersection point of the rays from the cameras is determined. Using an evaluation experiment, we verified the accuracy of the proposed method. The wide angle of view provided by omnidirectional cameras can be fully exploited using this method.

Novel method to accurately align the laser sheet for planar and stereoscopic PIV

Several techniques including two-dimensional (2D) and three-dimensional (3D) calibration are used for the calibration of two-component two-dimensional (2C-2D) particle image velocimetry (PIV) and three-component two-dimensional (3C-2D) stereoscopic PIV (SPIV) systems. A major requirement of these techniques is to keep the calibration target exactly at the position of the laser sheet within the field of view (FOV), which is very difficult to achieve (Raffel et al., 2018). In 3C-2D SPIV, several methods offer different correction schemes based on the disparity between the FOV of two stereo cameras produced due to misalignment, to account for the misalignment error. These techniques adjust the calibration or the measured displacement field in different ways to reduce the error which may introduce an unintended error in the measurement position and/or velocity such as a bias in the measured three-component 3C displacements. This paper introduces a novel method to align the laser sheet with the calibration target so that the uncertainty in displacement measurements is minimal. Ideally, it should be of the order of the uncertainty associated with PIV measurement so that no ad hoc post-correction scheme is required.

Verification of a calibration method for 3D screw thread metrology

The novel approach for holistic screw thread calibrations developed by the Physikalisch-Technische Bundesanstalt was published in 2019. A significant achievement has been made in order to meet increasing demands in manufacturing processes and quality assurance, particularly when workpieces with complex geometries are under inspection. This article deals with the verification of the previously presented three-dimensional calibration procedure for screw threads. Screw thread pitch diameters, the lead and flank angles are compared to those determined by the standardized method based on line-like, rather two-dimensional measurements and evaluation. In order to provide a reliable basis for the verification, one thread gauge was calibrated under laboratory conditions for precision metrology. Additionally, calibrations were conducted by three alternating operators on three different coordinate measuring machines to investigate the influence by user and machine. The resulting normalized errors of screw thread determinants under test and reference values are significantly smaller than 0.5 which indicates a high level of agreement.

Research on Robot Hand-Eye Calibration Method Based on Three-Dimensional Calibration Block

Research on Robot Hand-Eye Calibration Method Based on Three-Dimensional Calibration Block

Measurements of the 277 nm photon detection efficiency of the OnSemi MicroFJ-60035 silicon photomultiplier

The article describes a method for absolute calibration of the photon detection efficiency of the OnSemi/SensL MicroFJ-60035 silicon photomultiplier by the Newport Power/Energy Meter 841-PE with the 883-UV photodiode sensor head, and the PicoQuant PLS-270 fast diode source of 277 nm ultraviolet emission. The dependences of the power of the detected emission and the number of ultraviolet photons on the distance to the source were obtained. The photon detection efficiency of the silicon photomultiplier was measured to be approximately 8% compared to the 9.6% level claimed by the manufacturer. It was also shown that, within the experimental setup, absorption of the 277 nm emission at paths in the air shorter than 1 m is not significant, and the angular distribution of the emission source is homogeneous. The obtained three-dimensional calibration surface of the dependence of the irradiance on the distance to the detector and the source intensity will be employed for development of a novel camera of the TAIGA-IACT telescope array.

Camera calibration and orientation for PCB jet printing inspection

To assess the quality of printed solder joints in the jet printing of printed circuit boards, a calibrated camera is used to reconstruct the solder volume via photogrammetry as a specific task of computer vision. This requires a procedure for calibration and orientation determination due to restrictions within the image acquisition process. We herein consider a novel application area called an ultra-close range normal case photogrammetry, where a camera acquires small objects at small operating distances and fields of depth. Because the camera cannot rotate or translate in the z-direction, we propose and evaluate four calibration procedures in terms of their capability in a normal case calibration within the ultra-close range. To set up an optimal calibration pipeline, a three-dimensional (3D) calibration field is used for single and multi-image calibrations. To enhance the accuracy and to simplify the assignment of 3D coordinates to the detected markers, we propose a geometry-based estimation of the lens model to undistort the image points. Close-range applications utilize spacer rings and extension tubes to enlarge the magnification and reduce the operating distance. We also examine the influence of these extensions on the intrinsics of the camera and the reconstruction result. Additionally, we demonstrate the dependence of the accuracy on the lens model in terms of radial and tangential distortions and the number of distortion coefficients regarding the reprojection error epsilon _{repro}. Finally, we provide recommendations for a lens configuration for ultra-close range normal case calibrations and measurements, based on the calibration and reconstruction results, which are evaluated by the 2D reprojection error epsilon _{repro} and the 3D reconstruction error epsilon _{recon} obtained from a second independent calibration field.

Three-Dimensional Calibration for Routine Analyses of Bromide and Nitrate Ions as Indicators of Groundwater Quality in Coastal Territories

Nitrate and bromide ions are generally considered indicators of anthropogenic pollution and seawater intrusion, respectively, in the groundwater of coastal territories. The analysis of these species is generally carried out with routine chromatographic analyses which generally afford partially merged or poorly resolved peaks. In the present paper a simple method for the correct evaluation of their concentration in water is reported. This method does not imply utilization of other instruments or technologies, only the mathematical elaboration of the data obtained from routine analysis of standard solutions containing the two species. Standard binary solutions of nitrate and bromide ions at different concentrations, ranging between 0.1 and 2 mM, were analyzed by means of ion chromatography. Splitting two partially merged chromatographic peaks and considering each resulting area as originating from a single species produces “measured” concentration values which differ from the nominal ones. Such a procedure generates errors (one per species) which can be written as a function of the above mentioned “measured” concentrations and which can be graphically represented by means of a surface in a three-dimensional (3D) space. In this way, “measured” concentrations of bromide and nitrate ions can be corrected by calculating the errors generated under the experimental conditions at which the chromatographic separation is performed. Notably, this is analogous with the two-dimensional (2D) calibration normally carried out for analytical purposes. Indeed, both methods allow estimation of the unknown concentration of species in solution by correlating the instrumental response with the concentration of standard solutions.

Store Separation: Photogrammetric Solution for the Static Ejection Test

The process of developing and certifying aircraft and aeronautical systems requires the execution of experimental flight test campaigns to determine the actual characteristics of the system being developed and/or validated. In this process, there are many campaigns that are inherently dangerous, such as the store separation. In this particular case, the greatest risk is the collision of the store with the fuselage of the aircraft. To mitigate the risks of this campaign, it is necessary to compare the actual trajectory of a separation with its simulated estimates. With such information, it is possible to decide whether the next store release can be done with the required safety and/or whether the model used to estimate the separation trajectory is valid or not. Consequently, exact determination of the trajectory of the separation is necessary. Store separation is a strategic, relevant, and complex process for all nations. The two main techniques for determining the quantitative store trajectory data with 6DoF (six degrees of freedom) are photogrammetry and instrumented telemetry packages (data obtained from inertial sensors that are installed in the store). Each presents advantages and disadvantages. In regard to photogrammetry, several market solutions can be used to perform these tests. However, the result of the separation trajectory is only obtained after the test flight, and therefore, it is not possible to safely carry out more than one on the same flight. In this context, the development and validation of a solution that will allow the realization of near real-time separation analysis are in fact an innovative and original work. This paper discusses the development and validation, through actual static ejection tests, of the components that will compose a new onboard optical trajectory system for use in store separation campaigns. This solution includes the implementation of a three-dimensional (3D) calibration field that allows calibration of the optical assembly with just one photo per optical assembly, development of a complete analytical model for camera calibration, and development of specific software for identification and tracking of targets in two-dimensional (2D) coordinate images and three-dimensional (3D) coordinate trajectory calculation. In relation to the calibration, the analytical model is based on a pinhole type camera and considers its intrinsic parameters. This allowed for a mean square error smaller than ±3.9 pixels @1σ. The 3D analysis software for 6DoF trajectory expression was developed using photogrammetry techniques and absolute orientation. The uncertainty associated with the position measurement of each of the markers varies from ±0.02 mm to ±8.00 mm @1σ, depending on the geometry of the viewing angles. The experiments were carried out at IPEV (Flight Test Research Institute)/Brazil, and the results were considered satisfactory. We advocate that the knowledge gained through this research contributes to the development of new methods that permit almost real-time analysis in store separation tests.

Research on multi-camera calibration and point cloud correction method based on three-dimensional calibration object

The single camera measurement system can't obtain all the surface information of the object limited by the field of view, thus it can't achieve complete measurement of the object. Multi-camera system can overcome this difficulty. But it is difficult to unify the coordinate system of distinct cameras. In order to solve this problem, a global calibration method of multi-camera system is proposed. A three-dimensional cube calibration object is designed. Every camera is only calibrated on one surface of the cube calibration object. Because different surfaces of the cube calibration object are in a unified world coordinate, the coordinates of the feature points on different surfaces are naturally in the unified world coordinate system. Thus global calibration can be completed by calibrating multiple cameras at the same time. In addition, to minimize the error of calibration, a correction method is proposed. The correction parameters are obtained by the deviation between the world coordinates and the reconstructed coordinates of the feature points on calibration object. The parameters are applied to the measurement to improve the accuracy of the whole point cloud. Experiments are carried out on a multi-camera measurement system, and the results show that the method proposed in this paper is effective and feasible.

Group geometric calibration and rectification for circular multi-camera imaging system

Calibration on multi-camera imaging system in circular arrangement is a challenge task, because the preliminary shared feature points are absent among opposite viewpoints in the calibration procedure. In this paper, we propose a scheme of group geometric calibration and ideal rectification for circular multi-camera imaging system. In this scheme, a three-dimensional (3D) calibration object with new patterns is firstly designed to extract the extrinsic parameters. After that, the ideal camera projection matrix is estimated based on these parameters. Finally, we extend our scheme from static to dynamic scenario. In the experiments, our method has a superior performance over state-of-the-art calibration methods. Furthermore, we verify our scheme by application of 3D modeling and improvements can also be found. These results demonstrate that our method performance on such imaging system is applicable for future interactive visual applications.

Single-image calibration method for multiple virtual binocular vision system

The virtual binocular vision system (VBVS) based on single camera and mirrors has been paid increasing attention, with the advantages of high flexibility and compactness. However, in its calibration process, the conventional methods require several images and obtain different intrinsic parameters, which should be identical between different virtual cameras. To simplify the calibration process and obtain identical intrinsic parameters, a single-image calibration method for the VBVS based on one camera and mirrors is proposed. Through the single image including multiple sub-images of the calibration planes, the intrinsic parameters and distortion coefficients can be obtained. Then, the global calibration of multiple virtual binocular structures can be performed efficiently. To test the performance of the proposed approach, a VBVS composed of four pairs of virtual binocular structures was designed and the calibration experiments were performed using an artificial three-dimensional calibration target. Moreover, an accuracy comparison with the conventional method was carried out. The results exhibited the feasibility of this method and proved its accuracy.

Discriminating between Different Heavy Metal Ions with Fullerene-Derived Nanoparticles.

A novel type of graphene-like nanoparticle, synthesized by oxidation and unfolding of C60 buckminsterfullerene fullerene, showed multiple and reproducible sensitivity to Cu2+, Pb2+, Cd2+, and As(III) through different degrees of fluorescence quenching or, in the case of Cd2+, through a remarkable fluorescence enhancement. Most importantly, only for Cu2+ and Pb2+, the fluorescence intensity variations came with distinct modifications of the optical absorption spectrum. Time-resolved fluorescence study confirmed that the common origin of these diverse behaviors lies in complexation of the metal ions by fullerene-derived carbon layers, even though further studies are required for a complete explanation of the involved processes. Nonetheless, the different response of fluorescence and optical absorbance towards distinct cationic species makes it possible to discriminate between the presence of Cu2+, Pb2+, Cd2+, and As(III), through two simple optical measurements. To this end, the use of a three-dimensional calibration plot is discussed. This property makes fullerene-derived nanoparticles a promising material in view of the implementation of a selective, colorimetric/fluorescent detection system.

Extrinsic Calibration of a Laser Galvanometric Setup and a Range Camera.

Currently, galvanometric scanning systems (like the one used in a scanning laser Doppler vibrometer) rely on a planar calibration procedure between a two-dimensional (2D) camera and the laser galvanometric scanning system to automatically aim a laser beam at a particular point on an object. In the case of nonplanar or moving objects, this calibration is not sufficiently accurate anymore. In this work, a three-dimensional (3D) calibration procedure that uses a 3D range sensor is proposed. The 3D calibration is valid for all types of objects and retains its accuracy when objects are moved between subsequent measurement campaigns. The proposed 3D calibration uses a Non-Perspective-n-Point (NPnP) problem solution. The 3D range sensor is used to calculate the position of the object under test relative to the laser galvanometric system. With this extrinsic calibration, the laser galvanometric scanning system can automatically aim a laser beam to this object. In experiments, the mean accuracy of aiming the laser beam on an object is below 10 mm for 95% of the measurements. This achieved accuracy is mainly determined by the accuracy and resolution of the 3D range sensor. The new calibration method is significantly better than the original 2D calibration method, which in our setup achieves errors below 68 mm for 95% of the measurements.

Functional range of motion in the metacarpophalangeal joints of the hand measured by single axis electric goniometers.

The functional range of motion (fROM) of the metacarpophalangeal (MCP) joints during the performance of activities of daily living (ADL) has not yet been established. This study aimed to determine the fROM of all five digits and verify the accuracy and reproducibility of dynamic angle measurement using a single-axis electric goniometer (EG) during ADL movements of the hand. This was a cross-sectional study. In EG suitability testing, we first confirmed the angles of a three-dimensional calibration device 10 times, and then compared EG readings with those determined by tomosynthesis images. Next, we determined the fROM of the MCP joints by evaluating all five digits of the dominant hands of 10 healthy adults performing 16 ADL. Intra-rater reproducibility of MCP joint data during task performance was assessed in two healthy adults. Static measurements of the triangular object showed variance to be within one degree in 39 of 40 trials. Differences between angles measured by the EG and those depicted by radiograph were a range of plus or minus five degrees in 88 of 96 digits. The fROM values for the thumb and index, middle, ring, and little fingers were-7.5 to 35.3, 10.6 to 67.8, 4.0 to 79.9, 3.0 to 83.9, and 2.9-91.4 degrees of flexion, respectively. Flexion angle in the fROM of the index finger was significantly smaller than those of the ring and little fingers. The flexion and extension angles of the thumb were significantly smaller than those of the four ulnar fingers. The intra-rater correlation coefficients of two participants were high at 0.94 and 0.93, respectively. The method adopted in this study exhibited excellent accuracy and reproducibility and was therefore considered suitable for the real-time establishment of fROM flexion-extension angles of the MCP joints for all five digits. Our data are useful as a target arc of motion in the treatment of MCP joint disease or injury.