Multi-position calibration method for laser beam based on cyclicity of harmonic turntable
Introduction
3D precision measurement is of vital importance in a wide range of manufacturing applications, such as 3D shape detection, assembly debugging and reverse modeling [1], [2], [3], [4]. The contact probes or telescopes of traditional measurement systems have been replaced by collimated lasers or laser sensors [5], [6], [7]. The highly-accurate positioning of laser beam is a key aspect for 3D precision measurements. The accuracy of measurement system depends heavily on the calibration method of laser beam. However, it is difficult to directly and precisely measure the coordinate of laser spot by the contact measurement method, such as CMM and laser tracker.
Shao et al. proposed a calibration method for a vision guiding-based laser-tracking measurement system [8]. The functions of laser beam under the camera coordinate system and laser tracker coordinate system are successively obtained. The calibration accuracy is 1.46 mm at a range of 10 m. Hu et al. presented an extrinsic calibration of 2D laser rangefinder and camera from single shot based on minimal solution [9]. A trirectangular trihedron is used as the calibration target and the simplified perspective-three-point problem is solved to calculate the pose of laser rangefinder. Wu et al. proposed a calibration method for non-orthogonal shaft laser theodolite measurement system [10]. The laser beam is blocked in different places and the coordinates of the laser spots are directly measured by CMM. The manual aiming greatly reduces the measurement accuracy. Miao et al. presented a dynamic calibration method of the laser beam for non-orthogonal shaft laser theodolite measurement system [11]. The rotation errors of rotary tables is not taken into consideration and the maximum measurement deviation is 0.34 mm at a range of 5 m. The above calibration methods are suitable for the large-scale 3D measurement.
Sun et al. presented a calibration method for laser displacement sensors [12]. A linear array camera of the LDS is used for collecting images of planar target with featured lines and the world coordinates of calibration points are obtained by the cross ratio invariance principle. Yang et al. proposed a calibration method of laser beams direction for the inner diameter measuring device [13]. The laser beams rotate and translate in the plane and constitute the rotary rays. The direction calibration of laser beams can be completed by the sensors’ distance information and corresponding data processing method. Wu et al. proposed a calibration method of laser beam for articulated laser sensor [14]. A 1D linear displacement optical calibration device is employed to receive the laser spot and complete the coordinate transformation between 2D and 3D. The direction vector and fixed point of laser beam are obtained in the CMM coordinate system. Bi et al. presented a calibration method of laser beam direction for optical coordinate measuring system [15]. The sensor respectively moves at an equal step along X, Y and Z axes and the equations are established to calculate the unit direction vector of laser beam based on a standard sphere. However, the dynamic rotation errors of laser beam mounted on the turntable is not mentioned in the above papers.
Focusing on the highly-accurate positioning of laser beam in the whole measurement space, a multi-position calibration method for laser beam base on the cyclical error of harmonic turntable is proposed in this paper. The PSD is used to receive the laser spot and provide the 2D coordinate. The 3D coordinates of porcelain beads in two coordinate systems are used as common points to calculate the transformation relationship between the coordinate systems of PSD and CMM. The Fourier series function is used to establish the error model of rotation angle of turntable. The rotation angles in the whole measurement space are compensated to achieve highly-accurate positioning of laser beam.
The remainder of this paper is organized as follows. Section 2 introduces the flexible calibration field and the transformation relationship between the coordinate systems of PSD and CMM. In Section 3, the calibration principle of laser beam is introduced in detail. Section 4 analyzes the error model of rotation angle of turntable. In Section 5, the calibration method is tested and evaluated with real data experiments. The paper ends with some concluding remarks in Section 6.
Section snippets
Flexible calibration field
The flexible calibration field is constructed by CMM, PSD-based laser receiving board and collimated laser, as shown in Fig. 1 (a). Owing to the high measurement accuracy, the CMM coordinate system is used as the global coordinate system. The PSD-based laser receiving board is mainly made up of PSD, porcelain beads and enclosure panel, as shown in Fig. 1 (b). The PSD is utilized for receiving the laser spots and providing the 2D coordinates. The porcelain beads are used as the auxiliary
Calibration principle
The laser beam can be viewed as a spatial line. The equation of laser beam can be expressed aswhere (xL_W, yL_W, zL_W) is the coordinate of a fixed point on the laser beam and (i, j, k) is the direction vector of laser beam.
The final goal of calibration is to obtain (xL_W, yL_W, zL_W) and (i, j, k). The calibration process can be simply divided into two parts, including calibrating the fixed point on the laser beam and the direction vector of laser beam. Firstly, a set
Multi-position calibration
The calibrated laser is mounted on turntable to achieve flexible rotation. Considering the compactness of practical sensor, the size of turntable is the smaller the better. However, the smaller turntable leads the larger error of rotation angle. Therefore, it is difficult to achieve highly-accurate measurement that the laser beam is calibrated in only one position. Harmonic turntable is adopted in the sensor. According to the theory of harmonic gear drive, the error of rotation angle changes
Calibration of PSD-based laser receiving board
The PSD-based laser receiving board is calibrated by CCD imager, as shown in Fig. 3. The CCD imager can achieve non-contact measurement by optical imaging and contact measurement by probe, respectively. The measurement accuracy of CCD imager is 2.4µm +4l/1000 µm, where l is the measuring distance. The PSD is measured by optical imaging and the porcelain beads are measured by probe. The coordinates of porcelain beads in PSD coordinate system are calibrated and the calibration results are shown
Conclusions
In the application of 3D precision measurement, the fusion of collimated laser and turntables has encountered bottlenecks. Motivated by the increasing demands on the 3D precision measurement, the positioning of laser beam in the whole measurement space with highly-accurate is needed. Based on the cyclical angle error of harmonic turntable, this paper presents a multi-position calibration method for laser beam. A flexible calibration field constructed by CMM and PSD-based laser receiving board
CRediT authorship contribution statement
Jiehu Kang: Conceptualization, Methodology, Software, Validation, Writing - original draft. Bin Wu: Writing - review & editing, Supervision, Project administration. Zhen Zhang: Investigation, Validation. Zefeng Sun: Investigation, Validation. Jiang Wang: Investigation, Validation.
Declaration of Competing Interest
The authors declare that there are no conflicts of interest related to this article.
Acknowledgments
This work is supported by the National Natural Science Foundation of China under Grant No. 61771336, the Natural Science Foundation of Tianjin in China under Grant No. 18JCZDJC38600.
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