Results and Discussions To verify the proposed calibration method, the two methods were used for repeated calibration, and the repeatability of the two method’s results was compared to verify the calibration algorithm’s precision. Ten repeated experiments showed that the direction vectors based on the joint estimation had a smaller standard deviation and higher precision. Following calibration, the size of the measuring block was measured to verify the algorithm’s accuracy. The size of the gauge block was 25 mm, measurement error of the traditional method was 32.7 μm, and measurement error of the method proposed in this study was 25.2 μm (Fig. 8). To verify the stability of the calibration method, a total of ten repeated calibrations were performed, and the results of the ten repeated calibrations were used to measure the size of the gauge blocks. The average measurement error of the proposed method is 25.0 μm, while the average measurement error of the traditional method is 35.7 μm. Compared with the traditional method, the measurement error of this method was reduced by an average of 30% (Fig. 9). According to the experimental results, the proposed calibration method has a higher scanning direction calibration accuracy and good robustness.

In a visual measurement system, the scanning mechanism is used to move the vision sensors or the measured object to expand the measurement range, which is known as translation scanning. The measurement range of a single image, particularly for a line-structured light three-dimensional (3D) sensor, is only the light stripe formed by the intersection of the light plane and object. To achieve a 3D reconstruction of the measured object, a scanning mechanism must scan the entire surface of the light plane. In practical applications, line-structured light 3D sensors and translation scanning mechanisms are used in combination to measure flat objects and in defect detection, quality control, geometric dimension measurement, positioning, and other applications. However, before use, it is necessary to unify the coordinate systems of the scanning mechanism and sensor, that is, to calibrate the translation direction of the scanning mechanism. In the traditional calibration method, the checkerboard plane target is fixed, sensor is moved along the scanning direction, and camera captures target images. Subsequently, the extrinsic camera parameters corresponding to each image are estimated separately, and the 3D coordinates of the same feature point on each target image are calculated in the camera coordinate system. Finally, the 3D coordinates of the same feature point are fitted with a straight line, and the straight line’s direction vector is the scanning direction. Because of the different sharpness of the target images captured at different positions, the corresponding camera extrinsic parameters contain different noises for each image separately, introducing noise several times when calculating the 3D coordinates of feature points and then reducing the calibration accuracy.

First, the study analyzed and verified the disadvantages of the traditional calibration method, which introduces noise several times. In the verification experiment, the target was only translated by the high-precision stage; the orientation of the plane target relative to the camera remained unchanged, and the translation distance of the target was measured using the laser interferometer as the reference value. The ideal rotation matrix for each capture position should be identical to the initial capture position. However, the experimental results show that the rotation matrices estimated by the traditional methods are different (Fig. 3), and the estimated value of the target translation differs significantly from the reference value (Fig. 4). This proves that the traditional method introduces noise several times, decreasing the accuracy of the scanning-direction calibration. To reduce noise caused by different image sharpnesses, a scanning direction calibration method based on joint estimation was proposed. The scanning direction vector was added to the camera imaging model, and in the calibration process, the translation stage was used to move the plane target at a fixed distance. Therefore, the rotation matrix of the target relative to the camera coordinate system at each capture position remains unchanged, and the change in the translation vector is constrained by the translation stage’s movement distance. By adding constraints on the rotation matrix and translational vector, the 2D feature points on the plane target are expanded to 3D feature points, which are all combined for one homography estimation, and the noise caused by different image sharpnesses is reduced.

To improve the 3D reconstruction accuracy of line-structured light 3D sensors, this study first analyzes and verifies the shortcomings of the traditional scanning direction calibration method, which introduces noise several times, and then proposes a scanning direction calibration method based on joint estimation. The 2D feature points on the plane target are expanded to 3D feature points by adding constraints to the rotation matrix and translation vector, which realizes one joint homography estimation for all the calibration images and improves the calibration accuracy of the scanning direction. The experimental results show that this method improves the scanning direction calibration accuracy and reduces the sensor’s 3D reconstruction error.