Structured light vision is an optical 3D surface measurement technology, which features fast speed, high precision, and strong robustness. The traditional optical plane model theory generally regards the projection plane of line structured light as the ideal plane to determine spatial parameters of the optical plane. However, the distortion in the lens of the structured light emitter causes the light plane to bend. Therefore, in the traditional methods, the structured light emitter must be accurately calibrated to avoid nonlinear effects. Due to system assembly errors and complex calibration processes, it is difficult to convert the distorted optical surface into an ideal optical plane just by accurate calibration. The surface bending of line structured light should be fully considered to achieve high-precision line structured cursor setting under a large field of view.

To avoid the influence of lens distortion on calibration accuracy, we propose a new method for surface calibration of linear structured light based on building a surface grid model. First, the camera rays are tracked along the horizontal and vertical directions of the image respectively, and then the intersection depth between the camera rays and the optical surface can be converted into linear changes of the sub-pixel column coordinates or row coordinates of the optical fringe image respectively. The space line structured light surface is decomposed into multiple curves. Then, the grid points formed by the intersection of horizontal and vertical curves are fitted by an equal almost weighting method to obtain the surface grid of line structured light. The fitted surface grid of linear structured light corresponds to the pixel grid for ray-tracing in the image. Since the local surface of linear structured light can be regarded as a plane after differentiation, the center point of any sub-pixel light strip of non-image pixel grid points can be reconstructed in 3D by establishing the homologous relationship between pixel grid points and surface grid points.

By analyzing the computational cost of polynomials of different orders and the fitting accuracy of sample points, the optimal fitting order for ray-tracing is determined (Table 2). To analyze the algorithm robustness, we compare the calibration accuracy of the algorithm and the tracking range of rays under different numbers of calibration images (Table 3). Additionally, the comprehensive analysis and verification show that the proposed method improves the applicability of the calibration method to the distribution directions of down-line structured light in different scenes. By adding different noise levels to the calibrated images, the algorithm is verified to have sound anti-noise performance (Tables 4 and 5). The distance measurement error for any adjacent target with a distance of 55.00 mm is less than 0.08 mm, and the distance measurement accuracy for adjacent targets with a distance of 1133.85 mm can reach 0.50 mm (Table 7). The dimensional measurement accuracy of the 880 mm×715 mm standard body is higher (Table 8), which verifies that the proposed method has significant advantages in large-field dimensional measurement.

A new calibration method based on ray-tracing for surface grids of linear structured light is proposed. Since the lens distortion of the linear structured light emitter is unavoidable, the plane of the linear structured light is distorted into a light surface. To reduce the influence of optical plane distortion on calibration accuracy, for each optical plane in finite space, we simplify the distorted optical surface to multiple curves in space based on the ray-tracing model. Meanwhile, we build a surface grid model of linear structured light based on the principle of equal probability weighting and combine the bidirectional ray-tracing to realize the calibration of any distribution of linear structured light. Additionally, the high-precision reconstruction of the sub-pixel coordinates of the center point of the light strip is realized by employing the homologous relationship between the surface grid points of the linear structured light and the pixel grid points of the image.