The global pixel size calibration method for a dual telecentric imaging system based on a sphere array

To enhance visual measurement precision, this paper presents a precision steel ball array calibration board specifically designed for bi-telecentric imaging systems. The calibration board, consisting of a spherical target array and a base, enables camera-wide pixel size calibration. Based on this calibration board, we propose a comprehensive pixel size calibration method that first detects the spherical targets through sub-pixel detection and circle fitting to determine center positions and diameters. The pixel size at each circle center is then calculated using the nominal diameter. Subsequently, these center pixel sizes serve as skeleton points for thin-plate spline interpolation, yielding smooth camera-wide pixel size calibration results. Additionally, we develop a method for calculating distances between image feature points. In experimental measurements of gauge plug diameters at various positions within the camera field of view, the maximum mean absolute error did not exceed 0.021 mm—a 60 % reduction compared to conventional measurement methods. This approach effectively minimizes measurement errors caused by changes in the position of measured objects.