Objective  Aiming at the difficulty and high cost of regular calibration of line-scan camera internal parameters in industrial production lines or integrated equipment, a calibration method of line-scan camera internal parameters based on 2.5D calibration fan is proposed. The appropriate calibration object is designed, and the internal parameter calibration model of the linear array camera is established. The linear transformation theory is used to calculate the initial value of the model parameters, and the improved Levenberg-Marquardt (L-M) algorithm is used to optimize the camera parameters. The experimental results show that the internal parameters of the linear array camera calibrated by this method have high accuracy and good consistency. The maximum re-projection error is less than 0.28 pixel, and the average RMSE is 0.112 pixel.

  Methods  A specific 2.5D calibration fan was designed. The internal parameter calibration model of line-scan camera including lens distortion is constructed, which takes into account the two attitude angles of the target relative to the camera. The initial value of the model parameters is solved by the equation linear transformation method, and the improved L-M algorithm is used to accelerate the optimization of the camera parameters. The detailed calculation steps and data processing process are given, and the feasibility of the method is verified according to the simulation and measured data.

  Results and Discussions   The theoretical analysis and experimental results show that the linear array camera calibration method is simple and flexible, and a large number of feature point pairs with regular distribution can be obtained. The parameter calibration accuracy is not limited by the camera movement accuracy and specific direction. In addition, when the angle between the fan-bone surface and the target surface is less than 10 °, high-precision and high-consistency camera internal parameters can be obtained. The maximum value of the feature point reprojection error is better than 0.28 pixel, the average RMSE is 0.112 pixel, and the standard deviation is only 0.014 pixel.

  Conclusions  Line-scan cameras are often placed inside the equipment in a modular form with other sensors, and the regular calibration of the internal parameters of such cameras is costly and difficult. In view of this, an internal parameter calibration method of linear array camera based on 2.5D calibration fan is proposed. The 2.5D calibration fan has the advantages of both the three-dimensional measurement effect of the 3D target and the low cost and high precision of the 2D target. The number of feature points is large and the distribution is regular, which avoids the problem of easy loss of features, and the feature points and image points are easy to match. The constructed linear array camera calibration model takes into account the lens distortion error and the small angle attitude between the target surface and the image surface, so that the camera movement direction and the position of the calibration object are not strictly limited. Experiments show that the internal parameters of the camera calibrated by the fan bone with \theta < ±10° are the best, and the calibration results have high accuracy and good consistency. The reprojection error of 89 % feature points is less than 0.20 pixel, the maximum error is better than 0.28 pixel, and the average RMSE is 0.112 pixel. In addition, compared with the standard L-M algorithm, the improved L-M algorithm reduces the number of iterations by half without affecting the accuracy of parameter optimization.