Objective  Collimation measurement is one of the most widely used precision angle measurement and attitude measurement methods. By imaging the known reference target at infinity, the accurate angular relationship between the measured object and the reference target can be obtained. The measurement results have the advantages of high accuracy and high repeatability. Photoelectric autocollimator, electronic total station, theodolite and other measuring and calibration instruments all take collimation measurement as their main measurement principle. Due to the limitation of the calibration accuracy of the large-field-of-view and high-distortion optical system, the camera field of view used in precision collimation measurement is usually small, so there are great limitations in the application of large range angle measurement. Fisheye camera has the advantages of large field of view, small volume and light weight, so it should have a broad development prospect in the field of measurement and calibration. However, due to the large field of view and large distortion of the fisheye camera, there is a complex nonlinearity in the camera imaging process, and the asymmetry in lens processing has a more severe impact on the imaging model parameters. For this reason, a fisheye camera calibration method for high precision collimation measurement is proposed in this paper.

  Methods  A two-step fisheye camera calibration method for collimation measurement is proposed in this paper, which includes radial rough calibration based on interpolation and fine calibration based on grid compensation. This method uses interpolation instead of constructing camera model, which can effectively avoid the system error caused by inaccurate model and unreasonable parameter setting, and can restrain the asymmetry of lens processing and the deviation caused by optical system adjustment to a certain extent. Different from the commonly used performance indicators such as peak signal-to-noise ratio (PSNR) and structural similarity (SSIM), the mean reprojection error (MRE) selected in this paper can more effectively measure the camera calibration results under the condition of collimation measurement.

  Results and Discussions   According to the classical model of fisheye camera, four different virtual fisheye cameras are constructed for simulation experiments (Tab.1). The simulation result shows that the calibration effect of this method on the four virtual fisheye camera models is better than the calibration method proposed recently (Fig.8), and the calibration uncertainty can be increased by 82.63% compared with the traditional method. Then, a fisheye camera calibration prototype based on embedded platform is designed (Tab.2). The calibration experimental results of the prototype shows that the proposed method can effectively calibrate the real fisheye camera for collimation measurement (Fig.10). After the calibration method is applied to the real prototype built in this paper, the uncertainty of the solution of the incident vector of the prototype can be raised to arcseconds (Fig.11).

  Conclusions  A fisheye camera calibration method for high-precision collimation measurement is proposed. In the method, calibration process of fisheye camera for collimation measurement is divided into two parts of radial calibration and grid calibration. Firstly, two kinds of calibration sample points are collected with the help of high-precision turntable and collimator. Then the rough construction of the imaging model is completed by radial calibration. Finally, grid calibration is used to eliminate the error caused by the non-coincidence of rotation axis and optical axis in radial calibration, and further improve the calibration accuracy. Through simulation comparison experiments and prototype verification experiments, it is proved that this method has high calibration accuracy. Moreover, this method can be applied to the high-precision calibration of all kinds of real fisheye cameras for collimation measurement, and can provide technical support for the development of collimation measurement in the future.