To meet the performance indicator requirements of long focal length, far detection distance, and high agility, modern optoelectronic equipment usually adopts the discrete optical-mechanical design to integrate a series of complex optical-mechanical components and sensors such as off-axis three mirrors, scanning reflector, fast steering mirror, and inertial measuring unit (IMU). These optical-mechanical components and sensors dramatically lead to more complex optical paths, making the optical axis pointing accuracy increasingly more sensitive. On one hand, the relative positions between the optical and mechanical components are changed easily under the excitation of vibration and shock mechanical environment and thermal environment. On the other hand, there are also measurement errors in IMU sensors. Both of them will ultimately lead to the out-of-tolerance of optical axis pointing accuracy. Frequent reassembly will not only consume huge manpower and material resources but also seriously interface with the program progress. Additionally, the influence of the assembly and adjustment residuals for the discrete optical system on the pointing accuracy cannot be ignored. Compared with the traditional mechanical assembly and adjustment, the digital correction can realize the rapid calibration of optical axis pointing through the pointing error modeling and the sample data obtained by tests. Therefore, it has become more and more urgent for the discrete optical system to develop research on digital correction technology.

A digital correction method of optical axis pointing error based on star measurement is studied to realize the fast correction of the optical axis pointing error of discrete optical systems. A discrete optical system containing the scanning reflector, fixed reflector, and IMU sensor is taken as an example to conduct the studies. At first, the optical axis pointing model in the geodetic coordinate system is derived by the quaternion method. In the pointing model, a total of 11 error parameters caused by structural processing assembly errors and sensor measurement errors are taken into account. Then, the equations are linearized by the first-order approximation of Taylor series expansion of the error parameters trigonometric function terms, and the calibration model of the error parameters is further deduced through the least square fitting. In addition, the calibration datum for star targets is established and the position of the star datum in the geodetic coordinate system is computed based on astronomical navigation principles. Finally, the digital correction technology of the optical axis pointing error is verified through the star measurement experiment.

A total of 11 error parameters of the discrete optical system and the fitting accuracy are all obtained by combining the calibration model of error parameters and data of test samples (Table 2). The error angles between the calculated and theoretical optical axis vectors before and after correction are computed for all samples and are compared (Fig. 7). The root mean square (RMS) value of the pointing errors after calibration is 11.61″, which equals the fitting accuracy, indicating the fitting accuracy can represent the optical axis pointing accuracy after correction. Through comparative analysis, the RMS value of the pointing errors decreases from 398.15″ to 11.61″ and the pointing accuracy is improved by 97.1% after the digital correction is developed (Fig. 7). The qualitative and quantitative verification tests are carried out respectively to evaluate the improvement effect of the pointing accuracy. The location values of the building feature point obtained through the gyro theodolite are taken as the given to adjust the optical axis. There is a large deviation between the optical axis pointing and the building feature target before correction, while the deviation almost disappears after pointing error correction (Fig. 8). After correction, the missing distance of the target star can be obtained by adjusting the optical axis pointing to the target star in the target pointing mode (Fig. 9). The RMS value of the missing distance is 10.78″ (Fig. 10). Both qualitative and quantitative verification test results show a significant increase in the pointing accuracy after digital correction.

We propose a digital correction method for the optical axis pointing error to improve the pointing accuracy of the discrete optical system. The theoretical modeling and experimental verification are carried out carefully. In theoretical modeling, the optical axis pointing model of the discrete optical system is built by the quaternion method, and the calibration model of the error parameters is deduced through the Taylor series first-order approximation of the trigonometric function terms of the error parameters and the least square fitting method. In addition, the star calibration datum is established based on astronomical navigation principles. The verification experiments indicate that the optical axis and building feature point almost coincide after correction, and the pointing error between the optical axis and star datum reduces from 398.15″ to 11.61″ after correction, with the pointing accuracy being improved by more than 97.1%.