a laser communication system and an optical tracking system. The former is for information transmission between two satellites, and the latter is for pointing, acquisition, and tracking (PAT). The space laser communication system is advancing toward miniaturization and is lightweight. However, traditional optical tracking and sighting systems usually use gimbal turrets and gimbal turning mirrors to attain significant beam angles. Furthermore, such structures are large in size, large in inertia, poor in dynamic performance, slow in response time, and sensitive to vibration, which is not conducive to the installation of the carrier platform and the balance of the carrier posture. Compared with the traditional structure, Risley prisms are small in size, have excellent viewing axis adjustment function, and can realize large-angle deflection of the beam; therefore, the rotating biprism is more suitable for space laser communication. However, since Risley prisms are composed of two coaxial wedge prisms, there is no linear relationship between the outgoing light and the wedge prism s rotation angle, making it challenging to solve the outgoing beam of Risley prisms. Additionally, there are several error sources of Risley prisms, and the pointing is not sufficiently accurate. Therefore, it should be corrected to obtain a more precise pointing, which can be used in space laser communication.

A new method of correcting the pointing deviation of Risley prisms is proposed to aim at the problem of poor pointing accuracies, including the significant pointing error of Risley prisms and more error sources. This study uses a non-paraxial ray tracing method to establish a Risley prism pointing model and a two-dimensional turntable pointing model. Many points are uniformly chosen in the entire field of view, and the deviation between the rotating double prism s theoretical and actual output beams is compared. The Levenberg-Marquardt iterative algorithm corrects the rotation angle error, wedge angle, and refractive index of the front and back mirrors of Risley prisms. Higher-precision pointing is achieved by correcting the inaccuracy of the initial incident beam relative to the ideal optical axis and separately correcting the region with a small pitch angle to address the issue of low pointing accuracy in the area with a big pitch angle.

From the simulation findings of the final convergence of the Levenberg-Marquardt algorithm with various initial values, different initial values have little impact on the final optimization results of this experiment (Fig. 2). The entire field of view of Risley prisms is pitch angle 0°-29.22°, azimuth angle 0°-360°. After optimizing the whole area of view by the Levenberg-Marquardt algorithm, the maximum pointing deviation is 5.33 mrad and the average pointing deviation is 1.82 mrad (Fig. 6). It can be observed that the pointing error of the initial incident beam relative to the ideal optical axis will have a relatively large impact on the pointing accuracy of Risley prisms from the effect of the simulation error on the pointing deviation between the actual outgoing beam and the theoretical outgoing beam (Fig. 7). After adding the correction of the error of the initial incident beam relative to the ideal optical axis by the Levenberg-Marquardt algorithm, the maximum pointing deviation is 3.75 mrad and the average pointing deviation is 1.38 mrad (Fig. 8). After using the Levenberg-Marquardt algorithm to correct the points with a pitch angle of less than 15°, the maximum pointing deviation is 1.51 mrad and the average deviation is 0.84 mrad (Fig. 9).

In this study, the non-paraxial ray tracing method is used to develop the pointing model of Risley prisms. Numerous points are evenly chosen in the entire area, and a two-dimensional turntable pointing model is shown to accurately measure the actual outgoing beam of the Risley prisms. Comparison is made between the deviation of the theoretical and real output beams of Risley prisms. The rotation angle error, wedge angle, and refractive index of the front and rear mirrors of Risley prisms are corrected via the Levenberg-Marquardt iterative procedure. After correction in the entire field of view, the maximum pointing deviation changes from 8.37 mrad to 3.75 mrad, and the average pointing deviation changes from 4.00 mrad to 1.38 mrad. Moreover, the correction effect is better when the pitch angle is small. For example, after individually correcting the field of view area with the pitch angle less than 15°, the maximum pointing deviation becomes 1.51 mrad and the average deviation becomes 0.84 mrad. This method improves the pointing accuracy of Risley prisms, and it has a particular reference value for correcting the pointing deviation of Risley prisms.