Laser technology has gained widespread applications in various fields, such as communication, guidance, and precision machining. However, the accuracy of these applications is often compromised by beam pointing instability caused by uneven internal laser temperature and external environmental changes. Traditional methods of improving beam pointing stability, including using materials with low thermal expansion coefficients, adopting cooling systems and deformation mirrors, and reducing vibration, have proven to be limited in their effectiveness. More advanced lasers have internal beam pointing correction systems, but their performance is limited by their size, and they cannot correct pointing deviations caused by external factors. In view of these limitations, the use of an external beam pointing deviation correction system has emerged as a promising solution. The beam pointing deviation correction system based on fast steering mirrors (FSMs) is considered to be the most mature and effective approach. However, the Z-shaped beam path commonly used in these systems changes the propagation direction of the original beam, resulting in poor expansion performance. In this paper, we present a U-shaped beam pointing deviation correction system based on FSMs that does not change the original beam propagation direction. The system is modeled using geometric optics, including the mapping model from FSMs to four-term beam pointing deviations and the FSMs control model. To further enhance the system's performance, we propose a predictive control model, simplifying the model operation and improving the system responsiveness. Our results demonstrate that the constructed system exhibits excellent beam pointing deviation correction performance.

The beam pointing deviation correction system consists of three main components: detector, controller, and actuator. The detector consists of a uniform beam splitter and two vertically distributed high-accuracy position-sensitive detectors (PSDs). The non-uniform beam splitter diverts a small portion of the beam from the main beam into the detector, where deviations in the beam's position from the center of the PSDs can be detected and used to determine beam pointing deviations. The controller is a computer that implements four distinct models: a beam pointing deviation detection model, a FSM attitude control model, a beam pointing deviation prediction model, and a simplified FSM attitude control model. The beam pointing deviation detection model calculates the four beam pointing deviations from the position deviations of PSDs. The FSM attitude control model determines the control angles of the FSMs from the four beam pointing deviations to realize the correction of beam pointing deviations. The latter two models, i.e., the beam pointing deviation prediction model and the simplified FSM attitude control model, are constructed to achieve predictive correction of the beam pointing deviation. The beam pointing deviation prediction model is based on the mean deviation correction method and predicts future beam pointing deviations, while the simplified FSM attitude control model has a simpler operation and can rapidly obtain the control angle of the FSMs. The FSMs act as actuators, adjusting their attitude based on control signals to correct the beam pointing deviations and improve the beam pointing stability.

The constructed beam pointing deviation prediction model has a slight lag in the prediction of beam pointing deviations, but it still has a high accuracy and can filter the high-frequency signals in the pointing deviations (Fig. 4). Therefore, the attitude of the corrected FSMs can be calculated based on the predicted pointing deviations. The simplified FSM attitude control model has a reliable accuracy (Fig. 5). The error between the FSMs' control angles obtained from the simplified model and the results calculated based on geometrical optics is within 1 μrad. Therefore, the simplified model can be used to correct the beam pointing deviations. The experiments show that the constructed beam pointing deviation detection model and FSM attitude control model also have high accuracy. The beam pointing deviation correction system can effectively reduce the beam pointing deviations. Although the beam pointing deviations are not completely corrected due to the open-loop control without additional feedback, the errors of the beam pointing deviations in X and Y directions are reduced by 78.08% and 70.28%, respectively.

A U-shaped beam pointing deviation correction system is designed, and a beam pointing deviation model and a FSM attitude control model are constructed based on geometric optics. Two PSDs are used to detect the beam pointing deviations, and two FSMs are used to correct the beam pointing deviations. A predictive beam pointing deviation correction model is proposed. A beam pointing deviation prediction model based on the average deviation correction method is constructed to correct the attitudes of FSMs based on the predicted beam pointing deviations rather than the real-time detections. The calculation of the control angles of the FSMs is simplified. A mapping model is constructed to calculate the control angle, which avoids solving the control angle in the original FSM attitude control model and effectively improves the response performance of the system. At last, experiments demonstrate that the developed system and model can effectively reduce the beam pointing deviations. The pointing deviations of the beam are reduced by 78.08% and 70.28% in the X and Y directions, respectively.