快速反射镜姿态角的高精度解算

High-precision calculation for attitude angles of fast steering mirror

为了提高跟瞄转台出射激光的指向精度,研究了快速反射镜(FSM)姿态角与转台跟踪误差间的关系,提出了FSM姿态角的高精度解算方法。介绍了跟瞄转台出射激光的光路特点和FSM的工作原理;确定了坐标系中入射光与出射光的方向,依据坐标变换理论和光的反射定律,建立了FSM反射镜姿态角与转台跟踪误差间的函数关系。然后,推导出姿态角的解析表达式,描述了姿态角的空间分布规律,并从解析表达式中推出了近似表达式,确定了近似表达式引入的指向误差。最后,通过指向精度实验验证了姿态角解算方法的正确性。实验结果表明:在跟踪误差不超过(A 12.9′,E13.5′)时,应用姿态角解析表达式和近似表达式均能取得优于2.5″的指向精度;跟踪误差增大为(A38.6′,E37.8′)时,解析表达式对应的指向误差仍低于2.5″,而近似表达式对应的指向误差迅速增大为13.2″。得到的结果显示:FSM姿态角的解析表达式不存在原理误差,在任意跟踪误差下均能使出射激光具有高精度指向能力,且其形式简洁,满足伺服控制器快速运算的要求。

To improve the pointing precision of output laser for a tracking turntable, the relationship between the attitude angles of a Fast Steering Mirror （FSM） and the tracking error of a tracking turntable was re- searched and a high precision calculation method for attitude control angles of the FSM was proposed. The light path of the output laser of the tracking turntable and the operating principle of the FSM were intro- duced. Then, the directions of the incident light and emergent light were determined in different coordinate systems and the functional relationship between the attitude control angles and the tracking errors was derived based on the coordinate transformation theory and the reflection law of light. Furthermore, the analytical ex- pressions of the attitude control angles were obtained, and the space distribution characteristics of the attitude angle were explained. A set of approximation expressions of the attitude control angles were derived from the analytical expressions, and the extra pointing errors caused by the approximation expressions were studied.Finally, a pointing precision experiment was performed to verify the correctness of the formulas for calculating the attitude control angles. The experimental results show that both the analytical formulas and the approxi- mation formulas guarantee the pointing error to be less than 2. 5＂with the turntable tracking errors less than （A 12.9＇, E 13.5＇） . However, the approximation formulas cause the pointing errors to grow to 13.2＂ and the turntable tracking errors to grow to （A38.6＇, E 37.8＇）while the analytical formulas keep the pointing er- rors to be within 2.5＂. It demonstrates that as terse-form analytical formulas of the attitude control an- gles have no principle errors, it always can output the laser beam with high precision pointing ability under any turntable tracking errors, and they show simple forms and satisfy the requirement of rapid calculation of servo controllers.