球面射电望远镜主动反射面的形状调节算法

Shape Regulation Algorithm for the Active Reflection Surface of the Spherical Radio Telescope

摘要: 为获得天体电磁波经反射面反射后的最佳接收效果，中国科学院研制了500米口径球面射电望远镜。该望远镜在反射面板调节约束条件下，通过调节促动器的径向伸缩量，将反射面调节为工作抛物面，使得该工作抛物面尽量贴近理想抛物面。本文以基准球面的球心为原点建立空间直角坐标系，只对被观测天体位于Z轴上方(简称为情形1)和方位角为36.7953˚、仰角为78.169˚ (简称为情形2)进行建模与分析。对于情形1，该文设计了一种算法。该算法基于馈源舱到理想抛物面与基准球面交点的长度选取照明区域的主索节点。继之以非线性最小二乘法得到被选取的主索节点与理想抛物面方程的拟合，其拟合优度R² = 0.9995，均方根误差RMSE = 0.2085，求得的拟合抛物面较为理想。对于情形2，因天体位置变化，得到的馈源舱到理想抛物面与基准球面交点的长度有误差，该文将选取照明区域的主索节点的判断条件，即馈源舱到基准球面的所有主索节点的距离是否小于等于PM (馈源舱到理想抛物面与基准球面交点的长度)进行放缩，得到与状况1相同个数的主索节点坐标。然后用非线性最小二乘法进行拟合，得到近似理想抛物面。其拟合优度R² = 0.9983，均方根误差RMSE = 0.6965，拟合效果较好。

Abstract: In order to obtain the best receiving effect of celestial electromagnetic waves after being reflected by the reflector, the Chinese Academy of Sciences has developed a 500-meter caliber sphere radio telescope. The telescope adjusts the reflection surface to a working parabolic surface by adjusting the radial elongation of the actuator, making the working parabolic surface as close to the ideal parabolic surface as possible. In this paper, the spatial right-angle coordinate system is established from the center of the benchmark sphere as the origin, which only models and analyzes the observed objects located above the Z axis (referred to as situation 1) and an azimuth of 36.7953˚ and an elevation of 78.169˚ (situation 2). For situation 1, the algorithm is designed in the paper. The algorithm selects the main cable node of the illumination area based on the length of the feed compartment to the intersection between the ideal parabolic plane and the reference sphere. Following the nonlinear least squares method to obtain the fit of the selected main cable node and the ideal parabolic equation, its goodness of fit R² = 0.9995, root mean square error RMSE = 0.2085. The obtained fitted parabola is relatively ideal. For situation 2, due to the change of the object position, the selection of the judgment condition of the main cable node of the lighting area is whether the distance of the source compartment from the main cable node to the reference space is less than or equal to the length of the PM (feed compartment to the intersection between the ideal parabolic and the reference sphere) to obtain the same number of main cable node coordinates as situation 1. It is then fitted by nonlinear least squares to obtain an approximate ideal parabola. Its goodness-of-fit R² = 0.9983, root mean square error RMSE = 0.6965, and fitting effect is good.