Application and Optimization of Shape Adjustment Design Based on “FAST” Active Reflector Model

For the establishment of an ideal parabolic reflector adjustment model and the optimization of the reception effect of celestial electromagnetic waves reflected by the reflector, it is a major problem in the actual operation of the China Sky Eye FAST - 500 m aperture spherical radio telescope. This paper makes reasonable assumptions about the working state of the active reflector, determines the ideal paraboloid, and optimizes the mediation scheme of the reflector in combination with the specific situation, providing theoretical reference for the actual operation and testing. The ideal paraboloid is determined when the object to be observed is directly above the reference sphere. First of all, the FAST reflection principle is obtained by focusing analysis of concave mirror and working principle of active reflection panel. Combined with the relative displacement of the apex of the paraboloid and the reference sphere, the expansion length of the apex of the paraboloid is obtained, thus enhancing the adjustability of the model. Finally, the parabolic equation in the three-dimensional plane is obtained by rotating the two-dimensional parabola around the z-axis. When the object S to be observed is located, the ideal paraboloid is determined, and the reflective panel adjustment model is established. First, the virtual time angle coordinate system is established, and then the horizontal right angle coordinate system is established according to the position of FSAT. The paraboloid expression is obtained through the time angle coordinate and the horizontal right angle expression. Using the virtual coordinate system, the paraboloid whose vertex coincides with the center of the reflecting surface is defined as the reference paraboloid in this system, and the polar coordinate equation is obtained. For determining the movable points covered by the paraboloid, we establish a sphere coverage model and calculate the Euclidean distance to determine the number of specific coverage points. Determine the polar angle corresponding to the point according to the position coordinates of the cable point within the effective aperture. Then calculate the extreme length of the cable point after changing its position to obtain the actual expansion.