Research on Shape Adjustment of Large Aperture Reflector Based on Differential Equation

Abstract

The FAST active reflector can transform the reference state's spherical surface into the working condition's parabolic surface by adjusting the system so that the radio telescope has high sensitivity. This paper mainly studies the structure of the ideal paraboloid in the working state and the influence of various factors of the adjustment system on signal reception. The primary cable node distribution model is established based on the paraboloid equation and coordinate rotation. The optimization model, the difference method and the stochastic simulation are used to solve the problem. Firstly, the ideal paraboloid focus selection range is determined as an interval near the feed cabin according to the properties of the focused parallel rays of the paraboloid and the receiving area as the central disk. At the same time, considering the adjustment factors of the reflective panel, the ideal paraboloid endpoint is given. With the constraint interval, an optimization model can be established for the two variables, the distance d from the focal point to the feed cabin and the z-coordinate b of the vertex of the ideal parabola, with the perfect paraboloid and the reference sphere as close as possible as the objective function. It is formed by rotating around the central axis. Therefore, to simplify the operation, the plane because is selected to analyze the ideal parabola, and finally, the optimal solution is obtained by using the two-dimensional grid search algorithm as , , The resulting ideal paraboloid equation is . The FAST active reflector can transform the reference state's spherical surface into the working condition's parabolic surface by adjusting the system so that the radio telescope has high sensitivity. This paper mainly studies the structure of the ideal paraboloid in the working state and the influence of various factors of the adjustment system on signal reception. The primary cable node distribution model is established based on the paraboloid equation and coordinate rotation. The optimization model, the difference method and the stochastic simulation are used to solve the problem.The average vector of each reflective panel can be obtained according to Cramer's law. Then according to the reflection properties of the wave, the direction vector of the reflected electromagnetic wave can be obtained from the incident electromagnetic wave and the average vector. The end of the panel is projected to the feed along the direction of the reflected electromagnetic wave. The cabin's plane can obtain the area reflected from each panel to the plane of the feed cabin. To simplify the calculation and improve efficiency, the Monte Carlo stochastic simulation algorithm is used to obtain the reflected signal receiving ratio of the working paraboloid. The receiving ratio is that the signal receiving the effect of the working paraboloid is much better than that of the reference reflective spherical surface.