中文摘要：

在太空无重力工作环境下,星载索网天线反射面由张紧的网格平面拼合而成。为尽可能降低天线索网型面的原理误差,提出一种新的索网型面生成方法。方法要求抛物面索网天线型面在天线光学口径面上的投影为正三角形网格,索网反射面的型面结点均取在与理想抛物面同轴且等焦距的某映射抛物面上,投影正三角形的边长由天线反射面的焦距及型面设计的原理误差要求确定,映射抛物面的具体位置由投影正三角的边长及反射面的焦距确定。以空间任意三角形与抛物面之间的轴向方均根误差计算公式的推导为基础,讨论在天线光学口径面上投影面积为定值的空间三角形与抛物面之间轴向方均根误差取得极小值的条件,得出抛物面索网天线型面在天线光学口径面上投影为正三角形网格时原理误差最小的结论。索网型面设计的算例结果表明所提方法有效、实用。

英文摘要：

Space-borne mesh antenna works in space environment without gravity.Under the influence of the internal tension,reflectors of mesh antenna are approximated with flat facets.Aimed at minimizing the systematic approximation error of the reflector,a geometry design method for paraboloid reflectors of mesh antenna is developed.To subdivide a paraboloid surface,the first step of the geometric scheme is to subdivide the inscribed regular hexagon of the optical aperture circle into small equilateral triangles.Then the points of intersection of these triangles are projected or mapped on the paraboloid surface using a suitable origin of coordinates to obtain the final nodal coordinates of the facets.Based on the systematic approximation error requirement in design and the paraboloid focal length of the reflector,certain formulas are given to determine the side length of the triangles and the origin coordinates of the paraboloid when the mapping is done.With axial square mean error as the measure of reflector＇s precision,a formula is derived for calculating the systematic approximation error when a spatial arbitrary triangle is used to approximate part of a paraboloid reflector.And when the spatial triangle has a certain projected area on the optical aperture circle surface,the conditions for the spatial triangle to get the best approximation to the paraboloid reflector is discussed,which gives the result that when the best approximation is expected,the optical aperture circle surface should be divided into small equilateral triangles as far as possible.A comparison is done among all the design methods available in a geometry design example for a paraboloid reflector and results show the validity and feasibility of the proposed method.