Abstract: 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.

Key words: Approximation error, Paraboloid surface, Reflector antennas, Space-borne antenna, Cerium oxide, Impact toughness, Inclusion, Laser-arc hybrid welding, Microstructure