Surface Profile Accuracy of Deployable Mesh Reflectors Based on Focal Offset

A deployable structure based on the tension truss concept is used to develop unfurlable, large-aperture reflectors for space applications. The paraboloid surface of the reflector is approximated by a reflective mesh attached to a cable network consisting of triangular facets. Existing approaches try to minimize the root mean square error between the faceted surface and the local quadratic approximation of the paraboloid for designing the cable net. An alternate approach for computing the surface accuracy of the faceted reflector surface is proposed here based on the proximity of the reflected rays to the receiver of the antenna. The offset distance of reflected rays from the focus or offset error is a more geometrically relevant indicator for determining the accuracy of the facets. An offset paraboloid reflector of 3 m aperture diameter is designed for which the surface errors are computed using both the approaches. These errors are computed for individual facets, and their distribution throughout the reflector surface is compared.