Geometric modeling of metallic mesh sheet tailoring for an axissymmetric reflector. Part 1

For a parabolic reflector-type antenna, an attachment of a reflecting metallic mesh sheet in a manner ensuring the least possible impact on radiophysical properties of the device is a crucial problem. It is clear that under different selected schemes of tailoring, the specified problem is solved (approximately) in different ways. The scheme of tailoring gives rise to a problem of optimum tailoring. Optimum tailoring can be understood in different ways. There is a well-known approach based on reducing the RMSD as much as possible, (root-mean-square deviation from an ideal surface). We however take different criteria as a basis for optimization — the degree of homogeneity of tension for the metallic mesh in different areas of the reflector (for example, the degree of metallic mesh stretching near the technological center should be a certain fraction of its degree of tension on the periphery). Usually, it is assumed that an acceptable result is achieved if there is a maximum tension at all the points of the reflector within some pre-specified limits, and minimal — also within the desirable limits (own ones). In this paper, we solve a problem of optimal tailoring, and optimality suggests the following conditions: extreme distortion of the relative length should be as close to unity, while the closer to the center of the paraboloid, the "stricter" specified condition must be satisfied.