Internal twist and least-squares adjustment of four-cornered surface plates for reflector antennas

Surface plates with four adjustment screws, one at each corner, allow four degrees of freedom for their adjustment, including an internal nonplanar twist or warp. Thus the surface deformations of trapezoidal plates under enforced twists are investigated. A simple equation is derived, holding as a satisfactory approximation for various plate designs (solid plate, honeycomb, and skin-and-ribs). Measurements at four different experimental plates agree with it within 2 percent. This approximation is then used to develop a least-squares procedure for obtaining those adjustment amounts which minimize the root-mean-square (rms) deviation between the plate's surface and the desired telescope paraboloid. The resulting procedure is recommended for all telescopes with trapezoidal surface plates. Seven experimental plates of four different designs were tested in the lab, and the suggested least-squares procedure (as compared to a simple true-corner adjustment) improved the residuals by 27 percent. Measurements of some plates on a telescope gave also encouraging results.