Interpolation of reflector surfaces using deformed plate theory

Due to the advantages of shaping reflector antennas for high gain or contour beam applications, reflector surfaces have departed from being described by simple equations, and often require the assistance of some interpolation scheme for their characterization. Various interpolation tools are available for describing an arbitrary surface, but most can only handle a grid of equally spaced points (i.e., uniform grid). To reduce errors associated with under sampling a highly shaped reflector region, while maintaining a reasonable computational efficiency, it is desirable to have an interpolation scheme capable of handling a non-uniform grid, so that a more dense sampling can be used only where needed. We investigate the capabilities and limitations of the surface spline. The idea behind their method is that a plate, under the action of an appropriately chosen set of localized forces, will deform smoothly and can be made to pass through any reasonable set of coordinate points. Hence, this deformed plate can be used as an interpolation tool. A related interpolation method, the pseudo-spline interpolation, is also considered.