On Reflector Surface Compensation by Minimal Probing of Subreflector Field in Dual Reflector Antennas

This paper presents the results of a theoretical study on the feasibility of probing the field at a limited number of points on a small subreflector surface to obtain information about the main reflector surface distortion. This information is used to provide a phase error profile across the subreflector surface that can compensate for the main reflector errors. This can be achieved by using an array of elements such as patch antennas that can cause a phase shift between the incoming and outgoing field. The example of a flat subreflector and a parabolic main reflector (a Newtonian dual reflector system) is considered. The surface synthesis will utilize geometrical (ray) optics while the required analysis is based on physical optics. The subreflector is assumed to be a reflectarray covered with reconfigurable patch elements. The phase change on the subreflector can be detected by a small number of receiving patch elements. It is shown that by probing this change at a few selected positions on the subreflector, the full range of phase error can be recovered and subsequently used to change the phase of all the patch elements covering the subreflector plane to compensate for main reflector errors. This is done by using a version of sampling theorem on the circular aperture, which has been developed as part of this work. The sampling is performed on the phase error function on the circular aperture of the main reflector. A sampling method is developed, using Zernike polynomials, which provides for an exact retrieval of the coefficients of up to any given orders from a set of selected points on main aperture in polar coordinates. The corresponding points on subreflector are then obtained, and by probing the fields at these points, a set of phase values are determined that are then transferred back to the main reflector aperture for recovering the phase function. Once this function is recovered, the corresponding phase values at all the points on the subreflector are calculated and can be applied to the array of phase shifting patch elements to compensate for main surface errors. Numerical calculations and graphicexamples are provided.