Deformation measurement by single spherical near-field intensity measurement for large reflector antenna

This paper presents a new method to obtain the deformation distribution on the main reflector of an antenna only by measuring the electric intensity on a spherical surface with the focal point as the center of the sphere, regardless of phase. Combining the differential geometry theory with geometric optics method, this paper has derived a deformation-intensity equation to relate the surface deformation to the intensity distribution of a spherical near-field directly. Based on the Finite difference method (FDM) and Gauss-Seidel iteration, deformation has been calculated from intensity simulated by GO and PO method, respectively, with relatively small errors, which prove the effectiveness of the equation proposed in this paper. By means of this method , it is possible to measure the deformation only by scanning the electric intensity of a single hemispherical near-field whose area is only about $1/15$ of the aperture. And the measurement only needs a plane wave at any frequency as the incident wave, which means that both the signals from the outer space satellite and the far-field artificial beacon could be used as the sources. The scanning can be realized no matter what attitude and elevation angle the antenna is in because the size and angle of the hemisphere are changeable.