An Alternative Solution for the Reflector Surface Retrieval Problem

Abstract

Abstract-The retrieval of the surface profile of a reflector antenna is an important task, mainly for radio-astronomical applications. The microwave holography retrieves the reflector profile starting from a set of measured far-field data. The main step of this technique is the computation of the induced currents on the reflector surface. This requires the solution of a linear inverse problem which is strongly illconditioned. We propose a new technique, based on the Singular Value Decomposition, for the solution of this linear inversion problem. This technique supplies a flexible regularization scheme, able to take into account also the noise level of the data. The proposed procedure has been tested on a number of different cases, with field data generated by a commercial software.

A Microwave Holographic Procedure for Large Symmetric Reflector Antennas Using a Fresnel-Zone Field Data Processing

“…wherein J i is the Bessel function of the first kind. Based on the same consideration carried on in [18] we can neglect the coupling between the ith harmonic of the field t i (θ) and the (i − 2)th and (i + 2)th harmonics of the current (C i−2 and C i+2 ). Therefore, we are left with a new set of 2P + 1 decoupled equations…”

“…Equation (27) can be solved in the least-squares sense [12], by using a regularization procedure based on the SVD of the matrix L. In [18] the same method has been applied by the authors to the reflector surface retrieval problem, but using far field instead of Fresnel-field data. Therefore, the reader is referred to Section 4 of [18] for the details of this SVD regularization procedure. Once the least-squares solution A (i) LS has been computed, we can find the currents on the reflector as the sum of Fourier harmonics:…”

“…The main point is that, even though this discrete data problem is well posed, it turns out to be heavily ill conditioned [12], because (10) is ill-posed. Therefore, it needs to be solved through a suitable regularization procedure [18].…”

Contribution to the Development of Flat Fresnel Reflectors in W Band for New Imaging Applications

“…-In the case of parabolic reflectors, the position of the feeder is critical, and any axial or lateral deviation in the feeder position (away from the focal point), introduces an important reduction in the surface efficiency [4][5][6]. -In the case of a Fresnel reflector, it is known that at each plate zone, the central radial part provides the main contribution to the total reflected radiation (Figure 3), so from the point of view of the reflected signal, the position of the edge shape of each zone is not relevant because the edge is the zone part with the least contribution to the signal focusing.…”