This paper describes, analyzes, and implements an approach to far-field determination from phaseless measurements over two planar surfaces. A proper formulation of the problem is considered as a quadratic inverse one whose data is the square amplitude of the near field. A solution is introduced as the global minimum of an appropriate functional. Next, to perform such a minimization procedure, a finite dimensional representation of the field radiated by sources whose plane-wave spectrum becomes negligible outside a fixed angular domain is used. A detailed investigation of the properties of the mapping connecting the unknowns to the data makes it possible to analyze how to escape from the local minima possibly met in the course of the minimization procedure. To this end, the crucial role of the availability of phaseless data over two different sarfa,ces and of appropriate weights in the functional definition is emphasized, and a reliable iterative procedure converging on the solution, regardless of the starting point, is thus obtained. This property is confirmed by experimental results concerning near-zone data from a shaped reflector at 9 Ghz. It can be readily appreciated that when only the field intensity is detected the complexity and the cost of the equipment required for near-field techniques in antenna testing and diagnostics can be reduced to a very large extent.

The problem of determining the dielectric permittivity profile of buried objects starting from the knowledge of the scattered field is considered in the two-dimensional geometry when incomplete near-zone data are collected at a single frequency under a multiview/multistatic measurement configuration. In particular, attention is paid to the practical issues of the truncated observation domain and the presence of uncertainties on data. The problem is tackled with reference to the scalar polarization by linearization of the mathematical relationship between the unknown dielectric permittivity profile and the scattered field. A homogeneous, possibly lossy, half-space geometry for the subsurface modeling is adopted, thus leading to the so-called distorted Born approximation (DBA). A thorough investigation of the class of unknown functions that can be reliably retrieved is performed by dealing with singular value decomposition of the relevant linear operator. It results that even if sources and receivers are located at the interface, a very restricted set of profile variations can be reconstructed by a stable inversion algorithm. In particular, reduced vertical features of the buried objects with respect to the horizontal ones can be reconstructed under DBA. Moreover, the truncation of the observation domain further restricts this set, affecting mainly the vertical resolution. Numerical results confirming the validity of the analysis are also provided.

A shape reconstruction algorithm is formulated for the multimonostatic configuration and the 2-D geometry. The imaging algorithm is based on the Kirchhoff approximation, works in the frequency domain, and exploits the singular value decomposition tool to achieve a stable solution. The effectiveness of the reconstruction algorithm is shown by processing synthetic data in the time domain generated via a finite-difference time-domain code. A performance analysis of the solution algorithm is addressed with varying host medium and measurement configurations, also by processing synthetic data for a 3-D geometry. Finally, an experimental validation of the technique is performed due to data collected by a time-domain ground-penetrating radar for buried pipe detection and localization.

The possibility of determining the far field of radiating systems by measuring only the near-field amplitude is investigated. The main difficulties of the problem are examined in some detail and a new near-field/far-field transformation technique is developed, based on the measurement of the near-field amplitude over two surfaces surrounding the antenna under test. The accuracy of the far-field reconstruction results are related both to the distance between such surfaces and to some a priori information concerning the near-field phase and/or the radiating system. The information on the radiating system allows relaxation of the need for any information on the near-field phase provided that the distance between the measurement surfaces is high enough. Conversely, the knowledge of a more or less corrupted near-field phase allows reduction of such distances without affecting the accuracy of the far-field reconstruction. Numerical examples validating the effectiveness of the developed algorithm are provided for the planar scanning case.

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