Phaseless near-field techniques from a random starting point

In this paper we address the problem of reconstructing the far field radiated by focusing sources from the knowledge of square amplitude samples of the radiated field on more measurement lines in near zone. We show that it is possible to estimate the angular sector where the far field is significantly different from zero. This allows to adopt an efficient procedure for the reconstruction of the far field without the use of prior information about it. Such procedure exploits the quadratic inversion approach for phase retrieval and it consists of two steps. In the first step, it recovers only those samples of the radiation pattern significantly different from zero. Later, it reconstructs all the samples of the radiation pattern starting from an initial guess which is equal to the solution of the first step, where the radiation pattern is significantly different from zero, and zero otherwise. Numerical results show the feasibility of the technique, and its efficiency in terms of data required for convergence.