Reflector antenna diagnosis from phaseless data

The problem of determining the surface profile or a reflector antenna from only amplitude measurements arises whenever the phase cannot be accurately detected. We apply the quadratic approach to solve this "holography" problem by looking directly for the aperture field function from measurements of field intensities at the feed location under different defocusing conditions, which can be easily achieved in testing radioastronomical antennas. A suitable finite-dimensional approximation of the unknown function and two sets of square amplitude data are employed. The solution procedure consists of minimizing a nonquadratic functional and can be critically affected by the existence of local minima. This crucial problem is discussed and solved and the procedure is applied to both simulated and experimental data. The reliability of the whole algorithm is confirmed by the fact that results are obtained starting from completely random initial guesses. A viable and simple way to determine the positions of the individual panels making up large radioastronomical antennas is also employed.