The reconstruction of the relative phases and polarization of the electromagnetic field based on amplitude measurements

The problem of determining the relative phases among the components of a monochromatic electromagnetic field at a single point based on amplitude measurements only is addressed. The following questions are answered: (1) How is the phase information reconstructed from amplitude measurements? (2) Do amplitude measurements contain enough information to reconstruct the phases uniquely? (3) How many amplitude measurements are required? and (4) In what directions must the amplitude measurements be taken to ensure that the reconstructed phases are unique? To answer these questions, a more general problem in n dimensions, the special case where n=3 being the solution to the above problem, is proposed and solved