T. Isernia et al., PHASELESS NEAR-FIELD TECHNIQUES - UNIQUENESS CONDITIONS AND ATTAINMENT OF THE SOLUTION, Journal of electromagnetic waves and applications, 8(7), 1994, pp. 889-908
In this series of two papers we consider in its maximum generality the
problem of determining electromagnetic fields starting from phaseless
distributions on one or more surfaces. In this second part, novel uni
queness conditions for the solution of the problem, requiring in princ
iple a single scanning surface, are introduced. Then, all questions re
lated to the attainment of the generalized solution are discussed. The
geometrical properties of the functional set corresponding to the ran
ge of the quadratic operator relating the unknowns to the data are exa
mined. It is shown how to avoid both contingent local minima problems
and ill-conditioning questions. The crucial role of the dimension of t
he data representation space is emphasized. The main benefits of the p
roposed approach are in the numerical search for the solution, that is
the exact, closed form line search step in the minimization procedure
and the introduction of a proper metric change in the functional, are
stressed. A critical review of the results already obtained is perfor
med with a particular care to the key points of the method.