After briefly reviewing the properties of the squared amplitudes of radiated fields, a simple and effective necessary condition to test if a source of given size and structure can radiate or not a power pattern lying in a given mask is furnished. The criterion is shown to be also sufficient for linear arrays, thus allowing to reduce the overall problem to the synthesis of a nominal pattern.Then, new synthesis procedures, strongly relying on the properties of squared amplitude distributions and on the quadraticity of the operator relating the source to the power pattern, are introduced. They are implemented and tested in the cases of linear and planar uniform arrays, showing that thanks to a full exploitation of the properties of quadratic operators and of those of squared amplitude distributions, they allow one to achieve very efficient solutions to mask constrained synthesis problems.