What is the maximum attainable visibility by a partially coherent electromagnetic field in Young's double-slit interference?

What is the maximum visibility attainable in double-slit interference by an electromagnetic field if arbitrary - but reversible - polarization and spatial transformations are applied? Previous attempts at answering this question for electromagnetic fields have emphasized maximizing the visibility under local polarization transformations. I provide a definitive answer in the general setting of partially coherent electromagnetic fields. An analytical formula is derived proving that the maximum visibility is determined by only the two smallest eigenvalues of the 4x4 two-point coherency matrix associated with the electromagnetic field. This answer reveals, for example, that any two points in a spatially incoherent scalar field can always achieve full interference visibility by applying an appropriate reversible transformation spanning both the polarization and spatial degrees of freedom - without loss of energy. Surprisingly, almost all current measures predict zero-visibility for such fields. This counter-intuitive result exploits the higher dimensionality of the Hilbert space associated with vector - rather than scalar - fields to enable coherency conversion between the field's degrees of freedom. (C) 2017 Optical Society of America