Despite the fact that incandescent sources are usually spatially incoherent, it has been known for some time that a proper design of a thermal source can modify its spatial coherence. A natural question is whether it is possible to extend this analysis to electroluminescence and photoluminescence. A theoretical framework is needed to explore these properties. In this paper, we extend a general coherence-absorption relation valid at equilibrium to two non-equilibrium cases: luminescent bodies and anisothermal bodies. We then use this relation to analyse the differences between the isothermal and anisothermal cases and to study the near-field emission of an electroluminescent source.