Poincaré sphere of electromagnetic spatial coherence. For an arbitrary partially polarized and partially coherent beam two coherence Poincaré vectors and with the same length but different orientations are generally needed (Sphere A). If the beam is fully polarized the lengths of these vectors display the degree of coherence, , and their directions show the polarization state of the beam at points and , respectively (Sphere B). If the beam is uniformly polarized, these vectors coincide and a single coherence Poincaré vector is sufficient to represent the beam, with its length again showing the degree of coherence and the direction specifying the polarization state (Sphere C). At a single point the formalism reduces to the traditional polarization Poincaré sphere where the distance from the origin is given by the degree of polarization [1] (Sphere D).