Polarization overlap in interferometric visibility ($\mathcal{V}=2\sqrt{I_1{I}_2}|{\mathbf{e}}_1^{†}{\mathbf{e}}_2|/(I_1+I_2)$)

For perfectly temporally coherent beams with unit Jones vectors ${\mathbf{e}}_1,{\mathbf{e}}_2$, their interference term is proportional to the complex inner product ${\mathbf{e}}_1^{†}{\mathbf{e}}_2$. Their interferometric visibility is the displayed expression. Equal beam light intensities reduce it to the magnitude of the polarization overlap. Two linear polarizations at relative angle $\theta$ give $|\cos \theta |$; a linear and a circular polarization give $1/\sqrt{2}$. Perfect coherence does not remove loss of contrast from unequal intensities or orthogonal polarizations.