Coherence is a key issue involved in many topics of quantum and classical physics. At a fundamental level, coherence appears in two basic optical items, namely, interference and polarization. More specifically, the polarization state is the result of coherence for the superposition of waves with orthogonal directions of vibration, while interference is the result of coherence for the superposition of waves with nonorthogonal (usually parallel) directions of vibration.
The objective of this contribution is to develop a coherence-based relationship between interference and polarization focusing on the proper assessment of the amount of coherence.
We devote the following section to elaboration of the simpler two-dimensional case, i.e., the superposition of two scalar waves or two field components, as a suitable ground to sustain more complex situations. We examine several alternative formulations for the degrees of coherence, visibility, and polarization that are equivalent in the two-dimensional case but lead to diverging results for larger dimensions. Then we extend these ideas to more involved situations with a larger number of field components, such as the degree of polarization for three-dimensional waves and the degree of coherence for pairs of two-dimensional waves, where several approaches to the corresponding degrees of polarization and coherence currently coexist.
The multiplicity of degrees of coherence for dimensions larger than two need not be disturbing, and the coexistence can be peaceful and harmonious. Increasing the number of field components increases the degrees of freedom and the complexity of the problem so that a single measure of coherence may not be enough to account for all phenomena displayed by a richer situation.