We consider two partially correlated scalar light beams in a spatially unitary interference setup. We introduce a state vector in a Poincaré-sphere-like geometrical configuration that fully specifies such an optical system and its evolution under spatial unitary transformations. We also identify three particular unitary operations together with their geometrical representations that can be optically implemented to realize an arbitrary spatial unitary transformation. Our work forms an advantageous geometrical platform to characterize distinguishability, visibility, degree of coherence, and classical entanglement, as well as their spatial unitary evolutions, in scalar two-beam light interference.
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