
AbstractThe coherence of an optical beam having multiple degrees of freedom (DoFs) is described by a coherency matrixGspanning these DoFs. This optical coherency matrix has not been measured in its entirety to date—even in the simplest case of two binary DoFs whereGis a 4 × 4 matrix. We establish a methodical yet versatile approach—optical coherency matrix tomography—for reconstructingGthat exploits the analogy between this problem in classical optics and that of tomographically reconstructing the density matrix associated with multipartite quantum states in quantum information science. HereGis reconstructed from a minimal set of linearly independent measurements, each a cascade of projective measurements for each DoF. We report the first experimental measurements of the 4 × 4 coherency matrixGassociated with an electromagnetic beam in which polarization and a spatial DoF are relevant, ranging from the traditional two-point Young’s double slit to spatial parity and orbital angular momentum modes.
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