Measuring the complete complex correlation matrix of a partially coherent vector beam via self-referencing holography

Measuring the complete complex correlation matrix of a partially coherent vector beam is extremely important for transmission calculation, encryption, and decryption for free-space optical communication and optical imaging. Based on self-referencing holography, we introduce a simple and efficient setup to measure the complex-valued cross spectral density matrix of a partially coherent vector beam, without any priori assumptions or approximations of the source. To verify the feasibility of our method, 2  × 2 complex-valued cross spectral density components in the matrix function of particularly correlated radially polarized partially coherence beam have been measured. The experimental measurements are in good agreement with the theoretical model.