Tomography of Complex Coherence-Polarization Matrix of Random Vector Light for Phase Image Encoding

Random vector optical beams, also termed partially coherent vector beams (PCVBs), possess multiple controllable degrees of freedom (DOFs), such as polarization, phase, and degree of coherence, which make them crucial for diverse applications in optical encryption, metrology, and optical trapping. However, full experimental characterization of all of the DOFs of the PCVBs still faces a significant challenge. In this study, with the use of vector mode decomposition and an off-axis holography technique, we develop an efficient method for measuring the 4D cross-spectral density matrix (or called coherence-polarization matrix) of a PCVB, enabling one to retrieve all the second-order statistical characteristics and beyond. The principle of our method is thoroughly discussed, and we validate it in experiments to accurately recover the polarization, average intensity, and coherence state of two test beams. Furthermore, we explore a potential application of our measurement method in coherence-based phase image encoding and decoding. Our study offers promising potential in optical encryption, information transfer, and detection.