Single-Shot Direct Tomography of the Complete Transverse Amplitude, Phase, and Polarization Structure of a Light Field

We present a direct-tomography protocol that is capable of characterizing the transverse spatial profile of both the polarization and the complex amplitude of fully polarized vector light beams in a single-shot measurement. This protocol entails a sequence of steps: a coherent mode transformation, a weak polarization perturbation, and a polarization-resolved imaging process. The final readout is directly proportional to the complex-amplitude profile of the two polarization components of the vector beam. We experimentally demonstrate our direct measurement protocol on a variety of commonly used vector beams, including vector-vortex beams and full Poincare beams. Our method provides the capability of acquiring all the information needed to characterize a fully polarized vector beam in a single-shot measurement. Such a real-time complete-tomography protocol has the potential to create new opportunities in emerging applications of vector beams as well as the fundamental study of complex physical systems with multiple degrees of freedom.