Efficient Switchable Common Path Interferometer for Transmission Matrix Characterization of Scattering Medium

Transmission matrix can be used as an elegant tool to represent the light transmission characteristics of a scattering medium. In this paper, we propose a novel common path interferometer technique to measure the transmission matrix utilizing the polarization rotation of incident beam. Specifically, the horizontally polarized and vertically polarized components of the incident beam are used as signal light and reference light, respectively. By rotating the polarization of the incident beam, the ratio between the powers of signal and reference light can be freely adjusted and balanced. The phase shift method is employed to retrieve the transmission matrix of scattering medium. Once the transmission matrix is known, the polarization of the incident light beam can be rotated to switch off the reference and only the signal will remain. Focusing and manipulation of light through a ground glass has been experimentally demonstrated with the measured transmission matrix. An optical focus enhancement reaches 83% of the theoretical maximal value is obtained, which is about 30% improvement compared to the previous co-propagation method. The transmission matrix characterization method has the potential to become a general tool to harness the multiple scattering of light through complex medium.