Quantitative control over the intensity and phase of light transmitted through highly scattering media

We experimentally demonstrate the use of the transmission matrix (TM) to quantitatively control the amplitude and phase of the light transmitted through highly scattering media. This is achieved by measuring the absolute value of the TM elements. We also use the fact that the cross-correlations between the contributions of different input channels at the observation plane is important in describing the transmitted optical field. In addition, we demonstrate both quantitative control of the intensity at multiple output spatial modes, each with a different intensity, as well as a "dark" area of low intensity. Our experiments are carried out using a low cost (less than US$600) spatial binary amplitude modulator that we modify for phase-only operation, as well as a novel optical setup that enables independent control of a reference and control signal while maintaining interferometric stability. The optical implementation used in this paper will make such experiments widely accessible to many researchers. Furthermore, the results presented could serve as the foundation for many useful potential applications ranging from the biomedical sciences to optical communications.