Using state tomography for characterizing input principal modes in optically scattering medium

We propose two new methods to measure principal modes, or Eisenbud-Wigner-Smith eigenstates in optically scattering medium. Both methods use similar techniques as in quantum state tomography, and are based on direct measurement of temporal delays. The first method requires N² different input launching conditions, and only the mean signal delay of these input states are needed to obtain full information of the principal modes. When the mode delay differences are large and all modes are non-degenerate, a second method can be used, which only requires 3N - 2 input launching conditions.