Temporal response of a random medium from speckle intensity frequency correlations

We reconstruct the temporal response of a random medium by using speckle intensity frequency correlations. When the scattered field from a random medium is described by circular complex Gaussian statistics, we show that third-order correlations permit retrieval of the Fourier phase of the temporal response with bispectral techniques. Our experimental results for random media samples in the diffusion regime are in excellent agreement with the intensity temporal response measured directly with an ultrafast pulse laser and a streak camera. Our speckle correlation measurements also demonstrate sensitivity to inhomogeneous samples, highlighting the potential application for imaging within a scattering medium.