Wigner phase space distributions and coherence tomography

We demonstrate the measurement of path-length-resolved optical phase space distributions as a new framework for exploring the evolution of optical coherence in a turbid medium. This method measures joint transverse position and momentum (i.e., angle) distributions of the optical field, resolved by optical path length in the medium. The measured distributions are related to the Wigner phase space distribution function of the optical field, and can provide complete characterization of the optical coherence in multiple scattering media. Optical phase space distributions are obtained as contour plots which enable a visual as well as quantitative method of characterizing the spatial coherence properties and wavefront curvature of the input and scattered fields. By using a broad-band source in a heterodyne detection scheme, we observe transmission and backscatter resolved by path length in the random medium, effectively providing time resolution. New two-window heterodyne detection methods permit independent control of position and momentum resolution with a variance product that surpasses the uncertainty limit associated with Fourier transform pairs. Hence, high position and angular resolution can be simultaneously achieved. These techniques may provide new venues for using optical coherence in medical imaging.