Theoretical optimal modulation frequencies for scattering parameter estimation and ballistic photon filtering in diffusive media

The efficiency of using intensity modulated light for estimation of scattering properties of a turbid medium and for ballistic photon discrimination is theoretically quantified in this article. Using the diffusion model for modulated photon transport and considering a noisy quadrature demodulation scheme, the minimum-variance bounds on estimation of parameters of interest are analytically derived and analyzed. The existence of a variance-minimizing optimal modulation frequency is shown and its evolution with the properties of the intervening medium is derived and studied. Furthermore, a metric is defined to quantify the efficiency of ballistic photon filtering which may be sought when imaging through turbid media. The analytical derivation of this metric shows that the minimum modulation frequency required to attain significant ballistic discrimination depends only on the reduced scattering coefficient of the medium in a linear fashion for a highly scattering medium

Spectral Method for Multiplexed Phase Retrieval and Application in Optical Imaging in Complex Media

We introduce a generalized version of phase retrieval called multiplexed phase retrieval. We want to recover the phase of amplitude-only measurements from linear combinations of them. This corresponds to the case in which multiple incoherent sources are sampled jointly, and one would like to recover their individual contributions. We show that a recent spectral method developed for phase retrieval can be generalized to this setting, and that its performance follows a phase transition behavior. We apply this new technique to light focusing at depth in a complex medium. Experimentally, although we only have access to the sum of the intensities on multiple targets, we are able to separately focus on each ones, thus opening potential applications in deep fluorescence imaging and light deliver