Efficient framework of solving time-gated reflection matrix for imaging through turbid medium.

Imaging through turbid medium is a long pursuit in many research fields, such as biomedicine, astronomy and automatic vehicle, in which the reflection matrix-based method is a promising solution. However, the epi-detection geometry suffers from round-trip distortion and it is challenging to isolate the input and output aberrations in non-ideal cases due to system imperfections and measurement noises. Here, we present an efficient framework based on single scattering accumulation together with phase unwrapping that can accurately separate input and output aberrations from the noise-affected reflection matrix. We propose to only correct the output aberration while suppressing the input aberration by incoherent averaging. The proposed method is faster in convergence and more robust against noise, avoiding precise and tedious system adjustments. In both simulations and experiments, we demonstrate the diffraction-limited resolution capability under optical thickness beyond 10 scattering mean free paths, showing the potential of applications in neuroscience and dermatology.