Fig. 7: Working principle of the quantification of φk(ρ) in MST algorithm.
From: Tracing multiple scattering trajectories for deep optical imaging in scattering media
a Illustration of the first term of \(E({{{{{{\boldsymbol{\rho }}}}}}}_{i},{z}_{0};{{{{{{\boldsymbol{\rho }}}}}}}_{j},{z}_{k})\) in Eq. (3), which is the \({j}^{{{{{{\rm{th}}}}}}}\) column vector of the propagated reflection matrix \({{{{{{\boldsymbol{R}}}}}}}_{{z}_{0},{z}_{k}}\) with \(j=1,2\). b Illustration of phase correlation method for finding the phase functions \({\varphi }_{k}({{{{{{\boldsymbol{\rho }}}}}}}_{j})\). Examples of \(E\left({{{{{{\boldsymbol{\rho }}}}}}}_{i},{z}_{0};{{{{{{\boldsymbol{\rho }}}}}}}_{1},{z}_{k}\right)\) and \(E\left({{{{{{\boldsymbol{\rho }}}}}}}_{i},{z}_{0};{{{{{{\boldsymbol{\rho }}}}}}}_{2},{z}_{k}\right)\) are shown at the first row. After normalizing the respective Green’s functions (second row), only the object function remains along with \({\varphi }_{k}\left({{{{{{\boldsymbol{\rho }}}}}}}_{1}\right)\) and \({\varphi }_{k}\left({{{{{{\boldsymbol{\rho }}}}}}}_{2}\right)\). Based on the correlation of the two field images in the third row, an approximate phase function \({\varphi }_{k}\left({{{{{{\boldsymbol{\rho }}}}}}}_{2}\right)-{\varphi }_{k}\left({{{{{{\boldsymbol{\rho }}}}}}}_{1}\right)\) can be obtained. All the images in d represent phase maps. Note that the illustrations in a and b show only the first term in Eq. (3) for clarity.
