Journal of Biomedical OpticsOptical coherence propagation and imaging in a multiple scattering medium
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We present a formal, microscopic, solution of the wave propagation problem for an inhomogeneity embedded in an isotropically disordered, multiple scattering, homogeneous background. The inhomogeneity is described by a local change in the complex, dielectric autocorrelation function B(r,r8) [v4/c4^e*(r)e(r8)&ensemble for a wave of frequency w and velocity c. For the homogeneous background, we consider a dielectric autocorrelation function Bh(r−r8) arising from a colloidal suspension of small dielectric spheres. This autocorrelation function can be determined using a newly developed technique called phase space tomography for optical phase retrieval. This technique measures the optical Wigner distribution function I(R,k) defined as the Fourier transform, with respect to r, of the electric field mutual coherence function ^E*(R+r/2)E(R −r/2)&ensemble. The Wigner distribution function is the wave analog of the specific light intensity, Ic(R,k ˆ ), in radiative transfer theory which describes the number of photons in the vicinity of R propagating in direction k ˆ. The Wigner function describes coherence properties of the electromagnetic field which can propagate much longer than the transport mean-free-path l* and which are not included in radiative transfer theory. Given the nature of the homogeneous background, repeated light intensity measurements, which determine the optical phase structure at different points along the tissue surface, may be used to determine the size, shape, and internal structure of the inhomogeneity. In principle, this method improves the resolution of optical tomography to the scale of several optical wavelengths in contrast to methods based on diffusion approximation which have a resolution on the scale of several transport mean-free-paths.