Temporal correlation of waves scattered off or transmitted through a random medium has been for a long time a very efficient tool in studying space-time dynamics of a great variety of complex structures [1,2]. At the microscale, typical examples include the solutions of macromolecules and colloidal suspensions, gels, foams, granular materials, and biological tissues. Macroscopic structures range from atmospheric turbulence and internal waves in the ocean to ionospheric and interstellar plasmas.

In this work, an original model based on the first principles is constructed for the temporal correlation of wave field propagating in strongly scattering random media [3-5]. The predictions of this model are consistent, in general, with those of the diffusing-wave spectroscopy [1]. However, it is shown that by considering the wave vector as a free parameter that can vary at will, we can provide an additional dimension to the data, which results in a tomographic-type reconstruction of the full space-time dynamics of a complex structure, instead of a plain spectroscopic technique. In the Fourier space the problem is reduced to a spherical mean transform defined for a family of spheres containing the origin and therefore is easily invertible. Hopefully, the developed diffusing wave tomography technique may find many applications in various areas of soft condensed matter science, biomedical analysis, and geophysics, to name a few.

[1]   B. J. Berne and R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).

[2]   A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).

[3]   G. Samelsohn and E. Gruzdev, Phys. Rev. E 78, 036601 (2008).

[4]   G. Samelsohn, V. Freilikher, and M. Haridim, Phys. Rev. E 78, 066602 (2008).

[5]   G. Samelsohn, Waves Random Complex Media 19, 11 (2009).