Diffuse time tomography of strongly scattering random structures^†

Abstract

An original model of wave propagation in strongly scattering transparent random structures with arbitrary correlated disorder is derived from the first principles. In particular, it is shown that the mean arrival (or diffuse) time of a short narrowband pulse can be presented as a linear integral transform of the microstructure's power spectrum. Moreover, this integral transform is invertible, which allows one, in principle, to reconstruct the correlation function of a heterogeneous medium by measuring the angular distributions of the diffuse time for waves of different frequencies. This technique, called here the diffuse time tomography, is free of the intrinsic diffraction tomography limitations; the most important is the fact that it can be applied to strongly scattering structures.

Wave tomography of time-varying disordered structures

“…These are just the Ewald spheres constructed for different frequencies and propagation directions (the information contained actually in the wave vector k). The spherical mean operator is known to be invertible [11,12]. In particular, it may be converted into the classical Radon transform using a geometric inversion of the K-space with respect to a reference sphere centered at the origin [11].…”

Archives of Acoustics

“…The spherical mean operator is known to be invertible (Cormack, Quinto, 1980). In particular, it may be converted into the classical Radon transform by using a geometric inversion of the q-space with respect to a reference sphere centered at the origin (Yagle, 1992;Samelsohn, 2009).…”

Inverse scattering of random media

“…The well known algorithm of diffraction tomography, based on the invertible expression relating the power spectrum of the medium to the coherence function of the scattered field, is applicable only to weakly scattering media, where the scattered field may be evaluated in the framework of the Born or Rytov approximation [2,3]. Recently, we have developed a new concept called Diffuse Time Tomography (DTT) which is suitable to study strongly scattering disordered structures [4]. This new modality implies that a short narrowband pulse (with wave vector k) is transmitted through the sample, and the normalized impulse response function (photon time-offlight distribution) ( ) J t k is measured by the detector.…”