Sakadžić and Wang17 previously derived a transport equation which describes the propagation of correlation in a turbid medium under insonification by a monochromatic acoustic field. The authors state a diffusion approximation to this transport equation which is valid under a number of assumptions regarding the nature of the acoustic excitation and optical properties. The principle limitation is that phase increments accrued at successive scattering sites are uncorrelated which requires that , where is the product of the acoustic wavenumber and the optical transport mean free path . Other limitations, such as the maximum permissible acoustic pressure amplitude, are introduced by the convenient approximations in the derivation. A more detailed analysis of the requisite approximations is presented in the original work, where the model is experimentally validated, demonstrating a good agreement in the region of validity of the standard optical diffusion approximation. The diffusion approximation reads Display Formula
(7)where Display Formula
(8)where is the diffusion coefficient, is the reduced scattering coefficient, is the scattering anisotropy, is the correlation fluence in the medium, is an isotropic source term, is the pressure amplitude of the acoustic field, is the optical wavenumber in vacuo, is the refractive index of the medium, is the acoustic wavenumber, is the density of the medium, is the speed of sound in the medium, is the angular acoustic frequency, is the acousto-optic coefficient, is the amplitude of scatterer displacement relative to the acoustic field, and is the relative phase of scatterer motion to the acoustic field.