Correlation Transfer and Diffusion of Ultrasound-Modulated Multiply Scattered Light

Abstract

We develop a temporal correlation transfer equation (CTE) and a temporal correlation diffusion equation (CDE) for ultrasound-modulated multiply scattered light, which can be used to calculate the ultrasound-modulated optical intensity in an optically scattering medium with a nonuniform ultrasound field and a heterogeneous distribution of optical parameters. We present an analytical solution based on the CDE for scattering of the temporal autocorrelation function from a cylinder of ultrasound in an optically scattering slab. The CDE is valid for moderate ultrasound pressures on a scale comparable with the optical transport mean free path, which must be greater than the ultrasound wavelength and smaller than or comparable to the sizes of both ultrasonic and optical inhomogeneities. These equations should be applicable to a wide spectrum of conditions for ultrasoundmodulated optical tomography of soft biological tissues.

Acousto-optic effect in random media

“…The most general such model is based on the Maxwell equations for a dielectric whose permittivity is modulated by an acoustic wave [1]. Alternatively, for multiply-scattered light, a phenomenological theory based on the radiative transport equation (RTE) or the diffusion approximation (DA) to the RTE may be employed [18][19][20][21]. In this paper, we develop a first-principles theory of the acousto-optic effect.…”

Fast acousto-optic tissue sensing with tandem nanosecond pulses

“…The model predicts a linear relation between the acoustic power and the speckle contrast which is verified experimentally in [33]. All these theories assume homogeneous acoustic waves, except for Sakadžić et al [35][36][37] in which localized acoustic waves were used.…”

“…Sakadžić et al [32,[35][36][37] and Wang [26] developed an analytical solution for this autocorrelation function equation 2.2, mostly focusing on the first two mechanisms. For a single pathlength s the contribution to the autocorrelation function is given by [26]:…”

“…The AO signal is affected not only by optical absorption and scattering in the US focus but also in the rest of the object. Therefore quantitative estimation of the absorption coefficient requires the number of tagged and untagged photons and an algorithm that solves the inversion problem as in DOT [36,39,60,[79][80][81].…”

“…Especially the model of Wang et al is widely used in biomedical optics i.e. [41,42] and is supported by an analytical model [27,32,35,36].…”