Correlation transfer and diffusion of ultrasound-modulated multiply scattered light

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 ultrasound-modulated optical tomography of soft biological tissues.