Correlation transfer equation for multiply scattered light modulated by an ultrasonic pulse: an analytical model and Monte Carlo simulation

We present derivation of the temporal correlation transfer equation (CTE) for multiply scattered light modulated by an ultrasound pulse. The equation can be used to obtain the time-varying specific intensity of light produced by a pulsed and nonuniform ultrasound field in optically scattering media that have a heterogeneous distribution of optical parameters. We also develop a Monte Carlo algorithm that can simulate the spatial distribution of the time-dependent power spectrum density of light modulated by a focused ultrasound pulse in optically scattering media with heterogeneous distributions of optically scattering and absorbing objects. Derivation is based on the ladder diagram approximation of the Bethe-Salpeter equation that assumes moderate ultrasound pressures. We expect these results to be applicable to a wide spectrum of conditions in the ultrasound-modulated optical tomography of soft biological tissues.