Theoretical study on the mechanisms of ultrasonic modulation of multiply scattered light

An analytic model of the ultrasonic modulation of multiply scattered coherent light in scattering media is provided. The model is based on two mechanisms: the ultrasonic modulation of the index of refraction, which causes a modulation of the optical path lengths between consecutive scattering events, and the ultrasonic modulation of the displacements of Rayleigh scatterers, which causes a modulation of optical path lengths upon each scattering event. Multiply scattered light accumulates modulated optical path lengths along its path. Consequently, the intensity of the speckles that are formed by the multiply scattered light is modulated. In water solutions, for example, the contribution from the index of refraction is slightly less than the contribution from displacement when the scattering mean free path is less than a critical fraction of the acoustic wavelength, and it becomes increasingly greater than the contribution from displacement beyond this critical point.