Statistical properties of complex amplitude of ultrasonic speckles back scattered from a Gaussian interface

Some statistical properties of complex amplitude of the ultrasonic speckles back scattered from a Gaussian interface which is insonified by ultrasound is analyzed theoretically. Based on the condition of continuous interface, the mean functions and the variance functions of the real part and the imaginary part of the complex amplitude of the ultrasonic speckles are deduced. The further analyses show that when the roughness of a Gaussian interface becomes extremely small or extremely large, these functions change to be identical with that deduced from a smooth interface or a strongly scattering interface.