In accordance with the mathematical model for the DM procedure21 a propagation of the angular spectrum is carried out in the paraxial approximation of the light that crosses a phase object and the optical system of a microscope. The phase object is represented as two flat interfaces, 1 and 2, situated in the positions and in relation to an arbitrary plane. The interfaces 1 and 2 are characterized by the thickness functions and , respectively. If it is considered that the interfaces of the object fluctuate in time causing contrast fluctuations of the defocused image, i.e., the thickness function is time-dependent , then an expression for the mean square fluctuation for any defocus position can be obtained30Display Formula
(4)where is the focus position relative to an arbitrary plane and and are the wave numbers in a vacuum and in the medium, respectively. and are the fluctuation spectrums of each interface, with regard to its equilibrium state as , where denotes temporal average.