For a checkerboard depolarizer containing random polarization cell,we statistically analyse its modulation behaviour to partially coherent incident rays.Within the framework of 2? coherence matrix,the change of coherence and the associated polarization properties are consequently derived.Under the paraxial assumption,The propagation of such modulated beams passing through generic optical system including Gaussian apertures are discussed on the basis of the complex ABCD matrix theory,and the expressions of the statistical properties are shown in terms of coherence matrix elements to provide the impact of screen and propagation system structure parameters including the cell size and the distance to observations screen.