Polarization imaging has attracted extensive attention in recent years due to its ability to detect object polarization information and effectively suppress noise signals of background.The previous research on sinusoidal amplitude grating imaging is basically carried out under the conditions of fully coherent,incoherent or partially coherent illumination.While this paper is based on the unified theory of polarization coherence,and it takes the polarization state of light into account under the condition of partially coherent illumination,and designs a partially coherent light′s polarization imaging system illuminated by a sinusoidal amplitude grating,according to which the Stokes frequency domain calculation model is obtained,and a method for calculating the frequency domain relationship of the Stokes object image is provided.Also,the frequency response of the polarization imaging system is described by the transmission cross coefficient,the nonlinearity of the polarization imaging system is showed,direct component,the fundamental frequency and the second harmonic in the grating image intensity are analyzed,and a set of normalized Stokes parameters is given,under which the partial coherent light irradiates the sinusoidal amplitude grating on the image plane intensity map,and this paper uses MATLAB to draw several sets of Stokes image intensity maps under the ratio of the illumination coherence interval of the object to the diffraction pattern size of the imaging system are plotted,which extends the application of the sinusoidal trajectory analysis in the performance evaluation of the polarization imaging system.