Polarization imaging has attracted extensive attention in recent years due to its ability to detect object polarization information and effectively suppress noise signals of backgro und.The previous research on sinusoidal amplitude grating imaging is basically carried o ut under the conditions of fully coherent,incoherent or partially coherent illumination.Whi le this paper is based on the unified theory of polarization coherence,and it takes the polari zation 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 grati ng,according to which the Stokes frequency domain calculation model is obtained,and a method for calc ulating 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 coeffi cient,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 paramet ers 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 i ntensity maps under the ratio of the illumination coherence interval of the object to the diff raction pattern size of the imaging system are plotted,which extends the application of the sinusoidal traj ectory analysis in the performance evaluation of the polarization imaging system.