As an advanced imaging technique, the polarization imaging has attracted more and more interests and many applications have been developed in the fields, such as biomedical diagnostics, target identification and remote sensing due to its unique ability to detect the polarization information of objects. On the other hand, the grating with its periodic spatial structure has been used widely in various imaging systems including but not limited to holographic imaging, Talbot effect of self-imaging, and imaging spectrometer. Furthermore, a sinusoidal amplitude grating is of considerable interest in image analysis and optical system characterization. Although many techniques with applications of the gratings have been developed in the last decades, few investigations have been made to the sinusoidal amplitude grating in a polarization imaging system with arbitrary illumination condition of polarization and coherence. In this paper, the polarization imaging of a sinusoidal amplitude object illuminated with a partially polarized and partially coherent light is investigated. With the help of the unified theory of polarization and coherence, we have extended the use of sinusoidal trace analysis in the evaluation of optical system performance and presented theoretical analysis on the Stokes images of a sinusoidal amplitude grating.