As an advanced technology, polarization imaging has attracted widespread interests in recent years due to its unique ability to detect the polarization information of objects. With illumination of partially coherent and partially polarized light, the polarization imaging systems are in generally nonlinear systems because they do not possess a transfer matrix in the usual sense. Nonetheless, it is possible to apply a sinusoidal amplitude object at the input and to measure a periodic output. However, unlike the linear case, knowledge of the response of the polarization system to a sinusoidal input does not allow one to predict what the output will be for other types of inputs. To address the fundamental nonlinearity in evaluation of the Stokes images, we provide a frequency- domain calculation of Stoke images of a sinusoidal amplitude grating under partially polarized and partially coherent illumination, and propose a new concept referred to as transmission cross coefficients to describe its frequency response of polarization imaging system. Some of the implications of such analysis are also given for polarization imaging evaluation.