In this paper, we established a mathematical model for describing a partially coherent optical processing, and the error transfer formulas are also derived. The mathematical model could be used not only for estimating the error of a restoration image, but also for predicting the optimum source distribution. The necessary and sufficient condition for achieving non-error restoration image is obtained. And we also proved that for a truncation signal, the restoration image could be obtained with arbitrary precision by using an appropriate light source.