Abstract: Yield rate, reliability and electrical characteristics of ICs can be investigated to a certain degree by simulation of the transferring process from mask patterns to silicon image. Based on Gabor's method of "reduction to principal waves", a partially coherent imaging system is represented as a superposition of coherent imaging systems. A Gaussian convolution representing the inhibitor diffusion is subsequently applied to the aerial image. An accurate and fast method to calculate intensities of sparse aerial points is derived based on the early approaches. Two matrix decomposition methods, which take advantage of the fact that the transmission cross-coefficient (TCC) of a stepper is Hermitian, are also presented and discussed.