A method and apparatus of a novel modeling scheme for performing optical lithography simulation for a multi-tone mask with a plurality of mask tones is described. The method generates a transmission function matrix based on a setting of the multi-tone mask. The method applies the transmission function matrix to transform a formula for calculating light intensity from Abbe's form to Hopkins' form while maintaining the accuracy of Abbe's form. The method then computes the light intensity using the transformed formula.
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