Optical lithography is an indispensible step in the process flow of Design for Manufacturability (DFM). Optical lithography simulation is a compute intensive task and simulation performance, or lack thereof can be a determining factor in time to market. Thus, the efficiency of lithography simulation is of paramount importance. Coherent decomposition is a popular simulation technique for aerial imaging simulation. In this thesis, we propose an approximate simulation technique based on the 2D wavelet transform and use a number of optimization methods to further improve polygon edge detection. Results show that the proposed method suffers from an average error of less than 6% when compared with the coherent decomposition method. The benefits of the proposed method are (i) > 20X increase in performance and more importantly (ii) it allows very large circuits to be simulated while some commercial tools are severely capacity limited and cannot even simulate a circuit as small as ISCAS-85 benchmark C17. Approximate simulation is quite attractive for layout optimization where it may be used in a loop and may even be acceptable for final layout verification.