We propose a method that realizes the modified illumination by implementing a binary phase grating at the backside of a photomask. By modeling the relationship between the shape of a grating on the photomask and the light intensity at the pupil plane, we developed a program named MIDAS that finds the optimum grating pattern with a stochastic approach. After applying the program to several examples, we found that the program finds the grating pattern for the modified illumination that we want. By applying the grating at the backside of a photomask, the light efficiency of modified illumination may be improved.