Pupil energy balances have always been considered significant elements for emersion lithography generally due to the large angle of incidence and offset imaging field. Those imbalances impact on exposure uniformity and decay pattern resolution. To overcome such shortcomings, a study on pupil compensation is discussed in this manuscript. A computational method based on a constrained optimization solution is proposed. By using a self-designed optical model of a zoomed system incorporating axicon lenses, a series of computations are developed and discussed. Also, the validity of our compensation method has been fully verified by simulations under multiple illumination settings.