Freeform lens for off-axis illumination in optical lithography system

A method of designing a freeform lens for off-axis illumination (OAI) in an optical lithography system is proposed in this paper. Based on the Snell's law and conservation law of energy, a series of first-order partial differential equations are deduced. Coordinate relations are established with the energy mapping relations by the characteristics of the incident beam and the predetermined irradiance distribution on the target plane. The contours of the freeform lens are calculated by solving partial differential equations numerically. Moreover, the optical performance for OAI is simulated and analyzed. Simulation results show that the irradiance distributions can be well controlled with a maximum uniformity of 95.71% and a maximum efficiency of 99.04%. Tolerance analysis shows that the angular errors of the freeform lens are more sensitive than the coordinate errors.