A fast method for calculating the thermal effect in projection objective lenses

A new method is mentioned which can be used to simulate the thermal effect in the projection objective lens with fast speed. The method improves the solving period by separating the all solution to two steps: the first step is to obtain the transfer matrix between intensity distribution of the incident beam and thermal effect (including lens temperature and surface deformation). The second step is to express the intensity distribution with polynomial coefficients and multiply the fitting coefficients by the transfer matrix. The solving-time and the precision of the method are validated by analyzing the thermal effects on three different lenses with 0.2 s to get the node temperature and the Zernike coefficients of the surface deformation, while the general finite element analysis (FEA) method needs 600 s. Another advantage of the new method is that the solving-time isn't lengthened with more nodes. Temperature peak valley (PV) error is 0.002°C, and fitting error of Zernike coefficient is 0.005 nm. The accuracy can match the requirement of calculating system aberration.