论文部分内容阅读
为了加快投影物镜内部温度场和表面变形的求解速度,提出了一种快速求解算法。获得不同入射光强分布与透镜温度场及应变场之间的转换矩阵,对入射光强分布进行多项式分解,并将多项式系数与转换矩阵相乘实现镜片内部节点温度及表面面形变化的快速求解。通过求解三片不同类型透镜的节点温度与表面变形,验证了这一算法的求解精度与计算时间:直接进行有限元求解时,计算时间为600s;而快速求解法的求解时间缩短至0.2s,且它的计算时间不随节点数量的增多而增加。快速求解法对温度的求解精度可以达到0.002℃,对面形Zernike系数的求解精度可以达到0.005nm,能够满足像差求解过程对温度与面形求解精度提出的要求。
In order to speed up the solution of temperature field and surface deformation of projection lens, a fast algorithm is proposed. The transformation matrix between different incident light intensity distribution and lens temperature field and strain field is obtained, the incident light intensity distribution is decomposed by polynomial, and the polynomial coefficient is multiplied with the conversion matrix to realize the rapid solution of temperature and surface area change . The solution accuracy and calculation time of this algorithm are validated by solving the temperature and surface deformation of three different types of lens. The calculation time is 600s when the finite element method is used directly, and the solution time is shortened to 0.2s with the fast solution method. And its calculation time does not increase with the number of nodes. The precision of temperature solution can reach 0.002 ℃ by fast method, and the accuracy of Zernike coefficient can reach 0.005nm. It can meet the requirements of solving the temperature and surface shape accuracy.