Ma Bin, Li Lin, Thompson Kevin P, Rolland Jannick P
The Institute of Optics, University of Rochester, 275 Hutchinson Road, Rochester, New York 14627, USA.
Opt Express. 2011 Oct 24;19(22):21174-9. doi: 10.1364/OE.19.021174.
It has recently been shown that the coefficients that specify the aspheric departure from a spherical surface in high NA lithographic lenses routinely require more significant digits than are available in even double precision computers when they are described as part of a power series in aperture-squared. The Q-type aspheric description has been introduced to solve this problem. An important by-product of this new surface description is that it allows the slope of a surface to be directly constrained during optimization. Results show that Q-type aspheric surfaces that are optimized with slope constraints are not only more testable, an original motivation, but, they can also lead to solutions that are less sensitive to assembly induced misalignments for lithographic quality lenses. Specifically, for a representative NA 0.75 lens, the sensitivity to tilt and decenter is reduced by more than 3X, resulting in significantly higher lens performance in-use.
最近的研究表明，在高数值孔径光刻透镜中，当用孔径平方的幂级数来描述偏离球面的非球面系数时，其所需的有效数字位数通常比即使是双精度计算机所能提供的还要多。为了解决这个问题，引入了Q型非球面描述。这种新的表面描述的一个重要副产品是，它允许在优化过程中直接约束表面的斜率。结果表明，通过斜率约束优化的Q型非球面表面不仅更易于测试（这是最初的动机），而且对于光刻质量的透镜，它们还可以导致对装配引起的失准不太敏感的解决方案。具体而言，对于一个代表性的数值孔径为0.75的透镜，其对倾斜和偏心的敏感度降低了三倍多，从而在实际使用中显著提高了透镜性能。
