This study introduces a differential algebra (DA) method to the high-order aberration analysis of a multi-offset cylindrical lens. The axial field functions (AFF) of harmonic field components for a cylindrical lens are interpolated into an analytic expression using a Gaussian wavelet, which can be transferred into DA arguments and can be operated as per DA methodology. The tracing of one reference ray can enable the high-order aberration coefficients of the multi-offset cylindrical lens to be obtained. As an example, a monochromator (MC) with a multi-offset cylindrical lens is computed, and up to third rank aberration coefficients are obtained using the developed DA method. The software has been developed and tested extensively.

本研究将微分代数（DA）方法引入了多偏移量圆柱透镜的高阶像差分析中。使用高斯小波将圆柱透镜的谐波场分量的轴向场函数（AFF）内插到解析表达式中，该表达式可以转换为DA参数并可以按照DA方法进行操作。跟踪一条参考射线可以使多偏移量柱面透镜的高阶像差系数得以获得。作为示例，计算出具有多偏移量柱面透镜的单色仪（MC），并使用开发的DA方法获得多达三级像差系数。该软件已被广泛开发和测试。