A quadrupoles acceptance is a measure of its ability to catch ions with certain trajectories. One way to calculate acceptance is the method of ellipses. The method arose partly from a simplification that trajectories could be calculated for an electrode axis independently of others. It has been used to calculate the acceptance and transmission of sine-driven quadrupole mass filters for over 50 years. Although the method is straightforward, it is generally described with little detail or presented as a confusing string of equations. As such, it may not be decipherable by all practitioners. For this reason, the first half of this paper presents a practical explanation of the method of ellipses and the concepts that make it work. Only equations necessary to describe the method are introduced. The tutorial also prepares the reader for the second half, which presents an alternative approach for calculating acceptance based on an array of initial trajectories. The alternative approach is used to compare the acceptance of simplified sinusoidal and digital ion guides. The method of ellipses was applied to validate results of the new approach for calculation of acceptance.

中文翻译：

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正弦和数字离子导向器的接受和传输的教程和综合计算研究。

四极杆接受度是其捕获具有特定轨迹的离子的能力的度量。计算接受度的一种方法是椭圆法。该方法部分源于简化，即可以独立于其他方式计算电极轴的轨迹。它已被用于计算正弦驱动四极质量过滤器的验收和传输超过50年。尽管该方法简单明了，但通常描述得很少，或以令人困惑的一连串方程式形式呈现。因此，并非所有从业人员都能理解。因此，本文的前半部分对椭圆的方法和使椭圆起作用的概念进行了实用的解释。仅介绍描述该方法所需的方程式。本教程还为读者准备了下半年的内容，提出了一种基于初始轨迹数组来计算接受度的替代方法。另一种方法是比较简化的正弦波和数字离子导管的可接受性。应用椭圆法对新方法的验收结果进行验证。