CEITEC - Central European Institute of Technology, Brno University of Technology, Purkyňova 123, Brno 612 00, Czech Republic.
CEITEC - Central European Institute of Technology, Brno University of Technology, Purkyňova 123, Brno 612 00, Czech Republic; Institute of Physical Engineering, Brno University of Technology, Technická 2, Brno 616 69, Czech Republic.
Ultramicroscopy. 2018 Jun;189:95-101. doi: 10.1016/j.ultramic.2018.03.023. Epub 2018 Mar 29.
Standard 3D interpolation polynomials often suffer from numerical errors of the calculated field and lack of node points in the 3D solution. We introduce a novel method for accurate and smooth interpolation of arbitrary electromagnetic fields in the vicinity of the optical axis valid up to 90% of the bore radius. Our method combines Fourier analysis and Gaussian wavelet interpolation and provides the axial multipole field functions and their derivatives analytically. The results are accurate and noiseless, usually up to the 5th derivative. This is very advantageous for further applications, such as accurate particle tracing, and evaluation of aberration coefficients and other optical properties. The proposed method also enables studying the strength and orientation of all multipole field components. To illustrate the capabilities of the proposed algorithm, we present three examples: a magnetic lens with a hole in the polepiece, a saturated magnetic lens with an elliptic polepiece, and an electrostatic 8-electrode multipole.
标准的 3D 插值多项式通常会受到计算域的数值误差和 3D 解中节点缺失的影响。我们引入了一种新的方法，可以在光学轴附近精确且平滑地插值任意电磁场，其有效范围可达孔径的 90%。我们的方法结合了傅里叶分析和高斯小波插值，并提供了轴向多极场函数及其导数的解析表达式。结果准确且无噪声，通常可达第 5 阶导数。这对于进一步的应用非常有利，例如精确的粒子追踪、像差系数和其他光学性质的评估。所提出的方法还可以研究所有多极场分量的强度和方向。为了说明所提出算法的能力，我们展示了三个示例：磁极片上有孔的磁透镜、具有椭圆形磁极片的饱和磁透镜和静电 8 电极多极。
