Analytic solution for a quartic electron mirror

作者：Straton Jack C^*

来源：Ultramicroscopy, 2015, 148: 168-179.

DOI：10.1016/j.ultramic.2014.09.003

• Electron mirror
• Electron microscope
• Microscopy
• Aberration correction
• Jacobi cosine-amplitude functions

A converging electron mirror can be used to compensate for spherical and chromatic aberrations in an electron microscope. This paper presents an analytical solution to a diode (two-electrode) electrostatic mirror including the next term beyond the known hyperbolic shape. The latter is a solution of the Laplace equation to second order in the variables perpendicular to and along the mirror's radius (z(2) - r(2)/2) to which we add a quartic term (k lambda z(4)). The analytical solution is found in terms of Jacobi cosine-amplitude functions. We find that a mirror less concave than the hyperbolic profile is more sensitive to changes in mirror voltages and the contrary holds for the mirror more concave than the hyperbolic profile.

• 出版日期2015-1