Electron beams can be reflected by an electrode that is at a more negative potential than the cathode from which the beam is emitted. We want to design a mirror with a flat mirror electrode where the electrons are reflected at a plane very close to the electrode. The wave front of an electron can then be shaped when the mirror contains a surface topography or modulated potential. However, electron beams reflected by flat electron mirrors are usually characterized by high coefficients of chromatic and spherical aberration. When the mirror is combined with an electrostatic lens to form a tetrode mirror system, the situation deteriorates even further. This places a restrictive limit on the maximum aperture angle of the beam, and consequently also limits the attainable resolution at the image plane. We have numerically studied the dependence of these aberrations as a function of design parameters of the tetrode mirror consisting of a ground, lens, cap, and mirror electrode, and limited ourselves to only using flat electrodes with round apertures, at fixed electrode spacing. It turns out that the third order spherical aberration can be made negative. The negative third order aberration is then used to partially compensate the positive fifth order aberration. This way, a system configuration is obtained that, at 2 keV beam energy, provides a diffraction limited resolution of 7.6 nm at an image plane 25 mm from the mirror at beam semi-angles of 2.3 mrad, enabling an illumination radius of 40 μm at the mirror. The presented tetrode mirror design could spark innovative use of patterned electron mirrors as phase plates for electron microscopy in general, and for use as coherent beam splitters in Quantum Electron Microscopy in particular. An appendix presents a method to calculate the spot size of a focused beam in the presence of both third and fifth order spherical aberration coefficients, which is also applicable to Scanning (Transmission) Electron Microscopes with aberration correctors.

中文翻译：

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平面电子镜

电子束可以被一个电极反射，该电极的电位比发射电子束的阴极更负。我们想设计一个带有平面镜面电极的镜子，其中电子在非常靠近电极的平面上被反射。当镜子包含表面形貌或调制电位时，电子的波前可以被成形。然而，平面电子镜反射的电子束通常具有较高的色差和球差系数。当镜子与静电透镜结合形成四极镜系统时，情况会进一步恶化。这对光束的最大孔径角设置了限制性限制，因此也限制了图像平面上可达到的分辨率。我们已经通过数值研究了这些像差与由接地、透镜、帽和镜电极组成的四极管镜的设计参数的函数关系，并将我们自己限制为仅使用具有圆形孔径的扁平电极，电极间距固定。结果表明，可以使三阶球面像差为负。然后使用负三阶像差来部分补偿正五阶像差。通过这种方式，获得了一个系统配置，在 2 keV 光束能量下，在离反射镜 25 mm 的像平面上以 2.3 mrad 的光束半角提供 7.6 nm 的衍射极限分辨率，从而实现 40 μm 的照明半径镜子。所提出的四极镜设计可以激发图案电子镜的创新使用，作为一般电子显微镜的相位板，特别是用作量子电子显微镜中的相干分束器。附录介绍了一种在存在三阶和五阶球面像差系数的情况下计算聚焦光束光斑大小的方法，该方法也适用于带有像差校正器的扫描（透射）电子显微镜。