Krielaart M A R, Kruit P
Delft University of Technology, Faculty of Applied Sciences, Department of Imaging Physics, Lorentzweg 1, 2628 CJ Delft, The Netherlands.
Delft University of Technology, Faculty of Applied Sciences, Department of Imaging Physics, Lorentzweg 1, 2628 CJ Delft, The Netherlands.
Ultramicroscopy. 2022 Mar;233:113424. doi: 10.1016/j.ultramic.2021.113424. Epub 2021 Nov 24.
We have analyzed the possibilities of wave front shaping with miniature patterned electron mirrors through the WKB approximation. Based on this, we propose a microscopy scheme that uses two miniature electron mirrors on an auxiliary optical axis that is in parallel with the microscope axis. A design for this microscopy scheme is presented for which the two axes can be spatially separated by as little as 1 mm. We first provide a mathematical relationship between the electric potential and the accumulated phase modulation of the reflected electron wave front using the WKB approximation. Next, we derive the electric field in front of the mirror, as a function of a topographic or pixel wise excited mirror pattern. With this, we can relate the effect of a mirror pattern onto the near-field phase, or far field intensity distribution and use this to provide a first optical insight into the functioning of the patterned mirror. The equations can only be applied numerically, for which we provide a description of the relevant numerical methods. Finally, these methods are applied to find mirror patterns for controlled beam diffraction efficiency, beam mode conversion, and an arbitrary phase and amplitude distribution. The successful realization of the proposed methods would enable arbitrary shaping of the wave front without electron-matter interaction, and hence we coin the term virtual phase plate for this design. The design may also enable the experimental realization of a Mach-Zehnder interferometer for electrons, as well as interaction-free measurements of radiation sensitive specimen.
我们通过WKB近似分析了使用微型图案化电子镜进行波前整形的可能性。在此基础上，我们提出了一种显微镜方案，该方案在与显微镜轴平行的辅助光轴上使用两个微型电子镜。给出了这种显微镜方案的一种设计，其中两个轴在空间上的间距可小至1毫米。我们首先利用WKB近似给出了电势与反射电子波前累积相位调制之间的数学关系。接下来，我们推导了镜面前方的电场，它是地形或逐像素激发镜图案的函数。通过这个，我们可以将镜图案对近场相位或远场强度分布的影响联系起来，并利用这一点对图案化镜的功能提供初步的光学见解。这些方程只能通过数值方法应用，为此我们描述了相关的数值方法。最后，应用这些方法来寻找用于控制光束衍射效率、光束模式转换以及任意相位和幅度分布的镜图案。所提出方法的成功实现将能够在无电子与物质相互作用的情况下对波前进行任意整形，因此我们将这种设计称为虚拟相位板。该设计还可能实现电子马赫-曾德尔干涉仪的实验实现，以及对辐射敏感样本的无相互作用测量。
