Energy extension in three-dimensional atomic imaging by electron emission holography

Abstract

A method is introduced joining together forward-scattering diffraction data taken in a small angular window at different photoelectron energies. This method extends the usable range in phase space for three-dimensional image reconstruction. Examples based on theoretical simulations demonstrate that a spatial resolution of < 1 A is achievable. We also show that using a small angular window in the backscattering geometry eliminates splittings in the reconstructed image.PACS numbers: 68.35.Bs, 68.55.-a When forming three-dimensional atomic images from electron-emission holography [1][2][3][4][5], there are two objectives: (i) that the images are formed at the correct atomic positions and (ii) that the full width at half magnitude (FWHM) of the image is as small as possible. The FWHM defines the ability of a "microscope" to produce distinct images of two closely spaced objects. The best resolution of the current state-of-the-art conventional electron microscope is 2-3 A. In electron-emission holography, a limiting factor is the small angular range of usable data available in k space for image reconstruction. In the forward-scattering geometry, most systems have multiple focusing directions [6]. In such systems, the diffraction fringes in an angular cone around each focusing direction are dominated by the scattering of atoms situated along that particular direction [7,8]. Therefore, the relevant interference fringes for image reconstruction for atoms in a particular direction are limited to within the effective angular cone O r , which is much smaller than the full 0,2* opening [7,9]. In the backscattering geometry, deep cusps in the scattering factor of many materials limit the effective angular range to a small cone in the reconstruction process. As we shall see later, these cusps cause image peaks to be split [10]. Since the diffraction limit for resolution is Ar a =2.4;r/Afc«, where a is a Cartesian-coordinate index, the small range of applicable Ak limits the achievable spatial resolution.In this paper, we show how this serious limitation of the technique can be lifted through the use of multiple energies in which diffraction data in a given angular cone taken at different emission energies are connected to form an extended range. When used in conjunction with a variable energy source (e.g., a synchrotron radiation center or Kikuchi electrons), this method can reach a spatial resolution of less than 1 A in the direction of the emitter scatterer. This direction has a worse resolution (> 2.5 A) in single-energy image reconstructions [2-6, 9,10].For the purpose of image reconstruction, we use x-rayphotoemission-spectroscopy (XPS) diffraction spectra calculated by the multiple-scattering slab method in which the crystal is rotated while the directions of photon incidence and electron exit are held fixed. This collection mode eliminates the anisotropy in the unscattered wave from any initial atomic core level [9]. Since the reference wave in this collection mode is continuously varying, we introduce an image reconstr...

Digital in-line holography for biological applications

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