Abstract

Crystal diffraction is a well-established technique for high-resolution structural analysis of material science and biological samples. However, the recovered structure is a result of averaging over all the unit cells in the crystal, which smears out the imperfections, atomic defects, or asymmetries and chiral properties of the individual molecules. We propose Bragg holography, where a nano-crystal is imaged at a defocus distance allowing separation of the diffracted beams, without turning them into peaks. The presence of a reference wave gives rise to a Bragg hologram, which can be reconstructed by conventional holographic reconstruction algorithms. The recovered complex-valued wavefront contains the complete information about the atomic distribution in the crystal, including defects. Bragg holography is demonstrated for gold nano-crystals, and its feasibility for biological nano-crystals is shown.

Highlights

  • X-ray crystallography, where signal is averaged over thousands of unit cells, has been routinely applied for solving the molecular structure of biological and material science samples [1]

  • We propose Bragg holography, where a nano-crystal is imaged at a defocus distance allowing separation of the diffracted beams, without turning them into peaks

  • High-resolution imaging of material science and biological crystalline samples can be realized in an electron microscope by a number of established techniques, such as selected-area electron diffraction (SAED) and high-resolution transmission electron microscopy (HRTEM)

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Summary

Introduction

X-ray crystallography, where signal is averaged over thousands of unit cells, has been routinely applied for solving the molecular structure of biological and material science samples [1]. High-resolution imaging of material science and biological crystalline samples can be realized in an electron microscope by a number of established techniques, such as selected-area electron diffraction (SAED) and high-resolution transmission electron microscopy (HRTEM). Standard SAED yields data with good signal-to-noise ratio (SNR) and insensitivity to real space specimen drift; but this technique yields only structure factor amplitudes, and the corresponding phases must be obtained via other means, such as molecular replacement [5]. In 1992, Coene et al demonstrated the unambiguous high-resolution reconstruction of samples obtained from a focal series acquired in a transmission electron microscope (TEM), which has become a practical tool for image analysis in HRTEM [6]. Having access to the full wave allows numerical back-propagation to the specimen, with confidence that the reconstructed image signal can be directly related to the sample structure (including defects). The details, including some practical limitations and constraints, are the subject of this paper

Principle
Non-biological crystals
Biological crystals
Discussion
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