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Register a new userRelative roles of multiple scattering and Fresnel diffraction in the imaging of small molecules using electrons, Part II: Differential Holographic Tomography
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It has been argued that in atomic-resolution transmission electron microscopy (TEM) of sparse weakly scattering structures, such as small biological molecules, multiple electron scattering usually has only a small effect, while the in-molecule Fresnel diffraction can be significant due to the intrinsically shallow depth of focus. These facts suggest that the three-dimensional reconstruction of such structures from defocus image series collected at multiple rotational orientations of a molecule can be effectively performed for each atom separately, using the incoherent first Born approximation. The corresponding reconstruction method, termed here Differential Holographic Tomography, is developed theoretically and demonstrated computationally on several numerical models of biological molecules. It is shown that the method is capable of accurate reconstruction of the locations of atoms in a molecule from TEM data collected at a small number of random orientations of the molecule, with one or more defocus images per orientation. Possible applications to cryogenic electron microscopy and other areas are briefly discussed.
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The real-space multiple-scattering (RSMS) approach is applied to model non-resonant inelastic scattering from deep core electron levels over a broad energy spectrum. This approach is applicable to aperiodic or periodic systems alike and incorporates ab initio, self-consistent electronic structure and final state effects. The approach generalizes to finite momentum transfer a method used extensively to model x-ray absorption spectra (XAS), and includes both near edge spectra and extended fine structure. The calculations can be used to analyze experimental results of inelastic scattering from core-electrons using either x-ray photons (NRIXS) or electrons (EELS). In the low momentum transfer region (the dipole limit), these inelastic loss spectra are proportional to those from XAS. Thus their analysis can provide similar information about the electronic and structural properties of a system. Results for finite momentum transfer yield additional information concerning monopole, quadrupole, and higher couplings. Our results are compared both with experiment and with other theoretical calculations.
We demonstrate that beams originating from Fresnel diffraction patterns are self-accelerating in free space. In addition to accelerating and self-healing, they also exhibit parabolic deceleration property, which is in stark contrast to other accelerating beams. We find that the trajectory of Fresnel paraxial accelerating beams is similar to that of nonparaxial Weber beams. Decelerating and accelerating regions are separated by a critical propagation distance, at which no acceleration is present. During deceleration, the Fresnel diffraction beams undergo self-smoothing, in which oscillations of the diffracted waves gradually focus and smooth out at the critical distance.
Numerical simulation of Fresnel diffraction with fast Fourier transform (FFT) is widely used in optics, especially computer holography. Fresnel diffraction with FFT cannot set different sampling rates between source and destination planes, while shifted-Fresnel diffraction can set different rates. However, an aliasing error may be incurred in shifted-Fresnel diffraction in a short propagation distance, and the aliasing conditions have not been investigated. In this paper, we investigate the aliasing conditions of shifted-Fresnel diffraction and improve its properties based on the conditions.
Optical hyperspectral imaging based on absorption and scattering of photons at the visible and adjacent frequencies denotes one of the most informative and inclusive characterization methods in material research. Unfortunately, restricted by the diffraction limit of light, it is unable to resolve the nanoscale inhomogeneity in light-matter interactions, which is diagnostic of the local modulation in material structure and properties. Moreover, many nanomaterials have highly anisotropic optical properties that are outstandingly appealing yet hard to characterize through conventional optical methods. Therefore, there has been a pressing demand in the diverse fields including electronics, photonics, physics, and materials science to extend the optical hyperspectral imaging into the nanometer length scale. In this work, we report a super-resolution hyperspectral imaging technique that simultaneously measures optical absorption and scattering spectra with the illumination from a tungsten-halogen lamp. We demonstrated sub-5 nm spatial resolution in both visible and near-infrared wavelengths (415 to 980 nm) for the hyperspectral imaging of strained single-walled carbon nanotubes (SWNT) and reconstructed true-color images to reveal the longitudinal and transverse optical transition-induced light absorption and scattering in the SWNTs. This is the first time transverse optical absorption in SWNTs were clearly observed experimentally. The new technique provides rich near-field spectroscopic information that had made it possible to analyze the spatial modulation of band-structure along a single SWNT induced through strain engineering.
Ultrafast electron diffraction and time-resolved serial crystallography are the basis of the ongoing revolution in capturing at the atomic level of detail the structural dynamics of molecules. However, most experiments employ the classical ball-and-stick depictions, and the information of molecular quantum states, such as the density matrix, is missing. Here, we introduce a framework for the preparation and ultrafast coherent diffraction from rotational wave packets of molecules, and we establish a new variant of quantum state tomography for ultrafast electron diffraction to characterize the molecular quantum states. The ability to reconstruct the density matrix of molecules of arbitrary degrees of freedom will provide us with an unprecedentedly clear view of the quantum states of molecules, and enable the visualization of effects dictated by the quantum dynamics of molecules.
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