Electron tomography at 2.4 {\AA} resolution

Transmission electron microscopy (TEM) is a powerful imaging tool that has found broad application in materials science, nanoscience and biology(1-3). With the introduction of aberration-corrected electron lenses, both the spatial resolution and image quality in TEM have been significantly improved(4,5) and resolution below 0.5 {\AA} has been demonstrated(6). To reveal the 3D structure of thin samples, electron tomography is the method of choice(7-11), with resolutions of ~1 nm^3 currently achievable(10,11). Recently, discrete tomography has been used to generate a 3D atomic reconstruction of a silver nanoparticle 2-3 nm in diameter(12), but this statistical method assumes prior knowledge of the particle's lattice structure and requires that the atoms fit rigidly on that lattice. Here we report the experimental demonstration of a general electron tomography method that achieves atomic scale resolution without initial assumptions about the sample structure. By combining a novel projection alignment and tomographic reconstruction method with scanning transmission electron microscopy, we have determined the 3D structure of a ~10 nm gold nanoparticle at 2.4 {\AA} resolution. While we cannot definitively locate all of the atoms inside the nanoparticle, individual atoms are observed in some regions of the particle and several grains are identified at three dimensions. The 3D surface morphology and internal lattice structure revealed are consistent with a distorted icosahedral multiply-twinned particle. We anticipate that this general method can be applied not only to determine the 3D structure of nanomaterials at atomic scale resolution(13-15), but also to improve the spatial resolution and image quality in other tomography fields(7,9,16-20).Comment: 27 pages, 17 figure

An overview of optimal and sub-optimal detection techniques for a non orthogonal spectrally efficient FDM

Spectrally Efficient non orthogonal Frequency Division Multiplexing (SEFDM) Systems occupy less bandwidth than equivalent orthogonal FDM (OFDM). However, enhanced spectral efficiency comes at the expense of an increased complexity in the signal detection. In this work, we present an overview of different detection techniques that trade the error performance optimality for the signal recovery computational effort. Linear detection methods like Zero Forcing (ZF) and Minimum Mean Squared Error (MMSE) offer fixed complexity but suffer from a significant degradation of the Bit Error Rate (BER). On the other hand optimal receivers like Sphere Decoders (SD) achieve the optimal solution in terms of error performance. Notwithstanding, their applicability is severely constrained by the SEFDM signal dimension, the frequency separation between the carriers as well as the noise level in the system

Automatic Spatial Calibration of Ultra-Low-Field MRI for High-Accuracy Hybrid MEG--MRI

With a hybrid MEG--MRI device that uses the same sensors for both modalities, the co-registration of MRI and MEG data can be replaced by an automatic calibration step. Based on the highly accurate signal model of ultra-low-field (ULF) MRI, we introduce a calibration method that eliminates the error sources of traditional co-registration. The signal model includes complex sensitivity profiles of the superconducting pickup coils. In ULF MRI, the profiles are independent of the sample and therefore well-defined. In the most basic form, the spatial information of the profiles, captured in parallel ULF-MR acquisitions, is used to find the exact coordinate transformation required. We assessed our calibration method by simulations assuming a helmet-shaped pickup-coil-array geometry. Using a carefully constructed objective function and sufficient approximations, even with low-SNR images, sub-voxel and sub-millimeter calibration accuracy was achieved. After the calibration, distortion-free MRI and high spatial accuracy for MEG source localization can be achieved. For an accurate sensor-array geometry, the co-registration and associated errors are eliminated, and the positional error can be reduced to a negligible level.Comment: 11 pages, 8 figures. This work is part of the BREAKBEN project and has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 68686

Enhanced the Fast Fractional Fourier Transform (FRFT) scheme using the closed Newton-Cotes rules

The paper considers the fractional Fourier transform (FRFT)--based numerical inversion of Fourier and Laplace transforms and the closed Newton Cotes quadrature rules. It is shown that the fast FRFT of a QN-long weighted sequence is the composite of two fast FRFTs: the fast FRFT of a Q-long weighted sequence and the fast FRFT of an N-long sequence. The Newton-Cotes rules, the composite fast FRFT, and non-weighted fast Fractional Fourier transform (FRFT) algorithms are applied to the Variance Gamma distribution and the Generalized Tempered Stable (GTS) distribution for illustrations. Compared to the non-weighted fast FRFT, the composite fast FRFT provides more accurate results with a small sample size, and the accuracy increases with the number of weights (Q)