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Handbook of Infrared Detection Technologies. Quantum Opto-Mechanics with Micromirrors. Advances in Imaging and Electron Physics. The Essential Guide to Video Processing. Furthermore, the experimental geometry required is relatively simple with no requirement for mechanical tilting of the sample as in electron tomography 13 , 14 or accurate scanning at different depths along the optical axis as in scanning confocal electron microscopy 40 , However, it may still be useful to combine the approach described with specimen rotation to recover 3D data from very strongly scattering specimens at high resolution, for example, reconstruction of micron thick biological samples 42 , although we note that recent advances in model-based tomographic reconstructions can negate the need for back projection Although the depth resolution demonstrated in these initial results as described is not yet comparable to that obtained using electron tomography 44 , the data acquisition process is faster and minimal data post processing is required to recover quantitative 3D information.
Potentially, the greatest advantage of this method lies in its compatibility with in situ sample holders, which opens up the possibility of quantitative 3D phase reconstruction for samples in liquid 46 , gas 47 , or cryo 48 environments, without the requirement for a wide gap objective lens pole piece suitable for tomography.
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Ptychographic reconstruction also enables post-reconstruction numerical focusing. The tube walls show lattice fringes at 0. All power spectra shown in Fig. However, as the CNTs are curved and misoriented with respect to the incident beam direction, other higher-order reflections are not resolved Reconstructed phase in focus.
A lattice spacing of 0. Arrows indicate the compartment layers of the interior tube. An additional advantage of post-acquisition focusing lies in the fact that it readily provides data at an optimal defocus, which is beneficial for imaging beam sensitive materials where it is challenging to identify the optimum defocus under low-dose conditions Hence, this 3D feature of electron ptychography may facilitate low-dose 3D imaging of beam-sensitive specimens, especially in the life sciences and in studies of soft matter.
Compared to focused probe experiments 53 , 54 , the pixel size and image size of the reconstructed image in the current ptychographic geometry is dependent on the sampling of the diffraction patterns at the detector plane, the illumination size and the number of scanning positions.
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With current and proposed high-speed, high-sensitivity detectors operating at —10, frames per second 55 , it should be possible to record the same data at time intervals corresponding to important chemical dynamic processes, for example, in catalysis. To theoretically describe both lateral resolution and depth sectioning, the Ewald sphere construction for the optical configuration was used as shown in Supplementary Fig. The lateral and depth resolution in ptychography 24 with an incident plane wave along the optic axis are given as. In the experiments described, a convergent incident beam was used.
Due to the low signal-to-noise ratio outside the bright-field BF disk at the detector plane, only the central BF disk was used for reconstruction. With curved illumination as in this experiment, the effective maximum scattering angle is twice as large as that of the BF disk in the k x and k y directions Apart from the resolved reflection with a 0. However, to accurately evaluate the lateral resolution, a sample consisting of 3D CNT bundles is not optimal when compared to single crystals with precisely defined lattice spacings for example, Si and LaB 6 36 , For this reason, further detailed investigations of both experimental lateral and depth resolutions achievable using this method are currently in progress.
To evaluate depth resolution experimentally, the region of the CNT bundle showing lattice fringes with a spacing of 0. Evaluation of depth resolution. Lattice fringes, with a spacing of 0. The simulations show that there is a sample thickness limit even for light element materials, such as that used in the present experiment where the invMS can fully accommodate multiple scattering but where the WDD approach cannot.
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In contrast to the work of Yang et al. This process removes both microstructural defects as well as the catalyst particles within CNTs and enhances their graphitic structure The optical sectioning results are shown in Supplementary Fig. The WDD reconstruction shows contrast variations along the depth direction and a noticeable contrast reversal in the reconstructed phase data Supplementary Fig. Hence, the contrast reversal observed in WDD optical sectioning is likely due to dynamical scattering. However, this is not the case for reconstructions using the invMS approach.
It can be seen that invMS reconstruction recovers more faithful phase data Supplementary Fig. Therefore, while for 2D imaging the WDD has produced impressive results at atomic resolution, its 3D optical sectioning capability for thick samples is limited by multiple scattering. This is consistent with the theory underlying the WDD, which makes use of the multiplicative approximation. Overall, the invMS approach provides depth-resolved sectioning, which is robust to multiple scattering, although the attainable resolution has yet to be shown to be competitive with that achieved using the WDD and a focused probe.
Compared to experiments using a focused probe and an integrating high-speed pixelated detector 30 as used to record data for the recent WDD work 19 , 29 , the defocused probe used in invMS is incompatible with the optical conditions required for annular dark-field imaging. However, despite this disadvantage, the data acquisition described here does not necessarily require a high-speed pixelated detector 30 as used successfully in the WDD experiments 29 , the speed of which can practically limit the number of probe positions and hence the size of the final reconstruction in pixels.
In future, we anticipate extending this approach by using direct counting electron detectors that are designed to have a very wide dynamic range Using this type of detector, we expect that much weaker signals can be detected from weakly scattering objects under low-dose conditions and also that the signal in the dark-field region outside the BF disk will be recorded with useable signal to noise ratio. In this geometry, the scattering angle used in the reconstruction will be extended to the maximum collection angle acquired by the detector, which will improve both lateral and depth resolution.
In conclusion, we have demonstrated for the first time that defocused probe electron ptychography using an invMS method can provide depth-sectioned information from a 3D complex transmission function of a thick sample including both amplitude and phase. The method provides high contrast, quantitative phase maps at close to atomic lateral resolution and with a few tens of nanometers depth resolution.
This 3D electron ptychographic method is potentially applicable to in situ TEM experiments as it does not require mechanical tilting of the specimen through large angles as is the case for electron tomography. The additional capability to carry out post-acquisition focusing of the reconstruction coupled with high-dose efficiency 61 particularly when coupled to high-speed and high-sensitivity detectors 55 should provide a route to structural determination, using the recovered, fully quantitative ptychographic phase from thicker, radiation sensitive specimens.
In the future, we anticipate that this method will find a wide range of applications in 3D structure determination of thick objects, ranging from inorganic nanostructures, heterostructures or ferroic domain structures to biological macromolecules. This high-temperature process efficiently graphitized the multiwall CNTs In order to disperse the tubes with different geometries, dropping and drying was repeated several times.
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The iterative method for reconstruction used the ptychography algorithm with the invMS approach 22 is summarized below. The multislice method is widely used in electron microscope simulations. The corresponding diffraction pattern acquired in the experiment is labeled, I j. For brevity, we subsequently omit the coordinate, r. For the next iteration, the probe is moved to the next position in the data set and the newly updated object slice is used as initial estimate. For the experimental set-up from which data was collected, the slice thickness can be chosen such that the minimum separation makes two neighboring slices of the object lie outside of the bounds of the multiplicative approximation For a finer slice thickness and a larger total slice number, a greater number of unknown pixels in the specimen reconstruction need to be reconstructed.
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Therefore, both of these values are also dependent on the degree of the redundancy of the ptychographic data, similar to the over-sampling ratio as described elsewhere This experimental configuration ensures that the extent of the illumination was well defined and gives a probe diameter of about 5. In this configuration, the overlap between adjacent positions was calculated to be From the over-sampling ratio 62 , the degree of the redundancy of ptychographic data used here is estimated as:. All relevant data are available from the authors on reasonable request. All authors discussed the results and commented on the manuscript.
Supplementary Information accompanies this paper at doi: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. National Center for Biotechnology Information , U. Published online Jul Martinez , 6 Peter D. Nellist , 6 Xiaoqing Pan , 1, 7, 8 and Angus I. Author information Article notes Copyright and License information Disclaimer. Received Dec 9; Accepted Jun 6. To view a copy of this license, visit http: This article has been cited by other articles in PMC.
Abstract Knowing the three-dimensional structural information of materials at the nanometer scale is essential to understanding complex material properties. Introduction Techniques enabling three-dimensional 3D structure analysis, such as X-ray 1 or neutron diffraction 2 , and electron microscopy 3 , are invaluable tools for understanding the complex relationship between structure and function in materials. Open in a separate window. Theoretical lateral and depth resolutions To theoretically describe both lateral resolution and depth sectioning, the Ewald sphere construction for the optical configuration was used as shown in Supplementary Fig.
Discussion Compared to experiments using a focused probe and an integrating high-speed pixelated detector 30 as used to record data for the recent WDD work 19 , 29 , the defocused probe used in invMS is incompatible with the optical conditions required for annular dark-field imaging.
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Propagation between slices uses a Fresnel method: From the over-sampling ratio 62 , the degree of the redundancy of ptychographic data used here is estimated as: Data availability All relevant data are available from the authors on reasonable request. Electronic supplementary material Supplementary Information 1.
Supplementary Movie 1 8. Notes Competing interests The authors declare no competing financial interests. Footnotes Electronic supplementary material Supplementary Information accompanies this paper at doi: Contributor Information Peng Wang, Email: Structural studies by electron tomography: Electron tomography and holography in materials science. Science , aaf Three-dimensional atomic imaging of crystalline nanoparticles. A new approach for electron tomography: Goris B, et al.
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