Reconstruction of complex single-particle images using charge-flipping algorithm

Wu, Jinsong; Spence, John C. H.

doi:10.1107/s0108767304033525

Cited by 23 publications

(5 citation statements)

References 17 publications

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“…As in all X-ray experiments, the phase of the scattered amplitude is lost during the experiment, and must be recovered either using ab initio phase retrieval algorithms [14,15,16,17] or using a model with some a priori (e.g. symmetry) information [23].…”

Section: Homogeneous Nanowiresmentioning

confidence: 99%

“…One goal of CXDI is to allow for the 3D reconstruction of single, non-crystalline objects such as biomolecules [11] or amorphous materials [12]: in this case the smallangle scattering is measured, optionally in 3D using a tomographic approach [13], and the electronic density of the sample can be reconstructed using an inverse Fourier transform combined with phase retrieval algorithms [14,15,16,17].…”

Section: Introductionmentioning

confidence: 99%

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Analysis of strain and stacking faults in single nanowires using Bragg coherent diffraction imaging

et al. 2010

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Coherent diffraction imaging (CDI) on Bragg reflections is a promising technique for the study of three-dimensional (3D) composition and strain fields in nanostructures, which can be recovered directly from the coherent diffraction data recorded on single objects. In this article we report results obtained for single homogeneous and heterogeneous nanowires with a diameter smaller than 100 nm, for which we used CDI to retrieve information about deformation and faults existing in these wires. The article also discusses the influence of stacking faults, which can create artefacts during the reconstruction of the nanowire shape and deformation.

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Section: Homogeneous Nanowiresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of strain and stacking faults in single nanowires using Bragg coherent diffraction imaging

et al. 2010

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“…Since the diffraction pattern provides only |F ( Q)|, we need to obtain the associated phase before we can recover the molecular structure. There are iterative numerical algorithms that permit reconstructing the phase directly from the intensity data [17,18,[87][88][89][90][91][92][93][94][95][96][97][98][99][100][101]. These algorithms require intensity data sampled at twice the Nyquist frequency.…”

Section: B Phase-retrieval Algorithmmentioning

confidence: 99%

Computational studies of x-ray scattering from three-dimensionally-aligned asymmetric-top molecules

Pabst

Santra

2010

Phys. Rev. A

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We theoretically and numerically analyze x-ray scattering from asymmetric-top molecules three-dimensionally aligned using elliptically polarized laser light. A rigid-rotor model is assumed. The principal axes of the polarizability tensor are assumed to coincide with the principal axes of the moment of inertia tensor. Several symmetries in the Hamiltonian are identified and exploited to enhance the efficiency of solving the time-dependent Schrödinger equation for each rotational state initially populated in a thermal ensemble. Using a phase-retrieval algorithm, the feasibility of structure reconstruction from a quasiadiabatically aligned sample is illustrated for the organic molecule naphthalene. The spatial resolution achievable strongly depends on the laser parameters, the initial rotational temperature, and the x-ray pulse duration. We demonstrate that for a laser peak intensity of 5 TW/cm 2 , a laser pulse duration of 100 ps, a rotational temperature of 10 mK, and an x-ray pulse duration of 1 ps, the molecular structure may be probed at a resolution of 1Å. STEFAN PABST, PHAY J. HO, AND ROBIN SANTRA PHYSICAL REVIEW A 81, 043425 (2010)where the expansion coefficients [C(t)]The equation of motion for the expansion coefficients in the interaction picture (subscript I) readsIn the following, we assume we found [C L,I (t)] J 1 τ 1 M 1 J 0 τ 0 M 0 , the solution for the laser-only problem, i.e.,Ĥ rot +Ĥ L (t). Note that in the laser-only Hamiltonian no x-ray field is involved and we will drop the x-ray field indices in its solution.The interaction between the laser-aligned molecules and the x-ray field is taken into account by first-order perturbation theory. The solution of Eq. (7) becomesThe expectation values of interest can be calculated by043425-2 = − 1 2 2 J =0 J M=−J (−1) J +M [α pol ] [J ] L M U [J ] L −M (t), (18) | J τ M (t) has to be known to calculate the expectation values. However, | J τ M (t) can be written as a superposition of | J KM (t) [cf. Eq. (11)], and by using the same argument as for M, only | J KM (t) for K 0 are necessary to build all | J τ M (t) [cf. Eq. ( 13)]. This makes it attractive to propagate | J KM (t) rather than | J τ M (t) . Taking both symmetries together only the states | J KM (t) for 0 K,M J have to be propagated to understand the full system response, which can save up to a factor 4 in computational effort.The decoupling between even and odd K/τ states and M states also enhances efficiency and does not get destroyed by the presence of the interactionĤ L (t). Therefore, many [C L (t)] J τ M J KM remain zero throughout the alignment process. This holds for symmetric-top as good as for asymmetric-top rotors, since each |J τ M can be classified into the class E ± or O ± (cf. Sec. II A). The benefit is not just a speed-up by a factor 4; also the memory requirement to store [C L (t)] J τ M J KM , the matrixĤ L (t), and the matrices cos 2 θ lm is reduced by a factor 4. Memory size can become an issue on PCs when high J states are not negligible.

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“…Gábor Charge flipping (CF) is an amazingly simple ab initio structure solution method [1,2] that has already attracted useful applications [3][4][5][6]. It is based on the existence of extended zero plateaus in the ideal electron density, but not directly on atomicity.…”

Section: M33o03mentioning

confidence: 99%

How can we cope with negative scattering density?

Oszlányi¹,

Sütõ²

2006

Acta Cryst Sect A

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Reconstruction of complex single-particle images using charge-flipping algorithm

Cited by 23 publications

References 17 publications

Analysis of strain and stacking faults in single nanowires using Bragg coherent diffraction imaging

Analysis of strain and stacking faults in single nanowires using Bragg coherent diffraction imaging

Computational studies of x-ray scattering from three-dimensionally-aligned asymmetric-top molecules

How can we cope with negative scattering density?

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