Fraunhofer diffraction

In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when plane waves are incident on a diffracting object, and the diffraction pattern is viewed at a sufficiently long distance (a distance satisfying Fraunhofer condition) from the object (in the far-field region), and also when it is viewed at the focal plane of an imaging lens. In contrast, the diffraction pattern created near the diffracting object and (in the near field region) is given by the Fresnel diffraction equation. The equation was named in honor of Joseph von Fraunhofer although he was not actually involved in the development of the theory. This article explains where the Fraunhofer equation can be applied, and shows Fraunhofer diffraction patterns for various apertures. A detailed mathematical treatment of Fraunhofer diffraction is given in Fraunhofer diffraction equation. Equation Fraunhofer diffraction equation When a beam of light is partly blocked by an obstacle, som

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Refinement for single-nanoparticle structure determination from low-quality single-shot coherent diffraction data

Christoph Bostedt, Christophe Nicolas

With the emergence of X-ray free-electron lasers, it is possible to investigate the structure of nanoscale samples by employing coherent diffractive imaging in the X-ray spectral regime. In this work, we developed a refinement method for structure reconstruction applicable to low-quality coherent diffraction data. The method is based on the gradient search method and considers the missing region of a diffraction pattern and the small number of detected photons. We introduced an initial estimate of the structure in the method to improve the convergence. The present method is applied to an experimental diffraction pattern of an Xe cluster obtained in an X-ray scattering experiment at the SPring-8 Angstrom Compact free-electron LAser (SACLA) facility. It is found that the electron density is successfully reconstructed from the diffraction pattern with a large missing region, with a good initial estimate of the structure. The diffraction pattern calculated from the reconstructed electron density reproduced the observed diffraction pattern well, including the characteristic intensity modulation in each ring. Our refinement method enables structure reconstruction from diffraction patterns under difficulties such as missing areas and low diffraction intensity, and it is potentially applicable to the structure determination of samples that have low scattering power.

INT UNION CRYSTALLOGRAPHY2020

Femtosecond X-ray coherent diffraction of aligned amyloid fibrils on low background graphene

Henning Paul-Julius Stahlberg

Here we present a new approach to diffraction imaging of amyloid fibrils, combining a freestanding graphene support and single nanofocused X-ray pulses of femtosecond duration from an X-ray free-electron laser. Due to the very low background scattering from the graphene support and mutual alignment of filaments, diffraction from tobacco mosaic virus (TMV) filaments and amyloid protofibrils is obtained to 2.7 A and 2.4 A resolution in single diffraction patterns, respectively. Some TMV diffraction patterns exhibit asymmetry that indicates the presence of a limited number of axial rotations in the XFEL focus. Signal-to-noise levels from individual diffraction patterns are enhanced using computational alignment and merging, giving patterns that are superior to those obtainable from synchrotron radiation sources. We anticipate that our approach will be a starting point for further investigations into unsolved structures of filaments and other weakly scattering objects.

Springer Science and Business Media LLC2018

Polarization-sensitive optics diffraction tomography

Elizabeth Elena Antoine, Ahmed Ayoub, Joowon Lim, Demetri Psaltis, Amirhossein Saba Shirvan

Polarization of light has been widely used as a contrast mechanism in two-dimensional (2D) microscopy and also in some three-dimensional (3D) imaging modalities. In this paper, we report the 3D tomographic reconstruction of the refractive index (RI) tensor using 2D scattered fields measured for different illumination angles and polarizations. Conventional optical diffraction tomography (ODT) has been used as a quantitative, label-free 3D imaging method. It is based on the scalar formalism, which limits its application to isotropic samples. We achieve imaging of the birefringence of 3D objects through a reformulation of ODT based on vector diffraction theory. The off-diagonal components of the RI tensor reconstruction convey additional information that is not available in either conventional scalar ODT or 2D polarization microscopy. Finally, we show experimental reconstructions of 3D objects with a polarization-sensitive contrast metric quantitatively displaying the true birefringence of the samples. (C) 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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