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Ochner H, Szilagyi S, Edte M, Malavolti L, Rauschenbach S, Kern K. Phase Reconstruction of Low-Energy Electron Holograms of Individual Proteins. ACS NANO 2022; 16:18568-18578. [PMID: 36367752 PMCID: PMC9706659 DOI: 10.1021/acsnano.2c06897] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/12/2022] [Accepted: 10/27/2022] [Indexed: 06/16/2023]
Abstract
Low-energy electron holography (LEEH) is one of the few techniques capable of imaging large and complex three-dimensional molecules, such as proteins, on the single-molecule level at subnanometer resolution. During the imaging process, the structural information about the object is recorded both in the amplitude and in the phase of the hologram. In low-energy electron holography imaging of proteins, the object's amplitude distribution, which directly reveals molecular size and shape on the single-molecule level, can be retrieved via a one-step reconstruction process. However, such a one-step reconstruction routine cannot directly recover the phase information encoded in the hologram. In order to extract the full information about the imaged molecules, we thus implemented an iterative phase retrieval algorithm and applied it to experimentally acquired low-energy electron holograms, reconstructing the phase shift induced by the protein along with the amplitude data. We show that phase imaging can map the projected atomic density of the molecule given by the number of atoms in the electron path. This directly implies a correlation between reconstructed phase shift and projected mean inner potential of the molecule, and thus a sensitivity to local changes in potential, an interpretation that is further substantiated by the strong phase signatures induced by localized charges.
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Affiliation(s)
- Hannah Ochner
- Max
Planck Institute for Solid State Research, Heisenbergstrasse 1, DE-70569 Stuttgart, Germany
| | - Sven Szilagyi
- Max
Planck Institute for Solid State Research, Heisenbergstrasse 1, DE-70569 Stuttgart, Germany
| | - Moritz Edte
- Max
Planck Institute for Solid State Research, Heisenbergstrasse 1, DE-70569 Stuttgart, Germany
| | - Luigi Malavolti
- Max
Planck Institute for Solid State Research, Heisenbergstrasse 1, DE-70569 Stuttgart, Germany
| | - Stephan Rauschenbach
- Max
Planck Institute for Solid State Research, Heisenbergstrasse 1, DE-70569 Stuttgart, Germany
- Department
of Chemistry, University of Oxford, 12 Mansfield Road, Oxford OX1 3TA, U.K.
| | - Klaus Kern
- Max
Planck Institute for Solid State Research, Heisenbergstrasse 1, DE-70569 Stuttgart, Germany
- Institut
de Physique, École Polytechnique
Fédérale de Lausanne, 1015 Lausanne, Switzerland
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2
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Zhu L, Xin X, Chang H, Wang X, Tian Q, Zhang Q, Gao R, Liu B. Security enhancement for adaptive optics aided longitudinal orbital angular momentum multiplexed underwater wireless communications. OPTICS EXPRESS 2022; 30:9745-9772. [PMID: 35299393 DOI: 10.1364/oe.453264] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2022] [Accepted: 02/27/2022] [Indexed: 06/14/2023]
Abstract
The frozen-wave-based longitudinal orbital angular momentum multiplexing (LOAMM) system developed in [IEEE Photonics J.10, 7900416 (2018)10.1109/JPHOT.2017.2778238] has the potential to overcome the crosstalk effects induced by turbulence. In this paper, we propose a defocus measurement aided adaptive optics (DMA-AO) technique for turbulence compensation in a LOAMM underwater wireless optical communication (UWOC) system to investigate the enhancement of physical layer security. Relying on a phase retrieval algorithm and probe beam, three amplitude-only measurements obtained from different back focus planes can realize phase reconstruction of distorted OAM beams. Moreover, the so-called mixture generalized gamma-Johnson SB (GJSB) distribution is proposed to characterize the probability density function (PDF) of reference-channel irradiance of OAM. The GJSB allows for obtaining closed-form and analytically tractable expression for the probability of strictly positive secrecy capacity (SPSC) in a single input single output (SISO) system. Furthermore, the average secrecy capacity (ASC) and probability of SPSC for a multiple input multiple output (MIMO) system are investigated. Compared to the traditional OAM multiplexing system based on Laguerre-Gaussian (LG) beams, the LOAMM system with a probe beam assisted DMA-AO technique has potential advantages for improving the security performance in UWOC.
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Hagemann J, Salditt T. Divide and update: towards single-shot object and probe retrieval for near-field holography. OPTICS EXPRESS 2017; 25:20953-20968. [PMID: 29041506 DOI: 10.1364/oe.25.020953] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2017] [Accepted: 07/28/2017] [Indexed: 06/07/2023]
Abstract
We present a phase reconstruction scheme for X-ray near-field holographic imaging based on a separability constraint for probe and object. In order to achieve this, we have devised an algorithm which requires only two measurements - with and without an object in the beam. This scheme is advantageous if the standard flat-field correction fails and a full ptychographic dataset can not be acquired, since either object or probe are dynamic. The scheme is validated by numerical simulations and by a proof-of-concept experiment using highly focused undulator radiation of the beamline ID16a of the European Synchrotron Radiation Facility (ESRF).
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Hagemann J, Robisch AL, Osterhoff M, Salditt T. Probe reconstruction for holographic X-ray imaging. JOURNAL OF SYNCHROTRON RADIATION 2017; 24:498-505. [PMID: 28244446 PMCID: PMC5330293 DOI: 10.1107/s160057751700128x] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/20/2016] [Accepted: 01/25/2017] [Indexed: 06/06/2023]
Abstract
In X-ray holographic near-field imaging the resolution and image quality depend sensitively on the beam. Artifacts are often encountered due to the strong focusing required to reach high resolution. Here, two schemes for reconstructing the complex-valued and extended wavefront of X-ray nano-probes, primarily in the planes relevant for imaging (i.e. focus, sample and detection plane), are presented and compared. Firstly, near-field ptychography is used, based on scanning a test pattern laterally as well as longitudinally along the optical axis. Secondly, any test pattern is dispensed of and the wavefront reconstructed only from data recorded for different longitudinal translations of the detector. For this purpose, an optimized multi-plane projection algorithm is presented, which can cope with the numerically very challenging setting of a divergent wavefront emanating from a hard X-ray nanoprobe. The results of both schemes are in very good agreement. The probe retrieval can be used as a tool for optics alignment, in particular at X-ray nanoprobe beamlines. Combining probe retrieval and object reconstruction is also shown to improve the image quality of holographic near-field imaging.
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Affiliation(s)
- Johannes Hagemann
- Institut für Röntgenphysik, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - Anna-Lena Robisch
- Institut für Röntgenphysik, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - Markus Osterhoff
- Institut für Röntgenphysik, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - Tim Salditt
- Institut für Röntgenphysik, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
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5
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Abstract
Ptychography is now a well-established X-ray microscopy tool for synchrotron end-stations equipped with a scanning stage and a pixelated detector. Ptychographic phasing algorithms use information from coherent diffraction to deliver quantitative images of the specimen at a resolution higher than the scanning resolution. These algorithms have traditionally been implemented in software on a per-instrument basis in various degrees of user-friendliness and sophistication. Here, we present Ptypy, a ptychography software written with the intention to serve as a framework across the diverse sets of available instruments and usage cases. A distinctive feature of the software is its formalism, which provides a convenient abstraction of the physical model, thus allowing for concise algorithmic implementations and portability across set-up geometries. We give an overview of the supported usage cases, explain the abstraction layer and design principles, and provide a step-by-step guide describing how an algorithm may be realized in a concise and readable manner. The software capabilities are illustrated with reconstructions from visible light and X-ray data.
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Affiliation(s)
- B Enders
- Department of Physics & Institute of Medical Engineering, Technical University of Munich, 85747 Garching, Germany; Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley 94720, CA, USA
| | - P Thibault
- School of Physics and Astronomy , University of Southampton, Southampton SO17 1BJ , , UK
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Salditt T, Osterhoff M, Krenkel M, Wilke RN, Priebe M, Bartels M, Kalbfleisch S, Sprung M. Compound focusing mirror and X-ray waveguide optics for coherent imaging and nano-diffraction. JOURNAL OF SYNCHROTRON RADIATION 2015; 22:867-78. [PMID: 26134789 DOI: 10.1107/s1600577515007742] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2015] [Accepted: 04/20/2015] [Indexed: 05/23/2023]
Abstract
A compound optical system for coherent focusing and imaging at the nanoscale is reported, realised by high-gain fixed-curvature elliptical mirrors in combination with X-ray waveguide optics or different cleaning apertures. The key optical concepts are illustrated, as implemented at the Göttingen Instrument for Nano-Imaging with X-rays (GINIX), installed at the P10 coherence beamline of the PETRA III storage ring at DESY, Hamburg, and examples for typical applications in biological imaging are given. Characteristic beam configurations with the recently achieved values are also described, meeting the different requirements of the applications, such as spot size, coherence or bandwidth. The emphasis of this work is on the different beam shaping, filtering and characterization methods.
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Affiliation(s)
- Tim Salditt
- Institut für Röntgenphysik, Universität Göttingen, 37077 Göttingen, Germany
| | - Markus Osterhoff
- Institut für Röntgenphysik, Universität Göttingen, 37077 Göttingen, Germany
| | - Martin Krenkel
- Institut für Röntgenphysik, Universität Göttingen, 37077 Göttingen, Germany
| | - Robin N Wilke
- Institut für Röntgenphysik, Universität Göttingen, 37077 Göttingen, Germany
| | - Marius Priebe
- Institut für Röntgenphysik, Universität Göttingen, 37077 Göttingen, Germany
| | - Matthias Bartels
- Institut für Röntgenphysik, Universität Göttingen, 37077 Göttingen, Germany
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Wilke RN, Hoppert M, Krenkel M, Bartels M, Salditt T. Quantitative X-ray phase contrast waveguide imaging of bacterial endospores. J Appl Crystallogr 2015; 48:464-476. [PMID: 25844079 PMCID: PMC4379437 DOI: 10.1107/s1600576715003593] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2014] [Accepted: 02/20/2015] [Indexed: 01/22/2023] Open
Abstract
Quantitative X-ray phase contrast imaging uniquely offers quantitative imaging information in terms of electron density maps allowing for mass and mass density determinations of soft biological samples (‘weighing with light’). Here, it was carried out using coherent X-ray waveguide illumination, yielding values of the mass and mass density of freeze-dried bacterial endospores (Bacillus spp.). Quantitative waveguide-based X-ray phase contrast imaging has been carried out on the level of single, unstained, unsliced and freeze-dried bacterial cells of Bacillus thuringiensis and Bacillus subtilis using hard X-rays of 7.9 keV photon energy. The cells have been prepared in the metabolically dormant state of an endospore. The quantitative phase maps obtained by iterative phase retrieval using a modified hybrid input–output algorithm allow for mass and mass density determinations on the level of single individual endospores but include also large field of view investigations. Additionally, a direct reconstruction based on the contrast transfer function is investigated, and the two approaches are compared. Depending on the field of view and method, a resolution down to 65 nm was achieved at a maximum applied dose of below 5 × 105 Gy. Masses in the range of about ∼110–190 (20) fg for isolated endospores have been obtained.
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Affiliation(s)
- R N Wilke
- University of Göttingen, Institute for X-ray Physics, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - M Hoppert
- University of Göttingen, Institute of Microbiology and Genetics, Grisebachstrasse 8, 37077 Göttingen, Germany
| | - M Krenkel
- University of Göttingen, Institute for X-ray Physics, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - M Bartels
- University of Göttingen, Institute for X-ray Physics, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany ; Philips Research, Hamburg, Germany
| | - T Salditt
- University of Göttingen, Institute for X-ray Physics, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
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Hagemann J, Robisch AL, Luke DR, Homann C, Hohage T, Cloetens P, Suhonen H, Salditt T. Reconstruction of wave front and object for inline holography from a set of detection planes. OPTICS EXPRESS 2014; 22:11552-69. [PMID: 24921276 DOI: 10.1364/oe.22.011552] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
We illustrate the errors inherent in the conventional empty beam correction of full field X-ray propagation imaging, i.e. the division of intensities in the detection plane measured with an object in the beam by the intensity pattern measured without the object, i.e. the empty beam intensity pattern. The error of this conventional approximation is controlled by the ratio of the source size to the smallest feature in the object, as is shown by numerical simulation. In a second step, we investigate how to overcome the flawed empty beam division by simultaneous reconstruction of the probing wavefront (probe) and of the object, based on measurements in several detection planes (multi-projection approach). The algorithmic scheme is demonstrated numerically and experimentally, using the defocus wavefront of the hard X-ray nanoprobe setup at the European Synchrotron Radiation Facility (ESRF).
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