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Kandel S, Maddali S, Huang X, Nashed YSG, Jacobsen C, Allain M, Hruszkewycz SO. Imaging extended single crystal lattice distortion fields with multi-peak Bragg ptychography. OPTICS EXPRESS 2024; 32:19594-19610. [PMID: 38859091 DOI: 10.1364/oe.516729] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2023] [Accepted: 02/27/2024] [Indexed: 06/12/2024]
Abstract
Recent advances in phase-retrieval-based x-ray imaging methods have demonstrated the ability to reconstruct 3D distortion vector fields within a nanocrystal by using coherent diffraction information from multiple crystal Bragg reflections. However, these works do not provide a solution to the challenges encountered in imaging lattice distortions in crystals with significant defect content that result in phase wrapping. Moreover, these methods only apply to isolated crystals smaller than the x-ray illumination, and therefore cannot be used for imaging of distortions in extended crystals. We introduce multi-peak Bragg ptychography which addresses both challenges via an optimization framework that combines stochastic gradient descent and phase unwrapping methods for robust image reconstruction of lattice distortions and defects in extended crystals. Our work uses modern automatic differentiation toolsets so that the method is easy to extend to other settings and easy to implement in high-performance computers. This work is particularly timely given the broad interest in using the increased coherent flux in fourth-generation synchrotrons for innovative material research.
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2
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Hammarberg S, Dzhigaev D, Marçal LAB, Dagytė V, Björling A, Borgström MT, Wallentin J. Fast nanoscale imaging of strain in a multi-segment heterostructured nanowire with 2D Bragg ptychography. J Appl Crystallogr 2024; 57:60-70. [PMID: 38322717 PMCID: PMC10840305 DOI: 10.1107/s1600576723010403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2023] [Accepted: 12/03/2023] [Indexed: 02/08/2024] Open
Abstract
Developing semiconductor devices requires a fast and reliable source of strain information with high spatial resolution and strain sensitivity. This work investigates the strain in an axially heterostructured 180 nm-diameter GaInP nanowire with InP segments of varying lengths down to 9 nm, simultaneously probing both materials. Scanning X-ray diffraction (XRD) is compared with Bragg projection ptychography (BPP), a fast single-projection method. BPP offers a sufficient spatial resolution to reveal fine details within the largest segments, unlike scanning XRD. The spatial resolution affects the quantitative accuracy of the strain maps, where BPP shows much-improved agreement with an elastic 3D finite element model compared with scanning XRD. The sensitivity of BPP to small deviations from the Bragg condition is systematically investigated. The experimental confirmation of the model suggests that the large lattice mismatch of 1.52% is accommodated without defects.
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Affiliation(s)
- Susanna Hammarberg
- Synchrotron Radiation Research and NanoLund, Lund University, Box 118, Lund 22100, Sweden
| | - Dmitry Dzhigaev
- Synchrotron Radiation Research and NanoLund, Lund University, Box 118, Lund 22100, Sweden
| | - Lucas A. B. Marçal
- Synchrotron Radiation Research and NanoLund, Lund University, Box 118, Lund 22100, Sweden
- MAX IV Laboratory, Lund University, Lund 22100, Sweden
| | - Vilgailė Dagytė
- Solid State Physics and NanoLund, Lund University, Box 118, Lund 22100, Sweden
| | | | - Magnus T. Borgström
- Solid State Physics and NanoLund, Lund University, Box 118, Lund 22100, Sweden
| | - Jesper Wallentin
- Synchrotron Radiation Research and NanoLund, Lund University, Box 118, Lund 22100, Sweden
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3
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Wang T, Jiang S, Song P, Wang R, Yang L, Zhang T, Zheng G. Optical ptychography for biomedical imaging: recent progress and future directions [Invited]. BIOMEDICAL OPTICS EXPRESS 2023; 14:489-532. [PMID: 36874495 PMCID: PMC9979669 DOI: 10.1364/boe.480685] [Citation(s) in RCA: 10] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2022] [Revised: 12/10/2022] [Accepted: 12/10/2022] [Indexed: 05/25/2023]
Abstract
Ptychography is an enabling microscopy technique for both fundamental and applied sciences. In the past decade, it has become an indispensable imaging tool in most X-ray synchrotrons and national laboratories worldwide. However, ptychography's limited resolution and throughput in the visible light regime have prevented its wide adoption in biomedical research. Recent developments in this technique have resolved these issues and offer turnkey solutions for high-throughput optical imaging with minimum hardware modifications. The demonstrated imaging throughput is now greater than that of a high-end whole slide scanner. In this review, we discuss the basic principle of ptychography and summarize the main milestones of its development. Different ptychographic implementations are categorized into four groups based on their lensless/lens-based configurations and coded-illumination/coded-detection operations. We also highlight the related biomedical applications, including digital pathology, drug screening, urinalysis, blood analysis, cytometric analysis, rare cell screening, cell culture monitoring, cell and tissue imaging in 2D and 3D, polarimetric analysis, among others. Ptychography for high-throughput optical imaging, currently in its early stages, will continue to improve in performance and expand in its applications. We conclude this review article by pointing out several directions for its future development.
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Affiliation(s)
- Tianbo Wang
- Department of Biomedical Engineering, University of Connecticut, Storrs, CT 06269, USA
- These authors contributed equally to this work
| | - Shaowei Jiang
- Department of Biomedical Engineering, University of Connecticut, Storrs, CT 06269, USA
- These authors contributed equally to this work
| | - Pengming Song
- Department of Biomedical Engineering, University of Connecticut, Storrs, CT 06269, USA
- These authors contributed equally to this work
| | - Ruihai Wang
- Department of Biomedical Engineering, University of Connecticut, Storrs, CT 06269, USA
| | - Liming Yang
- Department of Biomedical Engineering, University of Connecticut, Storrs, CT 06269, USA
| | - Terrance Zhang
- Department of Biomedical Engineering, University of Connecticut, Storrs, CT 06269, USA
| | - Guoan Zheng
- Department of Biomedical Engineering, University of Connecticut, Storrs, CT 06269, USA
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4
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Li P, Allain M, Grünewald TA, Rommel M, Campos A, Carbone D, Chamard V. 4 th generation synchrotron source boosts crystalline imaging at the nanoscale. LIGHT, SCIENCE & APPLICATIONS 2022; 11:73. [PMID: 35338112 PMCID: PMC8956681 DOI: 10.1038/s41377-022-00758-z] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2021] [Revised: 01/05/2022] [Accepted: 03/01/2022] [Indexed: 06/12/2023]
Abstract
New 4th-generation synchrotron sources, with their increased brilliance, promise to greatly improve the performances of coherent X-ray microscopy. This perspective is of major interest for crystal microscopy, which aims at revealing the 3D crystalline structure of matter at the nanoscale, an approach strongly limited by the available coherent flux. Our results, based on Bragg ptychography experiments performed at the first 4th-generation synchrotron source, demonstrate the possibility of retrieving a high-quality image of the crystalline sample, with unprecedented quality. Importantly, the larger available coherent flux produces datasets with enough information to overcome experimental limitations, such as strongly deteriorated scanning conditions. We show this achievement would not be possible with 3rd-generation sources, a limit that has inhibited the development of this otherwise powerful microscopy method, so far. Hence, the advent of next-generation synchrotron sources not only makes Bragg ptychography suitable for high throughput studies but also strongly relaxes the associated experimental constraints, making it compatible with a wider range of experimental set-ups at the new synchrotrons.
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Affiliation(s)
- Peng Li
- Aix-Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel, Marseille, France
- Diamond Light Source, Harwell Science and Innovation Campus, Fermi Ave, Didcot, OX11 0DE, UK
| | - Marc Allain
- Aix-Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel, Marseille, France
| | - Tilman A Grünewald
- Aix-Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel, Marseille, France
| | - Marcus Rommel
- Nanofabrication Laboratory, Department of Microtechnology and Nanoscience, MC2, Chalmers University of Technology, SE-412 96, Gothenburg, Sweden
| | - Andrea Campos
- Aix Marseille Univ, CNRS, Centrale Marseille, FSCM (FR1739), CP2M, 13397, Marseille, France
| | - Dina Carbone
- MAX IV Laboratory, Fotongatan 2, 225 94, Lund, Sweden
| | - Virginie Chamard
- Aix-Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel, Marseille, France.
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5
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Revealing nano-scale lattice distortions in implanted material with 3D Bragg ptychography. Nat Commun 2021; 12:7059. [PMID: 34862390 PMCID: PMC8642407 DOI: 10.1038/s41467-021-27224-5] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2020] [Accepted: 11/01/2021] [Indexed: 11/18/2022] Open
Abstract
Small ion-irradiation-induced defects can dramatically alter material properties and speed up degradation. Unfortunately, most of the defects irradiation creates are below the visibility limit of state-of-the-art microscopy. As such, our understanding of their impact is largely based on simulations with major unknowns. Here we present an x-ray crystalline microscopy approach, able to image with high sensitivity, nano-scale 3D resolution and extended field of view, the lattice strains and tilts in crystalline materials. Using this enhanced Bragg ptychography tool, we study the damage helium-ion-irradiation produces in tungsten, revealing a series of crystalline details in the 3D sample. Our results lead to the conclusions that few-atom-large 'invisible' defects are likely isotropic in orientation and homogeneously distributed. A partially defect-denuded region is observed close to a grain boundary. These findings open up exciting perspectives for the modelling of irradiation damage and the detailed analysis of crystalline properties in complex materials.
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6
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Poulsen HF, Dresselhaus-Marais LE, Carlsen MA, Detlefs C, Winther G. Geometrical-optics formalism to model contrast in dark-field X-ray microscopy. J Appl Crystallogr 2021. [DOI: 10.1107/s1600576721007287] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022] Open
Abstract
Dark-field X-ray microscopy, DFXM, is a new full-field imaging technique that non-destructively maps the structure and local strain inside deeply embedded crystalline elements in three dimensions. In DFXM an objective lens is placed along the diffracted beam to generate a magnified projection image of the local diffracted volume. In this work, a general formalism based on geometrical optics is provided for the diffraction imaging, valid for any crystallographic space group. This allows the simulation of DFXM images based on micro-mechanical models. Example simulations are presented with the formalism, demonstrating how this may be used to design new experiments or to interpret existing ones. In particular, it is shown how modifications to the experimental design may tailor the reciprocal-space resolution function to map specific components of the deformation-gradient tensor. The formalism supports multi-length-scale experiments, as it enables DFXM to be interfaced with 3D X-ray diffraction. To illustrate the use of the formalism, DFXM images are simulated from different contrast mechanisms on the basis of the strain field around a straight dislocation.
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7
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Godard P. On the use of the scattering amplitude in coherent X-ray Bragg diffraction imaging. J Appl Crystallogr 2021. [DOI: 10.1107/s1600576721003113] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022] Open
Abstract
Lens-less imaging of crystals with coherent X-ray diffraction offers some unique possibilities for strain-field characterization. It relies on numerically retrieving the phase of the scattering amplitude from a crystal illuminated with coherent X-rays. In practice, the algorithms encode this amplitude as a discrete Fourier transform of an effective or Bragg electron density. This short article suggests a detailed route from the classical expression of the (continuous) scattering amplitude to this discrete function. The case of a heterogeneous incident field is specifically detailed. Six assumptions are listed and quantitatively discussed when no such analysis was found in the literature. Details are provided for two of them: the fact that the structure factor varies in the vicinity of the probed reciprocal lattice vector, and the polarization factor, which is heterogeneous along the measured diffraction patterns. With progress in X-ray sources, data acquisition and analysis, it is believed that some approximations will prove inappropriate in the near future.
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8
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Pelzer K, Schwarz N, Harder R. Removal of spurious data in Bragg coherent diffraction imaging: an algorithm for automated data preprocessing. J Appl Crystallogr 2021. [DOI: 10.1107/s1600576721000819] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022] Open
Abstract
Bragg coherent diffraction imaging (BCDI) provides a powerful tool for obtaining high-resolution structural information from nanocrystalline materials. Here a BCDI sample consisting of a large number of randomly oriented nanoscale crystals is considered. Ideally, only one crystal is oriented to produce a Bragg peak on the detector. However, diffraction from other crystals often produces additional signals on the detector. Before the measured diffraction patterns can be processed into structural images, scientists routinely need to manually identify and remove the `alien' intensities from sources other than the intended crystal. With the development of modern high-coherence storage rings, such as the upgraded Advanced Photon Source (APS), the already slow process of manual preprocessing will be untenable for the large volumes of data that will be produced. An automated method of identifying and deleting alien intensities is proposed. This method exploits the fact that BCDI of a perfect crystal produces diffraction data with inversion symmetry around the Bragg peak. This approach uses the machine learning clustering method DBSCAN to distinguish between diffraction from multiple sources, and then calculates cluster size and inversion symmetry to assess whether clusters of intensity belong to desired data or alien signals. This approach can dramatically reduce the amount of time spent manually processing data, allowing BCDI data processing capabilities to keep pace with the technological advances of fourth-generation synchrotron light sources.
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Favre-Nicolin V, Girard G, Leake S, Carnis J, Chushkin Y, Kieffer J, Paleo P, Richard MI. PyNX: high-performance computing toolkit for coherent X-ray imaging based on operators. J Appl Crystallogr 2020. [DOI: 10.1107/s1600576720010985] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022] Open
Abstract
The open-source PyNX toolkit has been extended to provide tools for coherent X-ray imaging data analysis and simulation. All calculations can be executed on graphical processing units (GPUs) to achieve high-performance computing speeds. The toolkit can be used for coherent diffraction imaging (CDI), ptychography and wavefront propagation, in the far- or near-field regime. Moreover, all imaging operations (propagation, projections, algorithm cycles…) can be implemented in Python as simple mathematical operators, an approach which can be used to easily combine basic algorithms in a tailored chain. Calculations can also be distributed to multiple GPUs, e.g. for large ptychography data sets. Command-line scripts are available for on-line CDI and ptychography analysis, either from raw beamline data sets or using the coherent X-ray imaging data format.
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Dzhigaev D, Svensson J, Krishnaraja A, Zhu Z, Ren Z, Liu Y, Kalbfleisch S, Björling A, Lenrick F, Balogh ZI, Hammarberg S, Wallentin J, Timm R, Wernersson LE, Mikkelsen A. Strain mapping inside an individual processed vertical nanowire transistor using scanning X-ray nanodiffraction. NANOSCALE 2020; 12:14487-14493. [PMID: 32530025 DOI: 10.1039/d0nr02260h] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Semiconductor nanowires in wrapped, gate-all-around transistor geometry are highly favorable for future electronics. The advanced nanodevice processing results in strain due to the deposited dielectric and metal layers surrounding the nanowires, significantly affecting their performance. Therefore, non-destructive nanoscale characterization of complete devices is of utmost importance due to the small feature sizes and three-dimensional buried structure. Direct strain mapping inside heterostructured GaSb-InAs nanowire tunnel field-effect transistor embedded in dielectric HfO2, W metal gate layers, and an organic spacer is performed using fast scanning X-ray nanodiffraction. The effect of 10 nm W gate on a single embedded nanowire with segment diameters down to 40 nm is retrieved. The tensile strain values reach 0.26% in the p-type GaSb segment of the transistor. Supported by the finite element method simulation, we establish a connection between the Ar pressure used during the W layer deposition and the nanowire strain state. Thus, we can benchmark our models for further improvements in device engineering. Our study indicates, how the significant increase in X-ray brightness at 4th generation synchrotron, makes high-throughput measurements on realistic nanoelectronic devices viable.
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Affiliation(s)
- Dmitry Dzhigaev
- Division of Synchrotron Radiation Research and NanoLund, Department of Physics, Lund University, P.O. Box 118, SE-221 00 Lund, Sweden.
| | - Johannes Svensson
- Electrical and Information Technology, Department of Engineering, Lund University, P.O. Box 118, SE-221 00 Lund, Sweden
| | - Abinaya Krishnaraja
- Electrical and Information Technology, Department of Engineering, Lund University, P.O. Box 118, SE-221 00 Lund, Sweden
| | - Zhongyunshen Zhu
- Electrical and Information Technology, Department of Engineering, Lund University, P.O. Box 118, SE-221 00 Lund, Sweden
| | - Zhe Ren
- Division of Synchrotron Radiation Research and NanoLund, Department of Physics, Lund University, P.O. Box 118, SE-221 00 Lund, Sweden.
| | - Yi Liu
- Division of Synchrotron Radiation Research and NanoLund, Department of Physics, Lund University, P.O. Box 118, SE-221 00 Lund, Sweden.
| | | | | | - Filip Lenrick
- Division of Synchrotron Radiation Research and NanoLund, Department of Physics, Lund University, P.O. Box 118, SE-221 00 Lund, Sweden.
| | | | - Susanna Hammarberg
- Division of Synchrotron Radiation Research and NanoLund, Department of Physics, Lund University, P.O. Box 118, SE-221 00 Lund, Sweden.
| | - Jesper Wallentin
- Division of Synchrotron Radiation Research and NanoLund, Department of Physics, Lund University, P.O. Box 118, SE-221 00 Lund, Sweden.
| | - Rainer Timm
- Division of Synchrotron Radiation Research and NanoLund, Department of Physics, Lund University, P.O. Box 118, SE-221 00 Lund, Sweden.
| | - Lars-Erik Wernersson
- Electrical and Information Technology, Department of Engineering, Lund University, P.O. Box 118, SE-221 00 Lund, Sweden
| | - Anders Mikkelsen
- Division of Synchrotron Radiation Research and NanoLund, Department of Physics, Lund University, P.O. Box 118, SE-221 00 Lund, Sweden.
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11
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Pedersen AF, Chamard V, Poulsen HF. Confocal Bragg ptychography for bulk specimens: a numerical demonstration. OPTICS EXPRESS 2020; 28:15770-15782. [PMID: 32549414 DOI: 10.1364/oe.391282] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/25/2020] [Accepted: 04/15/2020] [Indexed: 06/11/2023]
Abstract
We report on a new X-ray imaging method, which generalizes Bragg ptychography to 3D mapping of embedded crystalline volumes within thick specimens. The sample is probed by a pencil X-ray beam. The diffracted beam is magnified by an objective and passes through a slit in the image plane to be monitored by a 2D detector in the far-field of the image plane. The dimensions of the incoming beam and the slit opening define a confocal Bragg volume. Scanning the sample with respect to this probe volume, an iterative oversampling routine is used to reconstruct the shape and projected displacement field of extended internal volumes. This routine takes into account the pupil function and known aberrations of the lens. We demonstrate the method by a numerical study of a 3.5 µm grain comprising a wall of edge dislocations. With a probe volume of ∼0.12 µm3 and a compound refractive lens with a numerical aperture of 0.49×10-3 as the objective, the dislocations are fully resolved with a displacement sensitivity of ∼10 pm. The spatial resolution is 26×27×123 nm3 (rms), with the poor resolution along the optical axis being limited by the probe size. With a four times larger numerical aperture, the resolution becomes 16×8×123 nm3 (rms). The lens aberrations are found to be not critical.
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12
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Kandel S, Maddali S, Allain M, Hruszkewycz SO, Jacobsen C, Nashed YSG. Using automatic differentiation as a general framework for ptychographic reconstruction. OPTICS EXPRESS 2019; 27:18653-18672. [PMID: 31252805 PMCID: PMC6825598 DOI: 10.1364/oe.27.018653] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
Coherent diffraction imaging methods enable imaging beyond lens-imposed resolution limits. In these methods, the object can be recovered by minimizing an error metric that quantifies the difference between diffraction patterns as observed, and those calculated from a present guess of the object. Efficient minimization methods require analytical calculation of the derivatives of the error metric, which is not always straightforward. This limits our ability to explore variations of basic imaging approaches. In this paper, we propose to substitute analytical derivative expressions with the automatic differentiation method, whereby we can achieve object reconstruction by specifying only the physics-based experimental forward model. We demonstrate the generality of the proposed method through straightforward object reconstruction for a variety of complex ptychographic experimental models.
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Affiliation(s)
- Saugat Kandel
- Applied Physics, Northwestern University, Evanston, Illinois 60208,
USA
| | - S. Maddali
- Materials Science Division, Argonne National Laboratory, Lemont, IL 60439,
USA
| | - Marc Allain
- Aix Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel, Marseille,
France
| | | | - Chris Jacobsen
- Advanced Photon Source, Argonne National Laboratory, Lemont, Illinois 60439,
USA
- Department of Physics & Astronomy, Northwestern University, Evanston, Illinois 60208,
USA
- Chemistry of Life Processes Institute, Northwestern University, Evanston, Illinois 60208,
USA
| | - Youssef S. G. Nashed
- Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, Illinois 60439,
USA
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13
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Croset B. Influence of the elastic deformations on the form factor of polyhedral nanocrystals: the illustrative example of the pseudomorphic inclusion. J Appl Crystallogr 2019. [DOI: 10.1107/s1600576719002553] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022] Open
Abstract
Using an analytically tractable example, the pseudomorphic inclusion, this article examines the influence of elastic deformations on the form factor of polyhedral nanocrystals. A control parameter, the total amplitude of the variation of the complex density phase, is identified and it is shown that for low enough deformations the characteristic asymptotic behaviours as a function of the scattering vector associated with the polyhedral crystal shape are preserved, leading to a strong contrast in the dependence of the form factor on orientation. Using the sections method, it is explained why these results can be generalized to more realistic elastic situations.
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15
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Kim C, Chamard V, Hallmann J, Roth T, Lu W, Boesenberg U, Zozulya A, Leake S, Madsen A. Three-Dimensional Imaging of Phase Ordering in an Fe-Al Alloy by Bragg Ptychography. PHYSICAL REVIEW LETTERS 2018; 121:256101. [PMID: 30608794 DOI: 10.1103/physrevlett.121.256101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2018] [Indexed: 06/09/2023]
Abstract
We show three-dimensional images of phase ordering in a Fe_{55}Al_{45} alloy obtained by coherent x-ray diffraction Bragg ptychography. Fe-Al alloys display ordered phases where the atoms organize on sublattices resulting in the emergence of otherwise forbidden superlattice reflections. The degeneracy of the ordering results in antiphase domain boundaries that, in addition to the general lattice strain, provide phase shifts of the diffracted beam depending on the reflection. The reconstructed phase images can be separated into components originating from B2 phase domains and lattice strain by performing Bragg ptychography on both the (002) fundamental and the (001) superlattice reflections.
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Affiliation(s)
- Chan Kim
- European X-Ray Free-Electron Laser Facility, Holzkoppel 4, 22869 Schenefeld, Germany
| | - Virginie Chamard
- Aix-Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel, Marseille, France
| | - Jörg Hallmann
- European X-Ray Free-Electron Laser Facility, Holzkoppel 4, 22869 Schenefeld, Germany
| | - Thomas Roth
- European X-Ray Free-Electron Laser Facility, Holzkoppel 4, 22869 Schenefeld, Germany
| | - Wei Lu
- European X-Ray Free-Electron Laser Facility, Holzkoppel 4, 22869 Schenefeld, Germany
| | - Ulrike Boesenberg
- European X-Ray Free-Electron Laser Facility, Holzkoppel 4, 22869 Schenefeld, Germany
| | - Alexey Zozulya
- European X-Ray Free-Electron Laser Facility, Holzkoppel 4, 22869 Schenefeld, Germany
| | - Steven Leake
- ESRF-The European Synchrotron, 71 Avenue des Martyrs, 38000 Grenoble, France
| | - Anders Madsen
- European X-Ray Free-Electron Laser Facility, Holzkoppel 4, 22869 Schenefeld, Germany
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16
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Pedersen AF, Chamard V, Poulsen HF. Numerical study of Bragg CDI on thick polycrystalline specimens. OPTICS EXPRESS 2018; 26:23411-23425. [PMID: 30184842 DOI: 10.1364/oe.26.023411] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2018] [Accepted: 08/16/2018] [Indexed: 06/08/2023]
Abstract
Bragg coherent diffraction imaging (BCDI) is a powerful X-ray imaging technique for crystalline materials, providing high resolution maps of structure and strain. The technique is typically used to study a small isolated object, and is in general not compatible with a bulk polycrystalline sample, due to overlap of diffraction signals from various crystalline elements. In this paper, we present an imaging method for bulk samples, based on the use of a coherent source. The diffracted X-ray beam from a grain or domain of choice is magnified by an objective before being monitored by a 2D detector in the far field. The reconstruction principle is similar to the case of BCDI, while taking the magnification and pupil function into account. The concept is demonstrated using numerical simulations and reconstructions. We find that by using an object-lens distance shorter than the focal length, the numerical aperture is larger than in a traditional imaging geometry, and at the same time the setup is insensitive to small phase errors by lens imperfections. According to our simulations, we expect to be able to achieve a spatial resolution smaller than 20 nm when using the objective lens in this configuration.
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17
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Zhang Y, De Falco P, Wang Y, Barbieri E, Paris O, Terrill NJ, Falkenberg G, Pugno NM, Gupta HS. Towards in situ determination of 3D strain and reorientation in the interpenetrating nanofibre networks of cuticle. NANOSCALE 2017; 9:11249-11260. [PMID: 28753215 DOI: 10.1039/c7nr02139a] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Determining the in situ 3D nano- and microscale strain and reorientation fields in hierarchical nanocomposite materials is technically very challenging. Such a determination is important to understand the mechanisms enabling their functional optimization. An example of functional specialization to high dynamic mechanical resistance is the crustacean stomatopod cuticle. Here we develop a new 3D X-ray nanostrain reconstruction method combining analytical modelling of the diffraction signal, fibre-composite theory and in situ deformation, to determine the hitherto unknown nano- and microscale deformation mechanisms in stomatopod tergite cuticle. Stomatopod cuticle at the nanoscale consists of mineralized chitin fibres and calcified protein matrix, which form (at the microscale) plywood (Bouligand) layers with interpenetrating pore-canal fibres. We uncover anisotropic deformation patterns inside Bouligand lamellae, accompanied by load-induced fibre reorientation and pore-canal fibre compression. Lamination theory was used to decouple in-plane fibre reorientation from diffraction intensity changes induced by 3D lamellae tilting. Our method enables separation of deformation dynamics at multiple hierarchical levels, a critical consideration in the cooperative mechanics characteristic of biological and bioinspired materials. The nanostrain reconstruction technique is general, depending only on molecular-level fibre symmetry and can be applied to the in situ dynamics of advanced nanostructured materials with 3D hierarchical design.
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Affiliation(s)
- Y Zhang
- Queen Mary University of London, Institute of Bioengineering and School of Engineering and Material Science, London, E1 4NS, UK. and Photon Science, Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany
| | - P De Falco
- Queen Mary University of London, Institute of Bioengineering and School of Engineering and Material Science, London, E1 4NS, UK.
| | - Y Wang
- Queen Mary University of London, Institute of Bioengineering and School of Engineering and Material Science, London, E1 4NS, UK.
| | - E Barbieri
- Queen Mary University of London, Institute of Bioengineering and School of Engineering and Material Science, London, E1 4NS, UK.
| | - O Paris
- Institute of Physics, Montanuniversitaet Leoben, Leoben, Austria
| | - N J Terrill
- Diamond Light Source, Harwell Science and Innovation Campus, Harwell, UK
| | - G Falkenberg
- Photon Science, Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany
| | - N M Pugno
- Laboratory of Bio-Inspired & Graphene Nanomechanics, Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano, 77, 38123, Trento, Italy and Queen Mary University of London, Institute of Bioengineering and School of Engineering and Material Science, London, E1 4NS, UK. and Ket Lab, Edoardo Amaldi Foundation, Italian Space Agency, Via del Politecnico snc, 00133, Rome, Italy
| | - H S Gupta
- Queen Mary University of London, Institute of Bioengineering and School of Engineering and Material Science, London, E1 4NS, UK.
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18
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Dzhigaev D, Stankevič T, Bi Z, Lazarev S, Rose M, Shabalin A, Reinhardt J, Mikkelsen A, Samuelson L, Falkenberg G, Feidenhans'l R, Vartanyants IA. X-ray Bragg Ptychography on a Single InGaN/GaN Core-Shell Nanowire. ACS NANO 2017; 11:6605-6611. [PMID: 28264155 DOI: 10.1021/acsnano.6b08122] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The future of solid-state lighting can be potentially driven by applications of InGaN/GaN core-shell nanowires. These heterostructures provide the possibility for fine-tuning of functional properties by controlling a strain state between mismatched layers. We present a nondestructive study of a single 400 nm-thick InGaN/GaN core-shell nanowire using two-dimensional (2D) X-ray Bragg ptychography (XBP) with a nanofocused X-ray beam. The XBP reconstruction enabled the determination of a detailed three-dimensional (3D) distribution of the strain in the particular nanowire using a model based on finite element method. We observed the strain induced by the lattice mismatch between the GaN core and InGaN shell to be in the range from -0.1% to 0.15% for an In concentration of 30%. The maximum value of the strain component normal to the facets was concentrated at the transition region between the main part of the nanowire and the GaN tip. In addition, a variation in misfit strain relaxation between the axial growth and in-plane directions was revealed.
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Affiliation(s)
- Dmitry Dzhigaev
- Deutsches Elektronen-Synchrotron DESY , Notkestraße 85, D-22607 Hamburg, Germany
| | - Tomaš Stankevič
- Niels Bohr Institute, University of Copenhagen , Blegdamsvej 17, 2100 Copenhagen, Denmark
| | - Zhaoxia Bi
- NanoLund, Department of Physics, Lund University , P.O. Box 118, SE-221 00 Lund, Sweden
| | - Sergey Lazarev
- Deutsches Elektronen-Synchrotron DESY , Notkestraße 85, D-22607 Hamburg, Germany
- National Research Tomsk Polytechnic University (TPU) , pr. Lenina 30, 634050 Tomsk, Russia
| | - Max Rose
- Deutsches Elektronen-Synchrotron DESY , Notkestraße 85, D-22607 Hamburg, Germany
| | - Anatoly Shabalin
- Deutsches Elektronen-Synchrotron DESY , Notkestraße 85, D-22607 Hamburg, Germany
| | - Juliane Reinhardt
- Deutsches Elektronen-Synchrotron DESY , Notkestraße 85, D-22607 Hamburg, Germany
| | - Anders Mikkelsen
- NanoLund, Department of Physics, Lund University , P.O. Box 118, SE-221 00 Lund, Sweden
| | - Lars Samuelson
- NanoLund, Department of Physics, Lund University , P.O. Box 118, SE-221 00 Lund, Sweden
| | - Gerald Falkenberg
- Deutsches Elektronen-Synchrotron DESY , Notkestraße 85, D-22607 Hamburg, Germany
| | - Robert Feidenhans'l
- Niels Bohr Institute, University of Copenhagen , Blegdamsvej 17, 2100 Copenhagen, Denmark
| | - Ivan A Vartanyants
- Deutsches Elektronen-Synchrotron DESY , Notkestraße 85, D-22607 Hamburg, Germany
- National Research Nuclear University MEPhI (Moscow Engineering Physics Institute) , Kashirskoe shosse 31, 115409 Moscow, Russia
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19
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Pavlov KM, Punegov VI, Morgan KS, Schmalz G, Paganin DM. Deterministic Bragg Coherent Diffraction Imaging. Sci Rep 2017; 7:1132. [PMID: 28442775 PMCID: PMC5430781 DOI: 10.1038/s41598-017-01164-x] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2016] [Accepted: 03/23/2017] [Indexed: 11/09/2022] Open
Abstract
A deterministic variant of Bragg Coherent Diffraction Imaging is introduced in its kinematical approximation, for X-ray scattering from an imperfect crystal whose imperfections span no more than half of the volume of the crystal. This approach provides a unique analytical reconstruction of the object's structure factor and displacement fields from the 3D diffracted intensity distribution centred around any particular reciprocal lattice vector. The simple closed-form reconstruction algorithm, which requires only one multiplication and one Fourier transformation, is not restricted by assumptions of smallness of the displacement field. The algorithm performs well in simulations incorporating a variety of conditions, including both realistic levels of noise and departures from ideality in the reference (i.e. imperfection-free) part of the crystal.
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Affiliation(s)
- Konstantin M Pavlov
- School of Science and Technology, University of New England, Armidale, NSW, 2351, Australia. .,School of Physics and Astronomy, Monash University, VIC, 3800, Australia.
| | - Vasily I Punegov
- Komi Research Center, Ural Division, Russian Academy of Sciences, Syktyvkar, 167982, Russian Federation.,Syktyvkar State University, Syktyvkar, 167001, Russian Federation
| | - Kaye S Morgan
- School of Physics and Astronomy, Monash University, VIC, 3800, Australia.,Institute for Advanced Studies and Chair of Biomedical Physics, Technische Universität München, Bayern, 85748, Germany
| | - Gerd Schmalz
- School of Science and Technology, University of New England, Armidale, NSW, 2351, Australia
| | - David M Paganin
- School of Physics and Astronomy, Monash University, VIC, 3800, Australia
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20
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Hruszkewycz SO, Allain M, Holt MV, Murray CE, Holt JR, Fuoss PH, Chamard V. High-resolution three-dimensional structural microscopy by single-angle Bragg ptychography. NATURE MATERIALS 2017; 16:244-251. [PMID: 27869823 DOI: 10.1038/nmat4798] [Citation(s) in RCA: 38] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2015] [Accepted: 10/12/2016] [Indexed: 05/10/2023]
Abstract
Coherent X-ray microscopy by phase retrieval of Bragg diffraction intensities enables lattice distortions within a crystal to be imaged at nanometre-scale spatial resolutions in three dimensions. While this capability can be used to resolve structure-property relationships at the nanoscale under working conditions, strict data measurement requirements can limit the application of current approaches. Here, we introduce an efficient method of imaging three-dimensional (3D) nanoscale lattice behaviour and strain fields in crystalline materials with a methodology that we call 3D Bragg projection ptychography (3DBPP). This method enables 3D image reconstruction of a crystal volume from a series of two-dimensional X-ray Bragg coherent intensity diffraction patterns measured at a single incident beam angle. Structural information about the sample is encoded along two reciprocal-space directions normal to the Bragg diffracted exit beam, and along the third dimension in real space by the scanning beam. We present our approach with an analytical derivation, a numerical demonstration, and an experimental reconstruction of lattice distortions in a component of a nanoelectronic prototype device.
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Affiliation(s)
- S O Hruszkewycz
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - M Allain
- Aix-Marseille University, CNRS, Centrale Marseille, Institut Fresnel, 13013 Marseille, France
| | - M V Holt
- Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - C E Murray
- IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - J R Holt
- IBM Semiconductor Research and Development Center, Hopewell Junction, New York 12533, USA
| | - P H Fuoss
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - V Chamard
- Aix-Marseille University, CNRS, Centrale Marseille, Institut Fresnel, 13013 Marseille, France
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21
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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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22
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Mandula O, Elzo Aizarna M, Eymery J, Burghammer M, Favre-Nicolin V. PyNX.Ptycho: a computing library for X-ray coherent diffraction imaging of nanostructures. J Appl Crystallogr 2016. [DOI: 10.1107/s1600576716012279] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022] Open
Abstract
X-ray imaging techniques have undergone a remarkable development during the past decade, taking advantage of coherent X-ray sources. Among these techniques, ptychography allows reconstruction of the specimen and the illumination probe from a series of diffraction patterns without any prior knowledge about the sample. However, the reconstruction of the ptychographic data remains challenging and the reconstruction software is often not publicly available. Presented here is an open-source library for the reconstruction of two-dimensional ptychographic data, written in Python. This library implements existing algorithms, with examples of data reconstruction on both simulated and experimental (Bragg ptychography on heterogeneous strained InAs/GaAs nanowires) data sets. It can be used for educational (simulation) purposes or experimental data analysis, and also features an OpenCL version of the ptychography algorithm for high-performance computing.
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23
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Nave C, Sutton G, Evans G, Owen R, Rau C, Robinson I, Stuart DI. Imperfection and radiation damage in protein crystals studied with coherent radiation. JOURNAL OF SYNCHROTRON RADIATION 2016; 23:228-37. [PMID: 26698068 PMCID: PMC4733927 DOI: 10.1107/s1600577515019700] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2015] [Accepted: 10/18/2015] [Indexed: 05/11/2023]
Abstract
Fringes and speckles occur within diffraction spots when a crystal is illuminated with coherent radiation during X-ray diffraction. The additional information in these features provides insight into the imperfections in the crystal at the sub-micrometre scale. In addition, these features can provide more accurate intensity measurements (e.g. by model-based profile fitting), detwinning (by distinguishing the various components), phasing (by exploiting sampling of the molecular transform) and refinement (by distinguishing regions with different unit-cell parameters). In order to exploit these potential benefits, the features due to coherent diffraction have to be recorded and any change due to radiation damage properly modelled. Initial results from recording coherent diffraction at cryotemperatures from polyhedrin crystals of approximately 2 µm in size are described. These measurements allowed information about the type of crystal imperfections to be obtained at the sub-micrometre level, together with the changes due to radiation damage.
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Affiliation(s)
- Colin Nave
- Diamond Light Source Ltd, Harwell Science and Innovation Campus, Didcot OX11 0DE, UK
| | - Geoff Sutton
- Division of Structural Biology, Wellcome Trust Centre for Human Genetics, Roosevelt Drive, Oxford OX3 7BN, UK
| | - Gwyndaf Evans
- Diamond Light Source Ltd, Harwell Science and Innovation Campus, Didcot OX11 0DE, UK
| | - Robin Owen
- Diamond Light Source Ltd, Harwell Science and Innovation Campus, Didcot OX11 0DE, UK
| | - Christoph Rau
- Diamond Light Source Ltd, Harwell Science and Innovation Campus, Didcot OX11 0DE, UK
| | - Ian Robinson
- London Centre for Nanotechnology, University College London, 17–19 Gordon Street, London WC1H 0AH, UK
| | - David Ian Stuart
- Diamond Light Source Ltd, Harwell Science and Innovation Campus, Didcot OX11 0DE, UK
- Division of Structural Biology, Wellcome Trust Centre for Human Genetics, Roosevelt Drive, Oxford OX3 7BN, UK
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24
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Ferrand P, Allain M, Chamard V. Ptychography in anisotropic media. OPTICS LETTERS 2015; 40:5144-5147. [PMID: 26565820 DOI: 10.1364/ol.40.005144] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
This letter describes ptychography in the context of polarized light probing anisotropic specimen (i.e., showing properties of birefringence and/or diattenuation). We established an optimization strategy using a vectorial formalism. We propose a measurement scheme using a set of linearly polarized probes and linear polarization analyzers, which allows the retrieval of the full anisotropy map of the specimen.
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