The theory of super-resolution electron microscopy via Wigner-distribution deconvolution

Rodenburg, J. M.; Bates, R. H. T.

doi:10.1098/rsta.1992.0050

Cited by 225 publications

(64 citation statements)

References 45 publications

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“…This phase retrieval approach has been successfully used for in-situ [6,7] Recently, x-ray Bragg ptychography methods have been developed that eliminate the requirement for isolated crystals and accommodate a broader range of samples. Originally proposed for electron microscopy [9,10] and developed extensively with x-rays in the transmission geometry [11,12], the present form of ptychography consists of inverting a set of far-field diffraction intensity patterns collected from overlapping regions of the sample illuminated with a localized beam. Thus, specific regions of interest can be imaged in continuous samples.…”

Section: Introductionmentioning

confidence: 99%

“…Originally proposed for electron microscopy [9,10] and developed extensively with x-rays in the transmission geometry [11,12], the present form of ptychography consists of inverting a set of far-field diffraction intensity patterns collected from overlapping regions of the sample illuminated with a localized beam. Thus, specific regions of interest can be imaged in continuous samples.…”

Section: Introductionmentioning

confidence: 99%

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High-resolution three-dimensional structural microscopy by single-angle Bragg ptychography

et al. 2016

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We present an efficient method of imaging 3D nanoscale lattice behavior and strain fields in crystalline materials with a new methodology -three dimensional Bragg projection ptychography (3DBPP). In this method, the 2D sample structure information encoded in a coherent high-angle Bragg peak measured at a fixed angle is combined with the real-space scanning probe positions to reconstruct the 3D sample structure. This work introduces an entirely new means of three dimensional structural imaging of nanoscale materials and eliminates the experimental complexities associated with rotating nanoscale samples. We present the framework for the method and demonstrate our approach with a numerical demonstration, an analytical derivation, and an experimental reconstruction of lattice distortions in a component of a nanoelectronic prototype device.Inversion methods provide a powerful alternative to traditional objective-lens-based microscopy. Techniques that numerically invert coherent diffraction patterns into real space images have provided substantial gains in resolution and sensitivity in certain optical, electron, and x-ray microscopy experiments, especially where image-forming lenses are inefficient or difficult to incorporate. The resulting images, formed by inverting reciprocal space diffraction patterns, contain quantitative information that encodes local physical parameters such as permittivity, density, and atomic displacement at sub-beam-size spatial resolutions.When implemented with hard x-rays, these coherent diffraction imaging (CDI) techniques have enhanced our understanding of the internal structure of nano-and meso-scale materials, especially in operating environments that are difficult to access with other probes. Furthermore, x-ray microscopy methods based on Bragg diffraction are of particular interest because the sensitivity of x-rays to crystalline distortions in materials can be leveraged to reveal the interplay between structure and properties without disturbing environmental boundary conditions. However, the routine application of inversion methods to coherent hard x-ray Bragg diffraction is still limited by stringent experimental requirements and long measurement times.Given the potential impact of non-destructive 3D structural microscopy and the limitations of current 3D Bragg coherent x-ray inversion methods, advances in Bragg phase retrieval methods that facilitate the rapid imaging of crystal lattice behavior in realistic environments are critically important. Here, we introduce a new coherent Bragg diffraction imaging approach, three dimensional Bragg projection ptychography (3DBPP), that provides such a capability. 3DBPP enables 3D image reconstruction from a series of 2D Bragg diffraction patterns measured at a single incident beam angle, thus forming a new mode of inversion-based 3D strain-sensitive imaging. As we discuss in this article, 3DBPP is a hybrid real / reciprocal space technique that takes advantage of the high angle of separation between the incident and diffracted beam in a Bra...

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

High-resolution three-dimensional structural microscopy by single-angle Bragg ptychography

et al. 2016

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“…Unlike previous reconstruction schemes [14,15], prior knowledge of the complex-valued probe profile is not required for the reconstruction to succeed. Instead, the probe is extracted from the dataset along with the image of the specimen.…”

Section: Uvx 2008mentioning

confidence: 99%

High-resolution scanning coherent X-ray diffraction microscopy

Thibault

Dierolf

Menzel

et al. 2009

UVX 2008 - 9e Colloque Sur Les Sources Cohérentes Et Incohérentes UV, VUV Et X : Applications Et Développements Récents

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Abstract. Scanning transmission x-ray microscopy (STXM) and coherent diffractive imaging (CDI) are imaging techniques that have evolved quite separately. STXM features straightforward data analysis but its resolution is limited by the spot size on the specimen. As for CDI, its promises to reach resolutions below 10 nm are often hindered by many stringent requirements on the quality of the collected datasets and on the characteristics of the specimen. We describe a ptychographic imaging method that addresses these challenges by bridging the gap between CDI and STXM through the collection of coherent diffraction patterns at each point of a STXM scan. We demonstrate this approach in a hard X-ray experiment, obtaining a five-fold improvement in resolution compared to the focal spot dimensions. The reconstruction algorithm extracts from the data not only the complex-valued transmission function of the specimen but also the complete structure of the wavefield incident on it. The method is expected to allow high-resolution imaging of a wide range of materials and life science specimens.Coherent diffractive imaging (CDI) is the name given to the set of microscopy techniques that rely on coherence to produce high-resolution images. In its simplest form, CDI consists in reconstructing the image of an isolated specimen from the measurement of its far-field diffraction pattern. The method is especially well suited to X-ray microscopy as it effectively removes the need for high-quality highefficiency lenses. With X-rays, the method has been successfully demonstrated on a wide variety of specimens both in 2D and 3D [1][2][3][4][5][6]. In spite of its successes, CDI is still plagued with important difficulties. Reconstruction of the scattering object involves solving the infamous phase problem which, in many instances, is a computationally difficult inverse problem. In addition, sample preparation is complicated by the requirement that the specimen be completely isolated.Another powerful microscopy technique, scanning transmission X-ray microscopy (STXM), entails scanning a specimen through a focused X-ray beam and measuring the transmitted intensity at each raster point. Thefingering method is relatively simple and can be conveniently combined with other scanning techniques, such as X-ray fluorescence mapping. However, the resolution of the resulting image is limited by the spot size on the specimen. Increase in resolution thus largely depends on the technological challenge of manufacturing focusing optics.Here we describe an experimental technique that merges both approaches. The principles of this imaging method were first described a few decades ago by Hegerl and Hoppe [7], who called it "ptychography", and demonstrated since in a few experiments [8][9][10]. Like STXM, the method involves scanning the specimen with a small beam, and, as CDI, it requires measuring a full diffraction pattern at each raster point. The combination of the two techniques suggests an alternative name for this method: "scanning X-ray diffraction m...

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“…In his pioneering work Hoppe describes how finite coherent illumination can be used to restore the phase information from the interference pattern recorded between the Bragg peaks of a crystalline specimen. The method was further developed for non-periodic objects [10][11][12], combined with iterative phase retrieval algorithms [13,14] and finally demonstrated with visible light and x-rays [1,2,15]. In the following, we briefly review the basic principles of the method and present some recent results obtained with x-rays and visible laser light.…”

Section: Ptychography and Coherent Diffractive Imagingmentioning

confidence: 99%