A phase retrieval algorithm for shifting illumination

Rodenburg, J. M.; Faulkner, Helen Mary Louise

doi:10.1063/1.1823034

Cited by 812 publications

(487 citation statements)

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“…The numerical approaches that have successfully been used in transmission geometry ptychography experiments (i.e., difference MAP [27,28], ordered-subset (OS) / Ptychographic Iterative Engine algorithm (PIE) [29][30][31] or gradient-type iterations [31-33]) can be adapted to accommodate 3DBPP by incorporating a new gradient based on the cost function Q(ρ):…”

Section: Principles Of the 3d Bragg Projection Ptychographymentioning

confidence: 99%

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: Principles Of the 3d Bragg Projection Ptychographymentioning

confidence: 99%

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

et al. 2016

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“…This beam is moved across the specimen and intensities are recorded in the reciprocal plane ͑Fourier plane͒ for each specified position of the probe ͑R j ͒. The ptychographical iterative engine ͑PIE͒ algorithm 22 enables the reconstruction of the wave function in the object plane from the recorded intensities in reciprocal space. The PIE needs only the complex probe function and the probe positions relative to the object to retrieve the phase and amplitude of the exit wave front.…”

Section: ͒mentioning

confidence: 99%

“…18,19 In this Rapid Communication we demonstrate experimentally a method of accurately imaging large phase changes ͑Ͼ ͒ in the electron exit wave induced by objects of unlimited lateral dimensions for which there is no a priori information. The technique, called ptychography, [20][21][22][23] was first proposed by Hoppe in 1969 ͑Ref. 24͒ as a solution to the crystalline phase problem, wherein an aperture or a confined beam of illumination is moved over the specimen while multiple diffraction patterns are recorded from overlapping regions of the specimen.…”

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confidence: 99%

Wave-front phase retrieval in transmission electron microscopy via ptychography

et al. 2010

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There are many different strategies that allow the solving of the well-known phase problem corresponding to the loss of phase information during a physical measurement. In microscopy, and, in particular, in transmission electron microscopy, most of these strategies focus on the retrieval of high-resolution information with the importance of lower resolution data often overlooked. Ptychography offers a means to investigate such data. Ptychography is a robust diffractive imaging technique with fast convergence for phase retrieval but, until now, has not been applied at the nanoscale. In this paper, we use the ptychographical iterative engine to retrieve the phase change at the exit plane of metallic nanoparticles using a conventional transmission electron microscope. Ptychographical reconstructions yielded images with a phase resolution of / 10 and a spatial resolution of 1 nm. These results stand as a first step toward aberration-free lensless imaging. The technique lends itself to be an alternative to off-axis electron holography or focal series reconstruction. A very long-standing issue in transmission electron microscopy ͑TEM͒ has been how to measure accurately the phase of the electron wave emanating from the exit surface of the specimen. Because the wavelength of an electron is reduced as it passes through a potential well, the atomic potentials within the specimen can induce significant changes in its phase relative to its free-space propagation. Measurement of the induced phase change at the atomic scale or nanoscale has many important applications: for example, the measurement of the mean inner potential in materials ͑which depends upon the local chemical distribution 1 ͒, the measurement of magnetic fields around nanostructures, 2 or the measurement of internal electric fields within the specimen ͑e.g., at semiconductor junctions 3 ͒.Traditional TEM phase contrast is based upon an approximate version of Zernike's method 4 for thin and weakly scattering specimen. In essence, an interference image is created by adding the unscattered and phase-modified scattered terms. The resulting contrast is then a combination of amplitude and phase components. The transfer function of the lens is a serious limitation of this method, especially at low scattering angles ͑low-resolution components in the image͒, meaning that phase contrast works well only for relatively small-scale features, below about 1.0 nm. Furthermore, the weak-scattering approximation breaks down for all but the thinnest ͑few nanometers͒, light-element specimens.One technique that overcomes some of these limitations requires the recording of two or more images at different defoci of the objective lens, thus imaging a number of planes downstream of the object. As a wave propagates, only one phase distribution will be consistent with the measured changes of intensity. There are several methods for retrieving phase using such data. 5-8 However, because the wave intensity relies on local interference between wavelets in the Fresnel propagation integral,...

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“…a more complex attenuation pro le, will thus be studied. One possible design that may be particularly suited for high resolution ptychographic imaging of the Siemens star pattern using the Coherent Di ractive Imaging [41,197,297] and, in particular, its variant ptychography [81,249,296] needs to cope with di ration patterns spanning orders of magnitude which can be problematic for current photon counting detectors. In case of ptychography, this high dynamic range problem is more accentuated because both the strong signal from the primary beam and the weak di racted signal from the probed object need to be recorded.…”

Section: Discussionmentioning

confidence: 99%

Coherent X-ray diffractive imaging on the single-cell-level of microbial samples

Wilke

2015

Göttingen Series in X-Ray Physics

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A phase retrieval algorithm for shifting illumination

Cited by 812 publications

References 9 publications

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

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

Wave-front phase retrieval in transmission electron microscopy via ptychography

Coherent X-ray diffractive imaging on the single-cell-level of microbial samples

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