Wave-front phase retrieval in transmission electron microscopy via ptychography

Abstract

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,...

Embedded pupil function recovery for Fourier ptychographic microscopy

“…FPM and conventional ptychography differ in that in conventional ptychography, the probe illumination is spatially panned across the sample while the far field diffraction patterns are imaged and recorded. Traditional phase retrieval methods such as the ptychographic iterative engine (PIE) [11][12][13] rely on an accurate knowledge of the probe function to retrieve the object distribution, which might be inaccurately known due, for example, to the inaccurate or incomplete knowledge of features of the aperture (or focusing optics) that generates the illuminating beam [14].…”

Single-atom fabrication with electron and ion beams: From surfaces and two-dimensional materials toward three-dimensional atom-by-atom assembly

“…The two primary paradigms of nanotechnology-scanning probe-based fabrication and chemical synthesis and self-assembly-have been guiding the development of this field for more than two decades. Now, a third paradigm, the "atom forge" 81,82 -a toolbelt of electron-beam-based methods for direct atomic manipulation and atom-by-atom assembly-joins this field. (The University of Tennessee, Knoxville) with figure preparation and literature analysis.…”

“…This will, in turn, necessitate fully harnessing data flow from detectors, the creation of rapid image analytic tools to identify observed atomic structures from local imaging, also ptychography (imaging based on analyzing the diffraction signal from STEM), [80][81][82] and establishing common knowledge spaces to integrate information from multiple microscopic platforms (similar to research models in astronomy or genomics). This requires deconvolution of the microscope transfer function (a measure of resolution and performance) and calibration, so that materialsspecific phenomena are separated from instrumental factors.…”

Wavefront measurement techniques used in high power lasers

“…To overcome these disadvantages, Rodenburg [31] proposed an improved phase retrieval algorithm called PIE, which used a Wegener filterlike algorithm to reconstruct images iteratively from a set of diffraction patterns and extended it to an extended PIE (ePIE) algorithm to obtain an accurate model of the illumination and specimen functions simultaneously. PIE and ePIE are promising algorithms for imaging using X-rays [32,33] , electron beams [34,35] , and visible light [36,37] . Given that the CDI algorithms can directly measure the phase distribution of a laser beam from the recorded diffraction intensity, they are often used in various high power laser applications, including wavefront detection, large optical element measurement, and FSDs.…”