A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

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Principles Of Optics Electromagnetic Theory Of Propagation Interference And Diffraction Of Light

Rechargeable battery technologies have ignited major breakthroughs in contemporary society, including but not limited to revolutions in transportation, electronics, and grid energy storage The remarkable development of rechargeable batteries is largely attributed to in-depth efforts to improve battery electrode and electrolyte materials There are, however, still intimidating challenges of lower cost, longer cycle and calendar life, higher energy density, and better safety for large scale energy storage and vehicular applications Further progress with rechargeable batteries may require new chemistries (lithium ion batteries and beyond) and better understanding of materials electrochemistry in the various battery technologies In the past decade, advancement of battery materials has been complemented by new analytical techniques that are capable of probing battery chemistries at various length and time scales Synchrotron X-ray techniques stand out as one of the most effective methods that allow for near

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Synchrotron X-ray Analytical Techniques for Studying Materials Electrochemistry in Rechargeable Batteries

Angle-resolved photoemission spectroscopy (ARPES) is a powerful experimental technique in materials science, as it can directly probe electronic states inside solids in energy (E) and momentum (k) space. As an advanced technique, spatially-resolved ARPES using a well-focused light source (high-resolution ARPES microscopy) has recently attracted growing interests because of its capability to obtain local electronic information at micro- or nano-metric length scales. However, there exist several technical challenges to guarantee high precision in determining translational and rotational positions in reasonable measurement time. Here we present two methods of obtaining k-space mapping and real-space imaging in high-resolution ARPES microscopy. One method is for k-space mapping measurements that enables us to keep a target position on a sample surface during sample rotation by compensating rotation-induced displacements (tracing acquisition method). Another method is for real-space imaging measurements that significantly reduces total acquisition time (scanning acquisition method). We provide several examples of these methods that clearly indicate higher accuracy in k-space mapping as well as higher efficiency in real-space imaging, and thus improved throughput of high-resolution APRES microscopy.

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Accurate and efficient data acquisition methods for high-resolution angle-resolved photoemission microscopy.

Angle-resolved photoemission spectroscopy (ARPES) has emerged as a leading experimental probe for studying the complex phenomena in quantum materials, a subject of increasing importance The power of this technique stems from the directness and the richness of the momentum-resolved information it can provide, such as band dispersion, Fermi surface topology, and electron self-energy Over the past decade, the significantly improved energy and momentum resolution and carefully matched experiments have turned this technique into a sophisticated tool in characterizing the electronic structure of complex materials This revolution is mostly evident in the study of cuprate high-temperature superconductors More recently, this technique has played a critical role in advancing our understanding of the newly discovered iron-based superconductors and topological insulators In this paper we review some of the recent ARPES results and discuss the future perspective in this rapidly developing field

Angle-Resolved Photoemission Studies of Quantum Materials

A synchrotron radiation beamline in the photon energy range of 18-240 eV and an electron spectroscopy end station have been constructed at the 3 GeV Diamond Light Source storage ring. The instrument features a variable polarisation undulator, a high resolution monochromator, a re-focussing system to form a beam spot of 50 × 50 μm2, and an end station for angle-resolved photoelectron spectroscopy (ARPES) including a 6-degrees-of-freedom cryogenic sample manipulator. The beamline design and its performance allow for a highly productive and precise use of the ARPES technique at an energy resolution of 10-15 meV for fast k-space mapping studies with a photon flux up to 2 ⋅ 1013 ph/s and well below 3 meV for high resolution spectra.

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A facility for the analysis of the electronic structures of solids and their surfaces by synchrotron radiation photoelectron spectroscopy

We demonstrate an extension of the x-ray grating interferometer three modal imaging method to a generalized stepping scheme using a phase object with small, random features. The method allows the recovery of the absorption, scattering, and two-dimensional phase image of the sample from a raster scan of the phase object. An additional extension of the method to recover the effective wave-front curvature is also described. The technique provides fine sensitivity and high spatial resolution and has only low requirements on spatial and longitudinal coherence of the x-ray beam. Imaging modes and processing methods are explained, and an experimental demonstration of the technique is provided by imaging a feather and the quantitative characterization of a compound refractive lens.

X-ray multimodal imaging using a random-phase object

X-ray phase and dark-field imaging techniques provide complementary and inaccessible information compared to conventional X-ray absorption or visible light imaging. However, such methods typically require sophisticated experimental apparatus or X-ray beams with specific properties. Recently, an X-ray speckle-based technique has shown great potential for X-ray phase and dark-field imaging using a simple experimental arrangement. However, it still suffers from either poor resolution or the time consuming process of collecting a large number of images. To overcome these limitations, in this report we demonstrate that absorption, dark-field, phase contrast, and two orthogonal differential phase contrast images can simultaneously be generated by scanning a piece of abrasive paper in only one direction. We propose a novel theoretical approach to quantitatively extract the above five images by utilising the remarkable properties of speckles. Importantly, the technique has been extended from a synchrotron light source to utilise a lab-based microfocus X-ray source and flat panel detector. Removing the need to raster the optics in two directions significantly reduces the acquisition time and absorbed dose, which can be of vital importance for many biological samples. This new imaging method could potentially provide a breakthrough for numerous practical imaging applications in biomedical research and materials science.

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From synchrotron radiation to lab source: advanced speckle-based X-ray imaging using abrasive paper.

We present a method to measure the surface profile of hard X-ray reflective optics with nanometer height accuracy and sub-millimetre lateral resolution. The technique uses X-ray near-field speckle, generated by a scattering membrane translated using a piezo motor, to infer the deflection of X-rays from the surface. The method provides a nano-radian order accuracy on the mirror slopes in both the tangential and sagittal directions. As a demonstration, a pair of focusing mirrors mounted in a Kirkpatrick-Baez (KB) configuration were characterized and the results were in good agreement with offline metrology data. It is hoped that the new technique will provide feedback to optic manufacturers to improve mirror fabrication and be useful for the online optimization of active, nano-focusing mirrors on modern synchrotron beamlines.

At-wavelength metrology of hard X-ray mirror using near field speckle

A fast and accurate method to characterize the X-ray wavefront by rotating one of the two gratings of an X-ray shearing interferometer is described and investigated step by step. Such a shearing interferometer consists of a phase grating mounted on a rotation stage, and an absorption grating used as a transmission mask. The mathematical relations for X-ray Moire fringe analysis when using this device are derived and discussed in the context of the previous literature assumptions. X-ray beam wavefronts without and after X-ray reflective optical elements have been characterized at beamline B16 at Diamond Light Source (DLS) using the presented X-ray rotating shearing interferometer (RSI) technique. It has been demonstrated that this improved method allows accurate calculation of the wavefront radius of curvature and the wavefront distortion, even when one has no previous information on the grating projection pattern period, magnification ratio and the initial grating orientation. As the RSI technique does not require any a priori knowledge of the beam features, it is suitable for routine characterization of wavefronts of a wide range of radii of curvature.

Hongchang Wang

Papers

A facility for the analysis of the electronic structures of solids and their surfaces by synchrotron radiation photoelectron spectroscopy

X-ray multimodal imaging using a random-phase object

From synchrotron radiation to lab source: advanced speckle-based X-ray imaging using abrasive paper.

At-wavelength metrology of hard X-ray mirror using near field speckle

X-ray wavefront characterization using a rotating shearing interferometer technique.