Session F46: Instrumentation III: Scattering, Diffraction, Imaging

What is the diffraction limit? From Airy to Abbe using direct numerical integration.

The resolution of a conventional optical microscope is sometimes taken from Airy's point spread function (PSF), $0.61\lambda/NA$, and sometimes from Abbe, $\lambda/2NA$, where $NA$ is the numerical aperture\footnote{J. W. Strutt (Lord Rayleigh), \textit{Phil}. \textit{Mag}. \textbf{8}, 261 (1879)}, however modern fluorescence and near-field optical microscopies achieve spatial resolution far better than either of these limits\footnote{S. W. Hell, \textit{Science} \textbf{316}, 1153 (2007)}. There is a new category of 2D metamaterials called planar optical elements (POEs), which have a microscopic thickness ($<\lambda$), macroscopic transverse dimensions ($>100\lambda$), and are composed of an array of nanostructured light scatterers. POEs are found in a range of micro- and nano-photonic technologies\footnote{A. Kildishev, A. Boltasseva, \& V. Shalaev, \textit{Science} \textbf{339}, 1289 (2013)}, and will influence the future optical nanoscopy. With this pretext, we shed some light on the 'diffraction limit' by numerically evaluating Kirchhoff's scalar formulae (in their exact form) and identifying the features of highly non-paraxial, 3D PSFs. We show that the Airy and Abbe criteria are connected, and we comment on the design rules for a particular type of POE: the flat lens.   

Imaging of Biological Tissues by Visible Light CDI

Recent advances in the use of synchrotron and X-ray free electron laser (XFEL) based coherent diffraction imaging (CDI) with application to material sciences and medicine proved the technique to be efficient in recovering information about the samples encoded in the phase domain. The current state-of-the-art algorithms of reconstruction are transferable to optical frequencies, which makes laser sources a reasonable milestone both in technique development and applications. Here we present first results from table-top laser CDI system for imaging of biological tissues and reconstruction algorithms development and discuss approaches that are complimenting the data quality improvement that is applicable to visible light frequencies due to it's properties. We demonstrate applicability of the developed methodology to a wide class of soft bio-matter and condensed matter systems. This project is funded by DOD-AFOSR~under award No FA9550-14-1-0363 and the LANSCE Professorship at LANL.   

A New Experimental Approach in Digital Holographic Microscopy to Insight into Submicron-sized Particle's Scattering Properties.

A novel application of digital holographic microscopy is presented. In this work, a submicron-sized particle is illuminated by two different wavelengths. Then, a special filtering technique is used so that the one wavelength only contributes to form the hologram of the particle in a flow-through, contract-free manner and other to produce the scattering pattern of the illuminating wave in the same plane. Later, an algorithm is applied to separate these two overlapping information. The separated holographic information is used to reconstruct the image of the particle and scattering pattern is used to analyze redistribution of energy on the medium caused by the particle. This information is unique to the particle's shape and size, thus provides the insight into a particle's scattering properties simultaneously with an image of the particle.   

HOMER: the Holographic Optical Microscope for Education and Research

Holography was invented in 1948 by Dennis Gabor and has undergone major advancements since the 2000s leading to the development of commercial digital holographic microscopes (DHM). This noninvasive form of microscopy produces a three-dimensional (3-D) digital model of a sample without altering or destroying the sample, thus allowing the same sample to be studied multiple times. HOMER-the Holographic Optical Microscope for Education and Research-produces a 3-D image from a two-dimensional (2-D) interference pattern captured by a camera that is then put through reconstruction software. This 2-D pattern is created when a reference wave interacts with the sample to produce a secondary wave that interferes with the unaltered part of the reference wave. I constructed HOMER to be an efficient, portable in-line DHM using inexpensive material and free reconstruction software. HOMER uses three different-colored LEDs as light sources. I am testing the performance of HOMER with the goal of producing tri-color images of samples. I'm using small basic biological samples to test the effectiveness of HOMER and plan to transition to complex cellular and biological specimens as I pursue my interest in biophysics.   

Bayesian Library for the Analysis of Neutron Diffraction Data

During this talk, I will introduce the Bayesian Library for the Analysis of Neutron Diffraction Data. In this library we use of the DREAM [1] algorithm to effectively sample parameter space. This offers several advantages over traditional least squares fitting approaches. It gives us more robust estimates of the fitting parameters, their errors, and their correlations. It also is more stable than least squares methods and provides more confidence in finding a global minimum. I will discuss the algorithm and its application to several materials. I will show applications to both structural and magnetic diffraction patterns. I will present examples of fitting both powder and single crystal data. [1] Jasper A. Vrugt, Cajo J. F. ter Braak, Martyn P. Clark, James M. Hyman, and Bruce A. Robinson, WATER RESOURCES RESEARCH, VOL. 44, W00B09 (2008)   

On Polarized Neutron Scattering from a Prototypical NMR Spin-Modulated System

The potential for utilizing the scattering of polarized neutrons from nuclei whose spin has been modulated using nuclear magnetic resonance (NMR) has previously been considered by Buckingham (1). That work broadly considered the overall feasibility and utility of such experiments with a potential aim, for example, of studying slow structural changes such as those that occur in biological macromolecules. Here, from first principles, we present a more in-depth development of the differential scattering cross-sections that would arise in such measurements from a prototypical and simplified model target system containing non-interacting nuclei with non-zero spins. In particular, we investigate the modulation of the polarized scattering cross-sections following the application of RF pulses that impart initial transverse rotations to selected sets of spin-1/2 nuclei. The aim is to lay the foundation for enhancing scattering signals from chosen nuclei, so as to advance knowledge of macromolecular or liquid structure. (1) A.D. Buckingham, Chem. Phys. Letts. 2003(371):517-521   

Phase sensitive small angle neutron scattering

It is a well-known problem that information about the scattered wave is lost in scattering experiments because the measured quantity is the modulus squared of the complex wave function. This "phase problem" leads to ambiguity in determining the physical properties of the scattering sample. Small angle neutron scattering (SANS) is a useful technique for determining the structure of biomolecules, in particular proteins that cannot be crystallized and studied with x-ray crystallography. However, because the biomolecules are usually suspended in a liquid the observed scattering is an average of all possible orientations, making it difficult to obtain three dimensional structural information. In a proposed method polarized SANS and magnetic nanoparticle references attached to the sample molecules is used to obtain phase sensitive structural information and simultaneously circumvent the problem of orientational averaging (Majkrzak et al. J. Appl. Cryst. 47, 2014) If realized and perfected the technique is very promising for unambiguous determination of the three dimensional structure of biomolecules. We demonstrate the principles of our method and show the first experimental data obtained on a simple test system consisting of core shell magnetic nanoparticles.   

Current and Future Scientific Investigations at GP-SANS

The general-purpose small-angle neutron scattering beam line, GP-SANS, in operation since 2007, is optimized for investigation of structures with dimensions from 0.5 to 200 nm. ~Along with high neutron flux, sample environments can easily be integrated into the beam line providing the user a versatile temperature range from 30 mK to 1600 K. In addition, there are two cryomagnets (horizontal 4.5 T and vertical 8 T), pressure cells, stop flow cell, electrochemical cell, load frames and custom-build equipment available to users allowing for significant flexibility in experimental setup. GP-SANS has supported investigation of a diverse array of intriguing scientific topics, including polymer solutions, gel and blends, colloids, micelles, , molecular self-assembly and interactions in complex fluids, microemulsions, spin textures and magnetic domains in novel materials, porosity in geological materials and phase separation, grain growth, and orientation in metallurgical alloys.~   

Ptychographic coherent x-ray surface scattering imaging

Lensless x-ray coherent diffraction imaging enables the determination of nano-scaled structures in physical and biological sciences. Several coherent diffractive imaging (CDI) methods have been developed in both transmission and reflection modes such as Bragg CDI, plane-wave CDI, Fresnel CDI, coherent surface scattering imaging (CSSI) and so on. The grazing-incidence coherent surface scattering (CSSI) technique, which is recently developed by T. Sun et al., takes advantage of enhanced x-ray surface scattering and interference near total external reflection, and thereby overcomes some limitations that the transmission mode have. However, the sample size can be investigated is limited by x-ray beam size because the sample is supposed to be isolated. We incorporated ptychographic algorithm with coherent surface scattering imaging to overcome this limitation and make it more useful and applicable. The ptychographic coherent surface scattering imaging technique enables us to measure 2D roughness of the flat surface such as thin film and silicon wafer regardless of the surface area.   

Design and Characterization of a Novel Near Field Detector for Three Dimensional X-ray Diffraction

Three dimensional x-ray diffraction microscopy (3DXRD) is a powerful technique that provides crystallographic and spatial information of a large number of grains in a sample simultaneously. A key component of a 3DXRD experiment is the near field detector which provides high resolution spatial information of the sample. A novel design for a near field detector was developed and characterized. This design, called the Quad Near Field Detector, utilizes four quadrants, each with a dedicated scintillating phosphor and optical microscope. A novel translation stage for focusing the microscopes was developed, tested, and implemented. The near field detector was calibrated and characterized at the Cornell High Energy Synchrotron Source. A flood field correction was developed for the detector to correct for variations in intensity response. Diffraction data of all four quadrants was able to reproduce the crystal orientation of the ruby calibrant. In conclusion, the design and implementation of the Quad Near Field Detector was a success and will be a useful tool for future 3DXRD experiments.   

A novel design of coherent and efficient electron beam-splitter based on quantum interaction-free measurement

We propose the design and theoretical analysis of a novel coherent and efficient electron beam-splitter utilizing quantum interaction-free measurement. A coherent electron beam-splitter is a necessary component in electron interferometry, electron holography, and recently emerging quantum electron optics. For most of these applications, a coherent, highly efficient, lossless, and two-port beam-splitter is preferred, which currently available electron beam-splitters cannot readily provide. Our electron beam-splitter design combines a weak phase grating with a resonator. Beam-splitting is achieved by passing the electron beam through the weak phase grating multiple times in the resonator. The beam-splitting ratio is controlled by the number of passes through the grating. Higher-order diffractions can be suppressed by inserting an aperture in the diffraction plane. The loss introduced by the aperture can be arbitrarily low according to quantum interaction-free measurement, thus enabling a lossless, two-port electron beam-splitter. Moreover, this novel design is not limited to electron optics, and can be generalized to light, atom, and molecular optics.   

High-brightness electron beams for ultrafast electron microdiffraction and imaging

Currently the ultrafast electron diffraction has achieved sub-picosecond temporal resolution and atomic resolution. However, direct ultrafast imaging of a nanometer scale specimen through coherent single-particle diffraction has not been achieved largely due to insufficient intensity when tuned to a coherence length that matches the size of the specimen under the projected phase space density. Utilizing a recently implemented high-brightness electron source with flexible optical design, we test the performance of ultrafast electron microdiffraction and coherence imaging. We demonstrate the feasibilities of single-shot microdiffraction on a single micrometer-sized domain in Highly Ordered Pyrolytic Graphite (HOPG) and coherent diffractive imaging of 10 nm scale charge-ordered domain structures in single-crystal complex materials, as validated by the measured brightness at the sample plane. These initial results show that source-limited performance even from a sub-relativistic electron beamline can drastically improve the current performance of ultrafast electron imaging and diffraction.   

Imaging Acoustic Phonon Dynamics on the Nanometer-Femtosecond Spatiotemporal Length-Scale with Ultrafast Electron Microscopy

Coherent collective lattice oscillations known as phonons dictate a broad range of physical observables in condensed matter and act as primary energy carriers across a wide range of material systems. Despite this omnipresence, analysis of phonon dynamics on their ultrashort native spatiotemporal length scale – that is, the combined nanometer (nm), spatial and femtosecond (fs), temporal length-scales – has largely remained experimentally inaccessible. Here, we employ ultrafast electron microscopy (UEM) to directly image discrete acoustic phonons in real-space with combined nm-fs resolution. By directly probing electron scattering in the image plane (as opposed to the diffraction plane), we retain phase information critical for following the evolution, propagation, scattering, and decay of phonons in relation to morphological features of the specimen (i.e. interfaces, grain boundaries, voids, ripples, etc.). We extract a variety of morphologically-specific quantitative information from the UEM videos including phonon frequencies, phase velocities, and decays times. We expect these direct manifestations of local elastic properties in the vicinity of material defects and interfaces will aide in the understanding and application of phonon-mediated phenomena in nanostructures.   

Dark-Field Scanning Transmission Ion Microscopy \textit{via} Direct Detection of Transmitted Helium Ions with a Multichannel Plate

A multichannel plate was used as an ion sensitive transmission detector in a commercial helium ion microscope for annular dark-field imaging of nanomaterials, i.e. scanning transmission ion microscopy. In contrast to previous transmission helium ion microscopy approaches that used secondary electron conversion holders, our new approach directly detects transmitted helium ions on an annular detector. Monte Carlo simulations are used to predict detector collection angles at which annular dark-field images with atomic number contrast are obtained. We demonstrate atomic number contrast imaging \textit{via} scanning transmission ion imaging of silica-coated gold nanoparticles and magnetite nanoparticles. While the resolution of this transmission technique is limited by beam broadening in the substrate, we image magnetite nanoparticles with high contrast on a relatively thick silicon nitride substrate. We expect this new approach to annular dark-field scanning transmission ion microscopy will open avenues for more quantitative ion imaging techniques, such as direct mass-thickness determination, and advance fundamental understanding of underlying ion scattering mechanisms leading to image formation.   

Structure of deuterated liquid n-butanol by neutron diffraction and molecular dynamics simulations

Aliphatic alcohols are the simpler molecular liquids possessing a polar hydroxylic group and a nonpolar alkyl tail. While the structure of the smallest alcohols has been relatively well studied, no much attention has been paid to the temperature dependence of the pre-peak observed before the main diffraction peak. The role of H-bonding in causing this feature and the direct relation between the number of C atoms and their distance were discovered very early, suggesting a liquid picture constituted of straight chains joined by H-bonds with the formation of mesoscopic size clusters. X-rays and neutron diffraction measurements showed that the height of the pre-peak associated with the formation of H-bonds increases with temperature. To explain this counterintuitive effect, a complete diffraction study using two neutron diffractometers D4 and D16 (ILL, Grenoble, France) allowing to cover the range 0.01-23 {\AA}${\rm t}$1 and exploring a temperature range from 100 K (glassy butanol) to 400 K (moderately supercritical conditions) has been conducted. Molecular Dynamics simulations using the OPLS-AA potential were also carried out as a function of temperature and compared to experiment. Experimental and numerical results of liquid n-butanol and its glassy transition will be presented.