Diffraction Intensity Measurements Research Articles

Stochastic minibatch approach to the ptychographic iterative engine

The ptychographic iterative engine (PIE) is a widely used algorithm that enables phase retrieval at nanometer-scale resolution over a wide range of imaging experiment configurations. By analyzing diffraction intensities from multiple scanning locations where a probing wavefield interacts with a sample, the algorithm solves a difficult optimization problem with constraints derived from the experimental geometry as well as sample properties. The effectiveness at which this optimization problem is solved is highly dependent on the ordering in which we use the measured diffraction intensities in the algorithm, and random ordering is widely used due to the limited ability to escape from stagnation in poor-quality local solutions. In this study, we introduce an extension to the PIE algorithm that uses ideas popularized in recent machine learning training methods, in this case minibatch stochastic gradient descent. Our results demonstrate that these new techniques significantly improve the convergence properties of the PIE numerical optimization problem.

Measurement of inkjet droplet size based on Fraunhofer diffraction.

Inkjet printers have started to manufacture OLED/QLED pixel arrays for the display industry, and the precise measurement and control of ink droplet volume during the printing process has become important. We investigated the feasibility of Fraunhofer diffraction analysis as a volume measurement tool for fast-moving inkjet droplets. To confirm the basic idea, two Fraunhofer diffraction-based methods were used to calculate the wire diameters of well-known sized and steady-positioned metal wires. The first method was to curve-fit the whole measured diffraction intensity curve with the extensive Fraunhofer diffraction equation. The second one was to use the simple approximate diameter calculation equation with the measured position data of minimum diffraction intensity. The metal wire diameters calculated by the two methods showed less than 1.17% error. For the size measurement of fast-moving inkjet droplets, the first method showed 24.5 µm diameter and 7.7 pL volume, while the second method showed 25.4 µm diameter and 8.58 pL volume. We found that the second method was more suitable for real-time inkjet monitoring because its average computer calculation time was 33ms, and the first method took an average of 34ms, about 1000 times more CPU time. Hence, Fraunhofer diffraction analysis as an inkjet droplet volume measurement tool was feasible with a good balance of measurement time and measurement accuracy.

Single-pixel coherent diffractive imaging based on super-pixel holography

Quantitative phase imaging (QPI) is a powerful approach to study dynamics associated with both thickness and refractive index fluctuations. In this work, we propose a coherent diffractive QPI scheme based on single-pixel imaging structure and coherent modulation imaging. In this scheme, digital micro-mirror device with high refresh rate is employed for structured illumination. Synchronously, a single point detector is used to perform mode selected measurement of diffraction intensity. Based on the illumination structure and point signals, phase imaging is realized using a reweighted amplitude flow phase retrieval algorithm. Non-interference modality omits the reference arm, which simplifies the apparatus and improves the system robustness. This proposed technique is demonstrated by QPI of both digital binary and grayscale objects. The three-dimensional profile measurement of a plano-convex lens shows the possibility of phase retrieval for real objects. Accordingly our technique will promote the application of single-pixel phase imaging to biomedical imaging, x-ray diffraction imaging and three-dimensional profilometry.

In-situ estimation of emission wavelength of embedded InAs QDs using RHEED intensity measurements

We propose a method for estimating the emission wavelength of self-assembled InAs quantum dots (QDs) embedded in a capping layer using reflection high-energy electron diffraction (RHEED) intensity measurements. As QDs are capped with a Ga(In)As layer, the RHEED intensity of QDs decays, and the decay degree depends on the growth conditions of capping. The RHEED intensity decay was analyzed, and a relationship between the decay degree and photoluminescence peak energy of embedded QDs was determined. This relationship can be used to predict the emission wavelength of embedded QDs during capping, which is particularly useful for QD-based optical device fabrication.

Three-Dimensional Structure from Single Two-Dimensional Diffraction Intensity Measurement.

Conventional three-dimensional (3D) imaging methods require multiple measurements of the sample in different orientation or scanning. When the sample is probed with coherent waves, a single two-dimensional (2D) intensity measurement is sufficient as it contains all the information of the 3D sample distribution. We show a method that allows reconstruction of 3D sample distribution from a single 2D intensity measurement, at the z resolution exceeding the classical limit. The method can be practical for radiation-sensitive materials, or where the experimental setup allows only one intensity measurement.

Review of partially coherent diffraction imaging

Coherent diffraction imaging (CDI), a type of lensless imaging method, relies on the use of light source with high-degree coherence to compute highly resolved complex-valued objects. The coherence of light source consists of temporal coherence and spatial coherence. In practice, it is difficult to obtain a fully coherent source. Spatial decoherence can be generated in the following three scenarios: no synchronization mechanism for the whole radiation source, a finite (non-zero) point spread function of the detector, and the sample variation within exposure time. Partial temporal coherence means that the beam is not quasi-monochromatic, behaving as the energy spread of the illumination. The consequence of reduced degree of temporal and/or spatial coherence in CDI is the decrease of visibility in the measured diffraction intensity. A fundamental assumption of CDI is the full temporal and spatial coherence, and even a relatively small deviation from full coherence can prevent the phase retrieval algorithm from converging accurately. It is necessary to break the barrier of limited coherence by improving the experimental setups directly or optimizing the phase retrieval algorithms to mitigate decoherence. Based on the Wolf’s model of coherence-mode of light and the framework of CDI using partially coherent light proposed by Nugent et al., various methods have been proposed to solve the problems induced by low coherence. Those methods generally experience a similar development process, that is, from the requirement for measuring the spatial (coherent length or complex coherent factor) or temporal (spectrum distribution) coherence properties to without the need for such priori knowledge. Here in this work, the principles of partial coherent CDI, and the major progress of CDI with partial spatial- and temporal-coherent light are reviewed.

High-speed coherent diffraction imaging by varying curvature of illumination with a focus tunable lens.

A high-speed coherent diffraction imaging method is proposed by varying the curvature of illumination with a focus tunable lens. The imaging setup is free of conventional mechanical translation and takes only milliseconds to refocus by changing the electric signal applied on the lens. It is more compact and also an inexpensive alternative to coherent diffraction imaging with computerized translational stages. A detector that is kept at a fixed distance from the sample records diffraction patterns each time the spherical wavefront illuminations on the sample is changed with a control current. The complex wavefront of the object is then quantitatively recovered from the diffraction intensity measurements using an iterative phase retrieval algorithm. The feasibility of the proposed method is experimentally verified using various samples. Extremely short response time of the focus tunable lens makes the proposed method highly suitable for applications that requires high speed imaging.

Concurrent probing of electron-lattice dephasing induced by photoexcitation in 1T -TaSeTe using ultrafast electron diffraction

It has been technically challenging to concurrently probe the electrons and the lattices in materials during non-equilibrium processes, allowing their correlations to be determined. Here, in a single set of ultrafast electron diffraction patterns taken on the charge-density-wave (CDW) material 1T-TaSeTe, we discover a temporal shift in the diffraction intensity measurements as a function of scattering angle. With the help of dynamic models and theoretical calculations, we show that the ultrafast electrons probe both the valence-electron and lattice dynamic processes, resulting in the temporal shift measurements. Our results demonstrate unambiguously that the CDW is not merely a result of the periodic lattice deformation ever-present in 1T-TaSeTe but has significant electronic origin. This method demonstrates a novel approach for studying many quantum effects that arise from electron-lattice dephasing in molecules and crystals for next-generation devices.

Crystal plasticity modeling and neutron diffraction measurements of a magnesium AZ31B plate: Effects of plastic anisotropy and surrounding grains

This study used in-situ neutron diffraction measurements and Elastic ViscoPlastic Self-Consistent polycrystal plasticity model, which incorporates a Twinning and DeTwinning scheme (denoted by EVPSC-TDT), to examine the macro-and micro-mechanical behaviors of a rolled AZ31B plate subjected to uniaxial tension. Three specimens were specifically designed for minimum, maximum and intermediate twinning: (1) loading along the rolling direction, (2) loading along the plate normal, and (3) loading along the direction 45° with respect to the plate normal. Apart from the macroscopic stress strain response, the measured diffraction intensities and internal elastic strains were obtained to examine the activities of the deformation modes at the grain level. The diffraction intensity evolution signaled the volume fraction change of twinning, while the internal elastic strain evolution designated the stress partitioning among the grain orientations. The effect of the surrounding grains on the development of the internal elastic strain was investigated by identifying the corresponding deformation mechanisms. Notably, the corresponding modeling work revealed that the EVPSC-TDT model permitted the prediction of the strain hardening and anisotropic behavior along the directions with minimum, maximum and intermediate twinning at the macroscale, and the evolution of the diffraction intensities and internal strains at the microscale. The results provide a physical understanding of the effects of the load direction, texture and surrounding grains on the role of the deformation modes in hexagonal close-packed polycrystalline materials.

相干衍射成像研究进展: 叠层扫描相干衍射成像和相干调制成像

Coherent diffraction imaging(CDI) is a lensless computational imaging technique, which reconstructs the amplitude and phase of an object directly from diffraction intensity measurement by solving the phase problem using iterative algorithms. CDI can provide images at the diffraction limit resolution that is only determined by the wavelength of radiation source and the effective numerical aperture of the recorded data. Since CDI has no need for high quality imaging optics, it is suitable for short wavelength radiations such as deep ultraviolet, X-rays, and electron beam, for which imaging optics of high performance are difficult to make. Meanwhile, the past 20 years have seen rapid progress of new type of light sources (cold emission electron guns, 3rd and 4th generation synchrotron X-rays sources, and free-electron lasers), array detectors with single particle sensitivity and broad dynamic range. All those progresses greatly promote the development of CDI. At present, CDI has shown some unique advantages over traditional methods in some study of materials science and biology, and gradually becomes a mainstream technology for certain applications. This paper briefly summarized the history of CDI with a focus on ptychography and coherent modulation imaging.

Treatment of spatial resolution effects in neutron residual strain scanning

A semi-empirical method for treatment of spatial resolution effects in neutron strain scanning is proposed. The method is based on the description of neutron sampling volume as a Gaussian function perturbed by sample boundaries and other material heterogeneities. This approach results in a simple analytical model with a small number of free parameters, which can be determined from measured diffraction intensities and/or by neutron ray-tracing simulation, therefore no extra calibration measurements are necessary. Suitability of the method for treatment of pseudo strains arising near sample boundaries as well as due to strain gradients is demonstrated on the 4-point bending experiment with a ferritic steel sample of fine grained construction steel type S690QL.

Fabrication of Au/graphene oxide/Ag sandwich structure thin film and its tunable energetics and tailorable optical properties

Au/graphene oxide/Ag sandwich structure thin film was fabricated. The effects of graphene oxide (GO) and bimetal on the structure and optical properties of metal silver films were investigated by X-ray diffraction (XRD), optical absorption, and Raman intensity measurements, respectively. Compared to silver thin film, Au/graphene oxide/Ag sandwich structure composite thin films were observed with wider optical absorption peak and enhanced absorption intensity. The Raman signal for Rhodamine B molecules based on the Au/graphene oxide/Ag sandwich nanostructure substrate were obviously enhanced due to the bimetal layer and GO layer with tunable absorption intensity and fluorescence quenching effects.

Pushing the limits of crystallography.

A very serious concern of scientists dealing with crystal structure refinement, including theoretical research, pertains to the characteristic bias in calculated versus measured diffraction intensities, observed particularly in the weak reflection regime. This bias is here attributed to corrective factors for phonons and, even more distinctly, phasons, and credible proof supporting this assumption is given. The lack of a consistent theory of phasons in quasicrystals significantly contributes to this characteristic bias. It is shown that the most commonly used exponential Debye-Waller factor for phasons fails in the case of quasicrystals, and a novel method of calculating the correction factor within a statistical approach is proposed. The results obtained for model quasiperiodic systems show that phasonic perturbations can be successfully described and refinement fits of high quality are achievable. The standard Debye-Waller factor for phonons works equally well for periodic and quasiperiodic crystals, and it is only in the last steps of a refinement that different correction functions need to be applied to improve the fit quality.

Structure of the cyanobactin oxidase ThcOx from Cyanothece sp. PCC 7425, the first structure to be solved at Diamond Light Source beamline I23 by means of S-SAD.

Determination of protein crystal structures requires that the phases are derived independently of the observed measurement of diffraction intensities. Many techniques have been developed to obtain phases, including heavy-atom substitution, molecular replacement and substitution during protein expression of the amino acid methionine with selenomethionine. Although the use of selenium-containing methionine has transformed the experimental determination of phases it is not always possible, either because the variant protein cannot be produced or does not crystallize. Phasing of structures by measuring the anomalous diffraction from S atoms could in theory be almost universal since almost all proteins contain methionine or cysteine. Indeed, many structures have been solved by the so-called native sulfur single-wavelength anomalous diffraction (S-SAD) phasing method. However, the anomalous effect is weak at the wavelengths where data are normally recorded (between 1 and 2 Å) and this limits the potential of this method to well diffracting crystals. Longer wavelengths increase the strength of the anomalous signal but at the cost of increasing air absorption and scatter, which degrade the precision of the anomalous measurement, consequently hindering phase determination. A new instrument, the long-wavelength beamline I23 at Diamond Light Source, was designed to work at significantly longer wavelengths compared with standard synchrotron beamlines in order to open up the native S-SAD method to projects of increasing complexity. Here, the first novel structure, that of the oxidase domain involved in the production of the natural product patellamide, solved on this beamline is reported using data collected to a resolution of 3.15 Å at a wavelength of 3.1 Å. The oxidase is an example of a protein that does not crystallize as the selenium variant and for which no suitable homology model for molecular replacement was available. Initial attempts collecting anomalous diffraction data for native sulfur phasing on a standard macromolecular crystallography beamline using a wavelength of 1.77 Å did not yield a structure. The new beamline thus has the potential to facilitate structure determination by native S-SAD phasing for what would previously have been regarded as very challenging cases with modestly diffracting crystals and low sulfur content.

Enhanced diffraction of MeV γ-rays by mosaic crystals

The diffraction of γ-rays by mosaic Si crystals with thicknesses of 20, 40, and 80 mm and by a 2-mm-thick perfect Si crystal in a transmission Laue geometry was measured using a high-flux 60Co source with an intensity of 2.2 TBq. The measured diffraction intensities at 1.17 and 1.33 MeV using 40- and 80-mm-thick mosaic crystals were enhanced by a factor of approximately 8.6 compared with those of the perfect Si crystal. The integrated reflectivity is well described in statistical dynamical theory by taking into account γ-ray absorption inside the crystals.

Detection of twinning in macromolecular crystallography

Abstract The merohedrally or pseudo-merohedrally twinned crystals cannot be identified during diffraction pattern inspection at the stage of data collection. Several methods for identifying twinning and estimating the twin fraction are suitable for macromolecular crystals, and all are based on the statistical properties of the measured diffraction intensities. They can be based on either the overall statistical properties of the measured reflection intensities or on the comparison of reflection intensities related by the twinning operation. The application of various tests for identification of twinning and estimation of twinning fraction is discussed, with examples of diffraction data from the Protein Data Bank. Twinning makes the solution of crystal structures more difficult, but once initially solved, the atomic models can be properly refined by the existing programs.

Plasmonic metagratings for simultaneous determination of Stokes parameters

Measuring light’s state of polarization is an inherently difficult problem since the phase information between orthogonal polarization states is typically lost in the detection process. In this work, we bring to the fore the equivalence between normalized Stokes parameters and diffraction contrasts in appropriately designed phase-gradient birefringent metasurfaces and introduce a concept of all-polarization birefringent metagratings. The metagrating, which consists of three interweaved metasurfaces, allows one to easily analyze an arbitrary state of light polarization by conducting simultaneous (i.e., parallel) measurements of the correspondent diffraction intensities that reveal immediately the Stokes parameters of the polarization state under examination. Based on plasmonic metasurfaces operating in reflection at a wavelength of 800 nm, we design and realize phase-gradient birefringent metasurfaces and the correspondent metagrating, while experimental characterization of the fabricated components convincingly demonstrates the expected functionalities. We foresee the use of the metagrating in compact polarimetric setups at any frequency regime of interest.

Determination of the geometric corrugation of graphene on SiC(0001) by grazing incidence fast atom diffraction

We present a grazing incidence fast atom diffraction (GIFAD) study of monolayer graphene on 6H-SiC(0001). This system shows a Moiré-like 13 × 13 superlattice above the reconstructed carbon buffer layer. The averaging property of GIFAD results in electronic and geometric corrugations that are well decoupled; the graphene honeycomb corrugation is only observed with the incident beam parallel to the zigzag direction while the geometric corrugation arising from the superlattice is revealed along the armchair direction. Full-quantum calculations of the diffraction patterns show the very high GIFAD sensitivity to the amplitude of the surface corrugation. The best agreement between the calculated and measured diffraction intensities yields a corrugation height of 0.27 ± 0.03 Å.

Holograms recording with pulsed laser on diazonaphthoquinone-novolac-based photoresists and their nanocomposites

Direct write digital holography technique (DWDH) using a single 440-nm pulsed laser exposure has been proposed to record master holograms on commercially available positive-tone photoresist systems based on a mixture of diazonaphthoquinone and novolac resin (DNQ-novolac) of different thicknesses. The DNQ-novo- lac nanocomposite doped with copper nanoparticles (CuNPs) films was also used. The method for numerical evaluation of hologram quality based on reflected beam diffraction intensity measurements was proposed and verified. It was found that all investigated photoresist nanocomposites were sensitive enough to record holo- graphic structures at low single pulse laser exposures (from 3.3 to 18.0 mJ∕cm 2 ). Moreover, doping DNQ-novo- lac nanocomposite with CuNPs s increases its sensitivity to pulsed laser exposure by more than 30%. The potential of single pulsed laser exposures to record high quality master holograms on commercially available and metal nanoparticles doped photoresists with at least five times lower exposures values as compared to the continuous-wave laser exposures usually used to expose photoresist materials in holographic applications, opens the possibility to use pulsed lasers for quick master-originals origination for embossed holograms applying a DWDH technique or analog methods. © 2014 Society of Photo-Optical Instrumentation Engineers (SPIE) (DOI: 10.1117/1.OE.53.9 .097101)

Particle statistics in powder diffraction method

The statistical variation in observed powder diffraction intensity is often dominated by the limited number of crystallites that satisfy the diffraction condition. This effect has been termed with particle statistics in powder diffraction method [1]. We have reported experimental validation of the theory for particle statistics about symmetric reflection mode measurements, and proposed a new method to evaluate the crystallite size and its distribution by statistical analysis based on a generalized theoretical framework [2]. We have also demostrated improvement of structure refinement by application of the maximum likelihood estimation to statistical model explicitly taking the errors caused by the particle statistics into account [3]. As the formula suitable for the particle statistics about a continuously spinning flat specimen is still unclear, three kinds of diffraction intensity measurements, (1) in-plane (Φ)-scan, rocking angle (Ω)-scans for (2) stationary and (3) spinning flat specimens, have been conducted for standard powder samples of Si (NIST SRM640c) and lanthanum hexaboride (NIST SRM660a) at a synchrotron powder diffraction beamline BL-4B2 at the Photon Factory, KEK in Tsukuba. The statistical variance observed inΦ-scan and Ω-scan measurements for stationary specimens have shown cosecant dependence of the effective number of diffracting crystallites, just as predicted by the traditional theory. The statistical variance in Ω-scan measurements for spinning specimens has also shown a cosecant behaivior rather than the squared cosecant dependence suggested by de Wolff [1].