Theory and verification of moiréfringes for x-ray three-phase grating interferometer

Dual-phase and three-phase grating x-ray interference is a promising new technique for grating-based x-ray differential phase contrast imaging.Dual-phase grating interferometers have been relatively completely studied and discussed.In this paper,the corresponding imaging fringe formula of the three-phase grating interferometer is provided.At the same time,the similarities and differences between the three-phase grating interferometer and the dual-phase grating interferometer are investigated and verified,and that the three-phase grating interferometer can produce large-period moiréfringes without using the analyzing grating is demonstrated experimentally.Finally,a simple method of designing three-phase grating and multi-grating imaging systems from geometric optics based on the thin-lens theory of gratings is presented.These theoretical formulas and experimental results provide optimization tools for designing three-phase grating interferometer systems.

Wavelength Dependent Nonlinear Spectroscopic Study of Third Harmonic Generation Probed by Rotational Maker Fringes Method

Efficient third-order nonlinearities of the Zinc Oxide and Al-doped Zinc Oxide were studied by Third Harmonic Generation (Third Harmonic Generation) Maker fringes to establish the effect Aluminum of Aluminum doping (Al-doping) on the cubic nonlinearities. Adding the Al-dopant to the Zinc Oxide crystal structure results in changes that affect the optical and nonlinear characteristics. Presented results indicate that the magnitude of X(3) was enhanced at single experimental wavelengths;however, across the broadband experimental spectrum, the effect of Al-doping remained relatively constant. The observed enhancement of third-order nonlinearity was purely from the bound electronic response. The observation is attributed to increased charge carriers and spontaneous polarization in the Zinc Oxide and Al-doped Zinc Oxide crystal structure.

2D PHASE SHIFTING AND LOGICAL MOIRE USED IN FRINGES ANALYSIS

Phase Shifting And Logical Moire (PSALM) is a kind of computer image processing method which can be used in phase measurement and to obtain the shape, deformation and strain distribution of an object.This paper presents the structure and working procedure of a 2D phase measurement PSALM2D program and its application. When analyzing moire interferometric fringes,we can obtain 2D distribution of displacement and strain.When it is used in reflection moire we can measure the slope of a specimen.Satisfactory visualization and quantitative results are given by PSALM2D.

Moiré superlattices arising from growth induced by screw dislocations in layered materials

Moiré superlattices(MSLs) are modulated structures produced from homogeneous or heterogeneous two-dimensional layers stacked with a twist angle and/or lattice mismatch. Enriching the methods for fabricating MSL and realizing the unique emergent properties are key challenges in its investigation. Here we recommend that the spiral dislocation driven growth is another optional method for the preparation of high quality MSL samples. The spiral structure stabilizes the constant out-of-plane lattice distance, causing the variations in electronic and optical properties. Taking SnS_(2) MSL as an example, we find prominent properties including large band gap reduction(~ 0.4 e V) and enhanced optical activity. Firstprinciples calculations reveal that these unusual properties can be ascribed to the locally enhanced interlayer interaction associated with the Moiré potential modulation. We believe that the spiral dislocation driven growth would be a powerful method to expand the MSL family and broaden their scope of application.

A fringe jump counting method for the phase measurement in the HCN laser interferometer on EAST and its FPGA-based implementation

Electron density in fusion plasma is usually diagnosed using laser-aided interferometers. The phase difference signal obtained after phase demodulation is wrapped, which is also called a fringe jump. A method has been developed to unwrap the phase difference signal in real time using FPGA, specifically designed to handle fringe jumps in the hydrogen cyanide(HCN) laser interferometer on the EAST superconducting tokamak. This method is designed for a phase demodulator using the fast Fourier transform(FFT) method at the front end. The method is better adapted for hardware implementation compared to complex mathematical analysis algorithms, such as field programmable gate array(FPGA). It has been applied to process the phase measurement results of the HCN laser interferometer on EAST in real time. Electron density results show good confidence in the fringe jump unwrapping method. Further possible application in other laser interferometers, such as the POlarimeter-INTerferometer(POINT)system on EAST tokamak is also discussed.

Physics-informed deep learning for fringe pattern analysis

Recently,deep learning has yielded transformative success across optics and photonics,especially in optical metrology.Deep neural networks (DNNs) with a fully convolutional architecture (e.g.,U-Net and its derivatives) have been widely implemented in an end-to-end manner to accomplish various optical metrology tasks,such as fringe denoising,phase unwrapping,and fringe analysis.However,the task of training a DNN to accurately identify an image-to-image transform from massive input and output data pairs seems at best naive,as the physical laws governing the image formation or other domain expertise pertaining to the measurement have not yet been fully exploited in current deep learning practice.To this end,we introduce a physics-informed deep learning method for fringe pattern analysis (PI-FPA) to overcome this limit by integrating a lightweight DNN with a learning-enhanced Fourier transform profilometry (Le FTP) module.By parameterizing conventional phase retrieval methods,the Le FTP module embeds the prior knowledge in the network structure and the loss function to directly provide reliable phase results for new types of samples,while circumventing the requirement of collecting a large amount of high-quality data in supervised learning methods.Guided by the initial phase from Le FTP,the phase recovery ability of the lightweight DNN is enhanced to further improve the phase accuracy at a low computational cost compared with existing end-to-end networks.Experimental results demonstrate that PI-FPA enables more accurate and computationally efficient single-shot phase retrieval,exhibiting its excellent generalization to various unseen objects during training.The proposed PI-FPA presents that challenging issues in optical metrology can be potentially overcome through the synergy of physics-priors-based traditional tools and data-driven learning approaches,opening new avenues to achieve fast and accurate single-shot 3D imaging.

Fringe家族基因在癌症中作用的研究进展

Fringe家族基因由疯狂边缘基因(LFNG)、躁狂边缘基因(MFNG)和激进边缘基因(RFNG)组成。Fringe家族基因编码的蛋白可修饰Notch受体来调控Notch信号通路,从而发挥调节细胞增殖、分化和凋亡等生物学功能。Genecards数据库分析了Fringe家族基因的染色体位置及生物学功能等。UCSCXenaShiny数据库整合癌症细胞系百科全书(CCLE)、癌症基因组图谱(TCGA)和基因型-组织表达(GTEx)数据分析了Fringe家族基因在泛癌细胞系、TCGA肿瘤组织和相对应的GTEx正常组织中的差异表达与预后价值。本文就Fringe家族基因在癌症中的作用作一综述。

Metropolitan Housing Development in Urban Fringe Areas-A Case Study of Three Metropolitan Cities of South Africa: Johannesburg, Ekurhuleni and Tshwane

Purpose:The metropolitan cities of Johannesburg,Ekurhuleni and Tshwane play an important role in the economy of the Gauteng province in South Africa.The region constitutes to 22.4 percent of the total population of South Africa and has a strong presence and contributes in areas of manufacturing sector,financial and business services,retail and wholesale trade,etc.The rapid urban population,increase in the informal settlements and socio-economic opportunities has resulted in considerable urban sprawl in and around the urban fringe areas of these metropolitan cities.The urban fringe areas of these metros often come under the influence of rapid urbanization process and pressures.Coupled with the economical and potential land dynamics and lack of priority of spatial development guidelines,these areas attract rapid and haphazard development from communities and developers.Research Design/Methodology:This research is based on a qualitative approach through a comprehensive literature review that included content analysis of key documents on housing sector such as IDPs(Integrated Development Plans),Municipal Annual Reports,Growth Development Strategies,and among other sectoral documents on housing sector.Some of the key priority issues considered in the housing sector included:eradication of housing backlogs,spatial restructuring of housing,provision of choice in terms of location,tenure and housing typology.Findings:The current paper discusses the approaches of metropolitan housing development processes in three metropolitan cities of South Africa from Gauteng region,namely:Johannesburg,Ekurhuleni and Tshwane.The paper discusses the existing housing sectoral scenario along with the fringe areas in three cities with focus on:formal and informal settlements,housing segregation and the backlogs,current institutional arrangements,role of public private participation,and scope for alternate mechanisms.The paper concludes in discussion on sustainable development options for housing development in urban fringe areas.

Carrier fringe method of moire interferometry for tiny strain measurements in micro-field

In this paper, we demonstrate a new optical method for tiny strain measurements based on the principle of carrier fringes of moire interferometry. A cross-line grating with frequency of 1200 lp/mm is replicated on the specimen surface, and the strain can be deduced from the changes in carrier fringes before and after the deformation of an object. Four coherent laser beams are used to obtain the carrier fringe patterns of field U and V. Both theoretical analysis and numerical simulation indicate that the ideal accuracy of strain can be controlled within a range of ±1με. Case study of a plane extension experiment shows that the measurement accuracy of strain can be controlled within the range of ±10με. The average strain values of every row of field U and every column of field V can be obtained by using this method, and approximated strain of every pixel in the whole-field can be further acquired, and thus it is possible to measure tiny strains occurred in a micro-field. The technology in this paper can provide comprehensive information for analyzing related mechanical content in the field of MEMS.

Automatic abstraction of interference fringes with image technique

ion technique of interference fringes used in phase modulation and phase scanning modulation interferometer is presented. For the measurement of amplitudes of interference fringes, fringes are fitted and their central points are determined automatically according to their distribution rules. However, for the measurement of their phases, fringes should be recognized and processed with different calculating algorithms and least square optimization methods depending on the scanning modulation mode. When this technique is used for measurement of surface roughness, the measurement uncertainty is better than 5nm and the repeatability is less than 5%.

Optical/Digital Fringe Multiplication in Projection Moire

In this paper, the optical/digital fringe multiplication (O/DFM) is realized in projection moiré using digital image processing (DIP). Both deformed grating and reference grating are captured using a CCD camera. The reference grating can also be produced using DIP. With the O/DFM, the pattern is multiplied with an image processing software, which is developed using MATLAB 6.5. Also with DIP, the phase shifting can become much simpler, and the automation can be adopted. The multiplied pattern is much thinner and easier to read, and sensitivity of measurement can be enhanced.

The Formation of Fringes of Equal Chromatic Order across Double Clad Fiber in the Presence of High Power Lasers

Multiple-beam fringes of equal chromatic order interferometry is a powerful technique to extract optical properties over a continuous range of spectrum. In this paper we develop a theory for the spectral shape of the fringes of equal chromatic order (FECO) that are formed across a double-clad fiber. The modified single term Sellmeier dispersion formula is used to construct the refractive index dispersion curves for the liquid, claddings, and core. Expressions for the paraxial optical path length for several rays passing through the fiber and the liquid are developed. The condition of bright fringe is applied to get an analytical expression for the spectral shape of the FECO across a double-clad fiber with an elliptical/circular inner cladding. A potential application of this theory is to determine the dispersion of Kerr constant of the claddings and the core of the fiber. To illustrate the theory and its application, simulation examples are provided and discussed.

Recent progress on fabrication and flat-band physics in 2D transition metal dichalcogenides moiré superlattices

Moiré superlattices are formed when overlaying two materials with a slight mismatch in twist angle or lattice constant. They provide a novel platform for the study of strong electronic correlations and non-trivial band topology, where emergent phenomena such as correlated insulating states, unconventional superconductivity, and quantum anomalous Hall effect are discovered. In this review, we focus on the semiconducting transition metal dichalcogenides(TMDs) based moiré systems that host intriguing flat-band physics. We first review the exfoliation methods of two-dimensional materials and the fabrication technique of their moiré structures. Secondly, we overview the progress of the optically excited moiré excitons, which render the main discovery in the early experiments on TMD moiré systems. We then introduce the formation mechanism of flat bands and their potential in the quantum simulation of the Hubbard model with tunable doping, degeneracies, and correlation strength. Finally, we briefly discuss the challenges and future perspectives of this field.

Review of phonons in moiré superlattices

Moirépatterns in physics are interference fringes produced when a periodic template is stacked on another similar one with different displacement and twist angles.The phonon in two-dimensional(2D)material affected by moirépatterns in the lattice shows various novel physical phenomena,such as frequency shift,different linewidth,and mediation to the superconductivity.This review gives a brief overview of phonons in 2D moirésuperlattice.First,we introduce the theory of the moiréphonon modes based on a continuum approach using the elastic theory and discuss the effect of the moirépattern on phonons in 2D materials such as graphene and MoS_(2).Then,we discuss the electron-phonon coupling(EPC)modulated by moirépatterns,which can be detected by the spectroscopy methods.Furthermore,the phonon-mediated unconventional superconductivity in 2D moirésuperlattice is introduced.The theory of phonon-mediated superconductivity in moirésuperlattice sets up a general framework,which promises to predict the response of superconductivity to various perturbations,such as disorder,magnetic field,and electric displacement field.

Interaction of moiréexcitons with cavity photons in two-dimensional semiconductor hetero-bilayers

Moirématerials,composed of two single-layer two-dimensional semiconductors,are important because they are good platforms for studying strongly correlated physics.Among them,moirématerials based on transition metal dichalcogenides(TMDs)have been intensively studied.The hetero-bilayer can support moiréinterlayer excitons if there is a small twist angle or small lattice constant difference between the TMDs in the hetero-bilayer and form a type-Ⅱ band alignment.The coupling of moiréinterlayer excitons to cavity modes can induce exotic phenomena.Here,we review recent advances in the coupling of moiréinterlayer excitons to cavities,and comment on the current difficulties and possible future research directions in this field.

Investigations of moiréartifacts induced by flux fluctuations in x-ray dark-field imaging

X-ray dark-field imaging using a grating interferometer has shown potential benefits for a variety of applications in recent years.X-ray dark-field image is commonly retrieved by using discrete Fourier transform from the acquired phasestepping data.The retrieval process assumes a constant phase step size and a constant flux for each stepped grating position.However,stepping errors and flux fluctuations inevitably occur due to external vibrations and/or thermal drift during data acquisition.Previous studies have shown that those influences introduce errors in the acquired phase-stepping data,which cause obvious moiréartifacts in the retrieved refraction image.This work investigates moiréartifacts in x-ray dark-field imaging as a result of flux fluctuations.For the retrieved mean intensity,amplitude,visibility and dark-field images,the dependence of moiréartifacts on flux fluctuation factors is theoretically derived respectively by using a first-order Taylor series expansion.Results of synchrotron radiation experiments verify the validity of the derived analytical formulas.The spatial frequency characteristics of moiréartifacts are analyzed and compared to those induced by phase-stepping errors.It illustrates that moiréartifacts can be estimated by a weighted mean of flux fluctuation factors,with the weighting factors dependent on the moiréphase and different greatly for each retrieved image.Furthermore,moiréartifacts can even be affected by object’s features not displayed in the particular contrast.These results can be used to interpret images correctly,identify sources of moiréartifacts,and develop dedicated algorithms to remove moiréartifacts in the retrieved multi-contrast images.

Projecting Distortion Calibration and Evaluation of Coding Fringes in Structured Light System

Coded structured light is an accurate, fast 3D measurement approach with high sampling density, of which the encoded fringes are distorted when projected to curved surface. Focused on the demand of encoding, decoding, multiview registration and system calibration, we expect to obtain undistorted fringes from camera image. Therefore, in this paper, we analyze the accuracy and sampling density of projecting distortion calibration approach based on control point and fitting surface. Moreover, combining the characteristic of coded structured light system, we design encoded fringe projecting distortion calibration scheme based on simplified encoded structured light model. Primarily, we neglect the minor parameters that affect the calibration in structured light model to reduce complexity. Then, we build the correspondence between camera image points and projector image points and achieve the calibration. Finally, we design evaluation scheme of projecting distortion calibration with parallelism and equal interval, and verify the effectiveness and accuracy of the approach through visual effect and experimental data.

Epitaxial growth of trilayer graphene moiré superlattice

The graphene-based moiré superlattice has been demonstrated as an exciting system for investigating strong correlation phenomenon. However, the fabrication of such moiré superlattice mainly relies on transfer technology. Here, we report the epitaxial growth of trilayer graphene(TLG) moiré superlattice on hexagonal boron nitride(h BN) by a remote plasma-enhanced chemical vapor deposition method. The as-grown TLG/h BN shows a uniform moiré pattern with a period of ~ 15 nm by atomic force microscopy(AFM) imaging, which agrees with the lattice mismatch between graphene and h BN. By fabricating the device with both top and bottom gates, we observed a gate-tunable bandgap at charge neutral point(CNP) and displacement field tunable satellite resistance peaks at half and full fillings. The resistance peak at half-filling indicates a strong electron–electron correlation in our grown TLG/h BN superlattice. In addition, we observed quantum Hall states at Landau level filling factors ν = 6, 10, 14,..., indicating that our grown trilayer graphene has the ABC stacking order. Our work suggests that epitaxy provides an easy way to fabricate stable and reproducible two-dimensional strongly correlated electronic materials.

MoiréDirac fermions in transition metal dichalcogenides heterobilayers

Monolayer group-VIB transition metal dichalcogenides(TMDs)feature low-energy massive Dirac fermions,which have valley contrasting Berry curvature.This nontrivial local band topology gives rise to valley Hall transport and optical selection rules for interband transitions that open up new possibilities for valleytronics.However,the large bandgap in TMDs results in relatively small Berry curvature,leading to weak valley contrasting physics in practical experiments.Here,we show that Dirac fermions with tunable large Berry curvature can be engineered in moirésuperlattice of TMD heterobilayers.These moiréDirac fermions are created in a magnified honeycomb lattice with its sublattice degree of freedom formed by two local moirépotential minima.We show that applying an on-site potential can tune the moiréflat bands into helical ones.In short-period moirésuperlattice,we find that the two moirévalleys become asymmetric,which results in a net spin Hall current.More interestingly,a circularly polarized light drives these moiréDirac fermions into quantum anomalous Hall phase with chiral edge states.Our results open a new possibility to design the moiré-scale spin and valley physics using TMD moiréstructures.

Melting of electronic/excitonic crystals in 2D semiconductor moirépatterns:A perspective from the Lindemann criterion

Using the Lindemann criterion,we analyzed the quantum and thermal melting of electronic/excitonic crystals recently discovered in two-dimensional(2D)semiconductor moirépatterns.We show that the finite 2D screening of the atomically thin material can suppress(enhance)the inter-site Coulomb(dipolar)interaction strength,thus inhibits(facilitates)the formation of the electronic(excitonic)crystal.Meanwhile,a strong enough moiréconfinement is found to be essential for realizing the crystal phase with a wavelength near 10 nm or shorter.From the calculated Lindemann ratio which quantifies the fluctuation of the site displacement,we estimate that the crystal will melt into a liquid above a critical temperature ranging from several tens Kelvin to above 100 K(depending on the system parameters).