Exploring beam size measurement based on the Talbot effect at BEPCII.

Vertical beam size measurements were carried out at Beijing Electron-Positron Collider II (BEPCII) using a phase grating and an absorption grating based on the Talbot effect. The transverse coherence of synchrotron radiation is closely related to beam size. Due to the partial coherence of the synchrotron radiation source, the coherence length can be calculated by measuring the visibility decay of interferograms recorded at different distances behind the gratings. A vertical beam size of 68.19 ± 2 µm was obtained based on the relationship between the coherence length and beam size at the 3W1 beamline of BEPCII. A comparison of the vertical emittance derived from the grating Talbot method and the synchrotron radiation visible light interferometer method was presented. The vertical emittances from the two methods are 1.41 nm rad and 1.40 nm rad, respectively. The 0.1% difference indicates that the grating Talbot method for beam size measurement is reliable. This technique has great potential for small beam size measurement of fourth-generation synchrotron radiation light sources, considering its small diffraction limitation and simple experimental setups.

An Ultracompact Angular Displacement Sensor Based on the Talbot Effect of Optical Microgratings.

Here, we report an ultracompact angular displacement sensor based on the Talbot effect of optical microgratings. Periodic Talbot interference patterns were obtained behind an upper optical grating. By putting another grating within the Talbot region, the total transmission of the two-grating structure was found to be approximatively in a linear relationship with the relative pitch angle between the two gratings, which was explained by a transversal shift of the Talbot interference patterns. The influence of the grating parameters (e.g., the grating period, the number of grating lines and the gap between the two gratings) was also studied in both a simulation and an experiment, showing a tunable sensitivity and range by simply changing the grating parameters. A sensitivity of 0.19 mV/arcsec was experimentally obtained, leading to a relative sensitivity of 0.27%/arcsec within a linear range of ±396 arcsec with the 2 µm-period optical gratings. Benefitting from tunable properties and an ultracompact structure, we believe that the proposed sensor shows great potential in applications such as aviation, navigation, robotics and manufacturing engineering.

X-ray dynamical diffraction analogues of the integer and fractional Talbot effects.

The X-ray integer and fractional Talbot effect is studied under two-wave dynamical diffraction conditions in a perfect crystal, for the symmetrical Laue case of diffraction. The fractional dynamical diffraction Talbot effect is studied for the first time. A theory of the dynamical diffraction integer and fractional Talbot effect is given, introducing the dynamical diffraction comb function. An expression for the dynamical diffraction polarization-sensitive Talbot distance is established. At the rational multiple depths of the Talbot depth the wavefield amplitude for each dispersion branch is a coherent sum of the initial distributions, shifted by rational multiples of the object period and having its own phases. The simulated dynamical diffraction Talbot carpet for the Ronchi grating is presented.

Transmission of an X-ray beam through a two-dimensional photonic crystal and the Talbot effect.

Results of computer simulations of the transmission of an X-ray beam through a two-dimensional photonic crystal as well as the propagation of an X-ray beam in free space behind the photonic crystal are reported. The photonic crystal consists of a square lattice of silicon cylinders of diameter 0.5 µm. The amount of matter in the path of the X-ray beam rapidly decreases at the sides of the cylinder projections. Therefore the transmission is localized near the boundaries, and appears like a channeling effect. The iterative method of computer simulations is applied. This method is similar to the multi-slice method that is widely used in electron microscopy. It allows a solution to be obtained with acceptable accuracy. A peculiarity in the intensity distribution inside the Talbot period zT in free space was found when the intensity is approximately equal to the initial value at a distance 0.46zT, and it is shifted by half a period at distance 0.5zT. The reason for this effect is the existence of a periodic phase of the wavefunction of radiation inside the intensity peaks. Simulations with zero phase do not show this effect. Symmetry rules for the Talbot effect are discussed.

Formation and Applications of the Secondary Fiber Bragg Grating.

Being one of the most proven fiber optic devices, the fiber Bragg grating has developed continually to extend its applications, particularly in extreme environments. Accompanying the growth of Type-IIa Bragg gratings in some active fibers, a new resonance appears at the shorter wavelength. This new type of grating was named "secondary Bragg grating" (SBG). This paper describes the formation and applications of the SBGs. The formation of the SBG is attributed to the intracore Talbot-type-fringes as a result of multi-order diffractions of the inscribing beams. The SBG presents a variety of interesting characteristics, including dip merge, high-temperature resistance, distinct temperature response, and the strong higher-order harmonic reflection. These features enable its promising applications in fiber lasers and fiber sensing technology.

30-Lens interferometer for high-energy X-rays.

A novel high-energy multi-lens interferometer consisting of 30 arrays of planar compound refractive lenses is reported. Under coherent illumination each lens array creates a diffraction-limited secondary source. Overlapping such coherent beams produces an interference pattern demonstrating strong longitudinal functional dependence. The proposed multi-lens interferometer was tested experimentally at the 100 m-long ID11 ESRF beamline in the X-ray energy range from 30 to 65 keV. The interference pattern generated by the interferometer was recorded at fundamental and fractional Talbot distances. An effective source size (FWHM) of the order of 15 µm was determined from the first Talbot image, proving the concept that the multi-lens interferometer can be used as a high-resolution tool for beam diagnostics.

Design and Demonstration of an In-Plane Micro-Optical-Electro-Mechanical-System Accelerometer Based on Talbot Effect of Dual-Layer Gratings.

An ultrasensitive single-axis in-plane micro-optical-electro-mechanical-system (MOEMS) accelerometer based on the Talbot effect of dual-layer gratings is proposed. Based on the Talbot effect of gratings, the acceleration can be converted into the variation of diffraction intensity, thus changing the voltage signal of photodetectors. We investigated and optimized the design of the mechanical structure; the resonant frequency of the accelerometer is 1878.9 Hz and the mechanical sensitivity is 0.14 µm/g. And the optical grating parameters have also optimized with a period of 4 µm and a grating interval of 10 µm. The experimental results demonstrated that the in-plane MOEMS accelerometer with an optimal design achieved an acceleration sensitivity of 0.74 V/g (with better than 0.4% nonlinearity), a bias stability of 75 µg and an acceleration resolution of 2.0 mg, suggesting its potential applications in smartphones, automotive electronics, and structural health detection.

Vortex Filament Equation for a Regular Polygon in the Hyperbolic Plane.

The aim of this paper is twofold. First, we show the evolution of the vortex filament equation (VFE) for a regular planar polygon in the hyperbolic space. Unlike in the Euclidean space, the planar polygon is open and both of its ends grow up exponentially, which makes the problem more challenging from a numerical point of view. However, using a finite difference scheme in space combined with a fourth-order Runge-Kutta method in time and fixed boundary conditions, we show that the numerical solution is in complete agreement with the one obtained by means of algebraic techniques. Second, as in the Euclidean case, we claim that, at infinitesimal times, the evolution of VFE for a planar polygon as the initial datum can be described as a superposition of several one-corner initial data. As a consequence, not only can we compute the speed of the center of mass of the planar polygon, but the relationship also allows us to compare the time evolution of any of its corners with the evolution in the Euclidean case.

Numerical Analysis of the Light Modulation by the Frustule of Gomphonema parvulum: The Role of Integrated Optical Components.

Siliceous diatom frustules present a huge variety of shapes and nanometric pore patterns. A better understanding of the light modulation by these frustules is required to determine whether or not they might have photobiological roles besides their possible utilization as building blocks in photonic applications. In this study, we propose a novel approach for analyzing the near-field light modulation by small pennate diatom frustules, utilizing the frustule of Gomphonema parvulum as a model. Numerical analysis was carried out for the wave propagation across selected 2D cross-sections in a statistically representative 3D model for the valve based on the finite element frequency domain method. The influences of light wavelength (vacuum wavelengths from 300 to 800 nm) and refractive index changes, as well as structural parameters, on the light modulation were investigated and compared to theoretical predictions when possible. The results showed complex interference patterns resulting from the overlay of different optical phenomena, which can be explained by the presence of a few integrated optical components in the valve. Moreover, studies on the complete frustule in an aqueous medium allow the discussion of its possible photobiological relevance. Furthermore, our results may enable the simple screening of unstudied pennate frustules for photonic applications.

X-ray dynamical diffraction Talbot effect behind a crystal in free space.

The dynamical diffraction Talbot effect takes place inside a crystal, when a periodic object is illuminated by a plane or spherical X-ray wave which then falls on the crystal at an angle close to the Bragg angle for some reflection. Both theoretical consideration and numerical calculations show that the dynamical diffraction Talbot effect also takes place behind the crystal. The effect is accompanied by the dynamical diffraction pendulum effect and wave focusing. Expressions are found for the dynamical diffraction Talbot distance for areas before and after focusing. The spatial Fourier spectrum of the periodic object is obtained on the focusing plane. Detailed analysis when the periodic object is illuminated by a plane wave has shown new features of this effect. The dynamical diffraction Talbot effect in free space can be used to determine the structure of a periodic object, to determine the structure of an arbitrary object placed before or after the periodic object, and to determine structural defects and deformations of the crystal.

Spherical-wave X-ray dynamical diffraction Talbot effect inside a crystal.

Two-wave dynamical diffraction of an X-ray spherical wave in a crystal, when the wave passes through an object with a periodic amplitude transmission function, is considered. The behavior of the diffracted wave (spherical-wave Talbot effect) in the crystal is investigated. The Talbot effect inside the crystal is accompanied by the focusing effect and the pendulum effect. Peculiarities of the effect before the focus point, in the focusing plane and in the region after the focus point inside the crystal are revealed. An expression is found for the Talbot depth and the spherical-wave Talbot effect in these three regions is investigated. The spherical-wave dynamical diffraction Talbot effect in a crystal is compared with the classical spherical-wave Talbot effect and also with spherical-wave effects inside the crystal without a periodic object.

Observation of ultrasonic Talbot effect in perforated plates.

The Talbot effect using ultrasonic waves transmitted through a periodic perforated plate is presented. The ultrasonic wave-field at the exit of the perforated plate replicates the perforated pattern at the Talbot distance. Experimental results are validated by an analytical model. The measured propagating wave-field is consistent with the analytical results. The influence of the grating size and the filling fraction on the Talbot effect are also studied, and it is found that both parameters affect the formation of Talbot images.

Laser Surface Microstructuring of Biocompatible Materials Using a Microlens Array and the Talbot Effect: Evaluation of the Cell Adhesion.

A laser based technique for microstructuring titanium and tantalum substrates using the Talbot effect and an array of microlenses is presented. By using this hybrid technique; we are able to generate different patterns and geometries on the top surfaces of the biomaterials. The Talbot effect allows us to rapidly make microstructuring, solving the common problems of using microlenses for multipatterning; where the material expelled during the ablation of biomaterials damages the microlens. The Talbot effect permits us to increase the working distance and reduce the period of the patterns. We also demonstrate that the geometries and patterns act as anchor points for cells; affecting the cell adhesion to the metallic substrates and guiding how they spread over the material.

Analysis of red blood cell parameters by Talbot-projected fringes.

Red blood cell (RBC) anomalies are significant symptoms for identification of health disorders and several blood diseases, which involve the modification of the parameters and biophysical characteristics of such cells. The aim of this study is to measure the three-dimensional phase information of healthy RBCs and their parameters, such as cell diameter, thickness, and hemoglobin (Hb) content, using Talbot-projected fringes. The Talbot image of linear grating is projected onto an RBC slide. The deformed grating lines due to the shape and refractive index of RBCs are recorded by a CCD camera through a 20× microscope objective. Hilbert transform is used to extract the phase image from the deformed projected grating lines. Experimentally calculated values of diameter (8.2 µm), thickness (2.7 µm), and Hb content (28.7 pg/cell) are well within the limits available in the literature. The proposed system is robust and user-friendly and performs the imaging of RBCs with high axial and lateral resolution (2.19 µm).

Rapid, High-Resolution 3D Interference Printing of Multilevel Ultralong Nanochannel Arrays for High-Throughput Nanofluidic Transport.

3D interference printing enables the single-step production of multilayered ultralong nanochannel arrays with nanoscale regularity. The superior depth-of-focus of this technique realizes a state-of-the-art nanostructure which has intensively stacked 32 layers of inch-long, horizonontal nanochannels with sub-100 nm holes in a monolithic matrix (≈15 µm). This exceptional structure can be integrated into microfluidic devices, facilitating high-flux rheological platforms using nanocapillarity.

Talbot holographic illumination nonscanning (THIN) fluorescence microscopy.

Optical sectioning techniques offer the ability to acquire three-dimensional information from various organ tissues by discriminating between the desired in-focus and out-of-focus (background) signals. Alternative techniques to confocal, such as active structured illumination, exist for fast optically sectioned images, but they require individual axial planes to be imaged consecutively. In this article, an imaging technique (THIN), by utilizing active Talbot illumination in 3D and multiplexed holographic Bragg filters for depth discrimination, is demonstrated for imaging in vivo 3D biopsy without mechanical or optical axial scanning.