Analysis of period and visibility of dual phase grating interferometer

Dual phase grating interferometer may simultaneously achieve large field of view and high x-ray dose efficiency.Here,we develop a simple theoretical method to better understand the imaging process of the dual phase grating interferometer.The derivation process of fringe period and the optimal visibility conditions of the dual phase grating interferometer are given in detail.Then,we theoretically prove that the fringe period and optimal visibility conditions of the dual phase grating interferometer include that of the Talbot interferometer.By comparing our experimental results with those of other researchers,we find that when the positions of phase gratings are far away from the positions where the fringe visibility is optimal,the fringe period of the dualπ-phase grating interferometer is twice the theoretical results under the illumination of polychromatic x-ray.This conclusion may explain the contradictory research results of dual phase grating interferometer among different researchers.

X-ray phase-sensitive microscope imaging with a grating interferometer:Theory and simulation

A general theoretical framework is presented to explain the formation of the phase signal in an x-ray microscope integrated with a grating interferometer,which simultaneously enables the high spatial resolution imaging and the improved image contrast.By using this theory,several key parameters of phase contrast imaging can be predicted,for instance,the fringe visibility and period,and the conversion condition from the differential phase imaging(DPI)to the phase difference imaging(PDI).Additionally,numerical simulations are performed with certain x-ray optical components and imaging geometry.Comparison with the available experimental measurement[Appl.Phys.Lett.113063105(2018)]demonstrates the accuracy of this developed quantitative analysis method of x-ray phase-sensitive microscope imaging.

Fused-like angles:replacement for roll-pitch-yaw angles for a six-degree-of-freedom grating interferometer

Representation of orientation is important in a six-degree-of-freedom grating interferometer but only a few studies have focused on this topic.Roll-pitch-yaw angles,widely used in aviation,navigation,and robotics,are now being brought to the field of multi-degree-of-freedom interferometric measurement.However,the roll-pitch-yaw angles are not the exact definitions the metrologists expected in interferometry,because they require a certain sequential order of rotations and may cause errors in describing complicated rotations.The errors increase as the tip and tilt angles of the grating increase.Therefore,a replacement based on fused angles in robotics is proposed and named“fused-like angles.”The fused-like angles are error-free,so they are more in line with the definitions in grating interferometry and more suitable for six-degree-of-freedom measurements.Fused-like angles have already been used in research on the kinematic model and decoupling algorithm of the six-degree-of-freedom grating interferometer.

Symmetrical short-period and high signal-to-noise ratio heterodyne grating interferometer

A symmetrical heterodyne grating interferometer with both a short period and high signal-to-noise ratio is proposed. It possesses good immunity to environmental disturbances and can simultaneously achieve high resolution and stability. The experimental results show that the standard deviation of 24.67 nm can be realized for the long range of 10 mm. The measurement resolution of better than 2 nm is achieved with the theoretical resolution of 12 pm. Additionally, system stability at less than 1.5 nm is obtained in just over 10 min. The measurement errors, including cosine error, nonlinear error and non-common path error, are discussed as well.

Comparative analysis of phase extraction methods based on phase-stepping and shifting curve in grating interferometry

Two phase extraction methods which are based separately on phase-stepping and shifting curve are mainly used in phase-sensitive imaging in gating interferometry to determine the x-ray phase shift induced by an object in the beam. In this paper, the authors perform a full comparative analysis and present the main virtues and limitations of these two methods according to the theoretical analysis of the grating interferometry.

Quantitative coherence analysis of dual phase grating x-ray interferometry with source grating

Dual phase grating x-ray interferometry is compatible with common imaging detectors,and abandons the use of an absorption analyzer grating to reduce the radiation dose.When using x-ray tubes,an absorbing source grating must be introduced into the dual phase grating interferometer.In order to attain a high fringe visibility,in this work we conduct a quantitative coherence analysis of dual phase grating interferometry to find how the source grating affects the fringe visibility.Theoretical analysis shows that with the generalized Lau condition satisfied,the fringe visibility is influenced by the duty cycle of the source grating and the transmission through the grating bar.And the influence of the source grating profile on the fringe visibility is independent of the phase grating type.Numerical results illustrate that the maximum achievable fringe visibility decreases significantly with increasing transmission in the grating bar.Under a given transmission,one can always find an optimal duty cycle to maximize the fringe visibility.These results can be used as general guidelines for designing and optimizing dual phase grating x-ray interferometers for potential applications.

Development of an HCN dual laser for the interferometer on EAST

A two-color continuous wave（CW） discharge-pumped far-infrared（FIR） hydrogen cyanide（HCN） laser was developed as the source of an interferometer for measuring the line-averaged electron density in the Experimental Advanced Superconducting Tokamak（EAST）. The output power of the dual laser system was about 120 m W from each laser on the 337 μm（0.89 THz）line. The polarization of each output beam was fixed using thin tungsten filaments and oscillated in the EH11 mode. Different megahertz intermediate frequencies（IF） and a slight frequency offset（～1 MHz） were generated in this system to replace the traditional rotating grating with～10 k Hz IF, and this can improve the time resolution of the interferometer significantly. The experimental result showed that different IF signals were obtained by successfully adjusting the cavity length. In particular, the beat frequency was captured at ～1.3 MHz by a Schottky mixer when the length of the resonant cavities was changed by 5 μm by an automatic adjustment system. In order to study the character of IF, a long time record of the IF signal was carried out,and the IF signal could be stabilized for a few minutes in the range of 2 MHz to 3 MHz. A realtime IF stability control system was initially designed for long pulse discharge experiments on the EAST. The ～MHz frequency response and good phase sensitivity of the dual laser HCN interferometer will allow the system to track fast density profiles and resolve fast MHD events,such as tearing/neoclassical tearing, disruptions, etc.

Model-driven CT reconstruction algorithm for nano-resolution x-ray phase contrast imaging

The low-density imaging performance of a zone plate-based nano-resolution hard x-ray computed tomography(CT)system can be significantly improved by incorporating a grating-based Lau interferometer. Due to the diffraction, however,the acquired nano-resolution phase signal may suffer splitting problem, which impedes the direct reconstruction of phase contrast CT(nPCT) images. To overcome, a new model-driven nPCT image reconstruction algorithm is developed in this study. In it, the diffraction procedure is mathematically modeled into a matrix B, from which the projections without signal splitting can be generated invertedly. Furthermore, a penalized weighted least-square model with total variation(PWLSTV) is employed to denoise these projections, from which nPCT images with high accuracy are directly reconstructed.Numerical experiments demonstrate that this new algorithm is able to work with phase projections having any splitting distances. Moreover, results also reveal that nPCT images of higher signal-to-noise-ratio(SNR) could be reconstructed from projections having larger splitting distances. In summary, a novel model-driven nPCT image reconstruction algorithm with high accuracy and robustness is verified for the Lau interferometer-based hard x-ray nano-resolution phase contrast imaging.

Recent Progress in Multiparameter Measurement Based on Extrinsic Fiber-Optic Fabry-Perot Interferometers and Fiber Gratings

This paper presents a review of recent progress in simultaneous measurement of multiparameters including strain, temperature, vibration, transverse load, based on the combinations of extrinsic fiber-optic Fabry-Perot interferometers and fiber gratings.

Design of a grating by a joint optimization method for a phase-shifting point diffraction interferometer

A grating is an important element of a phase-shifting point diffraction interferometer, and the grating constant and duty cycle have a great impact on the interferometer, so the design of a grating becomes significant. In order to measure the projection objective with a numerical aperture of 0.2, we present a joint optimization method of a pinhole and grating based on scalar diffraction and the finite difference time domain method. The grating constant and the film thickness are selected, and the duty cycle of the grating is optimized. The results show that in the grating processing the material chromium is adopted, the thickness is 200 nm, and the grating constant is 15 μm. When the duty cycle is 55%, the interference fringe contrast is the greatest. The feasibility of the design result is further verified by experiment.

An optical fiber magnetic field sensor based on fiber spherical structure interferometer coated by magnetic fluid

A novel magnetic field sensor based on optical fiber Mach-Zehnder interferometer(MZI) coated by magnetic fluid(MF) is proposed. The MZI consists of two spherical structures formed on standard single mode fiber(SMF). The interference wavelength and the power of the sensing structure are sensitive to the external refractive index(RI). Since RI of the MF is sensitive to the magnetic field, the magnetic field measurement can be realized by detecting the variation of the interference spectrum. Experimental results show that the wavelength and the power of interference dip both increase with the increase of magnetic field intensity.

A tension insensitive PbS fiber temperature sensor based on Sagnac interferometer

In this paper, a tension insensitive Pb S fiber temperature sensor based on Sagnac interferometer is proposed and demonstrated. The sensing mechanism of tension and temperature is analyzed. The relationships between the interference spectrum, temperature and tension are analyzed, respectively. The experimental temperature range is 36—70 °C. The experimental results show that the interference spectrum is red shifted, and its sensitivity is 53.89 pm/°C. In tension experiment, the tension range is 0—1 400 με. The experimental results show that there is no wavelength shift in the interference spectrum. The sensor is immune to tension cross-sensitivity compared with other sensors. It can be used for temperature testing in aerospace, chemistry and pharmacy.

FFPI-FBG hybrid sensor to measure the thermal expansion and thermo-optical coefficient of a silica-based fiber at cryogenic temperatures

In this Letter, a sensor consisting of a fiber Bragg grating（FBG） and a fiber Fabry–Perot interferometer（FFPI）sensor is developed to measure the coefficient of thermal expansion（CTE） and the thermo-optical coefficient（TOC） of a silica-based optical fiber at cryogenic temperatures. The FFPI is fabricated by welding together two acid-etched fibers. The temperature performance of the FFPI-FBG hybrid sensor is studied in the temperature range of 30–273 K. The CTE and TOC of the optical fiber at cryogenic temperatures are derived analytically and verified by experiments.

Measurement of small wavelength shifts based on total internal reflection heterodyne interferometry

This Letter presents a method of an optical sensor for measuring wavelength shifts. The system consists of a diffraction grating and a total internal reflection heterodyne interferometer. As a heterodyne light beam strikes a grating, the first-order diffraction beam is generated. The light penetrates into a total internal reflection prism at an angle larger than the critical angle. A wavelength variation will affect the diffractive angle of the first-order beam, thus inducing a phase difference variation of the light beam emerging from the total internal reflections inside the trapezoid prism. Both the experimental and theoretical results reveal that, for the first-order diffractive beam, the sensitivity and resolution levels are superior to 5°/nm and 0.006 nm, respectively, in the range of wavelength from 632 to 634 nm, and are superior to 3.1°/nm and 0.0095 nm in the range from 632 to 637 nm. For the theoretical simulation of the fourth-order diffractive beam, they are superior to 6.4 deg ∕nm and 0.0047 nm in the range from 632 to 637 nm.

An adaptive tensor voting algorithm combined with texture spectrum

An adaptive tensor voting algorithm combined with texture spectrum is proposed. The image texture spectrum is used to get the adaptive scale parameter of voting field. Then the texture information modifies both the attenuation coefficient and the attenuation field so that we can use this algorithm to create more significant and correct structures in the original image according to the human visual perception. At the same time, the proposed method can improve the edge extraction quality, which includes decreasing the flocculent region efficiently and making image clear. In the experiment for extracting pavement cracks, the original pavement image is processed by the proposed method which is combined with the significant curve feature threshold procedure, and the resulted image displays the faint crack signals submerged in the complicated background efficiently and clearly.