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 dual π -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.     

Fourier optics analysis of grating sensors with tilt errors

Dynamic diffraction gratings can be microfabricated with precision and offer extremely sensitive displacement measurements and light intensity modulation. The effect of pure translation of the moving part of the grating on diffracted order intensities is well known. This study focuses on the parameters that limit the intensity and the contrast of the interference. The effects of grating duty cycle, mirror reflectivities, sensor tilt and detector size are investigated using Fourier optics theory and Gaussian beam optics. Analytical findings reveal that fringe visibility becomes <0.3 when the optical path variation exceeds half the wavelength within the grating interferometer. The fringe visibility can be compensated by monitoring the interfering portion of the diffracted order light only through detector size reduction in the expense of optical power. Experiments were conducted with a grating interferometer that resulted in an eightfold increase in fringe visibility with reduced detector size, which is in agreement with theory. Findings show that diffraction grating readout principle is not limited to translating sensors but also can be used for sensors with tilt or other deflection modes.     

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. 113 063105 (2018)] demonstrates the accuracy of this developed quantitative analysis method of x-ray phase-sensitive microscope imaging.     

双能X射线光栅相衬成像的研究

X射线光栅相衬成像存在系统复杂、成像效率低、步进精度要求高、光栅加工难度大等问题.本文设计了一种双能阵列X射线源和双能分析光栅,并应用于X射线光栅相衬成像,提出了一种双能X射线光栅相衬成像系统,阐述了该成像系统的成像原理和相位信息提取方法.提出的成像系统不需要精密步进平台,精简了成像系统,避免了步进误差导致的成像质量降低问题;两次曝光就可以成像,提高了成像效率;双能阵列X射线源、双能分析光栅的应用避免了源光栅、分析光栅难以加工的问题.对提出的成像系统及其相位提取方法进行了仿真,仿真结果显示成像系统可以正常成像,提取到的检测样本的X射线相衬成像相位一阶导数分布与相关文献实验所得结果一致.     

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.     

Display of tilt information of vibrating object in time average mode using lateral shearing interferometry and interferometric grating

We have experimentally demonstrated vibration analysis of a reflecting object in time-average mode using shearing interferometry and interferometric grating. Experimental results show that time-average moiré fringes, formed between fringe pattern reflected from object and sinusoidal grating are modulated spatially by the amplitude of vibrating tilt. From the experimental results, information regarding tilt of vibrating objects can be determined.     

Imaging the ultrasmall-angle x-ray scattering distribution with grating interferometry

X-ray imaging with grating interferometry has previously been regarded as a technique providing information only in direct space. It delivers absorption, phase, and dark-field contrast, which can be viewed as parameters of the underlying but unresolved scattering distribution. Here, we present a method that provides the ultrasmall-angle x-ray scattering distribution and, thus, allows simultaneous access to direct and reciprocal space information.     

全息光栅制作中光栅掩模形状随曝光量及干涉场条纹对比度的变化规律

为了在光栅制作中对光栅掩模占宽比及槽深加以控制,结合光刻胶在显影过程中的非线性特性,建立了光栅掩模槽形演化的数学模型,由此分析和模拟曝光量、条纹对比度对光栅槽形的影响。结果表明:在显影条件确定时,光栅掩模占宽比随光刻胶曝光量的增大而减小,条纹对比度减小,则不仅使光栅占宽比减小,同时也是使光栅槽深减小的主要原因,这样做的前提是预先通过实验和计算确定出一个曝光量上限Ec。该方法能够反映光栅掩模形状的演化规律,为全息光栅参数预测和工艺控制提供依据。     

Generation of the derivative of out-of-plane displacements in the high-sensitivity grating interferometry configuration

A simple method for determining the surface slope of a specimen under test in the high-sensitivity grating interferometry setup is proposed. The information on the derivative of out-of-plane displacement is obtained by software subtraction of two primary interferograms: a conventional one and one with diffraction orders laterally displaced in the image plane. Very good coincidence between the theoretical and experimental results has been obtained. The method can be used for studying static and transient events depending on the fringe pattern analysis method used.     

Single-shot grating-based x-ray differential phase contrast imaging with a modified analyzer grating

X-ray grating interferometer has attracted widely attention in the past years due to its capability in achieving x-ray phase contrast imaging with low brilliance source. However, the widely used phase stepping information extraction method reduces system stability and prolongs data acquisition time by several times compared with conventional x-ray absorptionbased imaging. The mechanical stepping can be avoided by using a staggered grating, but at the cost of low vertical spatial resolution. In this paper, employing a modified staggered grating and the angular signal radiography, we proposed a single-shot grating-based x-ray differential phase contrast imaging with decent vertical spatial resolution. The theoretical framework was deduced and proved by numerical experiments. Absorption, phase, and scattering computed tomography can be performed without phase stepping. Therefore, we believe this fast and highly stable imaging method with decent resolution would be widely applied in x-ray grating-based phase contrast imaging.     

A mixed metal dielectric sandwiched grating for polarization-selective reflection

A mixed metal dielectric sandwiched grating is described for polarization-selective reflection. The novel grating is composed of substrate, metal slab, two dielectric grating layers, and covering layer. The polarization-selective grating is optimized by using rigorous coupled-wave analysis for the usual duty cycle of 0.5. With the optimized grating parameters, reflective efficiency of 96.49% can be diffracted into the −1st order for TE polarization. And two-port output of 48.26%/48.27% can be diffracted into the 0th and the −1st orders for TM polarization. Polarization-selective reflection with good performance can be obtained by the mixed metal dielectric sandwiched grating. The usual duty cycle of 0.5 makes it easy and simple to be fabricated for practical applications. Moreover, the polarization-selective beam splitter based on the mixed metal dielectric sandwiched grating has advantages of wide incident wavelength range for TE polarization and angular bandwidth for TM polarization.     

Connecting-layer-based polarizing beam splitter grating with high efficiency for both TE and TM polarizations

We describe a novel polarizing beam splitter (PBS) of transmission connecting-layer-based grating, which can show high efficiency for TE polarization in the ?1st order and TM polarization in the 0th order. According to the modal method, grating duty cycle and period are prescribed to obtain high efficiency for TM polarization. Using the rigorous coupled-wave analysis, grating depth and thickness of the connecting layer are optimized to achieve high efficiency for TE polarization. The presented PBS has advantages of wideband properties for incident wavelength and angle. Most importantly, the efficiency is improved greatly for TE polarization compared with the reported PBS based on fused-silica grating.     

软X射线位相型金透射光栅的设计与制作

根据衍射光栅的标量理论,计算并讨论了金透射光栅在软X波段衍射效率对光栅厚度和占宽比的依赖关系.结果表明,选择合适的光栅槽深和占宽比,高达 21.9%的衍射效率可能被获得,远高于振幅型光栅的+1级衍射效率10.14%.通过全息光刻与电镀转移技术制作的位相型金透射光栅由300nm的聚酰亚胺薄膜支撑,光栅槽深200nm,占宽比为0.55,周期为1μm,面积为20mm×5mm.在国家同步辐射装置上,测得其+1级透射衍射效率在波长λ=7.425nm时获得最大值,约为16%. 关键词： 透射位相光栅 全息光刻 电镀     

A novel 3D measuring method for discontinuous object by non-integral twin-frequency grating

A new 3D shape measurement method based on non-integral twin-frequency grating projection is proposed. In this paper, the projected composite grating is composed of two sinusoidal gratings, and the quotient of whose frequencies is not an integer. By using appropriate phase-shifting algorithms, two wrapped phases can be obtained from sixteen frames of the distorted grating patterns. In aid of appropriate phase unwrapping method, the unwrapped phase of high frequency fringe is obtained only from the relation of the two wrapped phases by a pixel-to-pixel phase unwrapping technique. Therefore the unwrapped phase of high frequency fringe pattern is independent of the low frequency fringe pattern, different from traditional integral twin-frequency grating projection methods in which the phase unwrapping error of low frequency fringe pattern may be propagated onto the unwrapped phase of high frequency fringe pattern. The new theory proves that the proposed method is applicable to measure discontinuous object, and has considerable measurement accuracy.     

A new real-time method of moiré interferometry for displacement derivative fringe patterns

A new method of moiré interferometry is proposed in this paper to obtain the strain fringe pattern in real time. The specimen grating is illuminated by dual beams whose optical path-difference is larger than the coherence length of the laser. The diffractions of the grating are sheared by a glass wedge to fulfil the optical differentiation. The principles based on wavefront analysis are shown and an experimental verification is reported.     

A novel approach to high-sensitivity grating interferometry

The authors propose a new approach for obtaining information about in-plane and out-of-plane displacements of an object tested using high-sensitivity grating interferometry. The interferences of each of the specimen grating diffraction orders with a reference beam are recorded separately. Computer addition and subtraction of the phase functions calculated from the interferograms give the in-plane and out-of-plane displacement values, respectively. The authors present their experimental work, and then compare their results with those obtained using a conventional grating interferometry approach.     

硬X射线相位光栅的设计与研制

针对在普通实验室和医院实现40—100keVX射线相衬成像的需求,考虑到成像系统参数、X射线源空间相干特性及光栅衍射效率,设计出硅基相位光栅结构参数.利用我们已发展的光助电化学刻蚀技术研制出直径为5英寸的相位光栅,其空间周期为5.6μm,线宽为2.8μm,深度为40—70μm.在理论分析的基础上,通过提高硅片两端有效工作电压和修正Lehmann电流密度公式,解决了实际刻蚀过程中出现的钻蚀问题.由实验结果可知,本方案对制作大面积高精度相位光栅十分有效。     

二维光栅角度信号响应函数研究

本文在平行相干光照明条件下,推导出了二维光栅剪切成像系统的角度信号响应函数,并描绘出了角度响应函数二维曲面.虽然光栅剪切成像系统常用的分束光栅有四种,分析光栅有三种,分析光栅和分束光栅之间还存在多种不同组合,但是产生的角度信号响应函数曲面却只有三种,即峰型位移曲面、谷型位移曲面和峰谷对称型位移曲面.其中峰型位移曲面和谷型位移曲面之间具有数值互补关系,由此还可以把峰型位移曲面和谷型位移曲面归纳为一种,最终只需要考虑两种位移曲面.这个理论结果无疑显著简化了人们对二维光栅剪切成像的认识,将对今后讨论定量提取二维角度信号的工作奠定基础.     

High-contrast interference pattern of amplified spontaneous emission from dyes under transient grating excitation

We demonstrate a high-contrast interference fringe pattern formed by amplified spontaneous emission (ASE) in a noncollinear two-beam self-diffraction setup by use of dyes. In the presence of a transient grating a stable interference pattern is observed in ASE induced by one- and two-photon absorption. The fringe visibility varies from 0.2 to 0.65 with a temporal delay in the two beams. The variation of the angle between the two exciting beams at the temporal overlap shows an increase in the fringe visibility with an increase in the angle.