相干X射线衍射成像三维重建的数字模拟研究

利用相干X射线衍射成像“过采样”采集样品的远场相干衍射图样, 结合相位重建迭代算法重建物空间样品信息. 三维重建过程中, 边界约束条件是相位重建算法中最为关键的部分. 本文采用数字模拟的方法, 利用灰度值图像作为物空间的样品, 研究并实现了边界条件的自动寻找, 重建结果显示比以往采用较“松”的边界约束更为精确. 利用噪声模拟方法, 研究了衍射图样中不同噪声类型的滤除对重建结果的影响. 研究发现传统的去噪方法在高噪声情况下不能直接应用于相干X射线衍射成像, 并找到了适用于相干X射线衍射成像噪声滤除的有效方法. 研究表明, 此方法能非常有效地降低噪声对重建结果的影响. 利用模拟三维纳米金颗粒作为样品, 完成了对纳米金颗粒中电子密度分布的三维重建, 在有随机噪声的影响下, 也得到了很好的重建结果, 并找到了成功实现三维重建的噪声限为信噪比不低于27. 关键词： X射线相干衍射成像 过采样 三维相位重建 显微成像     

相干衍射成像的相位复原及重建

相干衍射成像是一种对材料体密度敏感的超高分辨成像技术。相较于传统表面敏感的超高分辨成像技术,相干衍射成像利用了硬X射线的强穿透能力,可以深入材料体内部进行成像,且成像分辨能力可以根据成像布局进行调整,最高达到原子级空间分辨能力。这种灵活的空间分辨调整依赖于相干衍射成像独特的相位复原技术,即通过对图像成像强度的过采样,利用含约束的迭代算法同时获得光场的强度及相位,进而对样品进行重建;同时结合图像定向及组合技术,相干衍射成像可以实现对样品的三维重建。本文主要从成像原理、复原算法和重建方法介绍相干衍射成像技术,并结合实验进展及模拟研究展示该技术在多种重建情形下具备的诊断能力,以期较为全面地给出相干衍射成像技术的发展趋势。     

扫描相干衍射成像背景噪声分离算法研究

X射线扫描相干衍射成像(ptychography)是一种新型的无透镜成像方法,摆脱了传统透镜成像中聚焦元件对分辨率的限制,使理论分辨率只受到X射线波长和探测器数值孔径的限制.然而实验测量中的噪声限制了该方法对成像质量的改善,甚至最终导致图像重建失败.在研究了ptychography现有的相位恢复迭代算法后,本文提出了一种新型的图像重建迭代算法.该算法利用ptychography数据的高冗余性,通过梯度下降最小化技术,在重建样品和探针图像的同时还完成了背景噪声的同步迭代重建,实现了信号和噪声的盲分离功能.通过仿真模拟和实验数据重建,将该方法与传统的迭代算法进行了对比,结果表明新算法能够较好地实现信噪分离,显著提升ptychography的成像质量.     

代数迭代重建算法在折射衬度CT中的应用

X射线折射衬度CT是一种基于相位衬度的断层成像技术,特别适合对由轻元素组成的生物、医学样品进行成像,可以观察到常规吸收衬度CT无法观察到的软组织内部微细结构,是一种具有巨大发展潜力的新成像方法.迭代重建算法和解析重建算法是计算机断层成像技术中并行发展的两种算法,虽然已经提出了几种X射线折射衬度CT的解析重建算法,可是还未见X射线折射衬度CT迭代重建算法的报道.研究了代数迭代重建算法在X射线折射衬度CT中的应用,比较分析了不同的投影数据排列方式对于折射衬度CT重建图像的影响,并对实验数据进行了图像重建,获得了满意的CT图像.研究结果表明,在相位衬度CT中,迭代重建算法相对于解析重建算法而言,能减少投影次数,降低曝光剂量,减少对生物样品的辐射损伤,在生物样品成像和投影数据不完整的情况下具有明显的优势. 关键词： 衍射增强成像 代数迭代算法 CT重建 同步辐射     

X射线衍射增强成像中吸收、折射以及散射衬度的计算层析

X射线相位衬度成像是一种新型的X射线成像技术,通过记录射线穿过物体后相位的改变对物体进行成像,可以提供比传统的X射线吸收成像更高的图像衬度以及空间分辨力。衍射增强成像方法(Diffraction enhancedimaging,DEI)是X射线相位衬度成像方法之一,利用一块放置在物体和探测器之间的分析晶体提取物体的吸收、折射以及散射信息并进行成像。将衍射增强成像方法与计算机断层成像技术(Computerized Tomography)进行结合,利用吸收、散射以及折射信息,分别采用滤波反投影以及雷登(Radon)变换,对昆虫样品——蜜蜂进行计算层析重建,获得了好于X射线吸收计算层析的重建结果,验证了衍射增强成像信息分离计算层析的优越性。     

基于迭代重建算法的X射线光栅相位CT成像

基于光栅干涉仪的X射线成像技术可以同时获得样品内部的吸收信息、相位信息和散射信息,既保持了传统X射线衰减成像的优点,又拥有相衬成像和散射成像的优势.然而基于传统CT重建算法的X射线光栅成像需要采集大量完整的原始投影数据,数据采集时间过长从而使得物体接受很大的辐射剂量,难以在实际中应用.提出基于传统代数迭代重建算法的光栅成像技术.该方法利用现有X射线光栅成像系统采集少量原始投影数据,基于传统代数迭代重建算法,对旋转变化的相位数据进行CT重构,同时基于傅里叶变换的方法对微分相位数据进行相位恢复.模拟和实验结果表明,基于少量或不完备的原始投影数据,该方法能够准确重构成像对象的吸收、柑位和散射三维信息,同时还能对微分相位切片进行高信噪比的相位恢复,得到样品折射率实部衰减率,为X射线光栅成像技术在工业、生物和医学诊断等领域的应用提供理论和技术支撑.     

同轴X射线相位衬度计算机X射线断层摄影术研究

基于北京同步辐射装置(BSRF)开展了同轴X射线相位衬度计算机X射线断层摄影术(CT)研究.利用北京同步辐射的14 keV单色X射线作为光源,以高分辨能力的X射线胶片作为探测器,分别开展吸收衬度和同轴相位衬度成像的比较研究以及相位衬度计算机X射线断层摄影术研究.相位衬度计算机X射线断层摄影术重建采用Bronnikov提出的算法.结果显示,与传统的吸收衬度图像相比,相位衬度图像具有更好的衬度和更高的空间分辨力;实验获得人工样品和蝗虫的相位衬度计算机X射线断层摄影术重建图像.重建图像中可见样品的一些结构细节.实验结果表明,相位衬度X射线成像更适合于研究弱吸收或吸收差异很小的材料;利用北京同步辐射开展同轴X射线相位衬度计算机X射线断层摄影术研究是可行的.     

基于光栅相衬成像的扇束螺旋CT重建算法

X射线相位衬度成像具有极高的灵敏度,能探测到轻元素样品的内部结构,在医学、生物学和材料科学等众多领域显示出良好的应用前景。光栅成像模式可使用非相干光源进行X射线相位衬度成像,开创了非相干光源相衬成像新纪元。将螺旋CT的概念引入光栅相衬成像领域,将螺旋CT的高效率优势与光栅相位成像的高衬度优势相结合,发展X射线螺旋相位CT方法。通过分析螺旋轨迹非相干光源相位成像的特点,提出一种扇形束螺旋条件下的相位信息提取方法;而后借鉴希尔伯特滤波反投影重建算法的思想,得到扇形束螺旋相位CT重建算法。该算法利用折射角像直接重建物体的相位项。计算机仿真实验证明了该算法的有效性。     

相位恢复算法在量子关联衍射成像中的应用研究

随着研究工作的逐步深入,目前已经利用经典热光源实现了关联衍射成像,使得该技术有望在X射线以及中子衍射成像等方面得到广泛应用。在实验利用非相干光得到物体无透镜傅里叶变换频谱的基础上,采用误差消除与输入输出恢复算法,并结合过采样理论,实现了实验所用物体透射率函数的恢复。分别得到了纯振幅物体的振幅分布函数与纯相位物体的相位分布函数。此外,还讨论了实验所得傅里叶变换频谱的噪声等因素对图像恢复结果的影响。     

上海光源硬X射线相干衍射成像实验方法初探

相干X射线衍射成像方法是一种先进的成像技术,分辨率可达纳米量级.国际上大多数的同步辐射装置和自由电子激光装置都建立了该成像方法,并有将其作为主要成像技术的趋势.上海光源作为目前国内唯一的一台第三代同步辐射光源,尚未建立基于硬X射线的相干衍射成像实验平台.随着一批以波荡器为光源的光束线站投入使用,使得该方法的建立成为了可能.本文基于上海光源BL19U2生物小角散射线站,通过有效的光路设计,搭建了相干衍射实验平台,在12 keV和13.5 keV能量点均获得了硬X射线相干光束,并基于小孔衍射测量了入射光束的空间相干长度.该平台支持常规和扫描相干衍射实验模式,对小孔衍射图样及波带片扫描衍射图样实现了正确的相位重建,证明了该平台初步具备开展硬X射线相干衍射成像实验的能力.硬X射线相干衍射成像实验平台为国内首次建立,将为国内该实验方法的发展和应用提供有效的软硬件支持.     

Phase retrieval using an aperture-array filter under partially coherent illumination

Recently we have proposed a deterministic phase retrieval method using an aperture-array filter to reconstruct a complex-valued object from a single diffraction intensity pattern. We describe here the effect of quasi-monochromatic partially coherent illumination on the object reconstruction by the phase retrieval method, and then present the method of eliminating the effect of the partially coherent illumination from the diffraction intensity pattern via a simple Fourier deconvolution operation provided that the complex degree of spatial coherence of the illuminating beam is known. The usefulness of this method is shown in computer-simulated examples of the object reconstructions under Gaussian Schell-model partially coherent illumination.     

Retrieval of a complex-valued object from its diffraction pattern

It is commonly understood that the retrieval of a complex-valued object from its diffraction pattern using a support constraint is a difficult problem, the more so if the support is symmetric. In this Letter we show that, for just such a symmetric support, use of an iterative algorithm in which the basic iteration is specified by a difference map converges routinely. All that is required is sufficient oversampling in the diffraction pattern coupled with judicious choices of the parameters defining the difference map.     

Phase-coded aperture for optical imaging

For the optical spectrum region, we describe a novel phase-coded aperture imaging system that can be used in a computational imaging camera. The optical design includes a phase-only screen followed by a detector array. A specific diffraction pattern forms at the detector array when the wavefront from a point source object passes through the phase screen. Since diffraction effects cannot be ignored in the optical regime, an iterative phase retrieval method is used to calculate the phase coded screen. Correlation type processing can be applied for the image recovery. Computer simulation results are presented to illustrate the excellent imaging performance of this camera.     

A protocol for searching the most probable phase‐retrieved maps in coherent X‐ray diffraction imaging by exploiting the relationship between convergence of the retrieved phase and success of calculation

Coherent X‐ray diffraction imaging (CXDI) is a technique for visualizing the structures of non‐crystalline particles with size in the submicrometer to micrometer range in material sciences and biology. In the structural analysis of CXDI, the electron density map of a specimen particle projected along the direction of the incident X‐rays can be reconstructed only from the diffraction pattern by using phase‐retrieval (PR) algorithms. However, in practice, the reconstruction, relying entirely on the computational procedure, sometimes fails because diffraction patterns miss the data in small‐angle regions owing to the beam stop and saturation of the detector pixels, and are modified by Poisson noise in X‐ray detection. To date, X‐ray free‐electron lasers have allowed us to collect a large number of diffraction patterns within a short period of time. Therefore, the reconstruction of correct electron density maps is the bottleneck for efficiently conducting structure analyses of non‐crystalline particles. To automatically address the correctness of retrieved electron density maps, a data analysis protocol to extract the most probable electron density maps from a set of maps retrieved from 1000 different random seeds for a single diffraction pattern is proposed. Through monitoring the variations of the phase values during PR calculations, the tendency for the PR calculations to succeed when the retrieved phase sets converged on a certain value was found. On the other hand, if the phase set was in persistent variation, the PR calculation tended to fail to yield the correct electron density map. To quantify this tendency, here a figure of merit for the variation of the phase values during PR calculation is introduced. In addition, a PR protocol to evaluate the similarity between a map of the highest figure of merit and other independently reconstructed maps is proposed. The protocol is implemented and practically examined in the structure analyses for diffraction patterns from aggregates of gold colloidal particles. Furthermore, the feasibility of the protocol in the structure analysis of organelles from biological cells is examined.     

基于叠层衍射成像的二元光学元件检测研究

本文提出了一种基于叠层衍射成像(ptychography)的二元光学元件的检测方法,该方法可实现对二元光学元件表面微观轮廓的检测以及特征尺寸的标定.相比于传统的二元光学元件检测方法,其使用无透镜成像技术,简化了系统结构并可适用于特殊环境下的检测.该方法可直接通过采集多幅衍射图,利用叠层衍射成像迭代算法可精确地复原大尺寸待测元件的表面微观轮廓,提高大尺寸器件的检测效率.本文模拟仿真了台阶高度与噪声大小对纯相位台阶板复原结果的影响,并在光学实验中选取计算全息板为样品,复原样品的表面微观轮廓信息以及得到台阶高度.以白光干涉仪检测结果为标准,该方法在精度要求不太高的前提下,可获得令人满意的成像质量.     

Terahertz imaging with compressed sensing and phase retrieval

We describe a novel, high-speed pulsed terahertz (THz) Fourier imaging system based on compressed sensing (CS), a new signal processing theory, which allows image reconstruction with fewer samples than traditionally required. Using CS, we successfully reconstruct a 64 x 64 image of an object with pixel size 1.4 mm using a randomly chosen subset of the 4096 pixels, which defines the image in the Fourier plane, and observe improved reconstruction quality when we apply phase correction. For our chosen image, only about 12% of the pixels are required for reassembling the image. In combination with phase retrieval, our system has the capability to reconstruct images with only a small subset of Fourier amplitude measurements and thus has potential application in THz imaging with cw sources.     

Comparison of phase recovery methods in spiral speckle pattern interferometry correlation fringes

Spiral interferometry can be used as a solution to the problem of sign ambiguity presented in the conventional speckle pattern interferometric technique when the optical phase needs to be reconstructed from a single closed fringe system. Depressions and elevations of the topography corresponding to the object deformation are distinguished by the direction of rotation of the local spiral fringe pattern. In this work, we implement and compare several methods for optical phase reconstruction by analyzing a single image composed of spiral speckle pattern interferometry correlation fringes. The implemented methods are based on contour line demodulation, center line demodulation, Spiral Phase Quadrature Transform and the 2D Riesz transform with multivector structure. Contour line and center line demodulation approaches are exclusively dedicated to images containing a fringe system with spiral structure. The others are based on the 2D Riesz transform, these being well known approaches in conventional interferometry. We examine simulated experiments and analyze some of the emerging drawbacks for solving the phase reconstruction problem by using different mean values of speckle size and background noise levels. We also discuss several numerical procedures that may well improve the efficiency and robustness of the presented numerical implementations. The performance of the implemented demodulation methods is evaluated by using a universal image quality index and therefore a quantitative comparison is also presented.     

基于压缩感知与扩展小波树的自适应压缩成像

为了在现有的采样条件下,通过新的压缩采样方式获得计算量小且质量更好的图像,提出了基于压缩感知与扩展小波树的自适应压缩成像方法。首先将图像投影到分区控制的DMD上,获得图像在低分辨率下的测量值,并通过压缩感知重构算法重构出低分辨图像,接着利用扩展小波树预测重要小波位置,通过DMD在小波域采样获取图像的细节信息,最后由小波逆变换恢复高分辨率图像。将该方法与最小化全变分算法（TVAL3）和近来提出的基于扩展小波树的自适应成像算法（EWT-ACS）效果进行对比,实验结果表明,以boat图像为例,在压缩感知采样率为0.75,整体采样率为10%的无噪声条件下,该方法相较于TVAL3、EWT-ACS算法信噪比提高了4.63 dB和2.87 dB,在附加噪声条件下成像效果也较好。该方法能极大地降低压缩感知重建算法的运行时间,同时减少采样次数,具有较好的抗噪性。     

Experimental study on polarization holographic storage in genetic mutant BR-D96N film

The information storage is developing toward high speed access and massive stor-age capacity. Optical holographic storage has not only high speed parallel data access and high addressing speed without mechanical motion but also high storage density with multiplexed volume holographic storage[1]. In recent years, optical holographic storage is studied intensely in the field of information storage. It has been shown that the polari-zation of light could also be recorded with polarization hologra…