多层膜劳厄透镜的理论分析

Hard X-ray microscopy has found numerous applications in materials sciences, medicine, biology, environmental sciences and many other fields, its spatial resolution is limited by the focal spot size of X-ray focusing optics. Multilayer Laue lens (MLL) is a new type of diffractive focusing optics with high aspect ratios, in theory, it can focus hard X-ray to less than a nanometer. X-ray wave propagation and the error analysis inside an MLL must be described by dynamical diffraction theory, numerical approaches for complex partial differential equations have to be employed in calculating the diffraction efficiency and focal spot size. However, there is no currently readily available MLL numerical analysis software, which greatly increases the difficulty of design and optimization. For this problem, the project will establish mathematic model for the MLL with errors using dynamical diffraction theory, use the model to simulate the performance of MLL and choose the optimal scheme accordingly, develop a set of MLL focusing device to verify our model. Finally, the project will develop a novel MLL numerical analysis software with independent intellectual property rights, expecting to improve the efficiency of design, optimization and test at synchrotron radiation.

硬X射线显微镜在材料学、医学、生物学以及环境科学等诸多领域有着广泛的应用，其分辨率受到X射线聚焦元件聚焦光斑大小的限制。多层膜劳厄透镜是一种新型的大深宽比衍射型聚焦元件，理论上能够获得1nm以下的聚焦光斑。X射线在多层膜劳厄透镜中的传播以及误差分析必须运用衍射动力学来描述，对其聚焦性质的分析也必须通过数值计算的方法求解复杂的偏微分方程组，而目前并没有现成的多层膜劳厄透镜数值计算软件，极大的增加了对其进行优化设计的难度。针对此问题，本项目将运用衍射动力学理论建立起理想情况下以及加入各种误差后的多层膜劳厄透镜的数值计算模型，对其进行优化设计，并依据此方案研制出一套多层膜劳厄透镜聚焦装置，用以验证该理论，最后以此为基础发展出一种全新的、具有自主知识产权的多层膜劳厄透镜数值计算软件，期望能够提高多层膜劳厄透镜优化设计以及在同步辐射上调试的效率。

多层膜劳厄透镜（MLL）本质上是一种大深宽比的线性波带片，理论上其可以对硬X射线实现高效率的亚纳米量级的聚焦。X射线在MLL中的传播必须运用衍射动力学来描述，为了对MLL进行优化设计并且分析各种误差对其聚焦性能的影响，必须求解复杂的偏微分方程组，而目前并没有现成的MLL数值计算软件，极大的阻碍了MLL的发展。在本项目中，针对此问题，我们建立起了理想情况下以及加入各种误差（例如界面粗糙度、界面扩散、膜层位置误差、光源误差等）后MLL的衍射动力学计算模型，特别是针对膜层位置误差，基于耦合波理论，我们提出了一种新的动力学模型用以分析其MLL聚焦性能的影响；同时还对所建立起的衍射动力学模型进行了简化修改，形成了简洁的数值计算代码，能够提供给相关专业用户适用；利用所建立起的衍射动力学计算模型，对MLL进行了优化设计，得到了初步的MLL透镜，并对起进行了离线表征，结果显示该MLL透镜基本上能够实现衍射极限聚焦；针对Tilted MLL在实现衍射极限聚焦时衍射效率低和Wedged MLL镀制工艺难的问题，我们提出了一种新的MLL结构及其设计方法，即多倾斜角复合MLL，该结构能够极大的降低工艺难度，同时衍射效率接近Wedged MLL。