Fresnel zone plates are widely used for nanofocusing in x-ray microscopy. The focusing performance is described in terms of the resolution, related to the width of the smallest outermost zones, and the efficiency, governed by the thickness of the zones and therefore the amount of phase shift imparted onto the x-ray beam. The ratio of zone thickness to width, or “aspect ratio,” is limited in all methods of zone plate fabrication, requiring compromises between efficiency and resolution. We propose a new zone plate design method, which optimizes focusing efficiency within a set of practical constraints. This phasor-based method is used to optimize subject to a maximum aspect ratio the design of binary, multilevel, and kinoform zone plates. A truncated zone plate profile is proposed, which focuses more efficiently than binary or kinoform zone plates, with considerably higher manufacturability. Focused ion beam milling was used to fabricate the designed lenses in gold, and their relative efficiency was validated at a synchrotron hard x-ray beamline. Our phasor method provides rapid design optimization, producing the ultimate lens designs for a given manufacturing limit, and it is fully generalizable to incorporate any fabrication tolerances such as roughness, zone displacements, and zone wall inclination.

中文翻译：

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纵横比受限的X射线波带片的优化设计

菲涅耳波带片广泛用于 X 射线显微镜中的纳米聚焦。聚焦性能以分辨率和效率来描述，分辨率与最小最外区域的宽度相关，而效率则由区域的厚度以及施加到 X 射线束上的相移量决定。波带厚度与宽度的比率，或“纵横比”，在所有波带片制造方法中都受到限制，需要在效率和分辨率之间进行折衷。我们提出了一种新的波带片设计方法，可在一组实际约束条件下优化聚焦效率。这种基于相量的方法用于根据最大纵横比优化二元、多级和相息波带片的设计。提出了一种截断波带片轮廓，它比二元或开诺全息图波带片聚焦更有效，并且具有相当高的可制造性。使用聚焦离子束铣削来制造设计的金透镜，并在同步加速器硬 X 射线束线中验证了它们的相对效率。我们的相量方法提供快速的设计优化，针对给定的制造限制生成最终的透镜设计，并且它完全可以推广到包含任何制造公差，例如粗糙度、区域位移和区域壁倾斜度。