用衍射场叠加法分析四种误差下的X光波带片

Analysis of Influence of 4 Fabrication Errors on X-ray Zone Plates by Summing up Diffraction Fields

利用叠加所有圆环的解析近似衍射场的方法来计算和分析随机环带位置误差、宽度误差、扩散和粗糙度对X射线波带片的效率和分辨率的影响。用Strehl比来量化和衡量与理想波带片有偏差的波带片的性能,对两个波带片例子分别用Strehl极限确定了其能容许的四种误差极限。以一个Ni软X射线波带片为例,用叠加圆环衍射场的方法分析了随机环带位置误差和宽度误差对主焦点效率和分辨率的影响;以一个SiO2/Ni硬X射线溅射切片波带片为例,计算了两种材料的相互扩散和粗糙度对衍射效率和分辨率的影响。计算结果表明,四种误差越大,主焦点效率越小,分辨率越差,对第一个波带片例子而言,随机环带位置误差均方根和宽度误差均方根小于最外环宽度的30%;而对于第二个波带片例子,扩散区宽度和粗糙度均方根分别小于最外环宽度的105%和50%时,得到的Strehl比在Strehl极限之上。

The influence of random position error of zones, width error of zones, interdiffusion and roughness on the efficiency and resolution of X-ray zone plates （ZP） is analyzed by adding the analytic expression of the diffraction field of every ring. Strehl ratio is used to quantify and evaluate the performance of the zone plates deviating from perfect ones. The tolerances of the 4 errors mentioned above are gained by using Strehl limit in two examples. The influence of random zone position and width error of zones on the main focus efficiency and resolution of a Ni soft X-ray zone plate is calculated. And the influence of interdiffusion and roughness on the diffraction efficiency and resolution of a SiO2/Ni hard X-ray sputtered sliced zone plate is analyzed. It is showed that the efficiency of the main focus decreases and the resolution degrades with increasing the four errors. The root-mean-square of random position and width error of zones of the first zone plate need to be less than about 30% of the outmost zone width to generate a Strehl ratio higher than Strehl limit; the width of interdiffusion region and the root-mean-square roughness of the second zone plate need to be less than about 105% and 50% of the outmost zone width to generate a Strehl ratio higher than Strehl limit respectively.