We describe a method for obtaining the optimal design of a normal incidence Scanning Helium Microscope (SHeM). Scanning helium microscopy is a recently developed technique that uses low energy neutral helium atoms as a probe to image the surface of a sample without causing damage. After estimating the variation of source brightness with nozzle size and pressure, we perform a constrained optimisation to determine the optimal geometry of the instrument (i.e. the geometry that maximises intensity) for a given target resolution. For an instrument using a pinhole to form the helium microprobe, the source and atom optics are separable and Lagrange multipliers are used to obtain an analytic expression for the optimal parameters. For an instrument using a zone plate as the focal element, the whole optical system must be considered and a numerical approach has been applied. Unlike previous numerical methods for optimisation, our approach provides insight into the effect and significance of each instrumental parameter, enabling an intuitive understanding of effect of the SHeM geometry. We show that for an instrument with a working distance of 1 mm, a zone plate with a minimum feature size of 25 nm becomes the advantageous focussing element if the desired beam standard deviation is below about 300 nm.

中文翻译：

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一种扫描氦显微镜设计的约束优化方法

我们描述了一种获得法向入射扫描氦显微镜 (SHeM) 最佳设计的方法。扫描氦显微镜是最近开发的一种技术，它使用低能量中性氦原子作为探针，在不造成损坏的情况下对样品表面进行成像。在估计源亮度随喷嘴尺寸和压力的变化之后，我们执行约束优化来确定仪器的最佳几何形状（即，使强度最大化的几何形状）对于给定的目标分辨率。对于使用针孔形成氦微探针的仪器，源和原子光学是可分离的，拉格朗日乘数用于获得最佳参数的解析表达式。对于使用波带片作为焦点元件的仪器，必须考虑整个光学系统，并应用了数值方法。与以前的优化数值方法不同，我们的方法可以深入了解每个仪器参数的影响和重要性，从而能够直观地理解 SHeM 几何的影响。我们表明，对于工作距离为 1 毫米的仪器，如果所需的光束标准偏差低于约 300 纳米，则最小特征尺寸为 25 纳米的波带片将成为有利的聚焦元件。