A method for constrained optimisation of the design of a scanning helium microscope

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.