Theoretical model of the helium pinhole microscope

Abstract

In recent years, the development of neutral helium microscopes has gained increasing interest. The low energy, charge neutrality, and inertness of the helium atoms makes helium microscopy an attractive candidate for the imaging of a range of samples. The simplest neutral helium microscope is the so-called pinhole microscope. It consists of a supersonic expansion helium beam collimated by two consecutive apertures (skimmer and pinhole), which together determine the beam spot size and hence the resolution at a given working distance to the sample. Due to the high ionization potential of neutral helium atoms, it is difficult to build efficient helium detectors. Therefore, it is crucial to optimize the microscope design to maximize the intensity for a given resolution and working distance. Here we present an optimization model for the helium pinhole microscope system. We show that for a given resolution and working distance, there is a single intensity maximum. Further we show that with present-day state-of-the-art detector technology (ionization efficiency $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$), a resolution of the order of 600 nm at a working distance of 3 mm is possible. In order to make this quantification, we have assumed a Lambertian reflecting surface and calculated the beam spot size that gives a signal 100 cts/s within a solid angle of $0.02\ensuremath{\pi}$ sr, following an existing design. Reducing the working distance to the micron range leads to an improved resolution of around 40 nm.