Positron-positronium converters in reflection and transmission geometry for gravitational experiments with antihydrogen using Moiré deflectometry

In the context of the Antihydrogen Experiment: Gravity, Interferometry, Spectroscopy (AEgIS) located at CERN, positron-positronium converters with a high positron-positronium conversion efficiency have been designed in both reflection and transmission geometries. The converters utilize nanochanneled silicon target technology with positron conversion efficiencies up to around 50% and around 16%, at room temperature and in the absence of magnetic fields, for reflection and transmission respectively. The positron-positronium converters allow for the pulsed production of antihydrogen ($\overline{H}$) within the AEgIS experiment. This paper discusses the use of a pulsed $\overline{H}$ beam in a moiré deflectometer to perform a precise gravitational measurement on $\overline{H}$ at AEgIS. This work describes the principles and technical details of the current design of a moiré deflectometer using the pulsed $\overline{H}$ beam. The main goal of this work is to summarize the ongoing project of adding the described moiré deflectometer to the AEgIS experiment to further their efforts toward probing the material dependence of gravity and testing the weak equivalence principle (WEP).