The past two decades have witnessed an increasing focus on cold antimatter physics, with the development of the Antiproton Decelerator at CERN as a supply of low-energy antiprotons. Among the open questions concerning antimatter, the result of a gravity measurement on anti-atoms as a direct test of the weak equivalence principle has attracted the interest of several collaborations (AEgIS, GBAR, ALPHA). This work describes the use of a Talbot-Lau interferometer as a tool to perform a gravity measurement on antihydrogen. This device, composed of two or three material gratings, has been successfully used to reveal the wave behavior of different particle species and, in its classical limit, to perform inertial measurements on neutral and charged particles in the past. In order to study its suitability as a gravimeter for antimatter,
systematic effects which can prejudice the outcome of the measurement are analyzed in detail. These include misalignments of the interferometer and influences of external field gradients. Simple mathematical formulas which quantify their prominence are produced and tested via numerical simulations. State-of-the-art production rates of cold antihydrogen are used to calculate the time required to retrieve the sign of the gravitational acceleration of antimatter using this setup. The result is an estimation of the feasibility of this measurement in the framework of the AEgIS experiment
