In liquid rocket propulsion, liquid oxygen/liquid hydrogen (LOX/LH2) can be preferred propellants owing to the resulting high specific impulse. Typically in this case the fuel (LH2) enters the combustion chamber in pre-vaporized gaseous state and the oxidizer as droplets in the liquid state (LOX). The vaporization of the LOX droplets and the formation of a combustible mixture occur in the combustion chamber. These physical processes are directly connected to the chemical processes of combustion. That a single droplet is the basic element of spray combustion motivates microgravity experiments to be conducted in the Bremen Drop Tower to investigate the combustion process of a single oxygen droplet in a gaseous hydrogen environment. Microgravity conditions are useful to remove natural convection, ensuring spherical symmetry to more easily reveal the key physical phenomena. Experiments are planned for pressures up to 52 bar, which corresponds to supercritical conditions. The nominal, initial temperature of the LOX droplet and surrounding hydrogen gas will be 77 K. The droplet will be ignited by a laser induced plasma spark and the combustion will be observed by shadowgraphy, schlieren optics, OH-radical chemiluminescence as well as temporal and spatially resolved OH-planar laser induced fluorescence (OH-PLIF) diagnostics. Furthermore the experiments are compared to the results of numerical simulations developed in parallel. Of primary interest are the inverted character of the system with the fuel as the homogenous phase and the oxidizer as the dispersed phase as well as the transition from the ignition to the quasi-steady combustion flame. Preliminary simulations suggest the formation of two pre-mixed flames after ignition. Subsequently a third diffusion flame appears between the pre-mixed flames, which eventually die out. The paper describes the cryogenic experimental setup and the optical diagnostics. Initial results from the numerical simulations regarding the ignition process are discussed.