We realize textbook experiments on Bose-Einstein condensate tunnelling through thin repulsive potential barriers. In particular, we demonstrate atom tunnelling though a single optical barrier in the quantum scattering regime where the De Broglie wavelength of the atoms is larger than the barrier width. Such a beam splitter can be used for atom interferometry and we study the case of two barriers creating an atomic Fabry-Pérot cavity. Technically, the velocity of the atoms is reduced thanks to the use of a 39K Bose-Einstein condensate with no interactions. The potential barriers are created optically and their width is tunable thanks to the use of a digital micro-mirror device. In addition, our scattering experiments enable in-situ characterization of the optical aberrations of the barrier optical system.