We propose to build and operate a detector based on the emulsion film technology for the measurement of the gravitational acceleration on antimatter, to be performed by the AEgIS experiment (AD6) at CERN. The goal of AEgIS is to test the weak equivalence principle with a precision of 1% on the gravitational acceleration g by measuring the vertical position of the anni- hilation vertex of antihydrogen atoms after their free fall in a horizontal vacuum pipe. With the emulsion technology developed at the University of Bern we propose to improve the performance of AEgIS by exploiting the superior position resolution of emulsion films over other particle de- tectors. The idea is to use a new type of emulsion films, especially developed for applications in vacuum, to yield a spatial resolution of the order of one micron in the measurement of the sag of the antihydrogen atoms in the gravitational field. This is an order of magnitude better than what was planned in the original AEgIS proposal.