This paper suggests a novel method for determining the permeability of a membrane by spatially resolved measurements of the concentration profiles above and below the membrane. A compact diode laser absorption spectrometer is presented with a collimated measuring beam, allowing precise concentration measurements with a spatial resolution of 200 µm perpendicular to the laser beam. Measurements of the permeability of polyurethane coated polypropylene foils are presented, demonstrating the ability of fast and calibration-free measurements.