Realistic descriptions of surface reflectance have long been a topic of interest in both computer vision and computer graphics research. In this paper, we describe a novel and fast approach for the acquisition of bidirectional reflectance distribution functions (BRDFs). We develop a novel theory for directly measuring BRDFs in a basis representation by projecting incident light as a sequence of basis functions from a spherical zone of directions. We derive an orthonormal basis over spherical zones that is ideally suited for this task. BRDF values outside the zonal directions are extrapolated by re-projecting the zonal measurements into a spherical harmonics basis, or by fitting analytical reflection models to the data. We verify this approach with a compact optical setup that requires no moving parts and only a small number of image measurements. Using this approach, a BRDF can be measured in just a few minutes.