The hyperspectral component of bidirectional reflectance measurements, namely from several hundred wavelengths upwards, is attracting growing interest for numerous applications in both optics and computer graphics. In this paper, we present a motorized hyperspectral bidirectional reflectance measurement bench that performs in-plane and out-of-plane measurements for isotropic materials using a supercontinuum laser covering the visible and near infrared range, with a sub-nanometer spectral accuracy. We describe the complete data processing chain, including a method for assessing the alignment error of the measurement bench. From these measurements, we verify the principles of non-negativity, energy conservation and Helmholtz reciprocity. We introduce criteria also to evaluate the validity of the Lambertian hypothesis for the bidirectional reflectance and its deviation from reciprocity, obtained from the measurements directly. We show the need for spectral bidirectional reflectance measurements for certain materials, rejecting the separable function approximation.