The detector signals from a total integrated scatter (TIS) instrument, which uses a focusing Coblentz sphere, have been evaluated. Models for the calculation of correct reflectance and transmittance values for both scattering and nonscattering samples are presented. In particular, the correction for multiple reflections between sample and detector, the detector efficiency versus angle of incidence, and the symmetry properties of the Coblentz sphere have been investigated. Experimental results are compared with results obtained with an integrating sphere using a model for the correction of sphere asymmetry. The results show that the transmittance and reflectance values obtained with the TIS instrument and the integrating sphere agree only when the presented correction factors are properly taken into account. ©1995 American Institute of Physics.