The complete and accurate colorimetric characterization of fluorescent materials requires the use of a 'bispectrometer'; a two-monochromator instrument designed to provide a two-dimensional matrix of bispectral radiance factor values for any given sample. This paper presents the general principles of operation, and a definition of the properties measured by such an instrument; expressing the actual physical quantities measured as an approximation to corresponding theoretical quantities. Approaches to calibration are outlined, with particular attention to the need for separation of reflected and luminescent components. Finally, this paper describes the calculations required to reduce the bispectral data produced by the instrument to more familiar colorimetric terms.