The present paper proposes a generalized method to estimate the bispectral Donaldson matrices of fluorescent objects. We suppose that the matte surface of a fluorescent object is illuminated by each of light sources with different spectral-power distributions, and is observed by a spectral imaging system in a visible wavelength range. The Donaldson matrix is decomposed into three spectral functions of reflection, fluorescent excitation and fluorescent emission. We segment the visible wavelength into two ranges having (1) only reflection without luminescence and (2) both reflection and fluorescent emission. An iterative algorithm is presented to effectively estimate the three spectral functions on the residual minimization. The wavelength range of fluorescent emission is also estimated. The proposed method is reliable in the sense that the estimates are determined to minimize the average residual error to the observations. The feasibility of the method is shown in experiments using two fluorescent samples and four illuminants.