Estimation of bispectral Donaldson matrices of fluorescent objects by using two illuminant projections

This paper proposes a method for estimating the bispectral Donaldson matrices of fluorescent objects by using only two illuminant projections with continuous spectral power distributions. The Donaldson matrix represents the spectral radiance factor consisting of the sum of two components: a reflected radiance factor and a luminescent radiance factor. First, we describe the spectral characteristics of the observed matrix and model the matrix so that the luminescent radiance factor is separable into the emission and excitation wavelength components. We make no assumption as to the spectral shapes of any components, but derive a physical model that is useful for predicting the excitation spectral component from the reflected radiance component. An algorithm is developed to estimate the entire elements of the Donaldson matrix based on only two sets of spectral sensor outputs under two different illuminants. We suggest that the difference between the observed reflected radiance factors under the two different illuminants is not caused by the reflected radiance component, but only the luminescent radiance component. The algorithm is a sequential estimation of three radiance components of luminescent excitation, luminescent emission, and reflection. The feasibility of the proposed method is confirmed in experiments using a variety of fluorescent samples. The estimation accuracy is evaluated numerically in root-mean squared error and the color difference under the assumption of a viewing illuminant. An optimal selection of the illuminant pair is shown based on a simulation experiment using blackbody radiators with different color temperatures.