This chapter presents the applications of the matrix R theory for spectrum decomposition and reconstruction. We apply the method to spectra of seven illuminants and fourteen spectra used in the color rendering index (CRI) under the CIE 1931 or CIE 1964 standard observer. The common characteristics are derived and discussed. Based on these characteristics, we develop two methods for deriving two basis vectors that can be used to reconstruct various illuminants to some degree of accuracy. The first method uses the intuitive approach of averaging to generate basis vectors. The second method uses input tristimulus values to obtain the fundamental metamer via orthogonal projection, and the metameric black is obtained from a set of coefficients to scale the average metameric black. The coefficients are derived from ratios of input tristimulus values to average tristimulus values. These methods are applied to reconstruct 7 illuminants and 14 CRI spectra. The application of the metameric spectral reconstruction to the estimation of the fundamental metamer from an RGB or XYZ color scanner for accessing skin-tone reproducibility is also discussed.
Online access to SPIE eBooks is limited to subscribing institutions.