Estimation of Fluorescent Donaldson Matrices Using a Spectral Imaging System

Abstract

The present paper proposes a method to estimate the bispectral Donaldson matrices of fluorescent objects in a scene with a spectral imaging system. Multiple ordinary light sources with continuous spectral-power distributions are projected sequentially onto object surfaces without controlling the spectral shape of the illumination source. The estimation problem of the Donaldson matrices is solved as an optimization problem, where the residual error of observations by the spectral imaging system is minimized. The reflection, emission, and excitation spectral functions are estimated at each wavelength without using a basis function approximation. To improve the estimation efficiency, the output visible range is segmented into two types of wavelength ranges: one for only reflection and another for both reflection and emission. An iterative algorithm is then developed based on the wavelength segmentation and the physical excitation model. The usefulness of the proposed method is examined in experiments using different fluorescent objects and illuminants. We show the estimation accuracy of the Donaldson matrices, discuss the effective selection of illuminants, and demonstrate an application to spectral analysis and reconstruction of a fluorescent image.