Affordable method for measuring fluorescence using Gaussian distributions and bounded MESE

Abstract

We present an accurate and low-cost method for measuring fluorescence in materials. Our method outputs an estimate of the material’s Donaldson matrix, which is a commonly used two-dimensional spectral characterization of its fluorescence and reflectance properties. To find the estimate, only a few measurements of the material’s reflectance under a few illuminants are needed, which we demonstrate using low-cost optical components. Internally, our algorithm is based on representing each Donaldson matrix with a multivariate Gaussian mixture model and its diagonal with a bounded MESE (maximum entropy spectral estimate). It parametrizes and constrains the estimate in a robust and simple way, allowing the use of gradient-descent optimization. We evaluate our algorithm on a combination of real and synthetic data, and four examples of distinct optical components. We reach significantly lower errors than the current state of the art on the exact same inputs, our estimates do not suffer from artifacts such as oscillations of the spectra, and they are stable and robust.