Principal component analysis of refractive index spaces: a model-free approach to color analysis and color correction

Since the development of the first achromatic lenses back in the 18th century, dispersion models have been constant companions of optical designers. Various alternatives and extensions to the classical Abbe number and partial dispersion model have been proposed over the years, with the goal of making first- and higher order analysis and correction easier accessible. Hoogland's reformulation of the classical quantities allowed to visually select glasses and read optical powers for an apochromatic lens from a diagram, and Buchdahl dispersion coefficients have been used as basis for similar work in the infrared spectrum. In both cases however, model parameters must be tuned to arrive at the desired representation. Here we present a model-free approach using principal component analysis of normalized refractive index data at the system wavelengths. We show how it can be applied to understand simultaneously both the dispersion properties and color correction capabilities of a selection of glasses in any part of the optical spectrum, and how to derive favorable glass combinations for apochromatic and superapochromatic lenses including a prediction of residual color.