Chromatic Aberrations in Optical Systems: Prediction and Correction

Abstract

The variation of refractive index with wavelength, known as dispersion, was what redirected Isaac Newton from refractive telescope designs toward a reflective one, since he found the chromatic effect incurable. Later it was shown that different materials demonstrate different chromatic characteristics and refractive optical elements can compensate each other's chromatic contributions. This promoted the simple dispersion effect to the field of formulizing and categorizing chromatic aberrations and their corrections. In this study an introduction to this process is provided, where the historical aspects are followed by the mathematical derivation and description of different kinds of chromatic aberrations accompanied with a variety of approaches to correct the chromatic effects in different levels. The provided mathematical basis is employed in studying three distinctive topics. In the first one the flexibility of refractive elements is used to provide a middle-sized catadioptric telescope design with all-spherical surfaces. Employing a new combination of chromatic lens correctors, the image quality can be improved so that it becomes comparable to an equivalent aspheric Ritchey-Chrétien telescope design. As the second topic the atmospheric dispersion and its effect in extremely large telescopes are discussed, where a new atmospheric dispersion corrector design is proposed. In the third task the chromatic behavior in an inhomogeneous medium is considered. A new gradient refractive index lens model for the crystalline lens of the eye is established and a different approach in characterizing its chromatic effects is developed. These three research topics are underpinning the main goal of the theses, that is the role of chromatic aberration in image formation in various optical systems.