Color correction of monocentric lenses

Modern monocentric lenses are used in wide field-of-view and high-resolution optical devices. As many other refractive optical systems, monocentric lenses often require correction of chromatic aberration. Since monocentric lenses are essentially thick, methods of color correction for monocentric systems differ from those for thin lenses. Although this difference is taken into account in known chromatic aberration correction methods, which are specific for monocentric lenses, these methods are approximate and often result in significant errors in calculations. We present exact analytical paraxial theory of color correction for monocentric lens systems. The rigorous approach allows one to design achromatic and apochromatic monocentric lenses by algebraic calculations of modest complexity. The exact analytical calculations are especially useful for apochromatic lenses because the approximate methods lead to considerably inaccurate results. The outcome of computations according to the proposed theory is the set of design parameters of an optical system: radii of curvature of lenses, lens thicknesses, and air spaces.