Hyperchromatic systems are characterized by strong longitudinal chromatic aberrations that are quantitatively described by very small equivalent Abbe numbers. In this contribution, doublet systems are systematically studied with the aim of obtaining extreme values for the equivalent Abbe numbers. Both purely refractive combinations and hybrid systems of diffractive and refractive components are considered. Chromatic axial splitting is determined as a function of the optical powers of the individual components as well as the dispersion properties of the materials involved. In order to determine actual implementable configurations for extremely small equivalent Abbe numbers, a systematic ray-trace analysis is performed in addition to paraxial studies, taking into account geometric constraints on lens curvatures and considering also complete, continuous dispersion curves. As extreme values for systems with appropriate imaging quality, an equivalent Abbe number of ~=-2.5 is obtained for the purely refractive approach, and ~=0.4 for the hybrid case, which is more than 8 times smaller than the absolute value of a single diffractive lens.
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