Abstract

This study explores the design and optimization of cascaded double-hyperchromatic optical systems (i.e., ${2} \times {2}$ lenses), focusing on achieving an extremely linear axial spectral decomposition characterized by an exceptionally low equivalent Abbe number. The investigation involves two double hyperchromats, considering both purely refractive systems and hybrid configurations that combine refractive and diffractive elements. For purely refractive systems, alternating focal length signs of divergent and collective lenses are crucial to achieve significant axial chromatic dispersion. In hybrid systems, the position of the diffractive optical element (DOE) and the selection of focal lengths play key roles in obtaining extremely low equivalent Abbe numbers. The optimized systems demonstrate absolute equivalent Abbe numbers of 0.983 for purely refractive and 0.65 for hybrid systems—more than four times lower than the absolute Abbe number of a single diffractive element. Notably, even systems using standard materials exhibit significantly low equivalent Abbe numbers of 2.5 and 1.4 for pure refractive and hybrid configurations, respectively. These results offer promising opportunities for improving optical applications based on axial spectral decomposition, overcoming previous limitations of axial chromatic spreading.

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