Minimal equivalent Abbe number under the constraint of lens surface shapes for hyperchromatic doublet lenses

The minimum equivalent Abbe number can be used to describe the maximum axial dispersion achievable by a hyperchromatic doublet lens. In this study, the axial dispersion limit of such a doublet is investigated under the constraints of lens surface shapes. The paraxial formula with respect to lens curvature is organized to find the relationship between the equivalent Abbe number and the parameters of the glass material. Using data from an optical glass database, the minimum equivalent Abbe number is computed for different types of glass combinations. Ray tracing is then employed to simulate non-paraxial systems for validation purposes. The result reveals that the doublet exhibits an average minimum equivalent Abbe number of 10.5 when surface shape constraints are considered. The preferred glass combination tends toward H-ZPK2A for the first element and H-ZF73 for the second. Furthermore, this study presents the design of a chromatic confocal optical probe, which satisfies dispersion specifications and achieves an energy utilization efficiency 1.2 to 2.9 times that of the reference commercial probe across the measurement range. This research provides guidance for selecting suitable initial structures based on different dispersion requirements in hyperchromatic optical systems, thereby reducing the difficulty of subsequent optimization.