Applying slope constrained Qbfs aspheres for asphericity redistribution in the design of infrared transmission spheres.

An achromatic transmission sphere (TS) must be provided as an accessory for an infrared interferometer with a broadband wavelength channel. When designing an F/0.75 infrared TS using the one-asphere model of the two-lens-only package, the first surface was optimized as a strong asphere beyond our current testing ability, using either a slope-unconstrained Qbfs asphere equal to a conventional even asphere, or using a slope-constrained Qbfs asphere. We applied the asphere-splitting theory to redistribute the asphericity. Adopting only the slope-constrained Qbfs asphere, the strong asphere was successfully split into two weaker aspheres within our testing ability, getting a more manufacturable two-asphere TS solution. Besides, the TS solution with two weaker aspheres presented the same sensitivity to assembly errors compared to the solution with one strong asphere, as demonstrated by the analysis of the wavefront aberrations of the TS solutions. This phenomenon coincides well with the asphere-splitting theory, given that the total asphericity remains almost equivalent between the two solutions.