Exact equations to design a stigmatic singlet that meets the Herschel's condition

We present the exact equations to design a stigmatic singlet that meets the Herschel's condition. We determine analytically how must be the first and second refractive surface of the lens such that the singlet is stigmatic and meets Herschel's condition. To achieve this, we numerically solve a nonlinear differential equation. We show several illustrative examples of these new family lenses, and also we discuss their limitations.

Automated summary

The paper presents the precise equations needed to design a stigmatic singlet lens that meets Herschel's condition. The first and second refractive surfaces of the lens are determined analytically for this purpose, and a nonlinear differential equation is numerically solved. Illustrative examples of the new family lenses are shown, along with a discussion of their limitations.