Achromatic and sharp real imaging of a point by a single aspheric lens

By a single lens (two refracting surfaces, one dispersive medium) an achromatic real point image can be obtained. We show how such a lens brings a large aperture bundle of axial-parallel rays to the same sharp focus for two wavelengths, that is, for two refractive-index values. The normal of one of the two refracting surfaces is, in general, discontinuous at the axis. The numerical aperture which is practically attainable can be enhanced by off-axis steps in the refracting surfaces. The design principles for such lenses, computational formulas, and examples of results are given. Limitations and further possibilities are discussed.