General equation of the achromatic stigmatic singlet

The merge of two models is presented: the achromatic principle and the general equation of the stigmatic lens [ J. Opt. Soc. Am. A 39 , 1524 ( 2022 ) JOAOD6 0740-3232 10.1364/JOSAA.460993 ; Appl. Opt. 57 , 9341 ( 2018 ) APOPAI 0003-6935 10.1364/AO.57.009341 ]. The achromatic principle expresses the bases to design an optical imaging system rigorously free of chromatic aberrations for a given spectrum of electromagnetic waves. It has been applied only to Cartesian ovals. On the other hand, the equation of the stigmatic lens gives a perfect point image for a single wavelength. The merge consists of generalizing the equation of the stigmatic lens to be stigmatic for a given spectrum of electromagnetic waves based on the achromatic principle. The constraints to rigorously achieve the achromatic stigmatic singlet are studied in detail. No paraxial concepts are used, and no iteration process is required. An example of an achromatic stigmatic singlet is presented, and the results are as expected by theory.