Huygens' principle and Hilbert integral to propagate wavefronts through chromatic separated doublets.

We study the propagation of refracted wavefronts through chromatically separated doublets, considering an incident plane wavefront incoming to the optical system. Based on Huygens' principle and Hilbert integral, we define piecewise functions to fully represent the shape of wavefronts propagated through two conic lenses immersed in air, having a tiny distance of separation between them. Alternatively, by varying the design parameters such as curvature radii, axial thicknesses, and refractive indices, it is possible to reduce the size and modify the shape of the caustic surfaces for evaluating the circle of least confusion. Finally, we provide two different approaches to represent the shape of propagated wavefronts at the second order, which are related to the envelopes for all refracted rays.