Absence of a perfect intermediate reference wavefront for anamorphic systems

An exact reference wavefront for a single paraxial surface that provides two perpendicular remote image lines instead of a single focal point has not been provided in the recent literature. A naive estimate would state that it may have a toric form. We provide a proof for the nonexistence of an exact toric reference wavefront for intermediate spaces in cross-cylindic symmetrical optical systems where the two principal images do not coincide. As it will be shown, such a shape exists only at the second order in the coordinates x and y in departure from a plane. (C) 2020 Optical Society of America