If the mirror is made parabolic, to correct the spherical aberration, then it must necessarily suffer from coma and off-axis astigmatism.
In practice, the design may also include any number of flat fold mirrors, used to bend the optical path into more convenient configurations.
One way to look at this is to imagine the tertiary mirror, which suffers from spherical aberration, is replaced by a Schmidt telescope, with a correcting plate at its centre of curvature.
Paul's solution had a curved focal plane, but this was corrected in the Paul–Baker design, introduced in 1969 by James Gilbert Baker.
[3] The Paul–Baker design adds extra spacing and reshapes the secondary to elliptical, which corrects field curvature to flatten the focal plane.
A variation of the Korsch design is the Two-Mirror three-surface telescope[6] introduced by Shai Eisenberg and Earl T. Pearson in 1987.
A compact illustration of the Korsch telescope published in 1995 by Shai Eisenberg[7] is the solid version of the design with the use of total internal reflection (TIR) to integrate the fourth fold mirror without introducing vignetting.