Optical systems with translational invariance

The leading order monochromatic aberrations are investigated for the optical systems, which obey single-plane symmetry and translational invariance. These aberrations are classified from the symmetry principles for the wave aberration function. The Fermat's Principle is applied for a system made of generic cylindrical surfaces and a complete set of the aberration coefficients required for calculation of the aberrations for any paraxial ray is obtained. To demonstrate the applied value of the analytical results obtained the criteria of compensation of the leading aberrations for cylindrical analog of the Cassegrain telescope were found.