Aerodynamic requirements on airborne optical system have brought about the need to develop lower drag conformal domes. Because these domes typically deviate greatly from spherical surface descriptions, large amounts of aberrations are induced which vary with line of sight through the dome. Several solutions to this problem have been investigated, one of which is the use of translating phase plates to dynamically dial in the appropriate amount of aberration correction. Axially translating phase plates can be described as two nominally plane parallel phase plates with matched aspheric surfaces on their inner surfaces. When placed in contact, they behave as a single plane parallel plate, but when an axial separation is introduced, the optical ray passing through the first plate intersects the second plate at a different location resulting in both a change in optical path length and a set of induced aberrations. A mathematical derivation of the aberrations generated is performed for Zernike polynomial surfaces in the presence of both converging and collimated beams. Code V is used to verify the derived expression and the theory is used to describe the results of a previous conformal optics aberration correction technique.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.