Calculation of third-order misalignment aberrations with the Optical Plate diagram

The Optical Plate Diagram of C. R. Burch has been generalized to allow the calculation of third-order perturbation aberrations for nominally axially symmetrical optical systems. The plate method has the advantage of simplifying the third-order analysis of optical systems by removing the first-order considerations that complicate traditional approaches. This development is shown to be directly analogous to the original derivation of Shack and Thompson.