We give a complete description of the calculation of the eikonal coefficients of symmetric optical systems. First, we show how to express the eikonal coefficients of each component as functions of the component data and the position of the object and the stop. We decompose each eikonal into meridional and sagittal subseries, and we give a proof of the uniqueness of this decomposition. Second, we give simple formulas to calculate system eikonal coefficients of the sixth order in the direction cosines and a fast algorithm to obtain a good estimate of coefficients of orders higher than the sixth. We conclude with a discussion on pseudoaberrations and their uses and also a generalization of the Seidel formulas for the addition of aberrations.
© 1988 Optical Society of America
Original Manuscript: January 13, 1988
Manuscript Accepted: April 5, 1988
Published: August 1, 1988
C. H. F. Velzel and J. L. F. de Meijere, "Characteristic functions and the aberrations of symmetric optical systems. III. Calculation of eikonal coefficients," J. Opt. Soc. Am. A 5, 1237-1243 (1988)