Three pupil-coordinate definitions are considered for the description of aberrations. The corresponding sets of expressions for the third- and fifth-order image-aberration coefficients as well as the third-order pupil-aberration coefficients are presented. We show their interrelations and the connection with eikonal coefficients. One pupil-coordinate definition leads to the occurrence of 9 independent fifth-order image-aberration coefficients; the other two definitions lead to 12 independent fifth-order image-aberration coefficients. We find that the third-order image-aberration coefficients are independent of the choice of pupil-coordinate definition, whereas the third-order pupil-aberration coefficients and the fifth-order image-aberration coefficients do depend on this choice. We show that the case of ideal imaging may imply finite pupil aberrations.
© 1989 Optical Society of America
Original Manuscript: June 21, 1988
Manuscript Accepted: April 25, 1989
Published: October 1, 1989
L. F. de Meijere and C. H. F. Velzel, "Dependence of third- and fifth-order aberration coefficients on the definition of pupil coordinates," J. Opt. Soc. Am. A 6, 1609-1617 (1989)