Establishment of the Fifth Order Aberration Theory for Practical Use

I. General Theory (2)

Abstract

In the preceding paper, starting from the Herzberger-Focke's fifth order aberration theory, the author has defined the new practical aberration coefficients, which correspond to the Berek's coefficients in the region of the third order. In this paper, the various formulas of the aberration coefficients are considered.
The contents are: Relation between the aberration coefficients of image and those of pupil; shifting of pupil and object; curvatures of object, image and pupil surfaces; relations between the intrinsic and the total aberration coefficients; and the aberration coefficients based upon the exit pupil coordinates. Most of the formulas are derived from the Herzberger's theory, but some of them are supplied by the author.
Every transformation formula may be applied to both the intrinsic and the total aberration coefficients of any rotationally symmetrical system.