Abstract

The author here suggests the replacement of the customary image error theory by a new one which permits the analysis of the symmetry qualities of the image by means of a few diagrams. Three new functions are introduced: the deformations function, D, the asymmetry function, A, and the spherical aberration function, S. The distance, τ, of the caustic from the diapoints is given by

τ2+Sτ+Dζ2=0,

and D=S=0 gives a system free from aberration. S, D, and A, are developed as functions of a special kind of variable, for which the author suggests ηη0, ζζ0. Here, ζ and η are the direction cosines of the image ray with the optical axis and the perpendicular to it in the meridian plane; ζ0 and η0 are the corresponding angles for the principal ray of the bundle to be investigated.

Formulas are given for the development of these functions and for their connection with the characteristic function of the system.

© 1948 Optical Society of America

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