In the introduction we have generalized the definition of isoplanatism and established the corresponding representation for centered systems. In Part I we explain the theory for the meridional bundles, applying the general differential law for two independent wave surfaces. The angle of field may have any finite magnitude. After having found Eq. (35), we transform it conveniently, so that there appear in it only the intrinsic variables which are introduced for the bundles under consideration and the total aberration of aperture, obtaining the condition (42) in invariant form. This is a necessary and sufficient condition.
The explained theory is valid for optical systems more general than centered systems, viz., for those which have only a single plane of symmetry, in which the isoplanatic, linear element can have any direction.
Though we defer the general discussion of the conditions to a later paper in which the theory will be extended to extra-meridional bundles, we make a first analysis of formula (42) deducing from it (Sections II.9–17) some characteristic laws. The extension of the validity of the form of some conditions, for instance those of Herschel and Lihotzky-Staeble, for general values of fields, shows the principal ray is an axis of bundle even more important than the optical axis in the centered systems.
In the Appendix we shall present some comments on main aspects of the theory.
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