A new characteristic function is introduced which enables an immediate determination of the departures of imaging pencils of rays from homocentricity as well as of the deformations of the associated wave fronts from spherical form. This function is therefore well suited for investigations of aberration effects on the basis of geometrical optics or of diffraction theory.
Within the approximations of fourth-order theory, the new function is closely related to the Seidel eikonal of Schwarzschild, but unlike the latter it is defined in simple physical terms and is applicable whether the imaging of a point object or of an extended object is under investigation. The series development of this function is carried out in detail up to fourth order.
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