Summary In this paper the geometrical aberrations of a rotationally symmetrical optical system are dealt with in a new way, suggested by the wave-optical treatment of the image errors to be published subsequently. A spherical surface is introduced with its centre at the Gaussian image (situated at a radial distance σ from the axis) and passing through the centre of the exit-pupil. The actual wave-front deviates by an amount V (σ, γ, ) from this sphere, where γ andare plane polar co-ordinates upon the latter. The aberration function” V is expanded in terms γn cosm, whereas usually the characteristic function analogous to V is expanded in terms containing γn cosm . Thus a single aberration is defined now by an aberration function blnmσ2l+mγn cos m. As a consequence of this new definition the discussion of the aberration figures is simplified considerably. Also a simple classification of image errors of all orders is found, according to which the value of m determines the general type to which a given single aberration belongs (spherical aberration for m = 0, coma for m = 1, astigmatism for m = 2).

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latter waveoptical treatment of gaussian image way rotationally symmetrical optical system geometrical aberrations n cosm classification of image errors aberration function blnm2lmn cos characteristic function wavefront definition exitpupil spherical surface axis

B.R.A. Nijboer,.The diffraction theory of optical aberrations: Part I: General discussion of the geometrical aberrations. 10 (8),679-692.

B.R.A. Nijboer,"The diffraction theory of optical aberrations: Part I: General discussion of the geometrical aberrations" 10

B.R.A. Nijboer,"The diffraction theory of optical aberrations: Part I: General discussion of the geometrical aberrations"