IV. — Aberration diffraction effects

The image of a luminous point, given by a symmetrical optical system, will not itself be a point; and this will follow both from the nature of light and also from the necessary ‘ imperfections ’ of the system. A part only of the incident wave will pass through the system and diffraction phenomena will appear ; in addition the emergent wave will not be a portion of a sphere but will be distorted by the geometrical aberrations of the system. Diffraction theory would indicate that corresponding to a point source of light a system of luminous rings should be produced upon the image plane ; this was investigated by Airy in 1834 ; geometrical theory, on the other hand, leads to a consideration of several types and orders of aberration, the more common ones being better known as the 'Five Aberrations of Von Seidel.’ They are: Spherical Aberration, Coma, Astigmatism, Curvature of the Field and Distortion ; these are well known and they have been investigated by a number of writers. In the present paper a consideration is undertaken of the modification of the ‘ ideal ’ diffraction pattern produced by these geometrical aberrations. The method adopted depends upon the Eikonal Function of Bruns, and a summary of the properties of this function is given, therefore, in Part I of the paper ; Part II deals with the Aberration-Diffraction effects. Throughout Parts I and II of the paper it is assumed that the stops of the optical system are circular, with centres upon the axis of symmetry ; and this is generally the case. Occasionally, however, other stops are used, and in Part III of the paper is undertaken a consideration of the diffraction effects of such. The precise forms of aperture considered are the following :— 1. the usual circular aperture with the central portion stopped out—as suggested by Lord Rayleigh : 2. one (or two parallel) narrow rectangular apertures—as used for the determination of the diameters of large stars and for the separation of close double-stars : 3. a semi-circular aperture—as used in a heliometer.