A. Cox, A System of Optical Design (Focal, London, New York, 1964), p. 164.
M. Born and E. Wolf, Principles of Optics, 2nd ed (Pergamon, New York, 1964), p. 150.
M. Herzberger, Modern Geometrical Optics (Interscience, New York, London, 1958), Sec. 22; Ref. 1, pp. 149 and 169; and G. Schulz, Paradoxa aus der Optik (Barth, Leipzig, 1974), pp. 30–33 and 74–76.
Reference 1, Sec. 5.3.
W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, London, New York, San Francisco, 1974), p. 201.
H. H. Hopkins, Wave Theory of Aberrations (Clarendon, Oxford, 1950), pp. 137–138.
C. G. Wynne, "A Unit-Power Telescope for Projection Copying," in Optical Instruments and Techniques 1969, edited by J. Home Dickson (Oriel, Newcastle, 1970), pp. 429–434; S. Rosin, "Unit magnification optical system," Appl. Opt. 16, 2568–2571 (1977).
Reference 5, pp. 133 and 135.
Reference 1, Sec. 5.5.
L. van der Waerden, Moderne Algebra II, (Springer, Berlin, 1931), Secs. 73–74.
Reference 15, Sec. 71; and O. Th. Bürklen and F. Ringleb, Mathematische Formelsammlung, Sammlung Göschen Band 51 (Gruyter, Berlin, 1939), pp. 35–36.
Some of these parameters, especially s1, could be varied such that one or another of the properties of the solution is optimized. However, the purpose of this paper is not to find a relative or an absolute optimum, but to show the existence of an optical system having the property mentioned in the abstract. Therefore, in the following, only examples of such systems are shown.
a4bi/8r3i is the distance between surface i and the ri sphere in axis direction at the height a from the axis; therefore, bi/8r3i is a measure of the asphericity of surface i.