J. C. Maxwell, “On the general laws of optical instruments,” Vol. 1 of Scientific papers (Cambridge U. Press, Cambridge, UK, 1890), pp. 271–285.

For a general introduction to eikonal functions see Refs. 5-8.

M. Herzberger, Strahlenoptik (Springer, Berlin, 1931).

R. Luneburg, Mathematical Theory of Optics (University of California, Los Angeles, Calif., 1964).

H. A. Buchdahl, An Introduction to Hamiltonian Optics (Cambridge U. Press, Cambridge, UK, 1970).

A. Walther, The Ray and Wave Theory of Lenses (Cambridge U. Press, Cambridge, UK, 1995).

We assume, as is usual in this context, that it is, at least in principle, possible to design a lens that realizes any specified eikonal. See also Ref. 8, Sec. 22.1.

See, however, Sec. 7 and especially Ref. 18.

See, for instance, R. Kingslake, A History of the Photographic Lens (Academic, New York, 1989), p. 159.

R. Kingslake, A History of the Photographic Lens (Academic, New York, 1989), p. 161.

This result agrees with the work described in Chap. 2 of J. B. Lasché, “Aberration correction in zoom systems: theoretical results,” Ph.D. dissertation (University of Rochester, Rochester, N.Y., 1998).

See Ref. 8, Sec. 6.4.

Mock ray tracing is described in Ref. 8, Chap. 31. See also A. Walther, “Mock ray tracing,” J. Opt. Soc. Am. 60, 918–920 (1970), and “Irreducible aberrations of a lens used for a range of magnifications,” J. Opt. Soc. Am. A 6, 415–422 (1989).

[CrossRef]

See Ref. 8, p. 351, or W. H. Press, B. F. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1988), Sec. 9.6.

OSLO SIX is a registered trademark of Sinclair Optics Inc., Fairport, New York.

As pointed out by one of the referees, the separation between the design tasks is not complete. Section 4 shows that for the Donders system the coefficients Q1,Q4,Q7, and Q10 are still at our disposal. These coefficients affect the eikonals of both groups to be designed. So an iterative process involving the designs of both groups will be needed to find the optimum values of these coefficients.