A. Offner, “Unit power imaging catoptric anastigmat,” U.S. patent3,748,015 (24July1973).

L. H. J. F. Beckmann, D. Ehrlichmann, “Three-mirror off-axis systems for laser applications,” in International Optical Design Conference, G. W. Forbes, ed., Vol. 22 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1994), pp. 340–348.

For a description of Hamilton’s characteristic functions see, for example, H. A. Buchdahl, Introduction to Hamiltonian Optics (Dover, New York, 1993), Chap. 2.

An introduction to matrix methods for symmetric systems can be found in Sec. 6.2.1 of E. Hecht, Optics, 3rd ed. (Addison-Wesley, Reading Mass., 1998). A generalization of matrix optics for asymmetric systems is discussed in Sec. 4 of B. D. Stone, “Determination of initial ray configurations for asymmetric systems,” J. Opt. Soc. Am. A 14, 3415–3429 (1997).

A detailed derivation of Eq. (17) can be found in Sec. 10 of the book cited in Note 16 or in Sec. 2 of the paper referenced in Note 17. Equation (18) can be determined by a similar procedure.

The original works of Hamilton can be found in A. W. Conway, J. L. Synge, The Mathematical Papers of Sir William Rowan Hamilton (Cambridge U. Press, Cambridge, 1931).

M. Brunn, “Unobstructed all-reflecting telescopes of the Schiefspiegler type,” U.S. patent5,142,417 (25August1992).

C. T. Cotton, “Design of an all-spherical, three-mirror, off-axis telescope objective,” in International Optical Design Conference, G. W. Forbes, ed., Vol. 22 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1994), pp. 349–351.

The geometrical interpretation associated with Hamilton’s characteristic functions can be found in Chap. 2 of the reference cited in Note 16 or alternatively in J. L. Synge, Geometrical Optics, An Introduction to Hamilton’s Method (Cambridge U. Press, Cambridge, 1937), Sec. 6.

A detailed discussion of the geometric interpretation associated with the coefficients of degree two in the Taylor expansion of a characteristic function can be found in Sec. 2 of the paper cited in Note 17. Note that there is a subtle notational difference between that paper and this. In that paper the reference planes are taken to be perpendicular to the base ray segments in object and image space. When quantities associated with tilted object and image planes are discussed, they are denoted by the addition of a tilde (˜). Here we tilt the reference planes along with the object and the image planes; therefore a tilde is unnecessary and is not used.

See Sec. 6 of the book by Buchdahl cited in Note 16.

A discussion of the consequences of object and image tilts in the context of first-order optics can be found in Sec. 4 of the paper cited in Note 17.

A discussion of the consequences of object and image tilts in the context of second-order optics can be found in Sec. 3 of Ref. 10.

A detailed discussion of these conclusions can be found in Sec. 2.C.1 of Ref. 12.

D. Korsch, Reflective Optics (Academic, Boston, Mass., 1991), Chaps. 9, 12, and 13.

A. Kutter, Der Schiefspiegler (Fritz Weichhard, Biberach an der Riss, Germany, 1953). An edited and translated summary of this work can be found in A. Kutter, “The Schiefspiegler (oblique telescope),” Sky Telesc. Bull. A (1958).

B. Tatian, “A first look at computer design of optical systems without any symmetry,” in Recent Trends in Optical Systems Design: Computer Lens Design Workshop, C. Londono, R. E. Fischer, eds., Proc. SPIE766, 38–47 (1985).

K. P. Thompson, “Aberration fields in tilted and decentered optical systems,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 1980).

J. R. Rogers, “Vector aberration theory and the design of off-axis systems,” in International Lens Design Conference, W. H. Taylor, D. T. Moore, eds., Proc. SPIE554, 76–81 (1985).