Abstract

An analysis is made of two-mirror systems consisting of spherical reflecting surfaces. Solutions are found for those systems having zero third-order spherical aberration. It is shown that no practical solution exists for the configuration resembling the Cassegrainian telescope; there are three one-parameter families of solutions. These are given by c<sub>1</sub> = (<i>q</i>-1)/2<i>t</i><sub>0</sub><i>t</i><sub>1</sub> = (<i>t</i><sub>0</sub>-ƒ)/<i>q</i> c<sub>2</sub>=<i>q</i>/2ƒ <i>t</i><sub>0</sub>= (27ƒ/32) sec<sup>2</sup>θ <i>q</i>=-3[1+4 cos ⅔(θ+7πr)-1, where <i>c</i><sub>1</sub>, and <i>c</i><sub>2</sub> are the two curvatures; <i>t</i><sub>1</sub> the axial separation of the two reflecting surfaces; <i>t</i><sub>0</sub> the distance from a focus to the corresponding surface; and ƒ the focal length. The free parameter is θ and <i>r</i> = 0, 1, -1.

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  1. D. P. Feder, J. Opt. Soc. Am. 41, 630 (1951).
  2. F. C. Champion, Light (Blackie & Son Ltd., London, 1941), p. 41.
  3. L. E. Dickson, New First Course in the Theory of Equations (John Wiley & Sons, Inc., New York, 1939), pp. 42–45.
  4. G. A. Korn and T. M. Korn, in Mathematical Handbook for Scientists and Engineers (McGraw-Hill Book Company, New York, 1961), p. 23.

Champion, F. C.

F. C. Champion, Light (Blackie & Son Ltd., London, 1941), p. 41.

Dickson, L. E.

L. E. Dickson, New First Course in the Theory of Equations (John Wiley & Sons, Inc., New York, 1939), pp. 42–45.

Feder, D. P.

D. P. Feder, J. Opt. Soc. Am. 41, 630 (1951).

Korn, G. A.

G. A. Korn and T. M. Korn, in Mathematical Handbook for Scientists and Engineers (McGraw-Hill Book Company, New York, 1961), p. 23.

Korn, T. M.

G. A. Korn and T. M. Korn, in Mathematical Handbook for Scientists and Engineers (McGraw-Hill Book Company, New York, 1961), p. 23.

Other

D. P. Feder, J. Opt. Soc. Am. 41, 630 (1951).

F. C. Champion, Light (Blackie & Son Ltd., London, 1941), p. 41.

L. E. Dickson, New First Course in the Theory of Equations (John Wiley & Sons, Inc., New York, 1939), pp. 42–45.

G. A. Korn and T. M. Korn, in Mathematical Handbook for Scientists and Engineers (McGraw-Hill Book Company, New York, 1961), p. 23.

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