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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 57, Iss. 6 — Jun. 1, 1967
  • pp: 741–743

Two-Mirror Systems with Spherical Reflecting Surfaces

ORESTES N. STAVROUDIS  »View Author Affiliations

JOSA, Vol. 57, Issue 6, pp. 741-743 (1967)

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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 c1 = (q-1)/2t0t1 = (t0-ƒ)/q c2=q/2ƒ t0= (27ƒ/32) sec2θ q=-3[1+4 cos ⅔(θ+7πr)-1, where c1, and c2 are the two curvatures; t1 the axial separation of the two reflecting surfaces; t0 the distance from a focus to the corresponding surface; and ƒ the focal length. The free parameter is θ and r = 0, 1, -1.

ORESTES N. STAVROUDIS, "Two-Mirror Systems with Spherical Reflecting Surfaces," J. Opt. Soc. Am. 57, 741-743 (1967)

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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.

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