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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 17, Iss. 17 — Sep. 1, 1978
  • pp: 2677–2685

Three-mirror telescopes: design and optimization

Paul N. Robb  »View Author Affiliations


Applied Optics, Vol. 17, Issue 17, pp. 2677-2685 (1978)
http://dx.doi.org/10.1364/AO.17.002677


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Abstract

A set of equations is developed which yields the constructional parameters of three-mirror all-reflecting optical systems. An equation whose factors allow the shape of the image surface to be controlled is also derived. A method of optimizing the performance of three-mirror systems by varying the inputs to the design equations is described, and the results are compared with those obtained through a conventional numerical design optimization. The technique described is shown to be markedly superior to the usual optimization method of varying the constructional parameters of the system.

© 1978 Optical Society of America

History
Original Manuscript: July 15, 1977
Published: September 1, 1978

Citation
Paul N. Robb, "Three-mirror telescopes: design and optimization," Appl. Opt. 17, 2677-2685 (1978)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-17-17-2677


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References

  1. M. Paul, Rev. Opt. 14, 169 (1935).
  2. N. J. Rumsey, Optical Instruments and Techniques (Oriel, Newcastle upon Tyne, 1970), p. 516.
  3. J. G. Baker, IEEE Trans. Aerosp. Electron. Syst. AES-5, 261 (1969). [CrossRef]
  4. R. V. Shack, A. B. Meinel, J. Opt. Soc. Am. 56, 545 (1966).
  5. N. J. Rumsey, “Telescopic System Utilizing Three Axially Aligned Substantially Hyperbolic Mirrors,” U.S. Patent3,460,886 (1969).
  6. W. B. Wetherell, M. P. Rimmer, Appl. Opt. 11, 2817 (1972). [CrossRef] [PubMed]
  7. Both the coefficients and factors of the Petzval condition equation are formed through sums and differences of quantities having large absolute values. Double precision arithmetic may be required to obtain solutions which are not numerical noise.
  8. D. Korsch, J. Opt. Soc. Am. 63, 667 (1973). [CrossRef]
  9. G. A. and T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, New York, 1968), p. 25.
  10. P. N. Robb, J. Opt. Soc. Am. 66, 1037 (1976). [CrossRef]
  11. R. Fletcher, C. M. Reeves, Comput J. 7, No. 2, 149 (1964). [CrossRef]
  12. L. W. Cornwall, A. K. Rigler, Appl. Opt. 7, 1659 (1972). [CrossRef]
  13. ACCOS-V, a proprietary product of Scientific Calculations, Inc., Rochester, N.Y. (1977). Both the damped least squares and Gram-Schmidt orthogonolization methods were used.
  14. J. Meiron, Appl. Opt. 7, 667 (1968). [CrossRef] [PubMed]
  15. Note that the image surface introduces vignetting at half-field angles greater than approximately 0.7°. The design illustrated in Fig. 5 was intended to operate with a line field, i.e., as a scanning system. The vignetting produced by the focal plane in this case was insignificant.
  16. The cost to design these systems is very modest; most of the calculations required are to evaluate the figure of merit. Using the merit function of Ref. 10 and computing the optical aberration coefficients out through the seventh order, the time per configuration averaged 15 msec on a Univac 1110 computer. This works out to a cost of 0.54 cents per design configuration.

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