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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 19, Iss. 7 — Jul. 1, 2002
  • pp: 1398–1405

Method for deriving the complete solution set for three-mirror anastigmatic telescopes with two spherical mirrors

Andrew Rakich and Norman Rumsey  »View Author Affiliations

JOSA A, Vol. 19, Issue 7, pp. 1398-1405 (2002)

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The “plate-diagram” method of quantifying and manipulating the Seidel aberrations of an optical system has been used to develop a procedure that has successfully determined the complete solution set of three-mirror anastigmats in which two surfaces are left strictly spherical. The procedure also readily identified solutions in which the Petzval sum is zero, and four distinct families of flat-field three-mirror anastigmats with two mirrors strictly spherical have thus been found. The success of the method is strong support for the argument that algebraic approaches to optical design can yield results distinctly superior to currently favored optimization-based design methods, at least for some types of optical systems.

© 2002 Optical Society of America

OCIS Codes
(080.2720) Geometric optics : Mathematical methods (general)
(080.2740) Geometric optics : Geometric optical design

Original Manuscript: August 28, 2001
Revised Manuscript: January 23, 2002
Manuscript Accepted: January 23, 2002
Published: July 1, 2002

Andrew Rakich and Norman Rumsey, "Method for deriving the complete solution set for three-mirror anastigmatic telescopes with two spherical mirrors," J. Opt. Soc. Am. A 19, 1398-1405 (2002)

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  1. H. L. Aldis, “On the construction of photographic objectives,” Photograp. J. 24, 291–299 (1900).
  2. C. R. Burch, “On the optical see-saw diagram,” Mon. Not. R. Astron. Soc. 102, 159–165 (1942).
  3. C. R. Burch, “On aspheric anastigmatic systems,” Proc. Phys. Soc. 55, 433–444 (1943). [CrossRef]
  4. C. R. Burch, “Application of the plate diagram to reflecting telescope design,” Opt. Act 26, 493–504 (1979). [CrossRef]
  5. E. H. Linfoot, Recent Advances in Optics (Clarendon, Oxford, UK, 1955), pp. 229–259.
  6. M. Paul, “Systèmes correcteurs pour réflecteurs astronomiques,” Rev. d’Opt. 14, 169–202 (1935).
  7. N. J. Rumsey, “Pairs of spherical mirrors as field correctors for paraboloid mirrors,” Proc. Astron. Soc. Aust. 2, 22–23 (1971).
  8. N. J. Rumsey, “Pairs of spherical mirrors as prime focus correctors for the Anglo-Australian Telescope,” Proc. Astron. Soc. Aust. 2, 126–127 (1972).
  9. A. Rakich, “A complete survey of three-mirror anastigmatic reflecting telescope systems with one aspheric surface,” M.Sc. thesis (University of Canterbury, Canterbury, New Zealand, 2001).
  10. A. E. Conrady, Applied Optics and Optical Design (Dover, New York, 1953).
  11. J. G. Baker, “On improving the effectiveness of large telescopes,” Trans. Aerosp. Electron. Syst. 2, 261–272 (1969). [CrossRef]
  12. L. G. Cook, “Wide field of view three-mirror anastigmat (TMA) employing spherical secondary and tertiary mirrors,” in Recent Trends in Optical Systems Design: Computer Lens Design Workshop, C. Londoño, R. E. Fischer, eds., Proc SPIE766, 158–162 (1987).

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