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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 50, Iss. 4 — Apr. 1, 1960
  • pp: 388–393

Mirror-Image Kinematics

JOSEPH STILES BEGGS  »View Author Affiliations


JOSA, Vol. 50, Issue 4, pp. 388-393 (1960)
http://dx.doi.org/10.1364/JOSA.50.000388


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Abstract

A matrix [M] is derived for a system of plane first-surface mirrors which transforms a point or the direction cosines of a ray in the image space to the object space. If the general displacement of the mirror system is represented by the screw matrix [S], then the new position of a point image is given by the transformation [S][M][S]-l. This method facilitates designing the mirror supporting structure for minimum image shift due to structural deflections.

Citation
JOSEPH STILES BEGGS, "Mirror-Image Kinematics," J. Opt. Soc. Am. 50, 388-393 (1960)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-50-4-388


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References

  1. Michel Chasles, Bull. sci. math. phys. chim. 14, 321–326 (1830).
  2. Joseph Stiles Beggs, Ein Beitrag zur Analyse Raumlichen Mechanismen, Diss. Technische Hochschule, Hanover, Germany (1959).
  3. S. Falk, Z. angew. Math. Mech. 31, 152–153 (1951).
  4. H. Wagner, Optik 8, 456–472 (1951).
  5. T. Smith, Trans. Opt. Soc. 30, 68 (1928).
  6. See reference 5, p. 79.
  7. T. Y. Baker, Trans. Opt. Soc. 29, p. 49 (1927–1928).
  8. See reference 7, p. 187.
  9. Felicien Blottiau, Rev. opt. 33, 339 (1954).

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