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Applied Optics

Applied Optics


  • Vol. 6, Iss. 3 — Mar. 1, 1967
  • pp: 537–544

Operator Formulation of Plane Mirror Systems

Robert W. Schmieder  »View Author Affiliations

Applied Optics, Vol. 6, Issue 3, pp. 537-544 (1967)

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A terminology limited to point objects is introduced to distinguish between finite and infinite, transparent and opaque mirrors. A basic image-producing operator is defined, and its properties are examined in detail. An operational form of the basic operator is derived, two general definitions are presented, and a formal expression for the images of a system of plane mirrors is written. Some simple systems are analyzed in detail to illustrate the applications of the theory. Finally, indication is given of possible directions for future development of the subject, and of its relationship to existing mathematical theories.

© 1967 Optical Society of America

Original Manuscript: August 25, 1966
Published: March 1, 1967

Robert W. Schmieder, "Operator Formulation of Plane Mirror Systems," Appl. Opt. 6, 537-544 (1967)

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  1. J. S. Beggs, J. Opt. Soc. Am. 50, 388 (1960). [CrossRef]
  2. S. Walles, R. E. Hopkins, Appl. Opt. 3, 1447 (1964). [CrossRef]
  3. R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, 1964).
  4. W. Brouwer, Matrix Methods in Optical Instrument Design (W. A. Benjamin, New York, 1964).
  5. R. J. Pegis, M. M. Rao, Appl. Opt. 2, 1271 (1963); A. Walther, Appl. Opt. 3, 543 (1964). [CrossRef]
  6. G. R. Rosendahi, J. Opt. Soc. Am. 50, 287 (1960); J. Opt. Soc. Am. 50, 859 (1960). [CrossRef]
  7. A. Messiah, Quantum Mechanics (North Holland Publishing Co., Amsterdam, 1962), p. 1080.
  8. B. Van der Pol, H. Bremmer, Operational Calculus (Cambridge Univ. Press, Cambridge, 1959).
  9. C. S. Hastings, New Methods in Geometrical Optics (Macmillan Co., New York, 1927), p. 25.
  10. Ray tracing in plane systems is discussed in R. K. Luneburg, op. cit., Appx. II.
  11. J. P. C. Southall, Mirrors, Prisms, and Lenses (Dover Publications, Inc., New York, 1964), p. 37. This result follows from (14), because every factor of T(α)T(β) adds 2α− 2βto θ, and a finite number of images implies that θ+ N(2α− 2β) = θ+ k2π.
  12. F. J. H. Dibdin, Essentials of Light (Cleaver–Hume Press Ltd., London, 1961), p. 15.
  13. Faceted mirrors are discussed by H. A. E. Keitz, Light Calculations and Measurements (Philips Technical Library, 1955), p. 206.

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