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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 35, Iss. 8 — Mar. 10, 1996
  • pp: 1367–1371

High-accuracy optical computing based on interval arithmetic and the fixed-point theorem

Jun Tanida, Wataru Watanabe, and Yoshiki Ichioka  »View Author Affiliations


Applied Optics, Vol. 35, Issue 8, pp. 1367-1371 (1996)
http://dx.doi.org/10.1364/AO.35.001367


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Abstract

A method for high-accuracy analog optical computing based on interval arithmetic and the fixed-point theorem is considered. Two-variable simultaneous equations are studied to investigate the proposed method. An optical implementation is considered by the use of spatial coding of intervals, affine transformation, and image magnification. Computational simulation verifies the principle of the method.

© 1996 Optical Society of America

History
Original Manuscript: June 12, 1995
Revised Manuscript: November 9, 1995
Published: March 10, 1996

Citation
Jun Tanida, Wataru Watanabe, and Yoshiki Ichioka, "High-accuracy optical computing based on interval arithmetic and the fixed-point theorem," Appl. Opt. 35, 1367-1371 (1996)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-35-8-1367


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References

  1. D. G. Feitelson, Optical Computing (MIT, Cambridge, Mass., 1988), Chaps. 3 and 4, pp. 52–137.
  2. Ref. 1, Chap. 7, pp. 164–225.
  3. A. D. McAulay, Optical Computer Architectures (Wiley, New York, 1991), Chaps. 8-10, pp. 193–288.
  4. R. E. Moore, Interval Analysis (Prentice-Hall, Englewood Cliffs, N.J., 1966), Chap. 2, pp. 9–17.
  5. L. E. J. Brouwer, “U¨ber Abbildungen von Mannigfaltigkeiten,” Math. Ann. 71, 97–115 (1912).
  6. E. Kaucher, S. M. Rump, “E-Methods for fixed point equations f (x) = x,” Computing 28, 31–42 (1982).
  7. J. Tanida, A. Uemoto, Y. Ichioka, “Optical fractal synthesizer: concept and experimental verification,” Appl. Opt. 32, 653–658 (1993).

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