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Applied Optics

Applied Optics


  • Vol. 31, Iss. 11 — Apr. 10, 1992
  • pp: 1709–1716

Transformation of three-dimensional shuffle patterns

Josef Gigimayr  »View Author Affiliations

Applied Optics, Vol. 31, Issue 11, pp. 1709-1716 (1992)

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Formulas are presented for the transformation of three-dimensional shuffle patterns into the two-dimensional domain. The results are applied to the transformation of the interstage patterns of three-dimensional multistage interconnection networks into their isomorphic two-dimensional patterns (and vice versa). This paper explains material in J. Giglmayr, “Classification scheme for 3-D shuffle interconnection patterns,” Appl. Opt. 28, 3120–3128 (1989) and corrects some algebraic results.

© 1992 Optical Society of America

Original Manuscript: September 26, 1990
Published: April 10, 1992

Josef Gigimayr, "Transformation of three-dimensional shuffle patterns," Appl. Opt. 31, 1709-1716 (1992)

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  1. T. J. Cloonan, F. B. McCormick, M. J. Herron, F. A. P. Tooley, G. W. Richards, E. Kerbis, J. L. Brubaker, A. L. Lentine, “A 3D crossover switching network based on S-SEED arrays,” in Photonics Switching II, K. Tada, H. S. Hinton, eds., Vol. 29 of Springer Series on Electronics and Photonics (Springer-Verlag, Berlin, 1990), pp. 196–199. [CrossRef]
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  8. J. E. Eisele, R. M. Mason, Applied Matrix and Tensor Analysis (Wiley-Interscience, New York, 1970), Chap. 4, p. 216.
  9. J. Giglmayr, “Organization of k × k switches (k ≥ 4) interconnected by d-dimensional (d ≥ 2) regular optical patterns,” Appl. Opt. 30, 5119–5135.
  10. R. H. Bracewell, The Hartley Transform (Oxford U. Press, London, 1986), Chap. 7, p. 128 (German edition).

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