OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 31, Iss. 1 — Jan. 1, 1992
  • pp: 27–37

Upper bound on the diffraction efficiency of phase-only fanout elements

Ulrich Krackhardt, Joseph N. Mait, and Norbert Streibl  »View Author Affiliations

Applied Optics, Vol. 31, Issue 1, pp. 27-37 (1992)

View Full Text Article

Enhanced HTML    Acrobat PDF (1026 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



For one-dimensional binary-phase [(0, π) and (0, non-π)] fanout elements and for one-dimensional continuous or multilevel quantized phase fanout elements, an upper bound on diffraction efficiency is presented for fanouts ranging from 2 to 25. The upper bound is determined by optimizing with respect to the array phase the upper bound on diffraction efficiency for a coherent array. To determine the upper bound for binary-phase gratings, restrictions on the array phase are imposed. For fanouts that are >5, the upper bound on the diffraction efficiency for continuous phase fanouts ranges between 97 and 98%; for (0, π)-binary-phase fanouts the upper bound ranges between 83 and 84%; and for (0, non-π)-binary-phase, between 87 and 88%.

© 1992 Optical Society of America

Original Manuscript: January 28, 1991
Published: January 1, 1992

Ulrich Krackhardt, Joseph N. Mait, and Norbert Streibl, "Upper bound on the diffraction efficiency of phase-only fanout elements," Appl. Opt. 31, 27-37 (1992)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. N. Streibl, K.-H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. A. B. Miller, M. Murdocca, M. Prise, T. Sizer, “Digital optics,” Proc. IEEE 77, 1954–1969 (1989). [CrossRef]
  2. M. R. Feldman, C. C. Guest, “High efficiency hologram encoding for generation of spot arrays,” Opt. Lett. 14, 479–481 (1989). [CrossRef] [PubMed]
  3. J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989). [CrossRef]
  4. J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989). [CrossRef]
  5. F. Wyrowski, “Coding and quantization techniques in digital phase holography,” in Holographic Optics II: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1136, 215–219 (1989).
  6. H. P. Herzig, D. Prongué, R. Dändliker, “Design and fabrication of highly efficient fan-out elements,” Jpn. J. Appl. Phys. 29, L1307–L1309 (1990). [CrossRef]
  7. J. N. Mait, “Extensions to Dammann’s method of binary-phase grating design,” in Holographic Optics: Optically and Computer Generated, I. N. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1052, 41–46 (1989).
  8. A. Vasara, J. Turunen, J. Westerholm, M. R. Taghizadeh, “Stepped-phase kinoforms,” in Optics in Complex Systems, F. Lanzl, H.-J. Preuss, J. Weigelt, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1319, 298–299 (1990).
  9. F. Wyrowski, “Characteristics of diffractive optical elements/digital holograms,” in Computer and Optically Formed Holographic Optics, I. N. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1211, 2–10 (1990).
  10. R. L. Morrison, “Symmetries that simplify design of spot-array phase gratings,” in Annual Meeting Technical Digest, Vol. 15 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 86.
  11. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1986).
  12. A. Vasara, “Array generation with periodic Fourier-transform holograms,” licentiate thesis (Helsinki University of Technology, Espoo, Finland, 1989).
  13. H. Dammann, K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971). [CrossRef]
  14. U. Krackhardt, N. Streibl, “Design of Dammann-gratings for array generation,” Opt. Commun. 74, 31–34 (1989). [CrossRef]
  15. U. Killat, G. Rabe, W. Rave, “Binary phase gratings for star couplers with high splitting ratio,” Fiber Integr. Opt. 4, 159–167 (1982). [CrossRef]
  16. J. N. Mait, “Design of binary-phase and multiphase Fourier gratings for array generation,” J. Opt. Soc. Am. A 7, 1514–1528 (1990). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited