OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 18, Iss. 6 — Jun. 1, 2001
  • pp: 1371–1382

Variational approach to moiré pattern synthesis

Guy Lebanon and Alfred M. Bruckstein  »View Author Affiliations

JOSA A, Vol. 18, Issue 6, pp. 1371-1382 (2001)

View Full Text Article

Enhanced HTML    Acrobat PDF (2073 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Moiré phenomena occur when two or more images are nonlinearly combined to create a new superposition image. Moiré patterns are patterns that do not exist in any of the original images but appear in the superposition image, for example as the result of a multiplicative superposition rule. The topic of moiré pattern synthesis deals with creating images that when superimposed will reveal certain desired moiré patterns. Conditions that ensure that a desired moiré pattern will be present in the superposition of two images are known; however, they do not specify these images uniquely. The freedom in choosing the superimposed images can be exploited to produce various degrees of visibility and ensure desired properties. Performance criteria for the images that measure when one superposition is better than another are introduced. These criteria are based on the visibility of the moiré patterns to the human visual system and on the digitization that takes place when the images are presented on discrete displays. We propose to resolve the freedom in moiré synthesis by choosing the images that optimize the chosen criteria.

© 2001 Optical Society of America

OCIS Codes
(100.2000) Image processing : Digital image processing
(100.2650) Image processing : Fringe analysis
(100.3190) Image processing : Inverse problems
(120.4120) Instrumentation, measurement, and metrology : Moire' techniques

Original Manuscript: August 23, 2000
Revised Manuscript: January 18, 2001
Manuscript Accepted: January 29, 2001
Published: June 1, 2001

Guy Lebanon and Alfred M. Bruckstein, "Variational approach to moiré pattern synthesis," J. Opt. Soc. Am. A 18, 1371-1382 (2001)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. H. Giger, “Moirés,” Comput. Math. Appl. 12, 329–361 (1986). [CrossRef]
  2. Lord Rayleigh, “On the manufacture and theory of diffraction-gratings,” Philos. Mag. 81, 81–93 (1874). Published also in G. Indebetouw, R. Czarnek, Selected Papers on Optical Moiré and Applications Vol. 64 of SPIE Milestone Series (SPIE Press, Bellingham, Wash., 1992), pp. 3–15.
  3. O. Bryngdahl, “Characteristics of superposed patterns in optics,” J. Opt. Soc. Am. 66, 87–94 (1976). [CrossRef]
  4. I. Amidror, The Theory of the Moiré Phenomenon (Kluwer Academic, Dordecht, The Netherlands, 2000).
  5. M. Wasserman, G. Oster, C. Zwerling, “Theoretical interpretations of moiré patterns,” J. Opt. Soc. Am. 54, 169–175 (1964). [CrossRef]
  6. R. Courant, D. Hilbert, Methods in Mathematical Physics (Interscience, New York, 1953), Vol. 1.
  7. W. K. Pratt, Digital Image Processing, 2nd ed. (Wiley, New York, 1991).
  8. R. Ulichney, Digital Halftoning (MIT Press, Cambridge, Mass., 1987).
  9. M. Levine, Vision in Man and Machine (McGraw-Hill, New York, 1985).
  10. M. Taylor, “Visual discrimination and orientation,” J. Appl. Opt. 53, 763–765 (1963).
  11. G. Thomas, R. Finney, Calculus and Analytic Geometry, 9th ed. (Addison-Wesley, Reading, Mass., 1996).
  12. H. Sagan, Introduction to the Calculus of Variations (Dover, New York, 1969).
  13. B. K. P. Horn, M. J. Brooks, “The variational approach to shape from shading,” Comput. Vis. Graph. Image Process. 2, 174–203 (1986). [CrossRef]
  14. G. Strang, Introduction to Applied Mathematics (Wellesley–Cambridge Press, Wellesley, Mass., 1986).
  15. R. L. Burden, J. D. Faires, Numerical Analysis, 6th ed. (Brooks Cole, Pacific Grove, Calif., 1997).
  16. M. Naor, A. Shamir, “Visual cryptography,” in EUROCRYPT 1994, Lecture Notes in Computer Science (Springer-Verlag, New York, 1995), Vol. 950, pp. 1–12.

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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited