Experimental Mechanics

, Volume 28, Issue 4, pp 409–416 | Cite as

Exact interpretation of moiré fringe patterns in digital images

  • C. A. Lee
  • T. G. Richard
  • R. E. Rowlands


Geometric moiré enjoys the advantages of simplicity of technique and equipment, and the ability to use white light. However, resolution has been hampered by difficulties in employing more than 40 ℓ per mm. The present paper illustrates the aspects of a digital imaging system relevant to the determination of fractional fringes, and enables reliable analysis from extremely few fringes.

In applying digital imaging to moiré analysis it is imperative that not only the optical characterization but also the features of the image recording system be well understood. Digitization, spatial-averaging operation and the aperture modulation are the most significant features critical to the interpretation of the digital image recorded.

This paper seeks to illustrate the interaction of the moiré technique with the characteristics of a specific image recording system. Examples are presented which experimentally define the nature of moiré fringes recorded with a relatively standard digital imaging system. Further examples are presented which illustrate the influences of the features of this imaging system on the interpretation of the moiré pattern.


Mechanical Engineer Fluid Dynamics Digital Imaging Imaging System Significant Feature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols

an, bn

Fourier coefficients of transmittance functions for reference grating and specimen grating, respectively


width of the opaque bar of Ronchi gratings, undeformed and deformed


Fourier-transformation operator


spectra of transmittance function


light intensity at positionx


digitized light intensity


averaged light intensity


local maximum and minimum of intensity profile


average and amplitude of intensity variations


frequency-modulation function


fringe order


pitches of Ronchi gratings, underformed and deformed

rect (x, y)

rectangular functions


spatial-averaging function


transmittance function of overlapped gratings


transmittance function of reference gratings


transmittance function of specimen gratings


displacement vertical to the reference grating at positionx


spatial-frequency coordinates


Cartesian coordinates

convolution operator

δ (x)

dirac delta function


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Voloshin, A.S., Burger, C.P., Rowlands, R.E. andRichard, T.G., “Analysis of Partial Moiré Fringes in Experimental Stress Analysis by Using Digital-Image-Analysis Techniques”, experimental mechanics,26 (3),254–258 (1986).Google Scholar
  2. 2.
    Voloshin, A.S., Burger, C.P. andRowlands, R.E., “Composites Analysis by Fractional Moiré Fringe System,”J. Comp. Mat.,19 (6),513–525 (1985).Google Scholar
  3. 3.
    Seguchi, Y., Tomita, Y. andWatanabe, M., “Computer-aided Fringe-Pattern Analyzer—A Case of Photoelastic Fringe,” experimental mechanics,19 (10),362–370 (1979).Google Scholar
  4. 4.
    Robinson, D., “Automatic Fringe Analysis with a Computer Image-processing System,”Appl. Opt.,22 (14),2169–2177 (1983).Google Scholar
  5. 5.
    Peter, W.H., Ranson, W.F., Chu, T.C. andAnderson, J., “Application of Digital Correlation Method to Rigid Body Mechanics,”Opt. Eng. 22 (6),738–742 (1983).Google Scholar
  6. 6.
    He, Z.H., Sutton, M.A., Ranson, W.F. andPeters, W.H., “Two-dimensional Fluid-velocity Measurements by Use of Digital-speckle Correlation Techniques,” experimental mechanics,24 (2),117–121 (1984).Google Scholar
  7. 7.
    Voloshin, A.S. andBurger, C.P., “Half-fringe Photoelasticity: A New Approach to Whole-field Stress Analysis,” experimental mechanics,23 (3),304–313 (1983).Google Scholar
  8. 8.
    Hunter, A.R. and Martinson, R.H., “Fringe-intensity Interpretation Method for High Sensitivity Moiré Strain Analysis,” Proc. 1982 Joint SESA-JSME Conf. on Exp. Mech. SEM, 52–57 (1982).Google Scholar
  9. 9.
    Sciammarella, C.A. and Durelli, A.J., “Moiré Fringes As A Means of Analysing Strains,” J. Eng. Mech. Div., Proc. ASCE, 55–74 (Feb. 1961).Google Scholar
  10. 10.
    Post, D., “Moiré Interferometry, Handbook on Experimental Mechanics, Chap. 7, ed. A.L. Kobayashi, Prentice Hall, Englewood Cliffs, NJ, 314–384 (1987).Google Scholar
  11. 11.
    Sciammarella, C.A., “Basic Optical Law in the Interpretation of Moiré Patterns Applied to the Analysis of Strain—Part 1,” experimental mechanics,5 (5),154–160 (1965).Google Scholar
  12. 12.
    Ross, B.E., Sciammarella, C.A. andSturgen, D., “Basic Optical Law in the Interpretation of Moiré Patterns Applied to the Analysis of Strains—Part 2,” experimental mechanics,5 (6),161–166 (1965).Google Scholar
  13. 13.
    Zandman, F., Holister, G.S. andBrcic, V., “The Influence of Grid Geometry on Moiré Fringe Properties,”J. Strain Anal.,1,1–10 (Jan. 1965).Google Scholar
  14. 14.
    Post, D., “Sharpening and Multiplication of Moiré Fringes,” experimental mechanics,7 (4),154–159 (1965).Google Scholar
  15. 15.
    Patorski, K. andYokozeki, S., “Moiré Profile Prediction by Using Fourier Series Formalism,”Jap. J. Appl. Phys. 15 (3),443–456 (1976).Google Scholar
  16. 16.
    McKelvie, J., “On the Limits to the Information Obtainable from a Moiré Pattern,” Proc. 1986 SEM Conf. on Exp. Mech., SEM, 971–980 (1986).Google Scholar
  17. 17.
    Lee, A.C., “Moiré Data Interpretation by Digital Image Processing,” PhD Thesis, Univ. of Wisconsin (1988).Google Scholar
  18. 18.
    Burch, J.M. andForno, C., “The High Sensitivity Moiré Grid Technique for Studying Deformation in Large Objects,”Opt. Eng.,14 (2),178–185 (1975).Google Scholar
  19. 19.
    Hall, L. Ernest, “Computer Image Processing and Recognition” (1979).Google Scholar
  20. 20.
    Dinstein, I., Merklet, F., Lam, T. andWong, K., “Imaging System Response Linearization and Shading Correction,”Opt. Eng.,23 (6),788–793 (Nov./Dec. 1984).Google Scholar
  21. 21.
    De Boor, Carl, “A Practical Guide to SplinesAppl. Math. Sci., 27, Springer-Verlag, New York (1978).Google Scholar
  22. 22.
    De Boor, Carl and Rice, John R., “Cubic Spline Approximation I —Fixed Knots,” Comp. Sci., Dept. TR 20, Purdue Univ. (April 1968).Google Scholar
  23. 23.
    De Boor, Carl and Rice, John R., “Cubic Spline Approximation II —Variable Knots,” Comp. Sci. Dept. TR 21, Purdue Univ. (April 1968).Google Scholar
  24. 24.
    IMSL Library Reference Manual, IMSL S-R091-E08.1, IMSL Inc., Houston (Oct., 1981).Google Scholar
  25. 25.
    Fairchild CAM3000 & CCD3000 specifications, Fairchild Weston System Inc., CCD Imaging Div. (1986).Google Scholar

Copyright information

© Society for Experimental Mechanics, Inc. 1998

Authors and Affiliations

  • C. A. Lee
    • 1
  • T. G. Richard
    • 2
  • R. E. Rowlands
    • 2
  1. 1.Delco Moraine Division of General Motors CorporationDayton
  2. 2.Department of Engineering MechanicsUniversity of WisconsinMadison

Personalised recommendations