Abstract

A new algorithm for automatic analysis of Young’s fringes in speckle photography, applicable to fringe numbers >0.5, is developed. In the algorithm we first divide the diffraction pattern by the corresponding diffraction halo, then integrate the result over bands in various directions for detecting the fringe orientation, and use curve fitting for determining the fringe spacing. The algorithm has enabled fully automatic analysis of double-exposure specklegrams for a wide range of speckle displacement with improved accuracy. Contours of displacement and strain fields have also been plotted using the result of the analysis.

© 1990 Optical Society of America

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References

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  1. J. M. Huntley, “Speckle Photography Fringe Analysis by the Walsh Transform,” Appl. Opt. 25, 382–386 (1986).
    [CrossRef] [PubMed]
  2. B. Ineichen, P. Eglin, R. Dändliker, “Hybrid Optical and Electronic Image Processing for Strain Measurements by Speckle Photography,” Appl. Opt. 19, 2191–2195 (1980).
    [CrossRef] [PubMed]
  3. D. W. Robinson, “Automatic Fringe Analysis with a Computer Image-Processing System,” Appl. Opt. 22, 2169–2176 (1983).
    [CrossRef] [PubMed]
  4. R. Erbeck, “Fast Image Processing with a Microcomputer Applied to Speckle Photography,” Appl. Opt. 24, 3838–3841 (1985).
    [CrossRef] [PubMed]
  5. J. Georgieva, “Diffraction Halo Effect in Speckle Photography,” Appl. Opt. 25, 3970–3971 (1986).
    [CrossRef] [PubMed]
  6. C. Joenathan, R. S. Sirohi, “Enhancement of Sensitivity in In-Plane Measurement in Speckle Photography,” Appl. Opt. 25, 1380–1380 (1986).
    [CrossRef] [PubMed]
  7. C. Joenathan, R. S. Sirohi, “Elimination of Error in Speckle Photography,” Appl. Opt. 25, 1791–1793 (1986).
    [CrossRef] [PubMed]
  8. G. H. Kaufmann, “Digital Analysis of Speckle Photography Fringes: Processing of Experimental Data,” Appl. Opt. 21, 3411–3412 (1982).
    [CrossRef] [PubMed]
  9. I. Yamaguchi, “Fringe Formation in Speckle Photography,” J. Opt. Soc. Am. A 1, 81–86 (1984).
    [CrossRef]
  10. M. Pedretti, F. P. Chiang, “On the Lower Limit of One Beam Laser Speckle Interferometry,” Opt. Laser Technol. 11, 143–147 (1979).
    [CrossRef]

1986 (4)

1985 (1)

1984 (1)

1983 (1)

1982 (1)

1980 (1)

1979 (1)

M. Pedretti, F. P. Chiang, “On the Lower Limit of One Beam Laser Speckle Interferometry,” Opt. Laser Technol. 11, 143–147 (1979).
[CrossRef]

Chiang, F. P.

M. Pedretti, F. P. Chiang, “On the Lower Limit of One Beam Laser Speckle Interferometry,” Opt. Laser Technol. 11, 143–147 (1979).
[CrossRef]

Dändliker, R.

Eglin, P.

Erbeck, R.

Georgieva, J.

Huntley, J. M.

Ineichen, B.

Joenathan, C.

Kaufmann, G. H.

Pedretti, M.

M. Pedretti, F. P. Chiang, “On the Lower Limit of One Beam Laser Speckle Interferometry,” Opt. Laser Technol. 11, 143–147 (1979).
[CrossRef]

Robinson, D. W.

Sirohi, R. S.

Yamaguchi, I.

Appl. Opt. (8)

J. Opt. Soc. Am. A (1)

Opt. Laser Technol. (1)

M. Pedretti, F. P. Chiang, “On the Lower Limit of One Beam Laser Speckle Interferometry,” Opt. Laser Technol. 11, 143–147 (1979).
[CrossRef]

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Figures (18)

Fig. 1
Fig. 1

Elimination of modulation induced by a diffraction halo: (a) diffraction halo; (b) smoothed diffraction halo; (c) pattern of Young’s fringes before the division; (d) pattern of Young’s fringes after the division.

Fig. 2
Fig. 2

Summary of the analysis procedures.

Fig. 3
Fig. 3

Schematics of the proposed algorithm: (a) summation band and weighting function; (b) the distribution of the sum along band orientation; (c) projection in the fringe direction and curve fitting.

Fig. 4
Fig. 4

Automatic system for analysis of double-exposure speckle-grams.

Fig. 5
Fig. 5

Measurement results from known in-plane translation showing the stability of the analysis for various specklegram orientations. Average fringe numbers in the sampled area are (a) 2.30 and (b) 0.52.

Fig. 6
Fig. 6

Errors of the results vs number of Young’s fringes.

Fig. 7
Fig. 7

Young’s fringes with spacing larger than the diameter of the diffraction halo (taken from the screen of a monitor). The square shows the sampled area for analysis.

Fig. 8
Fig. 8

Relationship between the measured speckle displacement and the given object translation for coarse Young’s fringes.

Fig. 9
Fig. 9

Analysis result for a specklegram taken from in-plane rotation of a disk. Arrowed lines represent the object displacement vectors. Values of the displacements are shown beside the vectors in microns. The rotation angle is 0.06°.

Fig. 10
Fig. 10

Difference between the analysis results and the expected displacement field.

Fig. 11
Fig. 11

Illustration of the origin of the tilt in the analysis result.

Fig. 12
Fig. 12

Differences after compensation for the tilt effect.

Fig. 13
Fig. 13

Specklegram taken from an aluminum plate subjected to extension between exposures. The strain change measured by a resistance strain gauge is 1.6 × 10−3; imaging magnification is 0.35.

Fig. 14
Fig. 14

Analysis results using the new algorithm.

Fig. 15
Fig. 15

Analysis results using the FFT algorithm incorporated with interpolation.

Fig. 16
Fig. 16

Comparison between the cross sections of the displacement fields obtained (a) from Fig. 14 and (b) from Fig. 15.

Fig. 17
Fig. 17

Contours of the displacement field. The original data have been interpolated to a 201 × 101 array for plotting the contours. Unit in the figure is μm. (a) X-component, displacement interval between two adhesive contours is a constant of 5.7 μm; (b) Y-component interval is 2.1 μm.

Fig. 18
Fig. 18

Contours of strain fields. The original data have been interpolated to a 201 × 101 array for plotting the contours. Unit of strain in the figure is 10−3. (a) Tensile strain along the X-axis; (b) tensile strain along the Y-axis; (c) shearing strain.

Equations (6)

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J d ( X , Y ) = J 0 ( X , Y ) + J h ( X , Y ) [ 1 + γ cos ( 2 π X A x + Y A y λ o f o ) ] ,
J ( X , Y ) = ( J d - J 0 ) J h = 1 + γ cos ( 2 π X A x + Y A y λ o f o ) ,
G ( M , N ) = F ( M , N ) F o ( M , N ) = 1 + γ cos [ 2 π ( K m M + K n N + C ) ] ,
B ( θ ) = k = - k o k o N = 1 127 G { [ 64 + ( 64 - N ) tan θ + k + 0.5 ] , N } W { k } ,
W ( k ) = { W o - k , - k o k k o 0 , else .
P ( k ) = a + b cos ( 2 π c k ) ,

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