Abstract

I report on a new optical technique that uses the principles of speckle photography and wave-front shearing to obtain the measurement of surface strains. The strain information stored at each point on the object surface is read out on a point-wise basis. The method is developed from a theoretical point of view, and experimental results are presented.

© 1998 Optical Society of America

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References

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  1. E. Archbold, A. E. Ennos, “Displacement measurement from double-exposure laser photographs,” Opt. Acta 19, 253–271 (1972).
    [CrossRef]
  2. F. P. Chiang, R. M. Juang, “Laser speckle interferometry for plate bending problems,” Appl. Opt. 15, 2199–2204 (1976).
    [CrossRef] [PubMed]
  3. K. A. Stetson, “Problem of defocusing in speckle photography, its connection to hologram interferometry, and its solution,” J. Opt. Soc. Am. 66, 1267–1270 (1976).
    [CrossRef]
  4. K. A. Stetson, I. R. Harrison, “Determination of the principal surface strains on arbitrary deformed objects via tandem speckle photography,” in Proceedings of the Sixth International Conference on Experimental Stress Analysis, Düsseldorf, Germany, 1978 (The Society for Experimental Stress Analysis, Bethel, Conn., 1978), pp. 149–154.
  5. P. M. Boone, “Measurement of displacement, strain, and stress by holography,” in The Engineering Uses of Coherent Optics, E. R. Robertson, ed. (Cambridge U. Press, Cambridge, UK, 1976), pp. 81–98.
  6. P. Jacquot, P. K. Rastogi, “Speckle motions by rigid-body movements in free-space geometry: an explicit investigation and extension to new cases,” Appl. Opt. 18, 2022–2032 (1979).
    [CrossRef] [PubMed]
  7. P. K. Rastogi, P. Jacquot, “Speckle metrology techniques: a parametric examination of the observed fringes,” Opt. Eng. 21, 411–426 (1982).
    [CrossRef]
  8. E. Diez, D. Chambless, J. Turner, “Image processing techniques in laser speckle photography,” Exp. Mech. 26, 230–237 (1986).
    [CrossRef]
  9. D. W. Robinson, “Automatic fringe analysis with a computer image-processing system,” Appl. Opt. 22, 2169–2176 (1983).
    [CrossRef] [PubMed]
  10. H. D. Navone, G. H. Kaufmann, “Two-dimensional digital processing of speckle photography fringes. 3. Accuracy in angular determination,” Appl. Opt. 26, 154–156 (1987).
    [CrossRef] [PubMed]
  11. R. Erbeck, “Fast image processing with a microcomputer applied to speckle photography,” Appl. Opt. 24, 3838–3841 (1985).
    [CrossRef] [PubMed]
  12. F. Ansari, G. Ciurpita, “Automated fringe measurement in speckle photography,” Appl. Opt. 26, 1688–1692 (1987).
    [CrossRef] [PubMed]
  13. J. M. Huntley, “Fast transforms for speckle photography fringe analysis,” Opt. Lasers Eng. 7, 149–161 (1987).
    [CrossRef]
  14. S. Toyooka, Y. Iwaasa, M. Kawahashi, K. Hosoi, M. Suzuki, “Automatic processing of Young’s fringes in speckle photography,” Opt. Lasers Eng. 6, 203–212 (1985).
    [CrossRef]
  15. R. Hofling, “Fringe analysis by automatic image fitting and its application to speckle pattern photography,” Opt. Lasers Eng. 11, 49–63 (1989).
    [CrossRef]
  16. P. K. Rastogi, “Techniques of displacement and deformation measurements in speckle metrology,” in Speckle Metrology, R. S. Sirohi, ed. (Dekker, New York, 1993), Chap. 2, pp. 41–98.
  17. M. Pedretti, F. P. Chiang, “On the lower limit of one beam laser speckle interferometry,” Opt. Laser Technol. 11, 143–147 (1979).
    [CrossRef]
  18. J. B. Chen, F. P. Chiang, “Statistical analysis of whole-field filtering of specklegram and its upper limit of measurement,” J. Opt. Soc. Am. A 1, 845–849 (1984).
    [CrossRef]
  19. K. A. Stetson, “Analysis of double-exposure speckle photography with two-beam illumination,” J. Opt. Soc. Am. 64, 857–861 (1974).
    [CrossRef]

1989 (1)

R. Hofling, “Fringe analysis by automatic image fitting and its application to speckle pattern photography,” Opt. Lasers Eng. 11, 49–63 (1989).
[CrossRef]

1987 (3)

1986 (1)

E. Diez, D. Chambless, J. Turner, “Image processing techniques in laser speckle photography,” Exp. Mech. 26, 230–237 (1986).
[CrossRef]

1985 (2)

R. Erbeck, “Fast image processing with a microcomputer applied to speckle photography,” Appl. Opt. 24, 3838–3841 (1985).
[CrossRef] [PubMed]

S. Toyooka, Y. Iwaasa, M. Kawahashi, K. Hosoi, M. Suzuki, “Automatic processing of Young’s fringes in speckle photography,” Opt. Lasers Eng. 6, 203–212 (1985).
[CrossRef]

1984 (1)

1983 (1)

1982 (1)

P. K. Rastogi, P. Jacquot, “Speckle metrology techniques: a parametric examination of the observed fringes,” Opt. Eng. 21, 411–426 (1982).
[CrossRef]

1979 (2)

1976 (2)

1974 (1)

1972 (1)

E. Archbold, A. E. Ennos, “Displacement measurement from double-exposure laser photographs,” Opt. Acta 19, 253–271 (1972).
[CrossRef]

Ansari, F.

Archbold, E.

E. Archbold, A. E. Ennos, “Displacement measurement from double-exposure laser photographs,” Opt. Acta 19, 253–271 (1972).
[CrossRef]

Boone, P. M.

P. M. Boone, “Measurement of displacement, strain, and stress by holography,” in The Engineering Uses of Coherent Optics, E. R. Robertson, ed. (Cambridge U. Press, Cambridge, UK, 1976), pp. 81–98.

Chambless, D.

E. Diez, D. Chambless, J. Turner, “Image processing techniques in laser speckle photography,” Exp. Mech. 26, 230–237 (1986).
[CrossRef]

Chen, J. B.

Chiang, F. P.

Ciurpita, G.

Diez, E.

E. Diez, D. Chambless, J. Turner, “Image processing techniques in laser speckle photography,” Exp. Mech. 26, 230–237 (1986).
[CrossRef]

Ennos, A. E.

E. Archbold, A. E. Ennos, “Displacement measurement from double-exposure laser photographs,” Opt. Acta 19, 253–271 (1972).
[CrossRef]

Erbeck, R.

Harrison, I. R.

K. A. Stetson, I. R. Harrison, “Determination of the principal surface strains on arbitrary deformed objects via tandem speckle photography,” in Proceedings of the Sixth International Conference on Experimental Stress Analysis, Düsseldorf, Germany, 1978 (The Society for Experimental Stress Analysis, Bethel, Conn., 1978), pp. 149–154.

Hofling, R.

R. Hofling, “Fringe analysis by automatic image fitting and its application to speckle pattern photography,” Opt. Lasers Eng. 11, 49–63 (1989).
[CrossRef]

Hosoi, K.

S. Toyooka, Y. Iwaasa, M. Kawahashi, K. Hosoi, M. Suzuki, “Automatic processing of Young’s fringes in speckle photography,” Opt. Lasers Eng. 6, 203–212 (1985).
[CrossRef]

Huntley, J. M.

J. M. Huntley, “Fast transforms for speckle photography fringe analysis,” Opt. Lasers Eng. 7, 149–161 (1987).
[CrossRef]

Iwaasa, Y.

S. Toyooka, Y. Iwaasa, M. Kawahashi, K. Hosoi, M. Suzuki, “Automatic processing of Young’s fringes in speckle photography,” Opt. Lasers Eng. 6, 203–212 (1985).
[CrossRef]

Jacquot, P.

P. K. Rastogi, P. Jacquot, “Speckle metrology techniques: a parametric examination of the observed fringes,” Opt. Eng. 21, 411–426 (1982).
[CrossRef]

P. Jacquot, P. K. Rastogi, “Speckle motions by rigid-body movements in free-space geometry: an explicit investigation and extension to new cases,” Appl. Opt. 18, 2022–2032 (1979).
[CrossRef] [PubMed]

Juang, R. M.

Kaufmann, G. H.

Kawahashi, M.

S. Toyooka, Y. Iwaasa, M. Kawahashi, K. Hosoi, M. Suzuki, “Automatic processing of Young’s fringes in speckle photography,” Opt. Lasers Eng. 6, 203–212 (1985).
[CrossRef]

Navone, H. D.

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]

Rastogi, P. K.

P. K. Rastogi, P. Jacquot, “Speckle metrology techniques: a parametric examination of the observed fringes,” Opt. Eng. 21, 411–426 (1982).
[CrossRef]

P. Jacquot, P. K. Rastogi, “Speckle motions by rigid-body movements in free-space geometry: an explicit investigation and extension to new cases,” Appl. Opt. 18, 2022–2032 (1979).
[CrossRef] [PubMed]

P. K. Rastogi, “Techniques of displacement and deformation measurements in speckle metrology,” in Speckle Metrology, R. S. Sirohi, ed. (Dekker, New York, 1993), Chap. 2, pp. 41–98.

Robinson, D. W.

Stetson, K. A.

K. A. Stetson, “Problem of defocusing in speckle photography, its connection to hologram interferometry, and its solution,” J. Opt. Soc. Am. 66, 1267–1270 (1976).
[CrossRef]

K. A. Stetson, “Analysis of double-exposure speckle photography with two-beam illumination,” J. Opt. Soc. Am. 64, 857–861 (1974).
[CrossRef]

K. A. Stetson, I. R. Harrison, “Determination of the principal surface strains on arbitrary deformed objects via tandem speckle photography,” in Proceedings of the Sixth International Conference on Experimental Stress Analysis, Düsseldorf, Germany, 1978 (The Society for Experimental Stress Analysis, Bethel, Conn., 1978), pp. 149–154.

Suzuki, M.

S. Toyooka, Y. Iwaasa, M. Kawahashi, K. Hosoi, M. Suzuki, “Automatic processing of Young’s fringes in speckle photography,” Opt. Lasers Eng. 6, 203–212 (1985).
[CrossRef]

Toyooka, S.

S. Toyooka, Y. Iwaasa, M. Kawahashi, K. Hosoi, M. Suzuki, “Automatic processing of Young’s fringes in speckle photography,” Opt. Lasers Eng. 6, 203–212 (1985).
[CrossRef]

Turner, J.

E. Diez, D. Chambless, J. Turner, “Image processing techniques in laser speckle photography,” Exp. Mech. 26, 230–237 (1986).
[CrossRef]

Appl. Opt. (6)

Exp. Mech. (1)

E. Diez, D. Chambless, J. Turner, “Image processing techniques in laser speckle photography,” Exp. Mech. 26, 230–237 (1986).
[CrossRef]

J. Opt. Soc. Am. (2)

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

Opt. Acta (1)

E. Archbold, A. E. Ennos, “Displacement measurement from double-exposure laser photographs,” Opt. Acta 19, 253–271 (1972).
[CrossRef]

Opt. Eng. (1)

P. K. Rastogi, P. Jacquot, “Speckle metrology techniques: a parametric examination of the observed fringes,” Opt. Eng. 21, 411–426 (1982).
[CrossRef]

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]

Opt. Lasers Eng. (3)

J. M. Huntley, “Fast transforms for speckle photography fringe analysis,” Opt. Lasers Eng. 7, 149–161 (1987).
[CrossRef]

S. Toyooka, Y. Iwaasa, M. Kawahashi, K. Hosoi, M. Suzuki, “Automatic processing of Young’s fringes in speckle photography,” Opt. Lasers Eng. 6, 203–212 (1985).
[CrossRef]

R. Hofling, “Fringe analysis by automatic image fitting and its application to speckle pattern photography,” Opt. Lasers Eng. 11, 49–63 (1989).
[CrossRef]

Other (3)

P. K. Rastogi, “Techniques of displacement and deformation measurements in speckle metrology,” in Speckle Metrology, R. S. Sirohi, ed. (Dekker, New York, 1993), Chap. 2, pp. 41–98.

K. A. Stetson, I. R. Harrison, “Determination of the principal surface strains on arbitrary deformed objects via tandem speckle photography,” in Proceedings of the Sixth International Conference on Experimental Stress Analysis, Düsseldorf, Germany, 1978 (The Society for Experimental Stress Analysis, Bethel, Conn., 1978), pp. 149–154.

P. M. Boone, “Measurement of displacement, strain, and stress by holography,” in The Engineering Uses of Coherent Optics, E. R. Robertson, ed. (Cambridge U. Press, Cambridge, UK, 1976), pp. 81–98.

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Figures (8)

Fig. 1
Fig. 1

Decorrelated speckle patterns produced by sampling of independent aperture positions.

Fig. 2
Fig. 2

Schematic of the geometry used to record the speckle shearograms.

Fig. 3
Fig. 3

Optical transform fringes obtained by point-wise filtering of the recorded speckle shearogram.

Fig. 4
Fig. 4

Two-quadrant three-dimensional display of the normalized autocorrelation function of a semicircular aperture of radius d/2; q is the distance between the lens and the image plane.

Fig. 5
Fig. 5

One-quadrant three-dimensional display of the moiré fringe pattern in the diffraction halo.

Fig. 6
Fig. 6

Layout of a speckle shearogram recording system.

Fig. 7
Fig. 7

Young’s moiré fringe patterns obtained by filtering through of two regions of a speckle shearogram.

Fig. 8
Fig. 8

Young’s moiré fringe patterns obtained by point-wise filtering of a speckle shearogram recorded in a split-lens arrangement. The reconstruction in (b) refers to the optical transform fringes obtained by use of a relatively more narrow laser beam than that used in (a).

Equations (31)

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δ r = δ x δ y ,
S = S x S y S z ,
Ω = CS ,
C = 1 0 0 1 - l o n o - m o n o ,
Ω ij = CS ij ,
S = S + δ S ,
Ω = C S ,
C = 1 0 0 1 - l o n o - m o n o .
C C .
( Σ Ω ij 2 ) 1 / 2 = λ D p 1 ,
( Σ Ω ij 2 ) 1 / 2 = λ D p 2 ,
Ω - Ω = C S - S .
δ Ω ij = k = 1 1 l = 1 2 m = 1 3   δ r jl lk C im S mk ,
= x y .
( Σ δ Ω ij 2 ) 1 / 2 = λ D p m ,
δ Ω 11 = δ x   S x x + δ y   S x y - l o n o δ x   S z x + δ y   S z y ,
δ Ω 21 = δ x   S y x + δ y   S y y - m o n o δ x   S z x + δ y   S z y .
δ r = δ x 0 .
δ Ω 11 = δ x S x x - l o n o S z x ,
δ Ω 21 = δ x S y x - m o n o S z x .
δ Ω 11 = δ x   S x x , δ Ω 21 = δ x   S y x ,
S x x 2 + S y x 2 1 / 2 = λ D δ xp m .
S x x = λ D δ xp m cos   ϕ , S y x = λ D δ xp m sin   ϕ ,
ρ = 2 dD q ,
S h = 1.22 λ D t ,
p m = λ D ∊δ x ,
= S x x 2 + S y x 2 1 / 2 .
p m dD q .
min = λ q δ xd = λ 1 + m f δ x ,
o min = λ 1 + m f m δ x .
p m 5 S h .

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