Abstract

Digital speckle-pattern interferometry systems for automatic measurement of deformations of a diffuse object are presented, which are based on a fringe scanning method with phase-shifted speckle interferograms. A digital speckle pattern before deformation of an object is recorded in the mass storage device of a computer facility. After deformation, four digital speckle patterns are recorded as changing the phase of reference light such as 0, π/2, π, and 3π/2, respectively. Four speckle interferograms, whose phases are shifted by 0, π/2, π, and 3π/2, are generated by calculating the square of the differences between speckle patterns before and after deformation. These interferograms are low-pass filtered to reduce speckle noise. The calculation of the arctangent with four phase-shifted speckle interferograms gives the optical path difference which is proportional to the deformation. A correction of the discontinuity of the calculated phase gives the numerical data of the deformation in the whole object area. Some experimental results for the measurement of out-of-plane, in-plane, and 3-D deformations are presented.

© 1985 Optical Society of America

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References

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  1. A. E. Ennos, “Speckle Interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer, Berlin, 1975), Vol. 9, pp. 203–253.
    [Crossref]
  2. J. N. Butters, J. A. Leendertz, “Speckle Pattern and Holographic Techniques in Engineering Metrology,” Opt. Laser Technol. 3, 26 (1971).
    [Crossref]
  3. O. J. Løkbrg, O. M. Holje, H. M. Pedersen, “Scan Converter Memory Used in TV-Speckle Interferometry,” Opt. Laser Technol. 8, 17 (1976).
    [Crossref]
  4. S. Nakadate, T. Yatagai, H. Saito, “Electronic Speckle Pattern Interferometry Using Digital Image Processing Techniques,” Appl. Opt. 19, 1879 (1980).
    [Crossref] [PubMed]
  5. S. Nakadate, T. Yatagai, H. Saito, “Computer-Aided Speckle Pattern Interferometry,” Appl. Opt. 22, 237 (1983).
    [Crossref] [PubMed]
  6. R. Dändliker, B. Ineichen, F. M. Mottier, “High Resolution Hologram Interferometry by Electronic Phase Measurement,” Opt. Commun. 9, 412 (1973).
    [Crossref]
  7. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital Wavefront Measuring Interferometer for Testing Optical Surfaces and Lenses,” Appl. Opt. 13, 2693 (1974).
    [Crossref] [PubMed]
  8. M. Takeda, H. Ina, S. Kobayashi, “Fourier-Transform Method of Fringe-Pattern Analysis for Computer-Based Topography and Interferometry,” J. Opt. Soc. Am. 72, 156 (1982).
    [Crossref]
  9. G. E. Sommargren, “Double-Exposure Holographic Interferometry Using Commonpath Reference Waves,” Appl. Opt. 16, 1736 (1977).
    [Crossref] [PubMed]
  10. P. Hariharan, B. F. Oreb, N. Brown, “Real-Time Holographic Interferometry: a Microcomputer System for the Measurement of Vector Displacements,” Appl. Opt. 22, 876 (1983).
    [Crossref] [PubMed]
  11. S. Nakadate, H. Saito, “Fringe Scanning Holographic and Speckle Interferometers for Deformation Measurements,” Kogaku (Jpn. J. Opt.) 13, 299 (1984), in Japanese.
  12. S. Nakadate, N. Magome, T. Honda, J. Tsujiuchi, “Hybrid Holographic Interferometer for Measuring Three-Dimensional Deformations,” Opt. Eng. 20, 246 (1981).
    [Crossref]
  13. S. Nakadate, T. Yatagai, H. Saito, “Digital Speckle-Pattern Shearing Interferometry,” Appl. Opt. 19, 4241 (1980).
    [Crossref] [PubMed]

1984 (1)

S. Nakadate, H. Saito, “Fringe Scanning Holographic and Speckle Interferometers for Deformation Measurements,” Kogaku (Jpn. J. Opt.) 13, 299 (1984), in Japanese.

1983 (2)

1982 (1)

1981 (1)

S. Nakadate, N. Magome, T. Honda, J. Tsujiuchi, “Hybrid Holographic Interferometer for Measuring Three-Dimensional Deformations,” Opt. Eng. 20, 246 (1981).
[Crossref]

1980 (2)

1977 (1)

1976 (1)

O. J. Løkbrg, O. M. Holje, H. M. Pedersen, “Scan Converter Memory Used in TV-Speckle Interferometry,” Opt. Laser Technol. 8, 17 (1976).
[Crossref]

1974 (1)

1973 (1)

R. Dändliker, B. Ineichen, F. M. Mottier, “High Resolution Hologram Interferometry by Electronic Phase Measurement,” Opt. Commun. 9, 412 (1973).
[Crossref]

1971 (1)

J. N. Butters, J. A. Leendertz, “Speckle Pattern and Holographic Techniques in Engineering Metrology,” Opt. Laser Technol. 3, 26 (1971).
[Crossref]

Brangaccio, D. J.

Brown, N.

Bruning, J. H.

Butters, J. N.

J. N. Butters, J. A. Leendertz, “Speckle Pattern and Holographic Techniques in Engineering Metrology,” Opt. Laser Technol. 3, 26 (1971).
[Crossref]

Dändliker, R.

R. Dändliker, B. Ineichen, F. M. Mottier, “High Resolution Hologram Interferometry by Electronic Phase Measurement,” Opt. Commun. 9, 412 (1973).
[Crossref]

Ennos, A. E.

A. E. Ennos, “Speckle Interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer, Berlin, 1975), Vol. 9, pp. 203–253.
[Crossref]

Gallagher, J. E.

Hariharan, P.

Herriott, D. R.

Holje, O. M.

O. J. Løkbrg, O. M. Holje, H. M. Pedersen, “Scan Converter Memory Used in TV-Speckle Interferometry,” Opt. Laser Technol. 8, 17 (1976).
[Crossref]

Honda, T.

S. Nakadate, N. Magome, T. Honda, J. Tsujiuchi, “Hybrid Holographic Interferometer for Measuring Three-Dimensional Deformations,” Opt. Eng. 20, 246 (1981).
[Crossref]

Ina, H.

Ineichen, B.

R. Dändliker, B. Ineichen, F. M. Mottier, “High Resolution Hologram Interferometry by Electronic Phase Measurement,” Opt. Commun. 9, 412 (1973).
[Crossref]

Kobayashi, S.

Leendertz, J. A.

J. N. Butters, J. A. Leendertz, “Speckle Pattern and Holographic Techniques in Engineering Metrology,” Opt. Laser Technol. 3, 26 (1971).
[Crossref]

Løkbrg, O. J.

O. J. Løkbrg, O. M. Holje, H. M. Pedersen, “Scan Converter Memory Used in TV-Speckle Interferometry,” Opt. Laser Technol. 8, 17 (1976).
[Crossref]

Magome, N.

S. Nakadate, N. Magome, T. Honda, J. Tsujiuchi, “Hybrid Holographic Interferometer for Measuring Three-Dimensional Deformations,” Opt. Eng. 20, 246 (1981).
[Crossref]

Mottier, F. M.

R. Dändliker, B. Ineichen, F. M. Mottier, “High Resolution Hologram Interferometry by Electronic Phase Measurement,” Opt. Commun. 9, 412 (1973).
[Crossref]

Nakadate, S.

S. Nakadate, H. Saito, “Fringe Scanning Holographic and Speckle Interferometers for Deformation Measurements,” Kogaku (Jpn. J. Opt.) 13, 299 (1984), in Japanese.

S. Nakadate, T. Yatagai, H. Saito, “Computer-Aided Speckle Pattern Interferometry,” Appl. Opt. 22, 237 (1983).
[Crossref] [PubMed]

S. Nakadate, N. Magome, T. Honda, J. Tsujiuchi, “Hybrid Holographic Interferometer for Measuring Three-Dimensional Deformations,” Opt. Eng. 20, 246 (1981).
[Crossref]

S. Nakadate, T. Yatagai, H. Saito, “Digital Speckle-Pattern Shearing Interferometry,” Appl. Opt. 19, 4241 (1980).
[Crossref] [PubMed]

S. Nakadate, T. Yatagai, H. Saito, “Electronic Speckle Pattern Interferometry Using Digital Image Processing Techniques,” Appl. Opt. 19, 1879 (1980).
[Crossref] [PubMed]

Oreb, B. F.

Pedersen, H. M.

O. J. Løkbrg, O. M. Holje, H. M. Pedersen, “Scan Converter Memory Used in TV-Speckle Interferometry,” Opt. Laser Technol. 8, 17 (1976).
[Crossref]

Rosenfeld, D. P.

Saito, H.

Sommargren, G. E.

Takeda, M.

Tsujiuchi, J.

S. Nakadate, N. Magome, T. Honda, J. Tsujiuchi, “Hybrid Holographic Interferometer for Measuring Three-Dimensional Deformations,” Opt. Eng. 20, 246 (1981).
[Crossref]

White, A. D.

Yatagai, T.

Appl. Opt. (6)

J. Opt. Soc. Am. (1)

Kogaku (Jpn. J. Opt.) (1)

S. Nakadate, H. Saito, “Fringe Scanning Holographic and Speckle Interferometers for Deformation Measurements,” Kogaku (Jpn. J. Opt.) 13, 299 (1984), in Japanese.

Opt. Commun. (1)

R. Dändliker, B. Ineichen, F. M. Mottier, “High Resolution Hologram Interferometry by Electronic Phase Measurement,” Opt. Commun. 9, 412 (1973).
[Crossref]

Opt. Eng. (1)

S. Nakadate, N. Magome, T. Honda, J. Tsujiuchi, “Hybrid Holographic Interferometer for Measuring Three-Dimensional Deformations,” Opt. Eng. 20, 246 (1981).
[Crossref]

Opt. Laser Technol. (2)

J. N. Butters, J. A. Leendertz, “Speckle Pattern and Holographic Techniques in Engineering Metrology,” Opt. Laser Technol. 3, 26 (1971).
[Crossref]

O. J. Løkbrg, O. M. Holje, H. M. Pedersen, “Scan Converter Memory Used in TV-Speckle Interferometry,” Opt. Laser Technol. 8, 17 (1976).
[Crossref]

Other (1)

A. E. Ennos, “Speckle Interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer, Berlin, 1975), Vol. 9, pp. 203–253.
[Crossref]

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Figures (25)

Fig. 1
Fig. 1

Schematic diagram of the fringe scanning speckle-pattern interferometer for measuring out-of-plane deformation.

Fig. 2
Fig. 2

Schematic illustration for the determination of an absolute fringe order number.

Fig. 3
Fig. 3

Speckle interferograms in nine deformation states of the 20-mm circular object which are obtained by five iterations of averaging over 3 × 3 sample points. The out-of-plane deformation increases gradually from (a) to (i).

Fig. 4
Fig. 4

Four phase-shifted speckle interferograms, (a)–(d), in the third state of deformation, whose phases are 0, π/2, π, and 3π/2, respectively.

Fig. 5
Fig. 5

Phase distribution proportional to the deformation between the adjacent deformation states shown in Fig. 3. Phases ranging from −π to π rad are displayed as 0–255 levels on the monitor.

Fig. 6
Fig. 6

Numerical values of the out-of-plane deformation in the ninth state of the object, which is obtained by correcting discontinuities of the phases shown in Figs. 5(a)–(i), and the results are summed: (a) contour and (b) perspective representations. The interval between contours is 0.3 μm.

Fig. 7
Fig. 7

Results from eight iterations of the median filtering within an 11 × 11 sample area in Fig. 6: (a) contour and (b) perspective representations. The interval between contours is 0.3 μm.

Fig. 8
Fig. 8

Second spatial derivative proportional to the bending moment of the deformation, which is obtained by polynomial fitting to the data in each horizontal line in Fig. 7; the polynomials are differentiated: (a) contour and (b) perspective representations. The interval between contours is 5 × 10−3 (1/m).

Fig. 9
Fig. 9

Normalized histograms of the deviations between the approximated first-order polynomials and the measured value of the deformation, where the object is tilted. Lines (a) and (b) result from the correction of phase discontinuities and median filtering, respectively. The standard deviations in lines (a) and (b) are 0.0639 × 2π and 0.0489 × 2π rad, respectively.

Fig. 10
Fig. 10

Schematic diagram of the fringe scanning speckle-pattern inteferometer for measuring in-plane deformation.

Fig. 11
Fig. 11

Low-pass filtered speckle interferograms in nine states of in-plane deformation of a brass plate with a hole. The deformations increase gradually from (a) to (i).

Fig. 12
Fig. 12

Phase distribution proportional to the in-plane deformation between adjacent states of the deformations shown in Fig. 11. Phases ranging from −π to π rad are displayed as 0–255 levels on the monitor.

Fig. 13
Fig. 13

Numerical value of the in-plane deformation in the ninth state of the object, which is obtained by correcting the phase discontinuities in Figs. 12(a)–(i); the results are summed: (a) contour and (b) perspective representations. The inteval between contours is 1 μm.

Fig. 14
Fig. 14

Numerical values of the deformation result from eight iterations of the median filtering within an 11 × 11 sample area: (a) contour and (b) perspective representations. The interval between contours is 1 μm.

Fig. 15
Fig. 15

First spatial derivative of the deformation in the horizontal direction, which is proportional to the strain or stress. A twentieth-order polynomial is fitted to the data on each horizontal line in Fig. 14 and the resultant polynomial is spatially differentiated: (a) contour and (b) perspective representations. The interval between contours is equal to 1 × 10−4 strains.

Fig. 16
Fig. 16

Schematic diagram of fringe scanning speckle-pattern shearing interferometry for 3-D deformation measurement.

Fig. 17
Fig. 17

Shearing camera for fringe scanning speckle-pattern shearing interferometry.

Fig. 18
Fig. 18

Vector diagram of three illuminating directions with direction cosines. I1 and I2 represent the unit vectors of illuminating beams from the He–Ne laser; I3 represents that from the Ar-ion laser shown in Fig. 16.

Fig. 19
Fig. 19

Four phase-shifted low-pass filtered speckle interferograms in the direction of I3 in Fig. 18.

Fig. 20
Fig. 20

Phase distribution proportional to 3-D deformation of the circular object in the direction of (a) I1, (b) I2, and (c) I3. The amount of shearing is 3.6 mm in the horizontal direction. Phases ranging from −π to π rad are displayed as 0–255 levels on the monitor.

Fig. 21
Fig. 21

Phase difference proportional to the spatial derivative of the deformation, which results from the correction of phase discontinuities and eight iterations of the median filtering within an 11 × 11 sample area: (a) contour and (b) perspective representations. The interval between contours is 2π rad.

Fig. 22
Fig. 22

Phase distributions proportional to 3-D deformation using the illuminating beams of (a) I1, (b) I2, and (c) I3 which are obtained by successive summation in the horizontal direction using data shown in Fig. 21.

Fig. 23
Fig. 23

The Z component w of 3-D deformation: (a) contour and (b) perspective representations. The interval between contours is 0.5 μm.

Fig. 24
Fig. 24

Second spatial derivative in the horizontal direction, 2w/∂x2, using the data shown in Fig. 23, which is proportional to the bending moment: (a) contour and (b) perspective representations. The interval between contours is 1 × 10−5 (1/m).

Fig. 25
Fig. 25

First spatial derivative of the in-plane deformation component in the horizontal direction, ∂u/∂x: (a) contour and (b) perspective representations. The interval between contours is 1 × 10−5 strains.

Equations (9)

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Φ = tan 1 [ I 4 I 2 I 1 I 3 ] .
d z = θ 2 π λ 2
d x = λ 2 sin θ ϕ 2 π ,
Θ i = 2 π λ i [ l i δ u + m i δ υ + ( 1 + n i ) δ w ] ,
Δ i = 2 π λ i [ l i δ u + m i υ + ( 1 + n i ) w ] .
Δ = A d ,
Δ = 1 2 π [ Δ 1 λ 1 Δ 2 λ 2 Δ 3 λ 3 ] , d = [ u υ w ] ,
A = [ l 1 m 1 1 + n 1 l 2 m 2 1 + n 2 l 3 m 3 1 + n 3 ]
d = A 1 Δ ,

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