Abstract

A metrology system is presented that measures internal three-dimensional (3-D) displacement fields. The system uses a stereo pair of flash x-ray heads and correlation analysis to measure the true deformation of a layer of x-ray-absorbent particles inside the specimen. The 3-D deformation field inside blocks of polyester was determined. The polyester blocks were impacted by a 9-mm steel ball bearing fired from a 9-mm-bore gas gun at a speed of 373.5 ± 3.0 m s-1. At a given time after impact, a short-duration (30 ns) flash x-ray pulse exposes the x-ray radiographs and freezes the events during impact. Thereafter, the x-ray radiographs are scanned into a personal computer and analyzed as in digital speckle photography.

© 1999 Optical Society of America

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References

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  1. P. Synnergren, H. T. Goldrein, W. G. Proud, “Application of digital speckle photography to flash x-ray studies of internal deformation fields in impact experiments,” Appl. Opt. 38, 4030–4036 (1999).
    [CrossRef]
  2. J. E. Field, “High-speed photography at the Cavendish,” in High-Speed Photography and Photonics, S. F. Ray, ed. (Focal, London, UK, 1997), Chap. 21, pp. 301–314.
  3. N. K. Bourne, L. C. Forde, J. C. F. Millett, J. E. Field, “Impact and penetration of a borosilicate glass,” J. Phys. IV France Colloq. C3 7, 157–162 (1997).
  4. J. Pryputniewicz, “Quantitative determination of displacements and strains from holograms,” in Holographic Interferometry, P. K. Rastogi, ed. (Springer-Verlag, Berlin, 1994).
    [CrossRef]
  5. Y. Wang, F. P. Chiang, “New moiré interferometry for measuring three-dimensional displacements,” Opt. Eng. 33, 2654–2658 (1994).
    [CrossRef]
  6. F. P. Chiang, D. W. Li, “Random (speckle) patterns for displacement and strain measurements: some recent advances,” Opt. Eng. 24, 936–943 (1985).
    [CrossRef]
  7. Z. L. Kahn-Jetter, T. C. Chu, “Three-dimensional displacement measurements using digital image correlation and photogrammic analysis,” Exp. Mech. 30, 10–16 (1990).
    [CrossRef]
  8. J. D. Helm, S. R. McNeill, M. A. Sutton, “Improved three-dimensional image correlation for surface displacement measurements,” Opt. Eng. 35, 1911–1920 (1996).
    [CrossRef]
  9. P. Synnergren, “Measurement of three-dimensional displacement fields and shape using electronic speckle photography,” Opt. Eng. 36, 2302–2310 (1997).
    [CrossRef]
  10. M. Sjödahl, L. R. Benckert, “Electronic speckle photography: analysis of an algorithm giving the displacement with subpixel accuracy,” Appl. Opt. 32, 2278–2284 (1993).
    [CrossRef] [PubMed]
  11. M. Sjödahl, “Electronic speckle photography: increased accuracy by nonintegral pixel shifting,” Appl. Opt. 33, 6667–6673 (1994).
    [CrossRef] [PubMed]

1999 (1)

1997 (2)

P. Synnergren, “Measurement of three-dimensional displacement fields and shape using electronic speckle photography,” Opt. Eng. 36, 2302–2310 (1997).
[CrossRef]

N. K. Bourne, L. C. Forde, J. C. F. Millett, J. E. Field, “Impact and penetration of a borosilicate glass,” J. Phys. IV France Colloq. C3 7, 157–162 (1997).

1996 (1)

J. D. Helm, S. R. McNeill, M. A. Sutton, “Improved three-dimensional image correlation for surface displacement measurements,” Opt. Eng. 35, 1911–1920 (1996).
[CrossRef]

1994 (2)

Y. Wang, F. P. Chiang, “New moiré interferometry for measuring three-dimensional displacements,” Opt. Eng. 33, 2654–2658 (1994).
[CrossRef]

M. Sjödahl, “Electronic speckle photography: increased accuracy by nonintegral pixel shifting,” Appl. Opt. 33, 6667–6673 (1994).
[CrossRef] [PubMed]

1993 (1)

1990 (1)

Z. L. Kahn-Jetter, T. C. Chu, “Three-dimensional displacement measurements using digital image correlation and photogrammic analysis,” Exp. Mech. 30, 10–16 (1990).
[CrossRef]

1985 (1)

F. P. Chiang, D. W. Li, “Random (speckle) patterns for displacement and strain measurements: some recent advances,” Opt. Eng. 24, 936–943 (1985).
[CrossRef]

Benckert, L. R.

Bourne, N. K.

N. K. Bourne, L. C. Forde, J. C. F. Millett, J. E. Field, “Impact and penetration of a borosilicate glass,” J. Phys. IV France Colloq. C3 7, 157–162 (1997).

Chiang, F. P.

Y. Wang, F. P. Chiang, “New moiré interferometry for measuring three-dimensional displacements,” Opt. Eng. 33, 2654–2658 (1994).
[CrossRef]

F. P. Chiang, D. W. Li, “Random (speckle) patterns for displacement and strain measurements: some recent advances,” Opt. Eng. 24, 936–943 (1985).
[CrossRef]

Chu, T. C.

Z. L. Kahn-Jetter, T. C. Chu, “Three-dimensional displacement measurements using digital image correlation and photogrammic analysis,” Exp. Mech. 30, 10–16 (1990).
[CrossRef]

Field, J. E.

N. K. Bourne, L. C. Forde, J. C. F. Millett, J. E. Field, “Impact and penetration of a borosilicate glass,” J. Phys. IV France Colloq. C3 7, 157–162 (1997).

J. E. Field, “High-speed photography at the Cavendish,” in High-Speed Photography and Photonics, S. F. Ray, ed. (Focal, London, UK, 1997), Chap. 21, pp. 301–314.

Forde, L. C.

N. K. Bourne, L. C. Forde, J. C. F. Millett, J. E. Field, “Impact and penetration of a borosilicate glass,” J. Phys. IV France Colloq. C3 7, 157–162 (1997).

Goldrein, H. T.

Helm, J. D.

J. D. Helm, S. R. McNeill, M. A. Sutton, “Improved three-dimensional image correlation for surface displacement measurements,” Opt. Eng. 35, 1911–1920 (1996).
[CrossRef]

Kahn-Jetter, Z. L.

Z. L. Kahn-Jetter, T. C. Chu, “Three-dimensional displacement measurements using digital image correlation and photogrammic analysis,” Exp. Mech. 30, 10–16 (1990).
[CrossRef]

Li, D. W.

F. P. Chiang, D. W. Li, “Random (speckle) patterns for displacement and strain measurements: some recent advances,” Opt. Eng. 24, 936–943 (1985).
[CrossRef]

McNeill, S. R.

J. D. Helm, S. R. McNeill, M. A. Sutton, “Improved three-dimensional image correlation for surface displacement measurements,” Opt. Eng. 35, 1911–1920 (1996).
[CrossRef]

Millett, J. C. F.

N. K. Bourne, L. C. Forde, J. C. F. Millett, J. E. Field, “Impact and penetration of a borosilicate glass,” J. Phys. IV France Colloq. C3 7, 157–162 (1997).

Proud, W. G.

Pryputniewicz, J.

J. Pryputniewicz, “Quantitative determination of displacements and strains from holograms,” in Holographic Interferometry, P. K. Rastogi, ed. (Springer-Verlag, Berlin, 1994).
[CrossRef]

Sjödahl, M.

Sutton, M. A.

J. D. Helm, S. R. McNeill, M. A. Sutton, “Improved three-dimensional image correlation for surface displacement measurements,” Opt. Eng. 35, 1911–1920 (1996).
[CrossRef]

Synnergren, P.

P. Synnergren, H. T. Goldrein, W. G. Proud, “Application of digital speckle photography to flash x-ray studies of internal deformation fields in impact experiments,” Appl. Opt. 38, 4030–4036 (1999).
[CrossRef]

P. Synnergren, “Measurement of three-dimensional displacement fields and shape using electronic speckle photography,” Opt. Eng. 36, 2302–2310 (1997).
[CrossRef]

Wang, Y.

Y. Wang, F. P. Chiang, “New moiré interferometry for measuring three-dimensional displacements,” Opt. Eng. 33, 2654–2658 (1994).
[CrossRef]

Appl. Opt. (3)

Exp. Mech. (1)

Z. L. Kahn-Jetter, T. C. Chu, “Three-dimensional displacement measurements using digital image correlation and photogrammic analysis,” Exp. Mech. 30, 10–16 (1990).
[CrossRef]

J. Phys. IV France Colloq. C3 (1)

N. K. Bourne, L. C. Forde, J. C. F. Millett, J. E. Field, “Impact and penetration of a borosilicate glass,” J. Phys. IV France Colloq. C3 7, 157–162 (1997).

Opt. Eng. (4)

Y. Wang, F. P. Chiang, “New moiré interferometry for measuring three-dimensional displacements,” Opt. Eng. 33, 2654–2658 (1994).
[CrossRef]

F. P. Chiang, D. W. Li, “Random (speckle) patterns for displacement and strain measurements: some recent advances,” Opt. Eng. 24, 936–943 (1985).
[CrossRef]

J. D. Helm, S. R. McNeill, M. A. Sutton, “Improved three-dimensional image correlation for surface displacement measurements,” Opt. Eng. 35, 1911–1920 (1996).
[CrossRef]

P. Synnergren, “Measurement of three-dimensional displacement fields and shape using electronic speckle photography,” Opt. Eng. 36, 2302–2310 (1997).
[CrossRef]

Other (2)

J. Pryputniewicz, “Quantitative determination of displacements and strains from holograms,” in Holographic Interferometry, P. K. Rastogi, ed. (Springer-Verlag, Berlin, 1994).
[CrossRef]

J. E. Field, “High-speed photography at the Cavendish,” in High-Speed Photography and Photonics, S. F. Ray, ed. (Focal, London, UK, 1997), Chap. 21, pp. 301–314.

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Figures (4)

Fig. 1
Fig. 1

Schematic of the stereo x-ray setup.

Fig. 2
Fig. 2

Photographs of the set-up: (a) gun and (b) target zone. (1) Steel boxes containing the x-ray heads, (2) the breech of the gun, (3) the polyester specimen in its holder, and (4) the x-ray film cartridges.

Fig. 3
Fig. 3

(a) Photograph of a polyester sample with an internal seeded layer of lead particles. (b) Positions of the lead layers of the four specimens situated at z = 0, 2, 4, 6 mm.

Fig. 4
Fig. 4

Measured 3-D deformation of the polyester samples 45 µs after impact. The radiographs in the left column show the in-plane displacement components due to the impact of a 9-mm ball bearing at 375 m s-1. The arrows show the magnitude and direction of the displacements. The right column gives the out-of-plane (z-direction) movements. The top row is from the specimen seeded at z = 0, and the remaining rows from specimens 2, 4, and 6, respectively. The ball bearing is centered at x = 14 mm in all four shots. The different projections of the shifted lead layers and the ball onto the film gives the appearance that the ball hits the target at different positions, which is not the case.

Equations (7)

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N=cos α0sin α010-sin α0cos α.
OXS1P¯ = ξOXS1PXP1¯
-n11X1-n21Y1+n31L1=1/ξn31L1-OZ1-x,-n12X1-n22Y1+n32L1=1/ξn32L1-OZ1-y,-n13X1-n23Y1+n33L1=1/ξn33L1-OZ1-z,
X1=L1x cos α+z sin αL1-OZ1+x sin α-z cos α, Y1=L1yL1-OZ1+x sin α-z cos α.
X2=L2x cos α-z sin αL2-OZ2+x sin α-z cos α, Y2=L2yL2-OZ2+x sin α-z cos α.
X1+U1=L1x+ucos α+z+wsin αL1-OZ1+x+usin α-z+wcos α, Y1+V1=L1y+vL1-OZ1+x+usin α-z+wcos α,
X2+U2=L2x+ucos α-z+wsin αL2-OZ2-x+usin α-z+wcos α, Y2+V2=L2y+vL2-OZ2-x+usin α-z+wcos α.

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