Abstract

An optical system for the parallel evaluation of in-plane and out-of-plane deformations is described. The object is illuminated from two different directions and imaged onto a CCD sensor. Each illumination interferes with its corresponding reference beam. This produces two sensitivity vectors. The references have different directions in order to produce two-directional spatial carriers. Two separate interferograms of an object under test in its undeformed and deformed states are recorded. The Fourier method is used for the quantitative evaluation. The measurements along different sensitivity vectors are separated in the Fourier domain. The phases of the two interferograms are obtained from the complex amplitudes, and the two-dimensional deformation is calculated from the phases. Two different arrangements (with and without a lens system) are presented together with some experimental results.

© 1997 Optical Society of America

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References

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  1. C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).
  2. R. Jones, C. Wikes, Holographic and Speckle Interferometry, 2nd ed., Vol. 6 of Cambridge Studies in Modern Optics (Cambridge U. Press, Cambridge, 1989).
  3. M. Kujawinska, J. Wojciak, “Spatial phase shifting techniques of fringe pattern analysis in photomechanics,” in Second International Conference on Photomechanics and Speckle Metrology: Moiré Techniques, Holographic Interferometry, Optical NDT, and Applications to Fluid Mechanics, F. Chiang, ed., Proc. SPIE1554B, 503–513 (1991).
  4. D. C. Williams, N. S. Nassar, J. E. Banyard, M. S. Virdiee, “Digital phase-step interferometry: a simplified approach,” Opt. Laser Technol. 23, 147–150 (1991).
    [CrossRef]
  5. G. Pedrini, B. Pfister, H. J. Tiziani, “Double pulse-electronic speckle interferometry,” J. Mod. Opt. 40, 89–96 (1993).
    [CrossRef]
  6. G. Pedrini, H. J. Tiziani, “Double pulse-electronic speckle interferometry for vibration analysis,” Appl. Opt. 33, 7857–7863 (1994).
    [CrossRef] [PubMed]
  7. W. W. Macy, “Real time fringe-pattern analysis,” Appl. Opt. 22, 3898–3901 (1983).
    [CrossRef]
  8. M. Takeda, I. Hideki, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72, 156–160 (1982).
    [CrossRef]
  9. U. Schnars, “Direct phase determination in hologram interferometry with use of digitally recorded holograms,” J. Opt. Soc. Am. A 11, 2011–2015 (1994).
    [CrossRef]
  10. G. Pedrini, Y. L. Zou, H. J. Tiziani, “Digital Double Pulse-Holographic Interferometry for Vibration Analysis,” J. Mod. Opt. 42, 367–374 (1995).
    [CrossRef]
  11. G. Pedrini, H. J. Tiziani, “Digital double pulse-holographic interferometry using Fresnel and image plane holograms,” Measurement 15, 251–260 (1995).
    [CrossRef]
  12. G. Pedrini, H. J. Tiziani, Y. Zou, “Digital double pulse-TV-holography,” Opt. Laser Eng. 26, 199–219 (1997).
    [CrossRef]
  13. R. Dändliker, “Two-reference-beam holographic interferometry,” in Holographic Interferometry, P. K. Rastogi, ed., Vol. 68 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1994), pp. 75–108.
    [CrossRef]
  14. V. Linet, X. Bohineust, F. Dupuy, “Three dimensional dynamic analysis of parts of automobile body by holographic interferometry,” in Proceedings of the Third French–German Congress on Application of Holography, St. Louis, France, 20–22 November 1991.

1997

G. Pedrini, H. J. Tiziani, Y. Zou, “Digital double pulse-TV-holography,” Opt. Laser Eng. 26, 199–219 (1997).
[CrossRef]

1995

G. Pedrini, Y. L. Zou, H. J. Tiziani, “Digital Double Pulse-Holographic Interferometry for Vibration Analysis,” J. Mod. Opt. 42, 367–374 (1995).
[CrossRef]

G. Pedrini, H. J. Tiziani, “Digital double pulse-holographic interferometry using Fresnel and image plane holograms,” Measurement 15, 251–260 (1995).
[CrossRef]

1994

1993

G. Pedrini, B. Pfister, H. J. Tiziani, “Double pulse-electronic speckle interferometry,” J. Mod. Opt. 40, 89–96 (1993).
[CrossRef]

1991

D. C. Williams, N. S. Nassar, J. E. Banyard, M. S. Virdiee, “Digital phase-step interferometry: a simplified approach,” Opt. Laser Technol. 23, 147–150 (1991).
[CrossRef]

1983

1982

M. Takeda, I. Hideki, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72, 156–160 (1982).
[CrossRef]

Banyard, J. E.

D. C. Williams, N. S. Nassar, J. E. Banyard, M. S. Virdiee, “Digital phase-step interferometry: a simplified approach,” Opt. Laser Technol. 23, 147–150 (1991).
[CrossRef]

Bohineust, X.

V. Linet, X. Bohineust, F. Dupuy, “Three dimensional dynamic analysis of parts of automobile body by holographic interferometry,” in Proceedings of the Third French–German Congress on Application of Holography, St. Louis, France, 20–22 November 1991.

Dändliker, R.

R. Dändliker, “Two-reference-beam holographic interferometry,” in Holographic Interferometry, P. K. Rastogi, ed., Vol. 68 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1994), pp. 75–108.
[CrossRef]

Dupuy, F.

V. Linet, X. Bohineust, F. Dupuy, “Three dimensional dynamic analysis of parts of automobile body by holographic interferometry,” in Proceedings of the Third French–German Congress on Application of Holography, St. Louis, France, 20–22 November 1991.

Hideki, I.

M. Takeda, I. Hideki, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72, 156–160 (1982).
[CrossRef]

Jones, R.

R. Jones, C. Wikes, Holographic and Speckle Interferometry, 2nd ed., Vol. 6 of Cambridge Studies in Modern Optics (Cambridge U. Press, Cambridge, 1989).

Kobayashi, S.

M. Takeda, I. Hideki, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72, 156–160 (1982).
[CrossRef]

Kujawinska, M.

M. Kujawinska, J. Wojciak, “Spatial phase shifting techniques of fringe pattern analysis in photomechanics,” in Second International Conference on Photomechanics and Speckle Metrology: Moiré Techniques, Holographic Interferometry, Optical NDT, and Applications to Fluid Mechanics, F. Chiang, ed., Proc. SPIE1554B, 503–513 (1991).

Linet, V.

V. Linet, X. Bohineust, F. Dupuy, “Three dimensional dynamic analysis of parts of automobile body by holographic interferometry,” in Proceedings of the Third French–German Congress on Application of Holography, St. Louis, France, 20–22 November 1991.

Macy, W. W.

Nassar, N. S.

D. C. Williams, N. S. Nassar, J. E. Banyard, M. S. Virdiee, “Digital phase-step interferometry: a simplified approach,” Opt. Laser Technol. 23, 147–150 (1991).
[CrossRef]

Pedrini, G.

G. Pedrini, H. J. Tiziani, Y. Zou, “Digital double pulse-TV-holography,” Opt. Laser Eng. 26, 199–219 (1997).
[CrossRef]

G. Pedrini, H. J. Tiziani, “Digital double pulse-holographic interferometry using Fresnel and image plane holograms,” Measurement 15, 251–260 (1995).
[CrossRef]

G. Pedrini, Y. L. Zou, H. J. Tiziani, “Digital Double Pulse-Holographic Interferometry for Vibration Analysis,” J. Mod. Opt. 42, 367–374 (1995).
[CrossRef]

G. Pedrini, H. J. Tiziani, “Double pulse-electronic speckle interferometry for vibration analysis,” Appl. Opt. 33, 7857–7863 (1994).
[CrossRef] [PubMed]

G. Pedrini, B. Pfister, H. J. Tiziani, “Double pulse-electronic speckle interferometry,” J. Mod. Opt. 40, 89–96 (1993).
[CrossRef]

Pfister, B.

G. Pedrini, B. Pfister, H. J. Tiziani, “Double pulse-electronic speckle interferometry,” J. Mod. Opt. 40, 89–96 (1993).
[CrossRef]

Schnars, U.

Takeda, M.

M. Takeda, I. Hideki, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72, 156–160 (1982).
[CrossRef]

Tiziani, H. J.

G. Pedrini, H. J. Tiziani, Y. Zou, “Digital double pulse-TV-holography,” Opt. Laser Eng. 26, 199–219 (1997).
[CrossRef]

G. Pedrini, H. J. Tiziani, “Digital double pulse-holographic interferometry using Fresnel and image plane holograms,” Measurement 15, 251–260 (1995).
[CrossRef]

G. Pedrini, Y. L. Zou, H. J. Tiziani, “Digital Double Pulse-Holographic Interferometry for Vibration Analysis,” J. Mod. Opt. 42, 367–374 (1995).
[CrossRef]

G. Pedrini, H. J. Tiziani, “Double pulse-electronic speckle interferometry for vibration analysis,” Appl. Opt. 33, 7857–7863 (1994).
[CrossRef] [PubMed]

G. Pedrini, B. Pfister, H. J. Tiziani, “Double pulse-electronic speckle interferometry,” J. Mod. Opt. 40, 89–96 (1993).
[CrossRef]

Vest, C. M.

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).

Virdiee, M. S.

D. C. Williams, N. S. Nassar, J. E. Banyard, M. S. Virdiee, “Digital phase-step interferometry: a simplified approach,” Opt. Laser Technol. 23, 147–150 (1991).
[CrossRef]

Wikes, C.

R. Jones, C. Wikes, Holographic and Speckle Interferometry, 2nd ed., Vol. 6 of Cambridge Studies in Modern Optics (Cambridge U. Press, Cambridge, 1989).

Williams, D. C.

D. C. Williams, N. S. Nassar, J. E. Banyard, M. S. Virdiee, “Digital phase-step interferometry: a simplified approach,” Opt. Laser Technol. 23, 147–150 (1991).
[CrossRef]

Wojciak, J.

M. Kujawinska, J. Wojciak, “Spatial phase shifting techniques of fringe pattern analysis in photomechanics,” in Second International Conference on Photomechanics and Speckle Metrology: Moiré Techniques, Holographic Interferometry, Optical NDT, and Applications to Fluid Mechanics, F. Chiang, ed., Proc. SPIE1554B, 503–513 (1991).

Zou, Y.

G. Pedrini, H. J. Tiziani, Y. Zou, “Digital double pulse-TV-holography,” Opt. Laser Eng. 26, 199–219 (1997).
[CrossRef]

Zou, Y. L.

G. Pedrini, Y. L. Zou, H. J. Tiziani, “Digital Double Pulse-Holographic Interferometry for Vibration Analysis,” J. Mod. Opt. 42, 367–374 (1995).
[CrossRef]

Appl. Opt.

J. Mod. Opt.

G. Pedrini, B. Pfister, H. J. Tiziani, “Double pulse-electronic speckle interferometry,” J. Mod. Opt. 40, 89–96 (1993).
[CrossRef]

G. Pedrini, Y. L. Zou, H. J. Tiziani, “Digital Double Pulse-Holographic Interferometry for Vibration Analysis,” J. Mod. Opt. 42, 367–374 (1995).
[CrossRef]

J. Opt. Soc. Am. A

M. Takeda, I. Hideki, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72, 156–160 (1982).
[CrossRef]

U. Schnars, “Direct phase determination in hologram interferometry with use of digitally recorded holograms,” J. Opt. Soc. Am. A 11, 2011–2015 (1994).
[CrossRef]

Measurement

G. Pedrini, H. J. Tiziani, “Digital double pulse-holographic interferometry using Fresnel and image plane holograms,” Measurement 15, 251–260 (1995).
[CrossRef]

Opt. Laser Eng.

G. Pedrini, H. J. Tiziani, Y. Zou, “Digital double pulse-TV-holography,” Opt. Laser Eng. 26, 199–219 (1997).
[CrossRef]

Opt. Laser Technol.

D. C. Williams, N. S. Nassar, J. E. Banyard, M. S. Virdiee, “Digital phase-step interferometry: a simplified approach,” Opt. Laser Technol. 23, 147–150 (1991).
[CrossRef]

Other

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).

R. Jones, C. Wikes, Holographic and Speckle Interferometry, 2nd ed., Vol. 6 of Cambridge Studies in Modern Optics (Cambridge U. Press, Cambridge, 1989).

M. Kujawinska, J. Wojciak, “Spatial phase shifting techniques of fringe pattern analysis in photomechanics,” in Second International Conference on Photomechanics and Speckle Metrology: Moiré Techniques, Holographic Interferometry, Optical NDT, and Applications to Fluid Mechanics, F. Chiang, ed., Proc. SPIE1554B, 503–513 (1991).

R. Dändliker, “Two-reference-beam holographic interferometry,” in Holographic Interferometry, P. K. Rastogi, ed., Vol. 68 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1994), pp. 75–108.
[CrossRef]

V. Linet, X. Bohineust, F. Dupuy, “Three dimensional dynamic analysis of parts of automobile body by holographic interferometry,” in Proceedings of the Third French–German Congress on Application of Holography, St. Louis, France, 20–22 November 1991.

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Figures (7)

Fig. 1
Fig. 1

Experimental setup for 2-D measurements with the two-directional spatial carrier: O, object; L’s, lenses; AP, aperture; BS’s, beam splitters; M’s, mirrors.

Fig. 2
Fig. 2

Spectrum of a hologram recorded with a two-directional spatial carrier (two references).

Fig. 3
Fig. 3

Out-of-plane deformation of an edge-clamped plate. (a) and (b) are the phase maps that correspond to the displacement along the sensitivity vectors s 1 and s 2, respectively. (c) and (d) are the phase maps that correspond to the out-of-plane (along s 1 + s 2) and in-plane (along s 2 - s 1) displacements, respectively.

Fig. 4
Fig. 4

In-plane rotation of a plate. (a) and (b) are the phase maps that correspond to the displacement along the sensitivity vectors s 1 and s 2, respectively. (c) and (d) are the phase maps that correspond to the out-of-plane and in-plane displacements, respectively.

Fig. 5
Fig. 5

Experimental setup for 2-D measurements by use of two-reference digital holography.

Fig. 6
Fig. 6

Out-of-plane deformation of a plate. (a) Reconstruction of the digital hologram recorded, (b) phase maps that correspond to the displacement along the sensitivity vectors s 1 and s 2. (c) and (d) are the phase maps that correspond to the out-of-plane and in-plane displacements, respectively.

Fig. 7
Fig. 7

In-plane rotation of a plate. (a) Reconstruction of the digital hologram recorded with two references and two illuminations, (b) phase maps that correspond to the displacement along the sensitivities vectors s 1 and s 2. (c) and (d) are the phase maps that correspond to the out-of-plane and in-plane displacements, respectively.

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

r1x,y=r1x,yexp-2πisinθ1λx,
u1x,y=u1x,yexpiϕ1x,y,
I1=r1x, y2+u1x, y2+r1x, yu1*x, y+r1*x, yu1x, y,
I1x, y=r1x, y2+u1x, y2+r1x, yu1x, yexpiϕ1x, y+2πf1x+r1x, yu1x, yexp-iϕ1x, y+2πf1x,
r2x, y=r2x, yexp-2πisinθ2λy,
u2x, y=u2x, yexpiϕ2x, y,
I2x, y=r2x, y2+u2x, y2+r2x, yu2x, yexpiϕ2x, y+2πf2y+r2x, yu2x, yexp-iϕ2x, y+2πf2y.
Ix, y=I1x, y+I2x, y.
FTI=δfx, fy+U1fx, fyU1* fx, fy+U2fx, fyU2*fx, fy+U1fx-f1, fy+U1*fx+f1, fy+U2fx, fy-f2+U2*fx, fy+f2,
ϕ1x, y-2πxf1=arctanImv1Rev1,
ϕ2x, y-2πyf2=arctanImv2Rev2.
u1x, y=u1x, yexpiϕ1x, y,
u2x, y=u2x, yexpiϕ2x, y,
Δϕ1=ϕ1-ϕ1=2πλd·s1,
Δϕ2=ϕ2-ϕ2=2πλd·s2
si=ki-ko,  i=1, 2;
Δϕz=Δϕ1+Δϕ2=2πλd·s1+s2,
Δϕx=Δϕ2-Δϕ1=2πλd·s2-s1.

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