Abstract

The three deformation components x, y, z of a vibrating object are measured simultaneously by use of digital holography with a double-pulse ruby laser source. The object is illuminated from three different directions, each optically path matched with three reference beams such that three independent digital holograms are formed and added incoherently in one single CCD image. The optical phase difference between the two recordings taken for each hologram is quantitatively evaluated by the Fourier-transform method so that a set of three phase maps is obtained, representing the deformation along three sensitivity vectors. The total object deformation is obtained as a vector resultant from the data of the three phase maps. To give the full three-dimensional (3-D) description, the shape of the object is measured by the two-wavelength contouring method. Experiments are performed with a cylinder as the test object, transiently and harmonically excited. The 3-D deformation and shape measurement results are presented graphically.

© 1999 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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1999

1998

1997

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

G. Pedrini, H. J. Tiziani, “Quantitative evaluation of two-dimensional dynamic deformations using digital holography,” Opt. Laser Technol. 29, 249–256 (1997).
[CrossRef]

A. Fernadéz, A. J. Moore, C. Pérez-López, A. F. Doval, J. Blanco-García, “Study of transient deformations with pulsed TV holography: application to crack detection,” Appl. Opt. 36, 2058–2065 (1997).
[CrossRef]

1994

1992

1982

Blanco-García, J.

Doval, A. F.

Ettemeyer, A.

Z. Wang, T. Walz, H. R. Schubach, A. Ettemeyer, “Three-dimensional pulsed ESPI: technique of analysis of dynamic problems,” in Optical Measurement Systems for Industrial Inspection, M. Kujawinska, W. Osten, eds., Proc SPIE3824, (to be published).

Fernadéz, A.

Fröning, P.

Gren, P.

Gusev, M. E.

Ina, H.

Kerr, D.

Kobayashi, S.

Li, X.

Mendoza Santoyo, F.

Moore, A. J.

Pedrini, G.

G. Pedrini, P. Fröning, H. J. Tiziani, M. E. Gusev, “Pulsed digital holography for high-speed contouring that uses the two-wavelength method,” Appl. Opt. 38, 3460–3467 (1999).
[CrossRef]

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

G. Pedrini, H. J. Tiziani, “Quantitative evaluation of two-dimensional dynamic deformations using digital holography,” Opt. Laser Technol. 29, 249–256 (1997).
[CrossRef]

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

Pérez-López, C.

Rodríguez Vera, R.

Schedin, S.

Schubach, H. R.

Z. Wang, T. Walz, H. R. Schubach, A. Ettemeyer, “Three-dimensional pulsed ESPI: technique of analysis of dynamic problems,” in Optical Measurement Systems for Industrial Inspection, M. Kujawinska, W. Osten, eds., Proc SPIE3824, (to be published).

Spooren, R.

R. Spooren, “Double-pulse subtraction TV holography,” Opt. Eng. 31, 1000–1007 (1992).
[CrossRef]

Takeda, M.

Tiziani, H. J.

G. Pedrini, P. Fröning, H. J. Tiziani, M. E. Gusev, “Pulsed digital holography for high-speed contouring that uses the two-wavelength method,” Appl. Opt. 38, 3460–3467 (1999).
[CrossRef]

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

G. Pedrini, H. J. Tiziani, “Quantitative evaluation of two-dimensional dynamic deformations using digital holography,” Opt. Laser Technol. 29, 249–256 (1997).
[CrossRef]

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

Vest, C. M.

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

Walz, T.

Z. Wang, T. Walz, H. R. Schubach, A. Ettemeyer, “Three-dimensional pulsed ESPI: technique of analysis of dynamic problems,” in Optical Measurement Systems for Industrial Inspection, M. Kujawinska, W. Osten, eds., Proc SPIE3824, (to be published).

Wang, Z.

Z. Wang, T. Walz, H. R. Schubach, A. Ettemeyer, “Three-dimensional pulsed ESPI: technique of analysis of dynamic problems,” in Optical Measurement Systems for Industrial Inspection, M. Kujawinska, W. Osten, eds., Proc SPIE3824, (to be published).

Zou, Y.

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

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Eng.

R. Spooren, “Double-pulse subtraction TV holography,” Opt. Eng. 31, 1000–1007 (1992).
[CrossRef]

Opt. Laser Technol.

G. Pedrini, H. J. Tiziani, “Quantitative evaluation of two-dimensional dynamic deformations using digital holography,” Opt. Laser Technol. 29, 249–256 (1997).
[CrossRef]

Opt. Lasers Eng.

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

Other

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

Z. Wang, T. Walz, H. R. Schubach, A. Ettemeyer, “Three-dimensional pulsed ESPI: technique of analysis of dynamic problems,” in Optical Measurement Systems for Industrial Inspection, M. Kujawinska, W. Osten, eds., Proc SPIE3824, (to be published).

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Figures (7)

Fig. 1
Fig. 1

Experimental setup for three-dimensional measurement with simultaneous recording of three digital holograms corresponding to the illumination directions k1, k2, and k3. AP, aperture; BS, beam splitter; DL1 and DL2, delay lines; L, lenses, M, mirrors; NL, negative lens; PM, parabolic mirrors; R1, R2, and R3, reference beams; s1, s2, and s3, sensitivity vectors.

Fig. 2
Fig. 2

Schematic spectrum of hologram consisting of three incoherently added interference patterns (three references)

Fig. 3
Fig. 3

Dimensions and coordinate system for the test cylinder.

Fig. 4
Fig. 4

Measurement of the cylinder vibrating harmonically at 1092 Hz. The pulse separation was 150 µs. (a), (b), and (c) are wrapped phase maps corresponding to the illumination directions k1, k2, and k3 , respectively (see Fig. 1).

Fig. 5
Fig. 5

Deformation of the cylinder surface in (a) the normal direction and in (b) the tangential direction overlaid on the results from the shape contouring measurement. The cylinder was harmonically vibrating at 1092 Hz.

Fig. 6
Fig. 6

Transient bending wave propagation in the cylinder at 150 µs after impact by a shock pulse. (a), (b), and (c) are wrapped phase maps corresponding to the illumination directions k1, k2, and k3 , respectively, (see Fig. 1).

Fig. 7
Fig. 7

Deformation of the cylinder surface at 150 µs after impact by a shock pulse in (a) the normal direction and in (b) the tangential direction overlaid on the results from the shape contouring measurement.

Equations (12)

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Iξ, η=k=13 Ikξ, η=k=13 |Rkξ, η+Ukξ, η|2=k=13|Rkξ, η|2+|Ukξ, η|2+Rkξ, ηUk*ξ, η+Rk*ξ, ηUkξ, η,
Ukξ, η=ukξ, ηexpiϕkξ, η,
Rkξ, η=rkξ, ηexp-2πifkξξ+fkηη,
Iξ, η=k=13 Ikξ, η=k=13akξ, η+ckξ, ηexp2πifkξξ+fkηη+ck*ξ, ηexp-2πifkξξ+fkηη,
akξ, η=uk2ξ, η+rk2ξ, η,
ckξ, η=ukξ, ηrkξ, ηexpiϕkξ, η.
FTI=k=13Akfξ, fη+Ckfξ-fkξ, fη-fkη+Ck*fξ+fkξ, fη+fkη,
ϕkξ, η=arctanImckξ, ηReckξ, η,  k=1, 2, 3.
Δϕkξ, η=ϕkξ, η-ϕkξ, η,  k=1, 2, 3.
Δϕk=2π/λu·sk,
sk=kˆk-kˆ0,  k=1, 2, 3,
uxuyuz=λ2πs1xs1ys1zs2xs2ys2zs3xs3ys3z-1Δϕ1Δϕ2Δϕ3

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