Abstract

A method for whole-field noncontact measurement of displacement, velocity, and acceleration of a vibrating object based on image-plane digital holography is presented. A series of digital holograms of a vibrating object are captured by use of a high-speed CCD camera. The result of the reconstruction is a three-dimensional complex-valued matrix with noise. We apply Fourier analysis and windowed Fourier analysis in both the spatial and the temporal domains to extract the displacement, the velocity, and the acceleration. The instantaneous displacement is obtained by temporal unwrapping of the filtered phase map, whereas the velocity and acceleration are evaluated by Fourier analysis and by windowed Fourier analysis along the time axis. The combination of digital holography and temporal Fourier analyses allows for evaluation of the vibration, without a phase ambiguity problem, and smooth spatial distribution of instantaneous displacement, velocity, and acceleration of each instant are obtained. The comparison of Fourier analysis and windowed Fourier analysis in velocity and acceleration measurements is also presented.

© 2007 Optical Society of America

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2006 (3)

2005 (3)

2004 (3)

Y. Fu, C. J. Tay, C. Quan, and L. J. Chen, "Temporal wavelet analysis for deformation and velocity measurement in speckle interferometry," Opt. Eng. 43, 2780-2787 (2004).
[CrossRef]

F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, and G. Mills, "Vibration analysis by phase shifting digital holography," Opt. Rev. 11, 297-299 (2004).
[CrossRef]

K. Qian, "Windowed Fourier transform for fringe pattern analysis," Appl. Opt. 43, 2695-2702 (2004).
[CrossRef]

2003 (3)

1999 (2)

1998 (3)

1997 (1)

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

1996 (1)

1993 (1)

1991 (1)

S. L. Toh, H. M Shang, F. S. Chau, and C. J. Tay, "Flaw detection in composites using time-average shearography," Opt. Laser Technol. 23, 25-30 (1991).
[CrossRef]

1986 (1)

1982 (1)

1967 (1)

J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

1965 (1)

Appl. Opt. (11)

S. Nakadate, "Vibration measurement using phase-shifting time-average holographic interferometry," Appl. Opt. 25, 4155-4161 (1986).
[CrossRef] [PubMed]

J. M. Huntley and H. Saldner, "Temporal phase-unwrapping algorithm for automated interferogram analysis," Appl. Opt. 32, 3047-3052 (1993).
[CrossRef] [PubMed]

C. Joenathan, B. Franze, P. Haible, and H. J. Tiziani, "Speckle interferometry with temporal phase evaluation for measuring large-object deformation," Appl. Opt. 37, 2608-2614 (1998).
[CrossRef]

H. O. Saldner, N.-E. Molin, and K. A. Stetson, "Fourier-transform evaluation of phase data in spatially phase-biased TV holograms," Appl. Opt. 35, 332-336 (1996).
[CrossRef] [PubMed]

D. I. Farrant, G. H. Kaufmann, J. N. Petzing, J. R. Tyrer, B. F. Oreb, and D. Kerr, "Measurement of transient deformations with dual-pulse addition electronic speckle-pattern interferometry," Appl. Opt. 37, 7259-7267 (1998).
[CrossRef]

J. M. Huntley, G. H. Kaufmann, and D. Kerr, "Phase-shifted dynamic speckle pattern interferometry at 1 kHz," Appl. Opt. 38, 6556-6563 (1999).
[CrossRef]

S. Schedin, G. Pedrini, H. J. Tiziani, and F. M. Santoyo, "Simultaneous three-dimensional dynamic deformation measurements with pulsed digital holography," Appl. Opt. 38, 7056-7062 (1999).
[CrossRef]

G. Pedrini, I Alexeenko, W. Osten, and H. J. Tiziani, "Temporal phase unwrapping of digital hologram sequences," Appl. Opt. 42, 5846-5854 (2003).
[CrossRef] [PubMed]

K. Qian, "Windowed Fourier transform for fringe pattern analysis," Appl. Opt. 43, 2695-2702 (2004).
[CrossRef]

Y. Fu, C. J. Tay, C. Quan, and H. Miao, "Wavelet analysis of speckle patterns with a temporal carrier," Appl. Opt. 44, 959-965 (2005).
[CrossRef] [PubMed]

G. Pedrini, W. Osten, and M. E. Gusev, "High-speed digital holographic interferometry for vibration measurement," Appl. Opt. 45, 3456-3462 (2006).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Commun. (1)

G. H. Kaufmann, "Phase measurement in temporal speckle pattern interferometry using the Fouier transform method with and without a temporal carrier," Opt. Commun. 217, 141-149 (2003).
[CrossRef]

Opt. Eng. (3)

Y. Fu, C. J. Tay, C. Quan, and L. J. Chen, "Temporal wavelet analysis for deformation and velocity measurement in speckle interferometry," Opt. Eng. 43, 2780-2787 (2004).
[CrossRef]

C. Joenathan, B. Franze, P. Haible, and H. J. Tiziani, "Novel temporal Fourier transform speckle pattern shearing interferometer," Opt. Eng. 37, 1790-1795 (1998).
[CrossRef]

K. Qian and S. H. Soon, "Two-dimensional windowed Fourier frames for noise reduction in fringe pattern analysis," Opt. Eng. 44, 075601 (2005).
[CrossRef]

Opt. Laser Eng. (1)

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

Opt. Laser Technol. (1)

S. L. Toh, H. M Shang, F. S. Chau, and C. J. Tay, "Flaw detection in composites using time-average shearography," Opt. Laser Technol. 23, 25-30 (1991).
[CrossRef]

Opt. Lett. (4)

Opt. Rev. (1)

F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, and G. Mills, "Vibration analysis by phase shifting digital holography," Opt. Rev. 11, 297-299 (2004).
[CrossRef]

Other (5)

H. J. Tiziani, "Spectral and temporal phase evaluation for interferometry and speckle applications," in Trends in Optical Nondestructive Testing and Inspection, P. K. Rastogi and D. Inaudi, eds. (Elsevier, Amsterdam, 2000), pp. 323-343.
[CrossRef]

M. Cherbuliez and P. Jacquot, "Phase computation through wavelet analysis: yesterday and nowadays," in Fringe2001, W.Osten and W.Juptner, eds. (Elsevier, Paris, 2001), pp. 154-162.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice-Hall, 2002).

S. Mallat, A Wavelet Tour of Signal Processing (Academic, 1998).

M. Cherbuliez, "Wavelet analysis of interference patterns and signals: development of fast and efficient processing techniques," Thesis No. 2377 (Swiss Federal Institute of Technology Lausanne, 2001).

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Figures (8)

Fig. 1
Fig. 1

Schematic layout of the experimental setup.

Fig. 2
Fig. 2

(a) Typical digital hologram obtained on a cantilever beam; (b) spectrum of the digital hologram obtained; (c) typical original wrapped phase map indicating the relative displacement of the beam.

Fig. 3
Fig. 3

(a) Simulated phase variation with noise containing two vibration frequencies; (b) first derivative of (a) with and without noise; (c) first derivative of (a) after low-pass filtering; (d) first derivative of (a) obtained with a windowed Fourier ridge.

Fig. 4
Fig. 4

Second derivative of Fig. 3(a) (a) with and without noise, (b) after low-pass filtering, (c) obtained with a windowed Fourier ridge.

Fig. 5
Fig. 5

(a) Typical original wrapped phase at instant t = 0.0345  s , (b) wrapped phase after 2-D windowed Fourier filtering, (c) 3-D plot of displacement at instant t = 0.0345  s .

Fig. 6
Fig. 6

(a) Original phase variation of point A obtained by the proposed digital holography, (b) velocity on point A evaluated with a windowed Fourier ridge, (c) first derivative of (a) obtained by numerical differentiation, (d) velocity on point A obtained by low-pass filtering.

Fig. 7
Fig. 7

3-D plot of velocity at instant t = 0.0345  s obtained by (a) a windowed Fourier ridge and (b) Fourier analysis.

Fig. 8
Fig. 8

3-D plot of acceleration at instant t = 0.0345  s obtained by (a) a windowed Fourier ridge and (b) Fourier analysis.

Equations (10)

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I H ( x , y ) = | R H ( x , y ) | 2 + | U H ( x , y ) | 2 + R H ( x , y ) × U H * ( x , y ) + R H * ( x , y ) U H ( x , y ) ,
f max = 2 λ sin ( θ max 2 ) ,
Δ ϕ = 2 π z λ S ,
Δ ϕ = arctan Im [ U ( x , y ; t n ) U * ( x , y ; t 1 ) ] Re [ U ( x , y ; t n ) U * ( x , y ; t 1 ) ] ,
S f ( u , ξ ) = + f ( t ) g u , ξ * ( t ) d t ,
f ( t ) = 1 2 π + + S f ( u , ξ ) g u , ξ ( t ) d ξ d u ,
g u , ξ ( t ) = g ( t u ) exp ( j ξ t ) .
g ( t ) = exp ( t 2 / 2 σ 2 ) ,
S C p ( u , ξ ) = s 2 A x y ( u ) exp { j [ φ ( u ) ξ u ] } × ( g ^ { s [ ξ φ ( u ) ] } + ε ( u , ξ ) ) ,
ξ ( u ) = φ ( u ) ,

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