Abstract

opportunities for full field 2D amplitude and phase vibration analysis are presented. It is demonstrated that it is possible to simultaneously encode-decode 2D the amplitude and phase of harmonic mechanical vibrations. The process allows the determination of in plane and out of plane vibration components when the object is under a pure sinusoidal excitation. The principle is based on spatial multiplexing in digital Fresnel holography. Experimental results are presented in the case of an industrial application.

© 2005 Optical Society of America

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References

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  1. U. Schnars and W. Jüptner , “ Direct recording of holograms by a CCD target and numerical reconstruction ,” App. Opt.   33 , 179 – 181 ( 1994 ).
    [CrossRef]
  2. L. Yu and M.K. Kim , “ Wavelength scanning digital interference holography for variable tomographic scanning ,” Opt. Express   13 , 5621 – 5627 ( 2005 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-15-5621.
    [CrossRef] [PubMed]
  3. M. Paturzo , P. Ferraro , S. Grilli , D. Alfieri , P. De Natale , M. de Angelis , A. Finizio , S. De Nicola , G. Pierattini , F. Caccavale , D. Callejo , and A. Morbiato , “ On the origin of internal field in Lithium Niobate crystals directly observed by digital holography ,” Opt. Express   13 , 5416 – 5423 ( 2005 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-14- 5416.
    [CrossRef] [PubMed]
  4. N. Demoli and I. Demoli , “ Dynamic modal characterization of musical instruments using digital holography ,” Opt. Express   13 , 4812 – 4817 ( 2005 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-13-4812.
    [CrossRef] [PubMed]
  5. B. Javidi , I. Moon , S. Yeom , and E. Carapezza , “ Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography ,” Opt. Express   13 , 4492 – 4506 ( 2005 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-12-4492.
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  7. I. Yamaguchi , J. Kato , and S. Ohta , “ Surface shape measurement by phase shifting digital holography ,” Opt. Rev.   8 , 85 – 89 ( 2001 ).
    [CrossRef]
  8. F. Dubois , L. Joannes , and J.C. Legros , “ Improved three-dimensional imaging with a digital holographic microscope with a source of partial spatial coherence ,” Appl. Opt.   38 , 7085 – 7094 ( 1999 ).
    [CrossRef]
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    [CrossRef] [PubMed]
  10. P. Picart , J. Leval , D. Mounier , and S. Gougeon , “ Some opportunities for vibration analysis with time-averaging in digital Fresnel holography ,” Appl. Opt.   44 , 337 – 343 ( 2005 ).
    [CrossRef] [PubMed]
  11. J. Leval , P. Picart , J.-P. Boileau , and J.-C. Pascal , “ Full field vibrometry with digital Fresnel holography ,” Appl. Opt.   44 , 5763 – 5772 ( 2005 ).
    [CrossRef] [PubMed]
  12. P. Picart , E. Moisson , and D. Mounier , “ Twin sensitivity measurement by spatial multiplexing of digitally recorded holograms ,” Appl. Opt.   42 , 1947 – 1957 ( 2003 ).
    [CrossRef] [PubMed]
  13. P. Picart , B. Diouf , E. Lolive , and J.-M. Berthelot , “ Investigation of fracture mechanisms in resin concrete using spatially multiplexed digital Fresnel holograms ,” Opt. Eng.   43 , 1169 – 1176 ( 2004 ).
    [CrossRef]
  14. Technical data sheet available for example on http://www.polytec.com.

2005 (6)

L. Yu and M.K. Kim , “ Wavelength scanning digital interference holography for variable tomographic scanning ,” Opt. Express   13 , 5621 – 5627 ( 2005 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-15-5621.
[CrossRef] [PubMed]

M. Paturzo , P. Ferraro , S. Grilli , D. Alfieri , P. De Natale , M. de Angelis , A. Finizio , S. De Nicola , G. Pierattini , F. Caccavale , D. Callejo , and A. Morbiato , “ On the origin of internal field in Lithium Niobate crystals directly observed by digital holography ,” Opt. Express   13 , 5416 – 5423 ( 2005 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-14- 5416.
[CrossRef] [PubMed]

N. Demoli and I. Demoli , “ Dynamic modal characterization of musical instruments using digital holography ,” Opt. Express   13 , 4812 – 4817 ( 2005 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-13-4812.
[CrossRef] [PubMed]

B. Javidi , I. Moon , S. Yeom , and E. Carapezza , “ Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography ,” Opt. Express   13 , 4492 – 4506 ( 2005 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-12-4492.
[CrossRef] [PubMed]

P. Picart , J. Leval , D. Mounier , and S. Gougeon , “ Some opportunities for vibration analysis with time-averaging in digital Fresnel holography ,” Appl. Opt.   44 , 337 – 343 ( 2005 ).
[CrossRef] [PubMed]

J. Leval , P. Picart , J.-P. Boileau , and J.-C. Pascal , “ Full field vibrometry with digital Fresnel holography ,” Appl. Opt.   44 , 5763 – 5772 ( 2005 ).
[CrossRef] [PubMed]

2004 (1)

P. Picart , B. Diouf , E. Lolive , and J.-M. Berthelot , “ Investigation of fracture mechanisms in resin concrete using spatially multiplexed digital Fresnel holograms ,” Opt. Eng.   43 , 1169 – 1176 ( 2004 ).
[CrossRef]

2003 (3)

2001 (1)

I. Yamaguchi , J. Kato , and S. Ohta , “ Surface shape measurement by phase shifting digital holography ,” Opt. Rev.   8 , 85 – 89 ( 2001 ).
[CrossRef]

1999 (1)

1994 (1)

U. Schnars and W. Jüptner , “ Direct recording of holograms by a CCD target and numerical reconstruction ,” App. Opt.   33 , 179 – 181 ( 1994 ).
[CrossRef]

Alfieri, D.

Angelis, M. de

Berthelot, J.-M.

P. Picart , B. Diouf , E. Lolive , and J.-M. Berthelot , “ Investigation of fracture mechanisms in resin concrete using spatially multiplexed digital Fresnel holograms ,” Opt. Eng.   43 , 1169 – 1176 ( 2004 ).
[CrossRef]

Boileau, J.-P.

Caccavale, F.

Callejo, D.

Carapezza, E.

Demoli, I.

Demoli, N.

Diouf, B.

P. Picart , B. Diouf , E. Lolive , and J.-M. Berthelot , “ Investigation of fracture mechanisms in resin concrete using spatially multiplexed digital Fresnel holograms ,” Opt. Eng.   43 , 1169 – 1176 ( 2004 ).
[CrossRef]

Dubois, F.

Ferraro, P.

Finizio, A.

Gougeon, S.

Grilli, S.

Javidi, B.

Joannes, L.

Jüptner, W.

U. Schnars and W. Jüptner , “ Direct recording of holograms by a CCD target and numerical reconstruction ,” App. Opt.   33 , 179 – 181 ( 1994 ).
[CrossRef]

Kato, J.

I. Yamaguchi , J. Kato , and S. Ohta , “ Surface shape measurement by phase shifting digital holography ,” Opt. Rev.   8 , 85 – 89 ( 2001 ).
[CrossRef]

Kim, M.K.

Legros, J.C.

Leval, J.

Lolive, E.

P. Picart , B. Diouf , E. Lolive , and J.-M. Berthelot , “ Investigation of fracture mechanisms in resin concrete using spatially multiplexed digital Fresnel holograms ,” Opt. Eng.   43 , 1169 – 1176 ( 2004 ).
[CrossRef]

Moisson, E.

Moon, I.

Morbiato, A.

Mounier, D.

Natale, P. De

Nicola, S. De

Ohta, S.

I. Yamaguchi , J. Kato , and S. Ohta , “ Surface shape measurement by phase shifting digital holography ,” Opt. Rev.   8 , 85 – 89 ( 2001 ).
[CrossRef]

Pascal, J.-C.

Paturzo, M.

Picart, P.

Pierattini, G.

Schnars, U.

U. Schnars and W. Jüptner , “ Direct recording of holograms by a CCD target and numerical reconstruction ,” App. Opt.   33 , 179 – 181 ( 1994 ).
[CrossRef]

Torzynski, M.

Vukicevic, D.

Yamaguchi, I.

I. Yamaguchi , J. Kato , and S. Ohta , “ Surface shape measurement by phase shifting digital holography ,” Opt. Rev.   8 , 85 – 89 ( 2001 ).
[CrossRef]

Yeom, S.

Yu, L.

App. Opt. (1)

U. Schnars and W. Jüptner , “ Direct recording of holograms by a CCD target and numerical reconstruction ,” App. Opt.   33 , 179 – 181 ( 1994 ).
[CrossRef]

Appl. Opt. (4)

Opt. Eng. (1)

P. Picart , B. Diouf , E. Lolive , and J.-M. Berthelot , “ Investigation of fracture mechanisms in resin concrete using spatially multiplexed digital Fresnel holograms ,” Opt. Eng.   43 , 1169 – 1176 ( 2004 ).
[CrossRef]

Opt. Express (5)

Opt. Lett. (1)

Opt. Rev. (1)

I. Yamaguchi , J. Kato , and S. Ohta , “ Surface shape measurement by phase shifting digital holography ,” Opt. Rev.   8 , 85 – 89 ( 2001 ).
[CrossRef]

Other (1)

Technical data sheet available for example on http://www.polytec.com.

Supplementary Material (9)

» Media 1: MPG (1064 KB)     
» Media 2: MPG (911 KB)     
» Media 3: MPG (1402 KB)     
» Media 4: MPG (1608 KB)     
» Media 5: MPG (1586 KB)     
» Media 6: MPG (1251 KB)     
» Media 7: MPG (1092 KB)     
» Media 8: MPG (1321 KB)     
» Media 9: MPG (811 KB)     

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Figures (12)

Fig. 1.
Fig. 1.

Experimental set-up for simultaneous 2D vibration analysis

Fig. 2.
Fig. 2.

Multiplexed holograms of the car joint piece

Fig. 3.
Fig. 3.

2D vibration amplitude and phase at a frequency of 680 Hz

Fig. 4.
Fig. 4.

Mean quadratic velocities extracted from the experimental results

Fig. 5.
Fig. 5.

1064 Ko Movie 1 - Kinetic representation of Fresnel for 2D vibration at 340Hz [Media 9]

Fig. 6.
Fig. 6.

912 Ko Movie 2 - Kinetic representation of Fresnel for 2D vibration at 430Hz

Fig. 7.
Fig. 7.

1403 Ko Movie 3 - Kinetic representation of Fresnel for 2D vibration at 460Hz

Fig. 8.
Fig. 8.

1609 Ko Movie 4 - Kinetic representation of Fresnel for 2D vibration at 680Hz

Fig. 9.
Fig. 9.

1586 Ko Movie 5 - Kinetic representation of Fresnel for 2D vibration at 730Hz

Fig. 10.
Fig. 10.

1251 Ko Movie 6 - Kinetic representation of Fresnel for 2D vibration at 880Hz

Fig. 11.
Fig. 11.

1093 Ko Movie 7 - Kinetic representation of Fresnel for 2D vibration at 900Hz

Fig. 12.
Fig. 12.

1321 Ko Movie 8 - Kinetic representation of Fresnel for 2D vibration at 930Hz

Equations (12)

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

U ( t ) = u x sin ( ω 0 t + φ x ) i + u y sin ( ω 0 t + φ y ) j + u z sin ( ω 0 t + φ z ) k ,
A ( t ) = A 0 exp ( i ψ 0 ) exp [ 2 S . U ( t ) / λ ] ,
A R ( x , y , d 0 , t ) = i exp ( 2 i π d 0 / λ ) λ d 0 exp [ i π λ d 0 ( x 2 + y 2 ) ]
× k = 0 k = K 1 l = 0 l = L 1 H ( l p x , k p y , d 0 , t ) exp [ i π λ d 0 ( l 2 p x 2 + k 2 p y 2 ) ] exp [ 2 i π λ d 0 ( lx p x + ky p y ) ] .
A + 1 R ( x , y , d 0 , t ) MN λ 4 d 0 4 R * ( x , y ) exp [ iπλ d 0 ( u 0 2 + v 0 2 ) ]
× A 0 ( x , y ) exp [ i ψ 0 ( x , y ) ] exp [ 2 S . U ( t ) / λ ] * δ ( x λ u 0 d 0 , y λ v 0 d 0 ) .
ψ J i = ψ 0 ± Δ φ x sin ( θ ) sin ( ω 0 t j + φ x ) Δ φ z [ 1 + cos ( θ ) ] sin ( ω 0 t j + φ z ) ,
Δ φ A = 1 2 [ Δ ψ 13 _ A ] 2 + [ Δ ψ 23 _ A + Δ ψ 21 _ A ] 2 ,
φ A = arctan [ Δ ψ 13 _ A Δ ψ 23 _ A + Δ ψ 21 _ A ] ,
v A 2 = ω 0 2 πS s 0 T 0 v A ( x , y , t ) 2 dtdxdy ,
v z ( x , y , t ) = λ ω 0 4 π ( 1 + cos θ ) Δ φ z ( x , y ) cos ( ω 0 + φ z ) ,
v z ( x , y ,t ) = λ ω 0 4 π sin ( θ ) Δ φ x ( x , y ) cos ( ω 0 t + φ x ) .

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