Abstract

Features offered by the combination of time averaging and digital Fresnel holography are investigated. In particular, we introduce the concept of the zero-crossing phase of Bessel fringes, which allows a highly contrasted determination of the dark fringes in the hologram. We discuss some particularities of the digital reconstruction and show how time-averaged digital holography can be used to study vibration drifts. Experiment results are presented in the case of a loudspeaker under a sinusoidal excitation; digital and analogical holography are also compared.

© 2005 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  12. W. C. Wang, C. H. Hwang, S. Y. Lin, “Vibration measurement by the time-averaged electronic speckle pattern interferometry methods,” Appl. Opt. 35, 4502–4509 (1996).
    [CrossRef] [PubMed]
  13. See http://perso.wanadoo.fr/holographie/FR/index.html .

2003 (1)

2002 (1)

2000 (1)

1999 (1)

1996 (1)

1995 (1)

J. D. R. Valera, J. D. C. Jones, “Vibration analysis by modulated time-averaged speckle shearing interferometry,” Meas. Sci. Technol. 6, 965–970 (1995).
[CrossRef]

1994 (2)

O. J. Lokberg, H. M. Pedersen, H. Valo, G. Wang, “Measurement of higher harmonics in periodic vibrations using phase-modulated TV holography with digital image processing,” Appl. Opt. 33, 4997–5002 (1994).
[CrossRef] [PubMed]

H. M. Pedersen, O. J. Lokberg, H. Valo, G. Wang, “Detection of non-sinusoidal periodic vibrations using phase-modulated TV-holography,” Opt. Commun. 104, 271–276 (1994).
[CrossRef]

1989 (1)

B. Lu, X. Yang, H. Abendroth, H. Eggers, “Time-averaged subtraction method in electronic speckle pattern interferometry,” Opt. Commun. 70, 177–180 (1989).
[CrossRef]

1988 (1)

1976 (1)

O. J. Lokberg, K. Hogmoen, “Use of modulated reference wave in electronic speckle pattern interferometry,” J. Phys. E 9, 847–851 (1976).
[CrossRef]

1965 (1)

Abendroth, H.

B. Lu, X. Yang, H. Abendroth, H. Eggers, “Time-averaged subtraction method in electronic speckle pattern interferometry,” Opt. Commun. 70, 177–180 (1989).
[CrossRef]

Bevilacqua, F.

Brohinsky, W. R.

Cuche, E.

Depeursinge, C.

Eggers, H.

B. Lu, X. Yang, H. Abendroth, H. Eggers, “Time-averaged subtraction method in electronic speckle pattern interferometry,” Opt. Commun. 70, 177–180 (1989).
[CrossRef]

Hogmoen, K.

O. J. Lokberg, K. Hogmoen, “Use of modulated reference wave in electronic speckle pattern interferometry,” J. Phys. E 9, 847–851 (1976).
[CrossRef]

Hwang, C. H.

Javidi, B.

Jones, J. D. C.

J. D. R. Valera, J. D. C. Jones, “Vibration analysis by modulated time-averaged speckle shearing interferometry,” Meas. Sci. Technol. 6, 965–970 (1995).
[CrossRef]

Kato, J.

Lin, S. Y.

Lokberg, O. J.

H. M. Pedersen, O. J. Lokberg, H. Valo, G. Wang, “Detection of non-sinusoidal periodic vibrations using phase-modulated TV-holography,” Opt. Commun. 104, 271–276 (1994).
[CrossRef]

O. J. Lokberg, H. M. Pedersen, H. Valo, G. Wang, “Measurement of higher harmonics in periodic vibrations using phase-modulated TV holography with digital image processing,” Appl. Opt. 33, 4997–5002 (1994).
[CrossRef] [PubMed]

O. J. Lokberg, K. Hogmoen, “Use of modulated reference wave in electronic speckle pattern interferometry,” J. Phys. E 9, 847–851 (1976).
[CrossRef]

Lu, B.

B. Lu, X. Yang, H. Abendroth, H. Eggers, “Time-averaged subtraction method in electronic speckle pattern interferometry,” Opt. Commun. 70, 177–180 (1989).
[CrossRef]

Matsumura, T.

Moisson, E.

Mounier, D.

Pedersen, H. M.

O. J. Lokberg, H. M. Pedersen, H. Valo, G. Wang, “Measurement of higher harmonics in periodic vibrations using phase-modulated TV holography with digital image processing,” Appl. Opt. 33, 4997–5002 (1994).
[CrossRef] [PubMed]

H. M. Pedersen, O. J. Lokberg, H. Valo, G. Wang, “Detection of non-sinusoidal periodic vibrations using phase-modulated TV-holography,” Opt. Commun. 104, 271–276 (1994).
[CrossRef]

Picart, P.

Powell, R. L.

Stetson, K. A.

Tajahuerce, E.

Valera, J. D. R.

J. D. R. Valera, J. D. C. Jones, “Vibration analysis by modulated time-averaged speckle shearing interferometry,” Meas. Sci. Technol. 6, 965–970 (1995).
[CrossRef]

Valo, H.

H. M. Pedersen, O. J. Lokberg, H. Valo, G. Wang, “Detection of non-sinusoidal periodic vibrations using phase-modulated TV-holography,” Opt. Commun. 104, 271–276 (1994).
[CrossRef]

O. J. Lokberg, H. M. Pedersen, H. Valo, G. Wang, “Measurement of higher harmonics in periodic vibrations using phase-modulated TV holography with digital image processing,” Appl. Opt. 33, 4997–5002 (1994).
[CrossRef] [PubMed]

Wang, G.

O. J. Lokberg, H. M. Pedersen, H. Valo, G. Wang, “Measurement of higher harmonics in periodic vibrations using phase-modulated TV holography with digital image processing,” Appl. Opt. 33, 4997–5002 (1994).
[CrossRef] [PubMed]

H. M. Pedersen, O. J. Lokberg, H. Valo, G. Wang, “Detection of non-sinusoidal periodic vibrations using phase-modulated TV-holography,” Opt. Commun. 104, 271–276 (1994).
[CrossRef]

Wang, W. C.

Yamaguchi, I.

Yang, X.

B. Lu, X. Yang, H. Abendroth, H. Eggers, “Time-averaged subtraction method in electronic speckle pattern interferometry,” Opt. Commun. 70, 177–180 (1989).
[CrossRef]

Appl. Opt. (3)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Phys. E (1)

O. J. Lokberg, K. Hogmoen, “Use of modulated reference wave in electronic speckle pattern interferometry,” J. Phys. E 9, 847–851 (1976).
[CrossRef]

Meas. Sci. Technol. (1)

J. D. R. Valera, J. D. C. Jones, “Vibration analysis by modulated time-averaged speckle shearing interferometry,” Meas. Sci. Technol. 6, 965–970 (1995).
[CrossRef]

Opt. Commun. (2)

B. Lu, X. Yang, H. Abendroth, H. Eggers, “Time-averaged subtraction method in electronic speckle pattern interferometry,” Opt. Commun. 70, 177–180 (1989).
[CrossRef]

H. M. Pedersen, O. J. Lokberg, H. Valo, G. Wang, “Detection of non-sinusoidal periodic vibrations using phase-modulated TV-holography,” Opt. Commun. 104, 271–276 (1994).
[CrossRef]

Opt. Lett. (3)

Other (1)

See http://perso.wanadoo.fr/holographie/FR/index.html .

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Figures (14)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Fringe pattern of the loudspeaker at low excitation.

Fig. 3
Fig. 3

Fringe pattern of the loudspeaker at moderate excitation.

Fig. 4
Fig. 4

Fringe pattern of the loudspeaker at high excitation.

Fig. 5
Fig. 5

Zero-crossing phase modulo 2π at low excitation.

Fig. 6
Fig. 6

Zero-crossing phase modulo 2π at moderate excitation.

Fig. 7
Fig. 7

Zero-crossing phase modulo 2π at high excitation.

Fig. 8
Fig. 8

Contour lines of the amplitude map at low excitation.

Fig. 9
Fig. 9

Contour lines of the amplitude map at moderate excitation.

Fig. 10
Fig. 10

Contour lines of the amplitude map at high excitation.

Fig. 11
Fig. 11

Classical reconstruction at low excitation.

Fig. 12
Fig. 12

Classical reconstruction at moderate excitation.

Fig. 13
Fig. 13

Classical reconstruction at high excitation.

Fig. 14
Fig. 14

Phase map of the drift over 30 min.

Tables (1)

Tables Icon

Table 1 Altitude of Contour Lines

Equations (19)

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H = O 0 + R * O + RO * ,
O ( x , y , d 0 ) = i exp ( - i 2 π d 0 / λ ) λ d 0 exp [ - i π λ d 0 ( x 2 + y 2 ) ] × - + - + A ( x , y ) exp [ - i π λ d 0 ( x 2 + y 2 ) ] × exp [ 2 i π λ d 0 ( x x + y y ) ] d x d y ,
H D ( l p x , k p y , d 0 ) = l p x - Δ x / 2 l p x + Δ x / 2 k p y - Δ y / 2 k p y + Δ y / 2 H ( x , y , d 0 ) d x d y .
Π Δ x , Δ y ( x , y ) = { 1 if             x Δ x / 2             and             y Δ y / 2 0 if not
H D ( l p x ,             k p y ,             d 0 ) = [ H ( x , y ,     d 0 ) * Π Δ x Δ y ( - x , - y ) ] ( l p x ,             k p y ) ,
A R ( X , Y , - d 0 ) = - 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 i = 0 l = L - 1 H D ( l p x ,             k p y ,             d 0 ) exp [ i π λ d 0 ( l 2 p x 2 + k 2 p 2 y ) ] exp [ - 2 i π λ d 0 ( l X p x + k Y p y ) ] ,
A + 1 R ( X ,     Y ,     - d 0 ) = 1 λ 2 d 0 2 exp [ i π λ d 0 ( X 2 + Y 2 ) ] × k = 0 k = K l = 0 l = L - 1 ( { exp [ - i π λ d 0 ( x 2 + y 2 ) ] R * ( x ,     y ) × F ( x λ d 0     y λ d 0 ) } * Π Δ x Δ y ( - x , - y ) ) ( l p x ,     k p y ) × exp [ i π λ d 0 ( l 2 p x 2 + k 2 p y 2 ) ] × exp [ - 2 i π λ d 0 ( l X p x + k Y p y ) ] ,
F ( x λ d 0 ,     y λ d 0 ) = - + - + F ˜ ( x , y ) exp [ 2 i π λ d 0 ( x x ) + y y ) ] d x d y = FT - 1 ( F ˜ ( x , y ) ( x λ d 0 , y λ d 0 ) ,
F ˜ ( x , y ) = A ( x , y ) exp [ - i π λ d 0 ( x 2 + y 2 ) ] ,
A + 1 R ( X , Y , - d 0 ) = λ 4 d 0 4 a R FT - 1 [ ( FT { F ˜ ( x - u λ d 0 , y - v λ d 0 ) × exp [ i π λ d 0 ( x 2 + y 2 ) ] } ( x λ d 0 , y λ d 0 ) ) ] × ( X λ d 0 , Y λ d 0 ) * FT - 1 [ Δ x Δ y sinc × ( - π Δ x x λ d 0 ) sinc ( - π Δ y y λ d 0 ) ] × ( X λ d 0 , Y λ d 0 ) * W ˜ NM ( X , Y ) ,
W ˜ NM ( X , Y ) = exp [ - i π ( N - 1 ) X p x λ d 0 - i π ( M - 1 ) Y p y λ d 0 ] × sin ( π N X p x / λ d 0 ) sin ( π X p x / λ d 0 ) sin ( π M Y p y / λ d 0 ) sin ( π Y p y / λ d 0 )
A + 1 R ( X , Y , - d 0 ) = λ 6 d 0 6 R * ( X , Y ) exp [ - i π λ d 0 ( u 2 + ν 2 ) ] A ( X - λ u d 0 ,             Y - λ ν d 0 ) * Π Δ x Δ y ( - X , - Y ) * W ˜ N M ( X , Y ) .
Δ ϕ ( t ) = Δ ϕ 0 + Δ ϕ m sin ( ω 0 t + ϕ 0 ) .
H D T ( l p x , k p y , d 0 ) = t 1 t 1 + T H D ( l p x , k p y , d 0 , t ) d t .
A + 1 R ( X , Y , - d 0 ) = λ 6 d 0 6 R * ( X , Y ) [ - i π λ d 0 ( u 2 + ν 2 ) ] × A mod ( X - λ u d 0 , Y - λ ν 0 ) * Π Δ x Δ y ( - X , - Y ) * W ˜ N M ( X , Y ) ,
A mod ( X , Y ) = A 0 ( x , y ) exp [ i ψ 0 ( X , Y ) + i Δ ϕ 0 ( X , Y ) ] × k J k [ Δ ϕ m ( X , Y ) ] sinc ( k ω 0 T 2 ) × exp ( i k ω 0 T 2 ) exp { i k [ ω 0 t 1 + ϕ 0 ( X , Y ) ] } .
lim T A mod ( X , Y ) = T A 0 ( X , Y ) exp [ i ψ 0 ( X , Y ) + i Δ ϕ 0 ( X , Y ) ] × J 0 [ Δ ϕ m ( X , Y ) ] exp [ i ϕ j ( X , Y ) ] .
ϕ J = { 0 if J 0 ( Δ ϕ m ) > 0 ± π if J 0 ( Δ ϕ m ) < 0 .
u z ( x , y ) = λ 2 π 1 1 + cos θ ω n ( x , y ) .

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