Abstract

In time-averaged digital holography (TADH), one records a hologram of a periodically oscillating object by using the exposure time typically much longer than the oscillating period. Problems arise when the total available exposure time is restricted or when the oscillation period is unknown. In this work we investigate effects of short exposure time to the quality of the recorded hologram and show that, to record high fidelity information in a shortest possible time, close estimates of the oscillating period and the phase are required. To that end we propose an advanced procedure based on short hologram exposures that allows obtaining such estimates. The procedure is efficient both in the number of recordings and their total exposure time.

© 2017 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
  4. N. Demoli, “Use of optical fiber bundle in digital image plane holography,” Opt. Quantum Electron. 45(8), 861–871 (2013).
    [Crossref]
  5. J. P. Chambard, V. Chalvidan, X. Carniel, and J. C. Pascal, “Pulsed TV – holography recording for vibration analysis applications,” Opt. Lasers Eng. 25, 343–360 (1996).
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    [Crossref] [PubMed]
  7. P. A. A. M. Somers and N. Bhattacharya, “A new method for processing time averaged vibration patterns: linear regression,” Strain 52(4), 264–275 (2016).
    [Crossref]
  8. M. Karray, P. Christophe, M. Gargouri, and P. Picart, “Digital holographic nondestructive testing of laminate composite,” Opt. Eng. 55(9), 095105 (2016).
    [Crossref]
  9. B. P. Thomas, S. A. Pillai, and C. S. Narayanamurthy, “Investigation on vibration excitation of debonded sandwich structures using time-average digital holography,” Appl. Opt. 56(13), F7–F13 (2017).
    [Crossref]
  10. G. O. Rosvold and O. J. Løkberg, “Effect and use of exposure control in vibration analysis using TV holography,” Appl. Opt. 32(5), 684–691 (1993).
    [Crossref] [PubMed]
  11. O. J. Løkberg, “ESPI – The ultimate holographic tool for vibration analysis?” J. Acoust. Soc. Am. 75, 1783–1791 (1984).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]

2017 (1)

2016 (2)

P. A. A. M. Somers and N. Bhattacharya, “A new method for processing time averaged vibration patterns: linear regression,” Strain 52(4), 264–275 (2016).
[Crossref]

M. Karray, P. Christophe, M. Gargouri, and P. Picart, “Digital holographic nondestructive testing of laminate composite,” Opt. Eng. 55(9), 095105 (2016).
[Crossref]

2015 (1)

2014 (1)

2013 (3)

2009 (1)

2007 (1)

J. Gladić, Z. Vučić, and D. Lovrić, “Reducing phase retrieval errors in Fourier analysis of 2-dimensional digital model interferograms,” Opt. Lasers Eng. 45(8), 868–876 (2007).
[Crossref]

2003 (2)

1999 (1)

1996 (2)

W.-C. Wang, C.-H. Hwang, and S.-Y. Lin, “Vibration measurement by the time-averaged electronic speckle pattern interferometry methods,” Appl. Opt. 35(22), 4502–4509 (1996).
[Crossref] [PubMed]

J. P. Chambard, V. Chalvidan, X. Carniel, and J. C. Pascal, “Pulsed TV – holography recording for vibration analysis applications,” Opt. Lasers Eng. 25, 343–360 (1996).

1993 (1)

1984 (1)

O. J. Løkberg, “ESPI – The ultimate holographic tool for vibration analysis?” J. Acoust. Soc. Am. 75, 1783–1791 (1984).
[Crossref]

1970 (1)

1965 (1)

Atlan, M.

Barton, J. S.

Bhattacharya, N.

P. A. A. M. Somers and N. Bhattacharya, “A new method for processing time averaged vibration patterns: linear regression,” Strain 52(4), 264–275 (2016).
[Crossref]

Carniel, X.

J. P. Chambard, V. Chalvidan, X. Carniel, and J. C. Pascal, “Pulsed TV – holography recording for vibration analysis applications,” Opt. Lasers Eng. 25, 343–360 (1996).

Chalvidan, V.

J. P. Chambard, V. Chalvidan, X. Carniel, and J. C. Pascal, “Pulsed TV – holography recording for vibration analysis applications,” Opt. Lasers Eng. 25, 343–360 (1996).

Chambard, J. P.

J. P. Chambard, V. Chalvidan, X. Carniel, and J. C. Pascal, “Pulsed TV – holography recording for vibration analysis applications,” Opt. Lasers Eng. 25, 343–360 (1996).

Christophe, P.

M. Karray, P. Christophe, M. Gargouri, and P. Picart, “Digital holographic nondestructive testing of laminate composite,” Opt. Eng. 55(9), 095105 (2016).
[Crossref]

Demoli, N.

Gargouri, M.

M. Karray, P. Christophe, M. Gargouri, and P. Picart, “Digital holographic nondestructive testing of laminate composite,” Opt. Eng. 55(9), 095105 (2016).
[Crossref]

Gautier, F.

Gladic, J.

J. Gladić, Z. Vučić, and D. Lovrić, “Reducing phase retrieval errors in Fourier analysis of 2-dimensional digital model interferograms,” Opt. Lasers Eng. 45(8), 868–876 (2007).
[Crossref]

D. Lovrić, Z. Vucić, J. Gladić, N. Demoli, S. Mitrović, and M. Milas, “Refined Fourier-transform method of analysis of full two-dimensional digitized interferograms,” Appl. Opt. 42(8), 1477–1484 (2003).
[Crossref] [PubMed]

Hand, D. P.

Hayasaki, Y.

Hwang, C.-H.

Isnard, V.

Jones, J. D. C.

Karray, M.

Leclercq, M.

Lin, S.-Y.

Løkberg, O. J.

G. O. Rosvold and O. J. Løkberg, “Effect and use of exposure control in vibration analysis using TV holography,” Appl. Opt. 32(5), 684–691 (1993).
[Crossref] [PubMed]

O. J. Løkberg, “ESPI – The ultimate holographic tool for vibration analysis?” J. Acoust. Soc. Am. 75, 1783–1791 (1984).
[Crossref]

Lovric, D.

J. Gladić, Z. Vučić, and D. Lovrić, “Reducing phase retrieval errors in Fourier analysis of 2-dimensional digital model interferograms,” Opt. Lasers Eng. 45(8), 868–876 (2007).
[Crossref]

D. Lovrić, Z. Vucić, J. Gladić, N. Demoli, S. Mitrović, and M. Milas, “Refined Fourier-transform method of analysis of full two-dimensional digitized interferograms,” Appl. Opt. 42(8), 1477–1484 (2003).
[Crossref] [PubMed]

Mestrovic, J.

Milas, M.

Mitrovic, S.

Moore, A. J.

Narayanamurthy, C. S.

Pascal, J. C.

J. P. Chambard, V. Chalvidan, X. Carniel, and J. C. Pascal, “Pulsed TV – holography recording for vibration analysis applications,” Opt. Lasers Eng. 25, 343–360 (1996).

Picart, P.

Pillai, S. A.

Powell, R. L.

Rosvold, G. O.

Skenderovic, H.

Somers, P. A. A. M.

P. A. A. M. Somers and N. Bhattacharya, “A new method for processing time averaged vibration patterns: linear regression,” Strain 52(4), 264–275 (2016).
[Crossref]

Sovic, I.

Stetson, K. A.

Stipcevic, M.

Thomas, B. P.

Verrier, N.

Vucic, Z.

J. Gladić, Z. Vučić, and D. Lovrić, “Reducing phase retrieval errors in Fourier analysis of 2-dimensional digital model interferograms,” Opt. Lasers Eng. 45(8), 868–876 (2007).
[Crossref]

D. Lovrić, Z. Vucić, J. Gladić, N. Demoli, S. Mitrović, and M. Milas, “Refined Fourier-transform method of analysis of full two-dimensional digitized interferograms,” Appl. Opt. 42(8), 1477–1484 (2003).
[Crossref] [PubMed]

Wang, W.-C.

Wilson, A. D.

Yamamoto, H.

Yamamoto, M.

Appl. Opt. (7)

J. Acoust. Soc. Am. (1)

O. J. Løkberg, “ESPI – The ultimate holographic tool for vibration analysis?” J. Acoust. Soc. Am. 75, 1783–1791 (1984).
[Crossref]

J. Opt. Soc. Am. (2)

Opt. Eng. (1)

M. Karray, P. Christophe, M. Gargouri, and P. Picart, “Digital holographic nondestructive testing of laminate composite,” Opt. Eng. 55(9), 095105 (2016).
[Crossref]

Opt. Lasers Eng. (2)

J. P. Chambard, V. Chalvidan, X. Carniel, and J. C. Pascal, “Pulsed TV – holography recording for vibration analysis applications,” Opt. Lasers Eng. 25, 343–360 (1996).

J. Gladić, Z. Vučić, and D. Lovrić, “Reducing phase retrieval errors in Fourier analysis of 2-dimensional digital model interferograms,” Opt. Lasers Eng. 45(8), 868–876 (2007).
[Crossref]

Opt. Lett. (4)

Opt. Quantum Electron. (1)

N. Demoli, “Use of optical fiber bundle in digital image plane holography,” Opt. Quantum Electron. 45(8), 861–871 (2013).
[Crossref]

Strain (1)

P. A. A. M. Somers and N. Bhattacharya, “A new method for processing time averaged vibration patterns: linear regression,” Strain 52(4), 264–275 (2016).
[Crossref]

Other (2)

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, NIST, 1972, p. 360.

J. M. Gere and S. P. Timoshenko, Mechanics of Materials, PWS Publishing Company, 1997.

Supplementary Material (3)

NameDescription
» Visualization 1: AVI (4969 KB)      Visualization 1
» Visualization 2: AVI (5027 KB)      Visualization 2
» Visualization 3: AVI (4869 KB)      Visualization 3

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Figures (12)

Fig. 1
Fig. 1 Displacement h( x ) (arbitrary units) of a uniform linear density cantilever beam of length L fixed at  x=0 , in its lowest oscillation mode.
Fig. 2
Fig. 2 Illustration of snapshots with respect to the vibration amplitude (sinusoid) of the object.
Fig. 3
Fig. 3 a) Schematics of the test setup, b) Photography of the object (OBJ) and the loudspeaker (LS).
Fig. 4
Fig. 4 a) Reconstructed hologram. b) Region of interest within the reconstructed hologram. c) One-dimensional vector of intensities along x axis obtained by averaging pixels with the same x coordinate in the region of interest.
Fig. 5
Fig. 5 Reconstructions of 10 consecutive holographic snapshots, each made with exposure time of 1 ms (up). Intensity profiles extracted from snapshots (down).
Fig. 6
Fig. 6 Numerical calculations of intensity profiles corresponding to measurements in Fig. 5.
Fig. 7
Fig. 7 Total cross-correlation between ten consecutive reconstructed holograms (each recorded with a 1 ms exposure and shown in Fig. 5) and corresponding theoretical predictions shifted in time by t 0 .
Fig. 8
Fig. 8 Reconstructed holograms (upper two rows), their intensity profiles (middle two rows) and simulations (bottom two rows) for exposures lasting 1, 2, 3, ..., 20 ms, starting at the oscillation node ( t 0 =0 ).
Fig. 9
Fig. 9 Deviation of the reconstructed time-averaged hologram from the reconstructed complete hologram, as a function of exposure time τ expressed in vibration periods T=10 ms. Several deviation functions for different starting times of the exposure within the period overlap (left). Maximum deviation as a function of the exposure time (right).
Fig. 10
Fig. 10 Reconstructed holograms for exposures of duration of 1,2,3,4, and 5 ms starting 2.5 ms after the equilibrium (top)s, extracted intensity profiles (middle), and calculated intensity profiles (bottom).
Fig. 11
Fig. 11 Measured fringe phases of 100 consecutive snapshots, taken every 0.1 ms, of the steel cantilever vibrating with period T=10 ms. Three series of phases are shown for different snapshot exposure times: 0.1 ms, 0.4 ms and 1 ms. Temporal development of fringe phases for the three exposure times is shown in Visualization 1, Visualization 2, and Visualization 3, respectively.
Fig. 12
Fig. 12 Simulations of the overall variance R 2 for an object periodically vibrating with the period of 10 ms. Simulations for N=4, 5, 7 and 10 points chosen uniformly within the period are drawn in different colors (left). Relative error of the period T E estimated by our method using N measured phases obtained from snapshots of the cantilever vibrating with period T=10 ms (right).

Equations (15)

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z( x,t )=h( x )sin[ 2π f 0 ( t t d ) ],
I( x,t )=a( x )+b( x )cos[ φ r ( x ) φ s ( x,t ) ],
M τ ( x )= 1 τ t 0 t 0 +τ exp[ iΦ( x )sin 2π T ( t t d ) ]dt
M τ ( x )= NT τ J 0 [ Φ( x ) ]+ 1 τ t 0 t 0 +ΔT exp[ iΦ( x )sin 2π T t ]dt.
M τ ( x )= 1 τ T 4 3T 4 exp[ iΦ( x )sin 2π T t ]dt= 1 π π 4 3π 4 exp[ iΦ( x )sinθ ]dθ = 1 π π/4 π/4 exp[ iΦ( x )cosθ ]dθ= J 0 [ Φ( x ) ] 
Φ( x )= A 0 [ 3 ( x L ) 2 2 ( x L ) 3 + 1 2 ( x L ) 4 ]
a uv ( k )= i=1 Nk ( u i u ¯ )( v i+k v ¯ )   ( i=1 Nk ( u i u ¯ ) 2 )( i=1 Nk ( v i u ¯ ) 2 ) , 
D=1| a uv ( 0 ) |.
Corr( t d )= 1 10 i=0 9 a u i ,  v i ( t d ) ( 0 ).
D( t ) = 0.02 ( τ/T ) 2 ( 1+ 2.3 τ/T ) .
ψ( t )=a+bsin( ωt+φ ),
ψ( t )=A+Bsin( 2π T t )+Ccos( 2π T t )
R 2 = i=0 N1 ( A+Bsin( ω t i )+Ccos( ω t i )ψ( t i ) ) 2 .
[ N sin( ω t i ) cos( ω t i ) sin( ω t i ) (sin( ω t i )) 2 sin( ω t i )cos( ω t i ) cos( ω t i ) sin( ω t i )cos( ω t i ) (cos( ω t i )) 2 ]×[ A B C ]=[ ψ( t i ) ψ( t i )sin( ω t i ) ψ( t i )cos( ω t i ) ]
cos( φ )= B B 2 + C 2 ; sin( φ )= C B 2 + C 2 .

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