Abstract

A method for separate recording of rationally related vibration frequencies is presented. To record and measure the mode shape of vibrations, a synchronized stroboscopic CCD camera is used. Synchronization and control of the camera acquisition for recording stroboscopic holographic sequence has been realized. The phase for different states of the object vibration is calculated using the Fourier-transform method. Experimental results are presented, and the advantages and disadvantages of the proposed method are discussed.

© 2009 Optical Society of America

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References

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  1. R. J. Collier, C. B. Burckhard, and L. H. Lin, Optical Holography (Academic, 1971), Chap. 5.
  2. C. M. Vest, Holographic Interferometry (Wiley, 1979).
  3. G. Pedrini, Y. L. Zou, and H. J. Tiziani, “Digital double pulse holographic interferometry for vibration analysis,” J. Mod. Opt. 42, 367-374 (1995).
    [CrossRef]
  4. G. Pedrini and H. J. Tiziani, “Digital holographic interferometry,” in Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, 2001), pp. 337-362, Chap. 6.
  5. S. Schedin, G. Pedrini, H. J. Tiziani, A. K. Aggarwal, and M. E. Gusev, “Highly sensitive pulsed digital holography for built-in defect analysis with a laser excitation,” Appl. Opt. 40, 100-103 (2001).
    [CrossRef]
  6. C. Perez-Lopez, F. Mendoza Santoyo, G. Pedrini, S. Schedin, and H. J. Tiziani, “Pulsed digital holographic interferometry for dynamic measurement of rotating objects with an optical derotator,” Appl. Opt. 40, 5106-5110 (2001).
    [CrossRef]
  7. P. Almoro, V. Garica, and C. Saloma, “Colored object recognition by digital holography and a hydrogen Raman shifter,” Opt. Express 15, 7176-7181 (2007).
    [CrossRef] [PubMed]
  8. E. Archbold and A. A. Ennos, “Observation of surface vibration modes by stroboscopic hologram interferometry,” Nature 217, 942-943 (1968).
    [CrossRef]
  9. M. Takeda, Hideki, and S. Kobayashi, “Fourier-transform method of fringe pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72 (1982).
    [CrossRef]
  10. Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, 2001).
  11. L. Onural, “Sampling of the diffraction field,” Appl. Opt. 39, 5929-5935 (2000).
    [CrossRef]
  12. A. D. Wilson and D. H. Strope, “Time-average holographic interferometry of a circular plate vibrating simultaneously in two rationally related modes,” J. Opt. Soc. Am. 60, 1162-1165 (1970).
    [CrossRef]
  13. C. S. Vikram, “Stroboscopic holographic interferometry of vibration simultaneously in two sinusoidal modes,” Opt. Commun. 11, 360-364 (1974).
    [CrossRef]
  14. K. A. Stetson, “A rigorous treatment of the fringes of hologram interferometry,” Optik (Jena) 29, 386-400 (1969).
  15. M. Miller, “Stroboscopic interferometry in ramp approximation,” Opt. Commun. 14, 406-408 (1975).
    [CrossRef]

2007

2001

2000

1995

G. Pedrini, Y. L. Zou, and H. J. Tiziani, “Digital double pulse holographic interferometry for vibration analysis,” J. Mod. Opt. 42, 367-374 (1995).
[CrossRef]

1982

M. Takeda, Hideki, and S. Kobayashi, “Fourier-transform method of fringe pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72 (1982).
[CrossRef]

1975

M. Miller, “Stroboscopic interferometry in ramp approximation,” Opt. Commun. 14, 406-408 (1975).
[CrossRef]

1974

C. S. Vikram, “Stroboscopic holographic interferometry of vibration simultaneously in two sinusoidal modes,” Opt. Commun. 11, 360-364 (1974).
[CrossRef]

1970

1969

K. A. Stetson, “A rigorous treatment of the fringes of hologram interferometry,” Optik (Jena) 29, 386-400 (1969).

1968

E. Archbold and A. A. Ennos, “Observation of surface vibration modes by stroboscopic hologram interferometry,” Nature 217, 942-943 (1968).
[CrossRef]

Aggarwal, A. K.

Almoro, P.

Archbold, E.

E. Archbold and A. A. Ennos, “Observation of surface vibration modes by stroboscopic hologram interferometry,” Nature 217, 942-943 (1968).
[CrossRef]

Burckhard, C. B.

R. J. Collier, C. B. Burckhard, and L. H. Lin, Optical Holography (Academic, 1971), Chap. 5.

Collier, R. J.

R. J. Collier, C. B. Burckhard, and L. H. Lin, Optical Holography (Academic, 1971), Chap. 5.

Ennos, A. A.

E. Archbold and A. A. Ennos, “Observation of surface vibration modes by stroboscopic hologram interferometry,” Nature 217, 942-943 (1968).
[CrossRef]

Garica, V.

Gusev, M. E.

Hideki,

M. Takeda, Hideki, and S. Kobayashi, “Fourier-transform method of fringe pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72 (1982).
[CrossRef]

Kobayashi, S.

M. Takeda, Hideki, and S. Kobayashi, “Fourier-transform method of fringe pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72 (1982).
[CrossRef]

Lin, L. H.

R. J. Collier, C. B. Burckhard, and L. H. Lin, Optical Holography (Academic, 1971), Chap. 5.

Miller, M.

M. Miller, “Stroboscopic interferometry in ramp approximation,” Opt. Commun. 14, 406-408 (1975).
[CrossRef]

Onural, L.

Pedrini, G.

S. Schedin, G. Pedrini, H. J. Tiziani, A. K. Aggarwal, and M. E. Gusev, “Highly sensitive pulsed digital holography for built-in defect analysis with a laser excitation,” Appl. Opt. 40, 100-103 (2001).
[CrossRef]

C. Perez-Lopez, F. Mendoza Santoyo, G. Pedrini, S. Schedin, and H. J. Tiziani, “Pulsed digital holographic interferometry for dynamic measurement of rotating objects with an optical derotator,” Appl. Opt. 40, 5106-5110 (2001).
[CrossRef]

G. Pedrini, Y. L. Zou, and H. J. Tiziani, “Digital double pulse holographic interferometry for vibration analysis,” J. Mod. Opt. 42, 367-374 (1995).
[CrossRef]

G. Pedrini and H. J. Tiziani, “Digital holographic interferometry,” in Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, 2001), pp. 337-362, Chap. 6.

Perez-Lopez, C.

Rastogi, P. K.

Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, 2001).

Saloma, C.

Santoyo, F. Mendoza

Schedin, S.

Stetson, K. A.

K. A. Stetson, “A rigorous treatment of the fringes of hologram interferometry,” Optik (Jena) 29, 386-400 (1969).

Strope, D. H.

Takeda, M.

M. Takeda, Hideki, and S. Kobayashi, “Fourier-transform method of fringe pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72 (1982).
[CrossRef]

Tiziani, H. J.

C. Perez-Lopez, F. Mendoza Santoyo, G. Pedrini, S. Schedin, and H. J. Tiziani, “Pulsed digital holographic interferometry for dynamic measurement of rotating objects with an optical derotator,” Appl. Opt. 40, 5106-5110 (2001).
[CrossRef]

S. Schedin, G. Pedrini, H. J. Tiziani, A. K. Aggarwal, and M. E. Gusev, “Highly sensitive pulsed digital holography for built-in defect analysis with a laser excitation,” Appl. Opt. 40, 100-103 (2001).
[CrossRef]

G. Pedrini, Y. L. Zou, and H. J. Tiziani, “Digital double pulse holographic interferometry for vibration analysis,” J. Mod. Opt. 42, 367-374 (1995).
[CrossRef]

G. Pedrini and H. J. Tiziani, “Digital holographic interferometry,” in Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, 2001), pp. 337-362, Chap. 6.

Vest, C. M.

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

Vikram, C. S.

C. S. Vikram, “Stroboscopic holographic interferometry of vibration simultaneously in two sinusoidal modes,” Opt. Commun. 11, 360-364 (1974).
[CrossRef]

Wilson, A. D.

Zou, Y. L.

G. Pedrini, Y. L. Zou, and H. J. Tiziani, “Digital double pulse holographic interferometry for vibration analysis,” J. Mod. Opt. 42, 367-374 (1995).
[CrossRef]

Appl. Opt.

J. Mod. Opt.

G. Pedrini, Y. L. Zou, and H. J. Tiziani, “Digital double pulse holographic interferometry for vibration analysis,” J. Mod. Opt. 42, 367-374 (1995).
[CrossRef]

J. Opt. Soc. Am.

M. Takeda, Hideki, and S. Kobayashi, “Fourier-transform method of fringe pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72 (1982).
[CrossRef]

A. D. Wilson and D. H. Strope, “Time-average holographic interferometry of a circular plate vibrating simultaneously in two rationally related modes,” J. Opt. Soc. Am. 60, 1162-1165 (1970).
[CrossRef]

Nature

E. Archbold and A. A. Ennos, “Observation of surface vibration modes by stroboscopic hologram interferometry,” Nature 217, 942-943 (1968).
[CrossRef]

Opt. Commun.

M. Miller, “Stroboscopic interferometry in ramp approximation,” Opt. Commun. 14, 406-408 (1975).
[CrossRef]

C. S. Vikram, “Stroboscopic holographic interferometry of vibration simultaneously in two sinusoidal modes,” Opt. Commun. 11, 360-364 (1974).
[CrossRef]

Opt. Express

Optik (Jena)

K. A. Stetson, “A rigorous treatment of the fringes of hologram interferometry,” Optik (Jena) 29, 386-400 (1969).

Other

Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, 2001).

G. Pedrini and H. J. Tiziani, “Digital holographic interferometry,” in Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, 2001), pp. 337-362, Chap. 6.

R. J. Collier, C. B. Burckhard, and L. H. Lin, Optical Holography (Academic, 1971), Chap. 5.

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

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Figures (5)

Fig. 1
Fig. 1

Experimental setup: (1) Nd-YAG laser, (2) beam splitter, (3) mirror, (4) spherical mirror, (5) object, (6) positive lens,  (7) aperture, (8) reference beam, (9) CCD camera, (10) personal computer, (11) electromagnetic exciter of mechanical vibrations, (12) sensor (accelerometer).

Fig. 2
Fig. 2

ω 1 / ω 2 = 1 / 3 pulse sequences setting an example to compensate for (a) low frequency ω 1 and (b) high frequency ω 2 .

Fig. 3
Fig. 3

Detailed sketch of loading and signal back answer system for the object: (1) disc, (2) loudspeaker (exciter of the vibrations), (3) accelerometer (sensor).

Fig. 4
Fig. 4

Interferograms of the pure resonant form: (a) oscillation ω 1 = 124 Hz , (b) oscillation ω 2 = 372 Hz .

Fig. 5
Fig. 5

Inteferograms (phase differences) of two modes resonant process as the phase scanning during the acquisitions of (b), (h), (k) revealed mode 372 Hz and (d) revealed mode 124 Hz .

Equations (9)

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I ( x , y ) = | R H ( x , y ) | 2 + | U H ( x , y ) | 2 + R H * ( x , y ) × U H ( x , y ) + U H * ( x , y ) × R H ( x , y ) ,
f max = 2 λ sin ( θ max 2 ) .
Δ φ = 2 π λ d · s ,
Δ φ = arctan Re ( U 1 ) Im ( U 2 ) Re ( U 2 ) Im ( U 1 ) Re ( U 1 ) Re ( U 2 ) + Im ( U 1 ) Im ( U 2 ) .
A ( r , t ) = 1 = n N A n ( r ) sin ( ω n t + φ n ) ,
t 1 = [ 2 ( p 1 ) π + θ φ ] / n ω 1 , t 2 = [ 2 ( p 1 ) π θ φ ] / n ω 1 ,
t 1 = [ 2 ( p 1 ) π + θ ] / ω 1 , t 2 = [ 2 ( p 1 ) π θ ] / ω 1 .
| M T | 2 = | 2 Δ t T SINC [ 1 2 s · A ( ω cos ( ω t 0 ) ) Δ t ] cos ( s · A sin ( ω t 0 ) ) | 2 ,
s · A cos ( ω t 0 ) Q 1 ,

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