Abstract

Vibration observation is a major application of digital speckle-pattern interferometry (DSPI), which is a variation on electronic speckle-pattern interferometry (ESPI). DSPI processes speckle patterns in a computer rather than with a frame grabber and analog electronics as in ESPI. A new method of observing vibration fringes is presented and compared with existing techniques as well as some variations on them. Fringe contrast and signal-to-noise ratio are used as a means of comparison since these quantities are dependent on the techniques used. This new technique involves continuously subtracting a reference frame containing only self-interference terms and no cross interference term from the time-averaged data frames of the vibrating object. This reference frame is created by vibrating a reference mirror at a high amplitude while the object is at rest. Comparisons of calculated fringe contrast with four other observation methods show that this method yields extremely good fringe contrast. Experimental results are shown for this new technique as well as for the most commonly used vibration-observation technique. These results show that the new technique is far superior to all the other methods for moderately unstable objects, which may slowly drift or deform in time.

© 1985 Optical Society of America

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References

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  1. K. Creath, “Digital speckle pattern interferometry (DSPI) using a 100 100 imaging array,” Proc. Soc. Photo-Opt. Instrum. Eng. 501, 292 (1984).
  2. J. N. Butters, J. A. Leendertz, “Speckle pattern and holographic techniques in engineering metrology,” Opt. Laser Technol. 3, 26 (1971).
    [CrossRef]
  3. A. Macovski, S. D. Ramsey, L. F. Schaefer, “Time-lapse interferometry and contouring using television systems,” Appl. Opt. 10, 2722 (1971).
    [CrossRef] [PubMed]
  4. R. Jones, C. Wykes, “General parameters for the design and optimization of electronic speckle pattern interferometers,” Opt. Acta 28, 949 (1981).
    [CrossRef]
  5. C. Wykes, “Use of electronic speckle pattern interferometry (ESPI) in the measurement of static and dynamic surface displacements,” Opt. Eng. 21, 400 (1982).
    [CrossRef]
  6. R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, 1983).
  7. G. Å. Slettemoen, “General analysis of fringe contrast in electronic speckle pattern interferometry,” Opt. Acta 26, 313 (1979).
    [CrossRef]
  8. O. J. Løkberg, “Advances and applications of electronic speckle pattern interferometry (ESPI),” Proc. Soc. Photo-Opt. Instrum Eng. 215, 92 (1980).
  9. O. J. Løkberg, G. Å. Slettemoen, “Electronic speckle pattern interferometry,” in Applied Optics and Optical Engineering, R. R. Shannon, J. C. Wyant, eds. (Academic, New York, to be published).
  10. A. E. Ennos, “Speckle interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin1975).
    [CrossRef]
  11. G. Å. Slettemoen, “Optimal signal processing in electronic speckle pattern interferometry,” Opt. Commun. 23, 213 (1977).
    [CrossRef]
  12. R. Jones, C. Wykes, “De-correlation effects in speckle-pattern interferometry. 2. Displacement dependent de-correlation and applications to the observation of machine-induced strain,” Opt. Acta 24, 533 (1977).
    [CrossRef]
  13. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975).
    [CrossRef]
  14. R. L. Powell, K. A. Stetson, “Interferometric vibration analysis by wavefront reconstruction,” J. Opt. Soc. Am. 55, 1593 (1965).
    [CrossRef]
  15. K. A. Stetson, R. L. Powell, “Interferometric hologram evaluation and real-time vibration analysis of diffuse objects,” J. Opt Soc. Am. 55, 1694 (1965).
    [CrossRef]
  16. S. Nakedate, T. Yatagai, H. Saito, “Digital speckle-pattern shearing interferometry,” Appl. Opt. 24, 4241 (1980).
    [CrossRef]
  17. K. Biedermann, L. Ek, “A recording and display system for hologram interferometry with low resolution imaging devices,” J.Phys. E 8, 571 (1975).
    [CrossRef]

1984 (1)

K. Creath, “Digital speckle pattern interferometry (DSPI) using a 100 100 imaging array,” Proc. Soc. Photo-Opt. Instrum. Eng. 501, 292 (1984).

1982 (1)

C. Wykes, “Use of electronic speckle pattern interferometry (ESPI) in the measurement of static and dynamic surface displacements,” Opt. Eng. 21, 400 (1982).
[CrossRef]

1981 (1)

R. Jones, C. Wykes, “General parameters for the design and optimization of electronic speckle pattern interferometers,” Opt. Acta 28, 949 (1981).
[CrossRef]

1980 (2)

O. J. Løkberg, “Advances and applications of electronic speckle pattern interferometry (ESPI),” Proc. Soc. Photo-Opt. Instrum Eng. 215, 92 (1980).

S. Nakedate, T. Yatagai, H. Saito, “Digital speckle-pattern shearing interferometry,” Appl. Opt. 24, 4241 (1980).
[CrossRef]

1979 (1)

G. Å. Slettemoen, “General analysis of fringe contrast in electronic speckle pattern interferometry,” Opt. Acta 26, 313 (1979).
[CrossRef]

1977 (2)

G. Å. Slettemoen, “Optimal signal processing in electronic speckle pattern interferometry,” Opt. Commun. 23, 213 (1977).
[CrossRef]

R. Jones, C. Wykes, “De-correlation effects in speckle-pattern interferometry. 2. Displacement dependent de-correlation and applications to the observation of machine-induced strain,” Opt. Acta 24, 533 (1977).
[CrossRef]

1975 (1)

K. Biedermann, L. Ek, “A recording and display system for hologram interferometry with low resolution imaging devices,” J.Phys. E 8, 571 (1975).
[CrossRef]

1971 (2)

J. N. Butters, J. A. Leendertz, “Speckle pattern and holographic techniques in engineering metrology,” Opt. Laser Technol. 3, 26 (1971).
[CrossRef]

A. Macovski, S. D. Ramsey, L. F. Schaefer, “Time-lapse interferometry and contouring using television systems,” Appl. Opt. 10, 2722 (1971).
[CrossRef] [PubMed]

1965 (2)

K. A. Stetson, R. L. Powell, “Interferometric hologram evaluation and real-time vibration analysis of diffuse objects,” J. Opt Soc. Am. 55, 1694 (1965).
[CrossRef]

R. L. Powell, K. A. Stetson, “Interferometric vibration analysis by wavefront reconstruction,” J. Opt. Soc. Am. 55, 1593 (1965).
[CrossRef]

Biedermann, K.

K. Biedermann, L. Ek, “A recording and display system for hologram interferometry with low resolution imaging devices,” J.Phys. E 8, 571 (1975).
[CrossRef]

Butters, J. N.

J. N. Butters, J. A. Leendertz, “Speckle pattern and holographic techniques in engineering metrology,” Opt. Laser Technol. 3, 26 (1971).
[CrossRef]

Creath, K.

K. Creath, “Digital speckle pattern interferometry (DSPI) using a 100 100 imaging array,” Proc. Soc. Photo-Opt. Instrum. Eng. 501, 292 (1984).

Ek, L.

K. Biedermann, L. Ek, “A recording and display system for hologram interferometry with low resolution imaging devices,” J.Phys. E 8, 571 (1975).
[CrossRef]

Ennos, A. E.

A. E. Ennos, “Speckle interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin1975).
[CrossRef]

Goodman, J. W.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975).
[CrossRef]

Jones, R.

R. Jones, C. Wykes, “General parameters for the design and optimization of electronic speckle pattern interferometers,” Opt. Acta 28, 949 (1981).
[CrossRef]

R. Jones, C. Wykes, “De-correlation effects in speckle-pattern interferometry. 2. Displacement dependent de-correlation and applications to the observation of machine-induced strain,” Opt. Acta 24, 533 (1977).
[CrossRef]

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, 1983).

Leendertz, J. A.

J. N. Butters, J. A. Leendertz, “Speckle pattern and holographic techniques in engineering metrology,” Opt. Laser Technol. 3, 26 (1971).
[CrossRef]

Løkberg, O. J.

O. J. Løkberg, “Advances and applications of electronic speckle pattern interferometry (ESPI),” Proc. Soc. Photo-Opt. Instrum Eng. 215, 92 (1980).

O. J. Løkberg, G. Å. Slettemoen, “Electronic speckle pattern interferometry,” in Applied Optics and Optical Engineering, R. R. Shannon, J. C. Wyant, eds. (Academic, New York, to be published).

Macovski, A.

Nakedate, S.

S. Nakedate, T. Yatagai, H. Saito, “Digital speckle-pattern shearing interferometry,” Appl. Opt. 24, 4241 (1980).
[CrossRef]

Powell, R. L.

K. A. Stetson, R. L. Powell, “Interferometric hologram evaluation and real-time vibration analysis of diffuse objects,” J. Opt Soc. Am. 55, 1694 (1965).
[CrossRef]

R. L. Powell, K. A. Stetson, “Interferometric vibration analysis by wavefront reconstruction,” J. Opt. Soc. Am. 55, 1593 (1965).
[CrossRef]

Ramsey, S. D.

Saito, H.

S. Nakedate, T. Yatagai, H. Saito, “Digital speckle-pattern shearing interferometry,” Appl. Opt. 24, 4241 (1980).
[CrossRef]

Schaefer, L. F.

Slettemoen, G. Å.

G. Å. Slettemoen, “General analysis of fringe contrast in electronic speckle pattern interferometry,” Opt. Acta 26, 313 (1979).
[CrossRef]

G. Å. Slettemoen, “Optimal signal processing in electronic speckle pattern interferometry,” Opt. Commun. 23, 213 (1977).
[CrossRef]

O. J. Løkberg, G. Å. Slettemoen, “Electronic speckle pattern interferometry,” in Applied Optics and Optical Engineering, R. R. Shannon, J. C. Wyant, eds. (Academic, New York, to be published).

Stetson, K. A.

K. A. Stetson, R. L. Powell, “Interferometric hologram evaluation and real-time vibration analysis of diffuse objects,” J. Opt Soc. Am. 55, 1694 (1965).
[CrossRef]

R. L. Powell, K. A. Stetson, “Interferometric vibration analysis by wavefront reconstruction,” J. Opt. Soc. Am. 55, 1593 (1965).
[CrossRef]

Wykes, C.

C. Wykes, “Use of electronic speckle pattern interferometry (ESPI) in the measurement of static and dynamic surface displacements,” Opt. Eng. 21, 400 (1982).
[CrossRef]

R. Jones, C. Wykes, “General parameters for the design and optimization of electronic speckle pattern interferometers,” Opt. Acta 28, 949 (1981).
[CrossRef]

R. Jones, C. Wykes, “De-correlation effects in speckle-pattern interferometry. 2. Displacement dependent de-correlation and applications to the observation of machine-induced strain,” Opt. Acta 24, 533 (1977).
[CrossRef]

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, 1983).

Yatagai, T.

S. Nakedate, T. Yatagai, H. Saito, “Digital speckle-pattern shearing interferometry,” Appl. Opt. 24, 4241 (1980).
[CrossRef]

Appl. Opt. (2)

S. Nakedate, T. Yatagai, H. Saito, “Digital speckle-pattern shearing interferometry,” Appl. Opt. 24, 4241 (1980).
[CrossRef]

A. Macovski, S. D. Ramsey, L. F. Schaefer, “Time-lapse interferometry and contouring using television systems,” Appl. Opt. 10, 2722 (1971).
[CrossRef] [PubMed]

J. Opt Soc. Am. (1)

K. A. Stetson, R. L. Powell, “Interferometric hologram evaluation and real-time vibration analysis of diffuse objects,” J. Opt Soc. Am. 55, 1694 (1965).
[CrossRef]

J. Opt. Soc. Am. (1)

J.Phys. E (1)

K. Biedermann, L. Ek, “A recording and display system for hologram interferometry with low resolution imaging devices,” J.Phys. E 8, 571 (1975).
[CrossRef]

Opt. Acta (3)

G. Å. Slettemoen, “General analysis of fringe contrast in electronic speckle pattern interferometry,” Opt. Acta 26, 313 (1979).
[CrossRef]

R. Jones, C. Wykes, “General parameters for the design and optimization of electronic speckle pattern interferometers,” Opt. Acta 28, 949 (1981).
[CrossRef]

R. Jones, C. Wykes, “De-correlation effects in speckle-pattern interferometry. 2. Displacement dependent de-correlation and applications to the observation of machine-induced strain,” Opt. Acta 24, 533 (1977).
[CrossRef]

Opt. Commun. (1)

G. Å. Slettemoen, “Optimal signal processing in electronic speckle pattern interferometry,” Opt. Commun. 23, 213 (1977).
[CrossRef]

Opt. Eng. (1)

C. Wykes, “Use of electronic speckle pattern interferometry (ESPI) in the measurement of static and dynamic surface displacements,” Opt. Eng. 21, 400 (1982).
[CrossRef]

Opt. Laser Technol. (1)

J. N. Butters, J. A. Leendertz, “Speckle pattern and holographic techniques in engineering metrology,” Opt. Laser Technol. 3, 26 (1971).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum Eng. (1)

O. J. Løkberg, “Advances and applications of electronic speckle pattern interferometry (ESPI),” Proc. Soc. Photo-Opt. Instrum Eng. 215, 92 (1980).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

K. Creath, “Digital speckle pattern interferometry (DSPI) using a 100 100 imaging array,” Proc. Soc. Photo-Opt. Instrum. Eng. 501, 292 (1984).

Other (4)

O. J. Løkberg, G. Å. Slettemoen, “Electronic speckle pattern interferometry,” in Applied Optics and Optical Engineering, R. R. Shannon, J. C. Wyant, eds. (Academic, New York, to be published).

A. E. Ennos, “Speckle interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin1975).
[CrossRef]

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, 1983).

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Plots of functions of Bessel functions. A, J02(4πa0/λ) for Cases I, III, and IV. B, [1/1.968] [1 − J0(4πa0/λ)]2 for Case II. C, [1/4] [1 + J0(4πa0/λ)]2 for Case V.

Fig. 2
Fig. 2

Calculated fringe contrast versus Bessel-function argument (4πa0/λ) with no electronic noise (σe2 = 0.000) for the five vibration-observation techniques discussed.

Fig. 3
Fig. 3

Calculated fringe contrast versus 4πa0/λ with σe2 = 0.004. This amount of noise enables 50 J02 fringes to be viewed.

Fig. 4
Fig. 4

Calculated fringe contrast versus 4πa0/λ with σe2 = 0.012.

Fig. 5
Fig. 5

Calculated fringe contrast versus 4πa0/λ with σe2 = 0.0004. This is the amount of noise present in the DSPI system described in this paper.

Fig. 6
Fig. 6

Schematic of a DSPI. The reference beam consists of a single-mode optical fiber placed in the center of the aperture that produces a specular spherical wave. The object beam is collimated and illuminates a diffuse object that is then imaged onto a detector array. The object is excited by an attached PZT. The PZT-actuated mirror is used to create a reference frame in Case III.

Fig. 7
Fig. 7

Vibration fringes observed using a single frame of data that has been high-pass filtered and squared before displaying. The object is a steel plate clamped on one side with a PZT exciting the other end. A, 7300-Hz resonance; B, 8560 Hz.

Fig. 8
Fig. 8

Vibration fringes observed by the method outlined in Case III. Same object and resonances as Fig. 7. Noise terms have been subtracted out using a reference frame created by vibrating a PZT-driven mirror at 800 Hz with object at rest (see Fig. 6).

Equations (21)

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C = B max B min B max + B min ,
C = S S + 2 N = α α + 2 ,
I ( x , y , t ) = | A 0 ( x , y ) | 2 + | A R ( x , y ) | 2 + 2 | A 0 ( x , y ) | | A R ( x , y ) | × Re ( exp { i [ ψ 0 ( x , y ) + ϕ 0 ( x , y , t ) ϕ R ( x , y , t ) ] } ) .
M n ( x , y ) = exp [ i ϕ R n ( x , y , t ) i ϕ 0 n ( x , y , t ) ] d t .
B n ( x , y ) = a n 2 [ | A 0 ( x , y ) | 2 + | A R ( x , y ) | 2 + 2 Re [ A R * ( x , y ) A 0 ( x , y ) M n ( x , y ) ] + N n ( x , y ) ] 2 ,
B ( x , y ) = I R 2 + I 0 2 + 4 Re [ ( A R * A 0 ) 2 ] | M | 2 + N 2 ( x , y ) = I R 2 + I 0 2 + 4 I R I 0 cos 2 ( ψ 0 ) | M | 2 + N 2 = I R 2 + I 0 2 + 2 I R I 0 | M | 2 + σ e 2 ,
α I = S N = 2 | M ( x , y ) | 2 I R I 0 I R 2 + I 0 2 + σ e 2 ,
B ( x , y ) = n = 1 2 { a n [ I n ( x , y ) + N n ( x , y ) ] } 2 ,
B ( x , y ) = ( { I R 1 ( x , y ) + I 01 ( x , y ) + 2 Re [ A R 1 * ( x , y ) × A 01 ( x , y ) M 1 ( x , y ) ] + N 1 ( x , y ) } { I R 2 ( x , y ) + I 02 ( x , y ) + 2 Re [ A R 2 * ( x , y ) A 02 ( x , y ) M 2 ( x , y ) ] + N 2 ( x , y ) } ) 2 .
B ( x , y ) = ( 2 Re { A R * ( x , y ) A 0 ( x , y ) [ M 1 ( x , y ) M 2 ( x , y ) ] } + [ N 1 N 2 ] ) 2 .
B ( x , y ) = 4 Re [ ( A R * A 0 ) 2 ] | M 1 ( x , y ) M 2 ( x , y ) | 2 + ( N 1 N 2 ) 2 = 4 I R I 0 cos 2 ( ψ 0 ) | M 1 ( x , y ) M 2 ( x , y ) | 2 + N 1 2 + N 2 2 = 2 I R I 0 | M 1 ( x , y ) M 2 ( x , y ) | 2 + 2 σ e 2 ,
α I I = | M 1 M 2 | 2 I R I 0 σ e 2 .
ψ ( x , y , t ) = exp { i [ ϕ ( x , y ) 4 π a 0 λ cos ( ω t ) ] } ,
M ( x , y ) = ( 1 T ) exp [ i ϕ ( x , y ) ] 0 T exp [ i 4 π a 0 λ cos ( ω t ) ] d t = exp ( i ϕ ) J 0 ( 4 π a 0 λ ) ,
2 | M ( x , y ) | 2 = J 0 2 ( 4 π a 0 λ ) .
| M 1 M 2 | 2 = 1 1.968 [ 1 2 J 0 ( 4 π a 0 λ ) [ cos ( Δ ϕ ) ] + J 0 2 ( 4 π a 0 λ ) ] .
| M 1 M 2 | 2 = 1 1.968 [ 1 J 0 ( 4 π a 0 λ ) ] 2 .
| M 1 M 2 | 2 = J 0 2 ( 4 π a 0 λ ) .
| M 1 M 2 | 2 = ( 4 4 ) J 0 2 ( 4 π a 0 λ ) cos 2 ( Δ ϕ 2 ) = J 0 2 ( 4 π a 0 λ ) cos 2 ( Δ ϕ 2 ) ,
| M 1 M 2 | 2 = 1 4 [ 1 + 2 J 0 ( 4 π a 0 λ ) cos ( Δ ϕ ) + J 0 2 ( 4 π a 0 λ ) ] .
| M 1 M 2 | 2 = 1 4 [ 1 + J 0 ( 4 π a 0 λ ) ] 2 .

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