Abstract

Temporal speckle pattern interferometry (TSPI) is an optical measurement procedurefor measuring the displacement of rough technical surfaces. The time-dependent speckle modulation due to optical path difference changes is tracked during the whole displacement of the surface and then evaluated pointwise without referring to neighboring pixels. This feature allows for its use as independent point sensors. This aspect of incremental phase tracking enables TSPI to be used to measure time-resolved mechanical vibrations. It also reduces the deteriorating effect of the decorrelation. Therefore large displacements can be measured. A concept for an inexpensive fiber-optical point sensor was developed and the theoretical accuracy for vibration measurement was investigated. The TSPI measurement of a loudspeaker membrane is compared with a high-precision vibrometer measurement. The first results show good agreement.

© 2006 Optical Society of America

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References

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  1. R. Jones and C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, 1983).
  2. R. S. Sirohi, Speckle Metrology (Dekker, 1993).
  3. A. E. Ennos, "Speckle interferometry," in Laser Speckle and Related Phenomena, Vol. 9 of Topics in Applied Physics, J.C.Dainty, ed. (Springer, 1975), pp. 203-253.
    [CrossRef]
  4. P. K. Rastogi, "Measurement of static surface displacements, derivatives of displacement, and three-dimensional surface shape--examples of applications to nondestructive testing," in Digital Speckle Pattern Interferometry and Related Techniques, P.K. Rastogi, ed. (Wiley, 2001), pp. 141-224.
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  8. C. Joenathan, B. Franze, P. Haible, and H. J. Tiziani, "Speckle interferometry with temporal phase evaluation: influence of decorrelation, speckle size, and nonlinearity of the camera," Appl. Opt. 38, 1169-1178 (1999).
    [CrossRef]
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    [CrossRef]
  11. H. J. Tiziani, B. Franze, and P. Haible, "Wavelength-shift speckle interferometry for absolute profilometry using a mode-hop free external cavity diode laser," J. Mod. Opt. 44, 1485-1496 (1997).
    [CrossRef]
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    [CrossRef]
  13. R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, 1965).
  14. J. M. Huntley, "Automated analysis of speckle intergerograms," in Digital Speckle Pattern Interferometry and Related Techniques, P.K.Rastogi, ed. (Wiley, 2001), pp. 59-139.
  15. E. A. Bedrosian, "Product theorem for Hilbert transforms," Proc. IEEE 51, 868-869 (1963).
    [CrossRef]
  16. S. L. Hahn, "Hilbert transformation," in The Transforms and Applications Handbook, A.D.Poularikas, ed. (CRC, 1996), pp. 463-629.
  17. P. Haible, M. P. Kothiyal, and H. J. Tiziani, "Heterodyne temporal speckle-pattern interferometry," Appl. Opt. 39, 114-117 (2000).
    [CrossRef]
  18. J. Kauffmann, M. Gahr, and H. J. Tiziani, "Noise reduction in speckle pattern interferometry," in Speckle Metrology, K. Gastinger, J. Lokberg, and S. Winter, eds., Proc. SPIE 4933, 9-14 (2003).
    [CrossRef]

2003 (1)

J. Kauffmann, M. Gahr, and H. J. Tiziani, "Noise reduction in speckle pattern interferometry," in Speckle Metrology, K. Gastinger, J. Lokberg, and S. Winter, eds., Proc. SPIE 4933, 9-14 (2003).
[CrossRef]

2001 (1)

H. J. Tiziani, "Progress in temporal speckle modulation," Optik 112, 370-380 (2001).
[CrossRef]

2000 (1)

1999 (1)

1998 (2)

1997 (1)

H. J. Tiziani, B. Franze, and P. Haible, "Wavelength-shift speckle interferometry for absolute profilometry using a mode-hop free external cavity diode laser," J. Mod. Opt. 44, 1485-1496 (1997).
[CrossRef]

1993 (1)

T. Floureux, "Improvement of electronic speckle fringes by addition of incremental images," Opt. Laser Technol. 25, 255-258 (1993).
[CrossRef]

1982 (1)

1963 (1)

E. A. Bedrosian, "Product theorem for Hilbert transforms," Proc. IEEE 51, 868-869 (1963).
[CrossRef]

Bedrosian, E. A.

E. A. Bedrosian, "Product theorem for Hilbert transforms," Proc. IEEE 51, 868-869 (1963).
[CrossRef]

Bracewell, R.

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, 1965).

Ennos, A. E.

A. E. Ennos, "Speckle interferometry," in Laser Speckle and Related Phenomena, Vol. 9 of Topics in Applied Physics, J.C.Dainty, ed. (Springer, 1975), pp. 203-253.
[CrossRef]

Floureux, T.

T. Floureux, "Improvement of electronic speckle fringes by addition of incremental images," Opt. Laser Technol. 25, 255-258 (1993).
[CrossRef]

Franze, B.

Gahr, M.

J. Kauffmann, M. Gahr, and H. J. Tiziani, "Noise reduction in speckle pattern interferometry," in Speckle Metrology, K. Gastinger, J. Lokberg, and S. Winter, eds., Proc. SPIE 4933, 9-14 (2003).
[CrossRef]

Hahn, S. L.

S. L. Hahn, "Hilbert transformation," in The Transforms and Applications Handbook, A.D.Poularikas, ed. (CRC, 1996), pp. 463-629.

Haible, P.

Huntley, J. M.

J. M. Huntley, "Automated analysis of speckle intergerograms," in Digital Speckle Pattern Interferometry and Related Techniques, P.K.Rastogi, ed. (Wiley, 2001), pp. 59-139.

Ina, H.

Joenathan, C.

Jones, R.

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

Kauffmann, J.

J. Kauffmann, M. Gahr, and H. J. Tiziani, "Noise reduction in speckle pattern interferometry," in Speckle Metrology, K. Gastinger, J. Lokberg, and S. Winter, eds., Proc. SPIE 4933, 9-14 (2003).
[CrossRef]

Kobayashi, S.

Kothiyal, M. P.

Rastogi, P. K.

P. K. Rastogi, "Measurement of static surface displacements, derivatives of displacement, and three-dimensional surface shape--examples of applications to nondestructive testing," in Digital Speckle Pattern Interferometry and Related Techniques, P.K. Rastogi, ed. (Wiley, 2001), pp. 141-224.

Sirohi, R. S.

R. S. Sirohi, Speckle Metrology (Dekker, 1993).

Takeda, M.

Tiziani, H. J.

Wykes, C.

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

Appl. Opt. (4)

J. Mod. Opt. (1)

H. J. Tiziani, B. Franze, and P. Haible, "Wavelength-shift speckle interferometry for absolute profilometry using a mode-hop free external cavity diode laser," J. Mod. Opt. 44, 1485-1496 (1997).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Laser Technol. (1)

T. Floureux, "Improvement of electronic speckle fringes by addition of incremental images," Opt. Laser Technol. 25, 255-258 (1993).
[CrossRef]

Optik (1)

H. J. Tiziani, "Progress in temporal speckle modulation," Optik 112, 370-380 (2001).
[CrossRef]

Proc. IEEE (1)

E. A. Bedrosian, "Product theorem for Hilbert transforms," Proc. IEEE 51, 868-869 (1963).
[CrossRef]

Proc. SPIE (1)

J. Kauffmann, M. Gahr, and H. J. Tiziani, "Noise reduction in speckle pattern interferometry," in Speckle Metrology, K. Gastinger, J. Lokberg, and S. Winter, eds., Proc. SPIE 4933, 9-14 (2003).
[CrossRef]

Other (8)

S. L. Hahn, "Hilbert transformation," in The Transforms and Applications Handbook, A.D.Poularikas, ed. (CRC, 1996), pp. 463-629.

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, 1965).

J. M. Huntley, "Automated analysis of speckle intergerograms," in Digital Speckle Pattern Interferometry and Related Techniques, P.K.Rastogi, ed. (Wiley, 2001), pp. 59-139.

C. Joenathan, "Speckle photography, shearography and ESPI," in Optical Measuring Techniques and Applications, P.K. Rastogi, ed. (Artech House, 1997), pp. 151-182.

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

R. S. Sirohi, Speckle Metrology (Dekker, 1993).

A. E. Ennos, "Speckle interferometry," in Laser Speckle and Related Phenomena, Vol. 9 of Topics in Applied Physics, J.C.Dainty, ed. (Springer, 1975), pp. 203-253.
[CrossRef]

P. K. Rastogi, "Measurement of static surface displacements, derivatives of displacement, and three-dimensional surface shape--examples of applications to nondestructive testing," in Digital Speckle Pattern Interferometry and Related Techniques, P.K. Rastogi, ed. (Wiley, 2001), pp. 141-224.

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Figures (9)

Fig. 1
Fig. 1

(a) Fiber-optical Michelson interferometer and (b) fiber-optical Fizeau interferometer.

Fig. 2
Fig. 2

(Color online) Reconstruction procedure. (a) Original signal with z ^ = 2 μ m and f m = 100   Hz . (b) Quadrature representation of the signal. (c) Hilbert transform of the signal. (d) Given vibration velocity sign and offset corrected. (e) Reconstructed instantaneous velocity.

Fig. 3
Fig. 3

(Color online) Reconstruction procedure. (a) Original signal with z ^ = 10 μ m and f m = 100   Hz . (b) Quadrature representation of the signal. (c) Hilbert transform of the signal. (d) Given vibration velocity with sign corrected. (e) Reconstructed instantaneous velocity.

Fig. 4
Fig. 4

(Color online) (a) Spectrum of the given vibration velocity with sign and offset correction. (b) Spectrum of the reconstructed instantaneous velocity. The signal could be low-pass filtered as indicated.

Fig. 5
Fig. 5

Relative deviation of the reconstruction versus sampling and carrier frequencies.

Fig. 6
Fig. 6

(a) Relative deviation of the reconstruction versus amplitude and vibration frequency and (b) relative deviation of the reconstruction with a 20   kHz low-pass filter.

Fig. 7
Fig. 7

Bidirectional laser–detector module with a pigtail.

Fig. 8
Fig. 8

(Color online) Voltage at the AD converter input corresponding to the intensity signal on the detector.

Fig. 9
Fig. 9

(Color online) Measured instantaneous vibration velocity. (a) Reconstruction. (b) Reconstruction with a low-pass filter.

Equations (18)

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I ( t ) = I 0 { 1 + m   cos [ ϕ ( t ) + ϕ 0 ] } .
z ( t ) = z ^   cos ( 2 π f m t + ϕ m ) ,
v ( t ) = d d t z ( t ) = 2 π f m z ^   sin ( 2 π f m t ) .
ϕ ( t ) = 4 π λ z ( t ) .
BW = 2 f m ( 4 π λ z ^ + 1 ) .
f O = a   cos [ ϕ ( t ) + ϕ 0 ] .
f Q = a   sin [ ϕ ( t ) + ϕ 0 ] .
ϕ ( t ) + ϕ 0 = unwrap ( arctan2 { sin [ ϕ ( t ) + ϕ 0 ] cos [ ϕ ( t ) + ϕ 0 ] } ) ,
f ( t ) = 4 π λ f m z ^   sin ( 2 π f m t ) .
f Q ( t ) = H { f O ( t ) } ,
f Q ( t ) = 2   Im [ A { f O ( t ) } ] .
A { } = F 1 { F { } h ( w ) } .
H { f ( t ) g ( t ) } = f ( t ) H { g ( t ) } .
H { cos [ ϕ ( t ) + 2 π f C t + ϕ 0 ] } = sin [ ϕ ( t ) + 2 π f C t + ϕ 0 ] .
I i = I 0 { 1 + m   cos [ 4 π z ^ λ   cos ( 2 π f m t i ) + 2 π f C t i + ϕ 0 ] } .
t i = i n t tot .
s = n t tot ,
dev rel = i ( x ˜ i x i ) 2 i ( x i ) 2 .

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