Abstract

A new electronic speckle pattern interferometric (ESPI) technique is introduced. The technique is based on a reference beam combined with a large aperture optical system. The basic principles are described and compared with conventional ESPI setups. The new interferometer is easy to adjust, it is invulnerable to dust and scratches on the optical components, and is very compact. It is well-suited for practical engineering applications. Light sensitivity and fringe quality are comparable with the conventional ESPI features. Superior fringe pattern can be obtained by use of a new speckle reduction technique to be described.

© 1980 Optical Society of America

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References

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  1. W. T. Cathey, U.S. Patent3,415,587 (10Dec.1968).
  2. J. P. Waters, Appl. Opt. 11, 630 (1972).
    [CrossRef] [PubMed]
  3. A. E. Ennos, in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer, Berlin, 1975), p. 202.
  4. G. Å. Slettemoen, Opt. Commun. 23, 213 (1977).
    [CrossRef]
  5. G. Å. Slettemoen, Opt. Acta 26, 313 (1979).
    [CrossRef]
  6. K. A. Stetson, Optik 29, 386 (1969).
  7. K. Biedermann, L. Ek, J. Phys. E: 8, 571 (1975).
    [CrossRef]
  8. E. N. Leith, J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).
    [CrossRef]
  9. A. Macovski, S. D. Ramsey, L. F. Schaefer, Appl. Opt. 10, 2722 (1971).
    [CrossRef] [PubMed]
  10. J. N. Butters, J. A. Leendertz, Meas. Control 4, 349 (1971).
  11. O. J. Løkberg, Appl. Opt. 18, 2377 (1979).
    [CrossRef] [PubMed]
  12. W. Martienssen, S. Spiller, Phys. Lett. A 24, 126 (1967).
    [CrossRef]
  13. J. C. Dainty, W. T. Welford, Opt. Commun. 3, 289 (1971).
    [CrossRef]
  14. O. J. Løkberg, K. Høgmoen, J. Phys. E: 9, 847 (1976).
    [CrossRef]
  15. O. J. Løkberg, K. Høgmoen, Appl. Opt. 15, 2701 (1976).
    [CrossRef] [PubMed]
  16. K. Høgmoen, O. J. Løkberg, Appl. Opt. 16, 1869 (1977).
    [CrossRef] [PubMed]
  17. O. J. Løkberg, K. Høgmoen, O. M. Holje, Appl. Opt. 18, 763 (1979).
    [CrossRef] [PubMed]

1979 (3)

1977 (2)

1976 (2)

O. J. Løkberg, K. Høgmoen, J. Phys. E: 9, 847 (1976).
[CrossRef]

O. J. Løkberg, K. Høgmoen, Appl. Opt. 15, 2701 (1976).
[CrossRef] [PubMed]

1975 (1)

K. Biedermann, L. Ek, J. Phys. E: 8, 571 (1975).
[CrossRef]

1972 (1)

1971 (3)

A. Macovski, S. D. Ramsey, L. F. Schaefer, Appl. Opt. 10, 2722 (1971).
[CrossRef] [PubMed]

J. N. Butters, J. A. Leendertz, Meas. Control 4, 349 (1971).

J. C. Dainty, W. T. Welford, Opt. Commun. 3, 289 (1971).
[CrossRef]

1969 (1)

K. A. Stetson, Optik 29, 386 (1969).

1967 (1)

W. Martienssen, S. Spiller, Phys. Lett. A 24, 126 (1967).
[CrossRef]

1962 (1)

Biedermann, K.

K. Biedermann, L. Ek, J. Phys. E: 8, 571 (1975).
[CrossRef]

Butters, J. N.

J. N. Butters, J. A. Leendertz, Meas. Control 4, 349 (1971).

Cathey, W. T.

W. T. Cathey, U.S. Patent3,415,587 (10Dec.1968).

Dainty, J. C.

J. C. Dainty, W. T. Welford, Opt. Commun. 3, 289 (1971).
[CrossRef]

Ek, L.

K. Biedermann, L. Ek, J. Phys. E: 8, 571 (1975).
[CrossRef]

Ennos, A. E.

A. E. Ennos, in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer, Berlin, 1975), p. 202.

Høgmoen, K.

Holje, O. M.

Leendertz, J. A.

J. N. Butters, J. A. Leendertz, Meas. Control 4, 349 (1971).

Leith, E. N.

Løkberg, O. J.

Macovski, A.

Martienssen, W.

W. Martienssen, S. Spiller, Phys. Lett. A 24, 126 (1967).
[CrossRef]

Ramsey, S. D.

Schaefer, L. F.

Slettemoen, G. Å.

G. Å. Slettemoen, Opt. Acta 26, 313 (1979).
[CrossRef]

G. Å. Slettemoen, Opt. Commun. 23, 213 (1977).
[CrossRef]

Spiller, S.

W. Martienssen, S. Spiller, Phys. Lett. A 24, 126 (1967).
[CrossRef]

Stetson, K. A.

K. A. Stetson, Optik 29, 386 (1969).

Upatnieks, J.

Waters, J. P.

Welford, W. T.

J. C. Dainty, W. T. Welford, Opt. Commun. 3, 289 (1971).
[CrossRef]

Appl. Opt. (6)

J. Opt. Soc. Am. (1)

J. Phys. E (1)

O. J. Løkberg, K. Høgmoen, J. Phys. E: 9, 847 (1976).
[CrossRef]

J. Phys. E: (1)

K. Biedermann, L. Ek, J. Phys. E: 8, 571 (1975).
[CrossRef]

Meas. Control (1)

J. N. Butters, J. A. Leendertz, Meas. Control 4, 349 (1971).

Opt. Acta (1)

G. Å. Slettemoen, Opt. Acta 26, 313 (1979).
[CrossRef]

Opt. Commun. (2)

G. Å. Slettemoen, Opt. Commun. 23, 213 (1977).
[CrossRef]

J. C. Dainty, W. T. Welford, Opt. Commun. 3, 289 (1971).
[CrossRef]

Optik (1)

K. A. Stetson, Optik 29, 386 (1969).

Phys. Lett. A (1)

W. Martienssen, S. Spiller, Phys. Lett. A 24, 126 (1967).
[CrossRef]

Other (2)

W. T. Cathey, U.S. Patent3,415,587 (10Dec.1968).

A. E. Ennos, in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer, Berlin, 1975), p. 202.

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Figures (6)

Fig. 1
Fig. 1

Schematic of an ESPI setup with a specular reference beam.

Fig. 2
Fig. 2

Wiener spectra of the different hologram terms at the TV camera. Sr0 is the reference–object cross-interference term, and S0 is the object self-interference term. The reference self-interference term Sr is indicated by the dotted line. The spectra have been drawn with a realistic reference–object intensity ratio. (a) Wiener spectrum with a circular aperture of radius equal to r. (b) Wiener spectrum with a double-slit aperture with slit widths equal to b. The x index denotes the direction parallel to the scanning of the TV camera, and z is the distance from the aperture to the photosurface of the TV camera.

Fig. 3
Fig. 3

Schematic of a speckle reference beam setup. M1, M2, and M3 are mirrors, and the electronic processor contains in addition to an amplifier and rectifier, a bandpass filter that only passes the signal due to cross-interference between the objects, while stopping the signal due to the self-interference from each of the objects.

Fig. 4
Fig. 4

Aperture element with 3½ periods of stripes, and Wiener spectra at the TV camera for a speckle reference beam setup. S1 and S2 are the Wiener spectra of the self-interference terms of objects 1 and 2, respectively. S12 is the Wiener spectrum of the useful object 1–object 2 cross-interference term, where the hatched spectrum passes the electronic bandpass filter. K is a proportionality constant equal to (λz)2/bh, and the x index denotes the direction parallel to the scan direction of the TV camera. z is the distance from the aperture to the photosurface of the TV camera.

Fig. 5
Fig. 5

Optical part of the simple ESPI setup based on a speckle reference beam.

Fig. 6
Fig. 6

Two time average patterns of a vibrating steel plate size 60 × 80 × 1 mm (the black cross is used for marking purposes). The resonant frequencies are 1549 Hz and 33,124 Hz, respectively. These patterns are recorded by ESPI with (a) a specular reference beam, (b) a speckle reference beam, and (c) a speckle reference beam and speckle reduction with an additional rotating aperture.

Equations (6)

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I m ( x , y ) = σ e 2 + ( g γ r I r ) 2 + ( g γ 0 I 0 ) 2 + 2 ( g γ r 0 ) 2 I r I 0 M ( x , y ) 2 ,
M ( x , y ) = t f ( t ) exp { i [ ϕ 0 ( x , y , t ) - ϕ r ( t ) ] } d t
γ r 0 2 = P ( ν ) 2 H tot 2 d ν P ( ν ) 2 d ν ,
γ 12 2 = [ P 1 ( ν ) 2 * P 2 ( ν ) 2 ] H tot 2 d ν [ P 1 ( ν ) 2 * P 2 ( ν ) 2 ] d ν ,
γ 1 2 = [ P 1 ( ν ) 2 * P 1 ( ν ) 2 ] H tot 2 d ν [ P 1 ( ν ) 2 * P 1 ( ν ) 2 ] d ν .
I m ( x , y ) = σ e 2 + ( g γ 1 I 1 ) 2 + ( g γ 2 I 2 ) 2 + 2 ( g γ 12 ) 2 I 1 I 2 M ( x , y ) 2 .

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