Abstract

Characteristics of the fringe pattern detected by an electronic speckle pattern interferometer, in conditions in which a test object deforms in an arbitrary direction and the speckle intensity is detected over a pixel area in the TV camera to be used, have been investigated from two aspects: speckle noise reduction and fringe contrast. The main result is that the fringes are obtained with high contrast and low speckle noise, if the speckle size is selected by the optical system so as to be smaller than the pixel size. This result is applicable to highly accurate measurements of the out-of-plane displacements of the test object, whose in-plane displacement is small.

© 1995 Optical Society of America

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References

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  1. A. E. Ennos, “Speckle interferometry,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1978), Vol. 16, pp. 233–288.
    [CrossRef]
  2. O. J. Lokberg, G. A. Slettemoen, “Interferometric comparison of displacements by electronic speckle pattern interferometry,” Appl. Opt. 20, 2630–2634 (1981).
    [CrossRef] [PubMed]
  3. S. Nakadate, T. Yatagai, H. Saito, “Computer-aided speckle pattern interferometry,” Appl. Opt. 22, 237–243 (1983).
    [CrossRef] [PubMed]
  4. R. R. Vera, D. Kerr, F. M. Santoyo, “Electronic speckle contouring,” J. Opt. Soc. Am. A 9, 2000–2008 (1992).
    [CrossRef]
  5. J. Kato, I. Yamaguchi, Q. Ping, “Automatic deformation analysis by a TV speckle interferometer using a laser diode,” Appl. Opt. 32, 77–83 (1993).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  7. G. A. Slettemoen, “First-order statistics of displayed speckle patterns in electronic speckle pattern interferometry,” J. Opt. Soc. Am. 71, 474–482 (1981).
    [CrossRef]
  8. G. A. Slettemoen, “General analysis of fringe contrast in electronic speckle pattern interferometry,” Opt. Acta 26, 313–327 (1979).
    [CrossRef]
  9. T. Yoshimura, “Statistical properties of dynamic speckles,” J. Opt. Soc. Am. A 3, 1032–1054 (1986).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

1993 (2)

1992 (1)

1991 (1)

1986 (1)

1983 (1)

1981 (2)

1979 (1)

G. A. Slettemoen, “General analysis of fringe contrast in electronic speckle pattern interferometry,” Opt. Acta 26, 313–327 (1979).
[CrossRef]

Chen, D. J.

Chiang, F. P.

Ennos, A. E.

A. E. Ennos, “Speckle interferometry,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1978), Vol. 16, pp. 233–288.
[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), pp. 9–75.
[CrossRef]

Kato, J.

Kerr, D.

Lokberg, O. J.

Mehta, C. L.

C. L. Mehta, “Theory of photoelectron counting,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1970), Vol. 8, pp. 373–440.
[CrossRef]

Nakadate, S.

Petersen, M. O.

Ping, Q.

Saito, H.

Santoyo, F. M.

Slettemoen, G. A.

Vera, R. R.

Yamaguchi, I.

Yatagai, T.

Yoshimura, T.

Appl. Opt. (4)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Opt. Acta (1)

G. A. Slettemoen, “General analysis of fringe contrast in electronic speckle pattern interferometry,” Opt. Acta 26, 313–327 (1979).
[CrossRef]

Other (3)

C. L. Mehta, “Theory of photoelectron counting,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1970), Vol. 8, pp. 373–440.
[CrossRef]

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 9–75.
[CrossRef]

A. E. Ennos, “Speckle interferometry,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1978), Vol. 16, pp. 233–288.
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Experimental setup of the out-of-plane displacement-sensitive interferometer. W, video signal that corresponds to the integrated intensity.

Fig. 2
Fig. 2

Dependences of the average ESPI signal on rs/D.

Fig. 3
Fig. 3

Dependences of the normalized standard deviation of the ESPI signal on rs/D.

Fig. 4
Fig. 4

Dependences of the fringe contrast on the in-plane displacement for the speckle sizes of 44.8 and 22.4 μm.

Fig. 5
Fig. 5

Dependences of the fringe contrast on rs/D as a function of the in-plane displacement.

Fig. 6
Fig. 6

ESPI signal of the out-of-plane displacements for the piezoelectric-transducer-driven vibrator. The applied voltage is (a) 6 V and (b) 12 V.

Equations (18)

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( I a - I b ) 2 = I a 2 + I b 2 - 2 I a I b .
I a ( X 1 ) I b ( X 2 ) = I a ( X 1 ) I b ( X 2 ) + E a ( X 1 ) E b * ( X 2 ) 2 .
I a ( X 1 ) I b ( X 2 ) = I 2 + E a o ( X 1 ) E b o * ( X 2 ) + E a r ( X 1 ) E b r * ( X 2 ) 2 .
E a o ( X 1 ) E b o * ( X 2 ) = ( I / 2 ) exp [ - X 1 - X 2 + M d x y 2 / ( 2 r s 2 ) ] exp ( i 2 k d z ) , E a r ( X 1 ) E b r * ( X 2 ) = ( I / 2 ) exp [ - X 1 - X 2 2 / ( 2 r s 2 ) ] ,
r s = 2 F 2 / ( k q ) .
( I a - I b ) 2 = I 2 [ 1 - cos ( 2 k d z ) ] ,
W = I ( X j ) H ( X j ) d X j ,
H ( X j ) = exp [ - 2 X j - X 2 / D 2 ] ,
W a 2 = I a ( X 1 ) I a ( X 2 ) H ( X 1 ) H ( X 2 ) d X 1 d X 2 , W a W b = I a ( X 1 ) I b ( X 2 ) H ( X 1 ) H ( X 2 ) d X 1 d X 2 .
( W a - W b ) 2 = f W 2 2 { 3 - exp ( - f | M d x y r s | 2 ) - 2 exp [ - ( 1 + f ) 4 | M d x y r s | 2 ] cos ( 2 k d z ) ,
f = [ 1 + ( D / r s ) 2 ] - 1 .
( W a - W b ) 2 = f W 2 [ 1 - cos ( 2 k d z ) ] .
σ 2 = ( W a - W b ) 4 - ( W a - W b ) 2 2 = 2 W a 4 - 8 W a 3 W b + 6 W a 2 W b 2 - f 2 W 4 ,
E a 1 E a 2 E a j E b 1 * E b 2 * E b j * = Σ E a 1 E b s * E a 2 E b t * E a j E b u * ,
W a 4 W 4 = 1 + 6 f + 3 f 3 + 128 f 2 ( f + 3 ) 2 + 24 f 3 ( f + 1 ) 2 , W a 3 W b W 4 = 1 + 9 f 2 + 3 f 2 2 + 80 f 2 ( f + 3 ) 2 + 12 f 3 ( f + 1 ) 2 , W a 2 W b 2 W 4 = 1 + 4 f + 3 f 2 2 + 64 f 2 ( f + 3 ) 2 + 9 f 3 ( f + 1 ) 2 .
σ 2 = [ 2 f 2 ( f 2 + 5 f + 1 ) / ( f + 1 ) 2 ] W 4 .
N = σ / A = [ 2 ( f 2 + 5 f + 1 ) ] 1 / 2 / ( f + 1 ) ,
C d = 2 exp [ - ( 1 + f ) M d x y / r s 2 / 4 ] 3 - exp ( - f M d x y / r s 2 ) ,

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