Abstract

Using a 1-D analysis of a double-exposed specklegram, we explore the influence of the diffraction halo removal in the numerical processing of data when it is done via discrete Fourier transform. Relative errors in displacements appear if the removal is not done, and they increase as fringe visibility and fringe density decrease. These errors are <0.5% for fringe densities larger than six fringes within the diffraction halo.

© 1981 Optical Society of America

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References

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  1. A. E. Ennos, “Speckle Interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer, Heidelberg, 1975), pp. 203–253.
    [CrossRef]
  2. J. M. Burch, J. M. J. Tokarski, Opt. Acta 15, 101 (1968).
  3. R. K. Erf, Ed., Speckle Metrology (Academic, New York, 1978).
  4. E. Archbold, A. E. Ennos, M. S. Virdee, “Speckle Photography for Strain Measurements—A Critical Assessment,” in First European Congress on Optics Applied to Metrology, Strasbourg, 1977, Vol. 136 (SPIE, Washington, D.C., 1978), pp. 258–264.
  5. G.H. Kaufmann, Opt. Laser Technol. 12, 207 (1980).
    [CrossRef]
  6. G. H. Kaufmann, A. E. Ennos, B. Gale, D. J. Pugh, J. Phys. E. 13, 579 (1980).
    [CrossRef]
  7. B. Ineichen, P. Eglin, R. Daendliker, Appl. Opt. 19, 2191 (1980).
    [CrossRef] [PubMed]
  8. E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, N.J., 1974).
  9. R. P. Khetan, F. P. Chiang, Appl. Opt. 15, 2205 (1976).
    [CrossRef] [PubMed]
  10. L. R. Rabiner, B. Gold, Theory and Application of Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).

1980 (3)

G.H. Kaufmann, Opt. Laser Technol. 12, 207 (1980).
[CrossRef]

G. H. Kaufmann, A. E. Ennos, B. Gale, D. J. Pugh, J. Phys. E. 13, 579 (1980).
[CrossRef]

B. Ineichen, P. Eglin, R. Daendliker, Appl. Opt. 19, 2191 (1980).
[CrossRef] [PubMed]

1976 (1)

1968 (1)

J. M. Burch, J. M. J. Tokarski, Opt. Acta 15, 101 (1968).

Archbold, E.

E. Archbold, A. E. Ennos, M. S. Virdee, “Speckle Photography for Strain Measurements—A Critical Assessment,” in First European Congress on Optics Applied to Metrology, Strasbourg, 1977, Vol. 136 (SPIE, Washington, D.C., 1978), pp. 258–264.

Brigham, E. O.

E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, N.J., 1974).

Burch, J. M.

J. M. Burch, J. M. J. Tokarski, Opt. Acta 15, 101 (1968).

Chiang, F. P.

Daendliker, R.

Eglin, P.

Ennos, A. E.

G. H. Kaufmann, A. E. Ennos, B. Gale, D. J. Pugh, J. Phys. E. 13, 579 (1980).
[CrossRef]

A. E. Ennos, “Speckle Interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer, Heidelberg, 1975), pp. 203–253.
[CrossRef]

E. Archbold, A. E. Ennos, M. S. Virdee, “Speckle Photography for Strain Measurements—A Critical Assessment,” in First European Congress on Optics Applied to Metrology, Strasbourg, 1977, Vol. 136 (SPIE, Washington, D.C., 1978), pp. 258–264.

Gale, B.

G. H. Kaufmann, A. E. Ennos, B. Gale, D. J. Pugh, J. Phys. E. 13, 579 (1980).
[CrossRef]

Gold, B.

L. R. Rabiner, B. Gold, Theory and Application of Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).

Ineichen, B.

Kaufmann, G. H.

G. H. Kaufmann, A. E. Ennos, B. Gale, D. J. Pugh, J. Phys. E. 13, 579 (1980).
[CrossRef]

Kaufmann, G.H.

G.H. Kaufmann, Opt. Laser Technol. 12, 207 (1980).
[CrossRef]

Khetan, R. P.

Pugh, D. J.

G. H. Kaufmann, A. E. Ennos, B. Gale, D. J. Pugh, J. Phys. E. 13, 579 (1980).
[CrossRef]

Rabiner, L. R.

L. R. Rabiner, B. Gold, Theory and Application of Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).

Tokarski, J. M. J.

J. M. Burch, J. M. J. Tokarski, Opt. Acta 15, 101 (1968).

Virdee, M. S.

E. Archbold, A. E. Ennos, M. S. Virdee, “Speckle Photography for Strain Measurements—A Critical Assessment,” in First European Congress on Optics Applied to Metrology, Strasbourg, 1977, Vol. 136 (SPIE, Washington, D.C., 1978), pp. 258–264.

Appl. Opt. (2)

J. Phys. E. (1)

G. H. Kaufmann, A. E. Ennos, B. Gale, D. J. Pugh, J. Phys. E. 13, 579 (1980).
[CrossRef]

Opt. Acta (1)

J. M. Burch, J. M. J. Tokarski, Opt. Acta 15, 101 (1968).

Opt. Laser Technol. (1)

G.H. Kaufmann, Opt. Laser Technol. 12, 207 (1980).
[CrossRef]

Other (5)

A. E. Ennos, “Speckle Interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer, Heidelberg, 1975), pp. 203–253.
[CrossRef]

R. K. Erf, Ed., Speckle Metrology (Academic, New York, 1978).

E. Archbold, A. E. Ennos, M. S. Virdee, “Speckle Photography for Strain Measurements—A Critical Assessment,” in First European Congress on Optics Applied to Metrology, Strasbourg, 1977, Vol. 136 (SPIE, Washington, D.C., 1978), pp. 258–264.

L. R. Rabiner, B. Gold, Theory and Application of Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).

E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, N.J., 1974).

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Figures (5)

Fig. 1
Fig. 1

Plot of normalized Iv(n) for v = 1.

Fig. 2
Fig. 2

Modulus of discrete Fourier transform for v = 1.

Fig. 3
Fig. 3

Plot of normalized Iv(n) for v = 0.55.

Fig. 4
Fig. 4

Modulus of discrete Fourier transform for v = 0.55.

Fig. 5
Fig. 5

Effect of fringe visibility on relative errors in displacements for different number of fringes: —, present work; - - -, calculated from fringe minima5; – –, calculated from fringe maxima.5

Equations (11)

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I ( x ) = 4 cos 2 ( π u x / λ L ) I 0 ( x ) ,
I 0 = { K [ 1 - ( u x / 2 L a ) ] 2 for x 2 L a / q , 0 for x > 2 L a / q ,
I v ( x ) = [ 4 1 - v 1 + v + 8 v 1 + v cos 2 ( π u x / λ L ) ] I 0 ( x ) ,
v = ( I max - I min ) / ( I max + I min ) ,
spacing of I v ( x ) / I 0 ( n ) - spacing of I v ( n ) spacing of I v ( n ) / I 0 ( n ) .
H ( w ) = n = 0 N - 1 x ( n ) exp ( i n w ) ,             w = 2 π l / N ,
x ( n ) = 1 N k = 0 N - 1 X ( k ) exp ( - i n w k ) ,             w k = 2 π k / N .
H ( w ) = 1 N k = 0 N - 1 X ( k ) n = 0 N - 1 exp [ i n ( w - w k ) ] .
H ( w ) = 1 N k = 0 N - 1 X ( k ) D ( w ) ,
D ( w ) = exp [ i w ( N - 1 ) / 2 + i w k / 2 ] sin ( N w / 2 ) sin ½ ( w - w k )
D ( w ) = { N if l = k , 0             otherwise .

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