Abstract

The present paper describes in details the operating principle of a completely new family of speckle interferometers: the double-focusing. This type of interferometer is sensitive to the same components of displacement given by holographic interferometry, i.e. the component along the bisector of the angle identified by the illumination and the observation directions. In addition, no external reference beam is necessary, with a consequent reduction of the complexity of the experimental setup. The only requirement for the correct functioning of this family of interferometers is that only a portion of the illuminated area undergoes a sensible deformation. The implementation can be indifferently carried out by adopting the classical Michelson or Mach-Zender configurations, but also a particularly compact in-line implementation can be realized.

© 2007 Optical Society of America

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References

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  1. A. E. Ennos, J. M. Burch, E. Archbold and P. A. Taylor, "Visual observation of surface vibration nodal patterns," Nature 222, 263-265 (1969).
    [CrossRef]
  2. J. A. Leendertz, "Interferometric displacement measurement on scattering surfaces utilizing speckle effect," J. Phys. E: J. Sci Instrum. 3, 214-218 (1970).
    [CrossRef]
  3. Y. Y. Hung, "Shearography: a novel and practical approach for nondestructive inspection," J. Nondestruct. Eval. 8, 55-67 (1989).
    [CrossRef]
  4. J. Chen and H. H. Hung, "Large-shear digital speckle interferometery based on liquid crystal phase modulator," Acta Opt. Sin. 24, 1292-1296 (2004).
  5. S. Waldner, "Removing the image-doubling in shearography by reconstruction of the displacement field," Opt. Commun. 27, 117-126 (1996).
    [CrossRef]
  6. K. A. Stetson, "The use of an image derotator in hologram interferometry and speckle photography of rotating objects," Exp. Mech. 18, 67-73 (1978).
    [CrossRef]
  7. J. W. Goodman, Introduction to Fourier Optics, (Roberts & Company Publisher, 2005).
  8. S. Donati and G. Martini, "Speckle-pattern intensity and phase: second order conditional statistics," J. Opt. Soc. Am. 69, 1690-1694 (1979).
    [CrossRef]
  9. J. W. Goodman, Speckle Phenomena in Optics, (Roberts & Company Publisher, 2007).
  10. M. Lehmann, "Decorrelation-induced phase errors in phase-shifting speckle interferometry," Appl. Opt. 36, 3657-3667 (1997).
    [CrossRef] [PubMed]
  11. J. M. Huntley, "Random phase measurement errors in digital speckle pattern interferometry," Proc. SPIE 2544, 246-257 (1995).

2004 (1)

J. Chen and H. H. Hung, "Large-shear digital speckle interferometery based on liquid crystal phase modulator," Acta Opt. Sin. 24, 1292-1296 (2004).

1997 (1)

1996 (1)

S. Waldner, "Removing the image-doubling in shearography by reconstruction of the displacement field," Opt. Commun. 27, 117-126 (1996).
[CrossRef]

1995 (1)

J. M. Huntley, "Random phase measurement errors in digital speckle pattern interferometry," Proc. SPIE 2544, 246-257 (1995).

1989 (1)

Y. Y. Hung, "Shearography: a novel and practical approach for nondestructive inspection," J. Nondestruct. Eval. 8, 55-67 (1989).
[CrossRef]

1979 (1)

1978 (1)

K. A. Stetson, "The use of an image derotator in hologram interferometry and speckle photography of rotating objects," Exp. Mech. 18, 67-73 (1978).
[CrossRef]

1970 (1)

J. A. Leendertz, "Interferometric displacement measurement on scattering surfaces utilizing speckle effect," J. Phys. E: J. Sci Instrum. 3, 214-218 (1970).
[CrossRef]

1969 (1)

A. E. Ennos, J. M. Burch, E. Archbold and P. A. Taylor, "Visual observation of surface vibration nodal patterns," Nature 222, 263-265 (1969).
[CrossRef]

Archbold, E.

A. E. Ennos, J. M. Burch, E. Archbold and P. A. Taylor, "Visual observation of surface vibration nodal patterns," Nature 222, 263-265 (1969).
[CrossRef]

Burch, J. M.

A. E. Ennos, J. M. Burch, E. Archbold and P. A. Taylor, "Visual observation of surface vibration nodal patterns," Nature 222, 263-265 (1969).
[CrossRef]

Chen, J.

J. Chen and H. H. Hung, "Large-shear digital speckle interferometery based on liquid crystal phase modulator," Acta Opt. Sin. 24, 1292-1296 (2004).

Donati, S.

Ennos, A. E.

A. E. Ennos, J. M. Burch, E. Archbold and P. A. Taylor, "Visual observation of surface vibration nodal patterns," Nature 222, 263-265 (1969).
[CrossRef]

Hung, H. H.

J. Chen and H. H. Hung, "Large-shear digital speckle interferometery based on liquid crystal phase modulator," Acta Opt. Sin. 24, 1292-1296 (2004).

Hung, Y. Y.

Y. Y. Hung, "Shearography: a novel and practical approach for nondestructive inspection," J. Nondestruct. Eval. 8, 55-67 (1989).
[CrossRef]

Huntley, J. M.

J. M. Huntley, "Random phase measurement errors in digital speckle pattern interferometry," Proc. SPIE 2544, 246-257 (1995).

Leendertz, J. A.

J. A. Leendertz, "Interferometric displacement measurement on scattering surfaces utilizing speckle effect," J. Phys. E: J. Sci Instrum. 3, 214-218 (1970).
[CrossRef]

Lehmann, M.

Martini, G.

Stetson, K. A.

K. A. Stetson, "The use of an image derotator in hologram interferometry and speckle photography of rotating objects," Exp. Mech. 18, 67-73 (1978).
[CrossRef]

Taylor, P. A.

A. E. Ennos, J. M. Burch, E. Archbold and P. A. Taylor, "Visual observation of surface vibration nodal patterns," Nature 222, 263-265 (1969).
[CrossRef]

Waldner, S.

S. Waldner, "Removing the image-doubling in shearography by reconstruction of the displacement field," Opt. Commun. 27, 117-126 (1996).
[CrossRef]

Acta Opt. Sin. (1)

J. Chen and H. H. Hung, "Large-shear digital speckle interferometery based on liquid crystal phase modulator," Acta Opt. Sin. 24, 1292-1296 (2004).

Appl. Opt. (1)

E: J. Sci Instrum. (1)

J. A. Leendertz, "Interferometric displacement measurement on scattering surfaces utilizing speckle effect," J. Phys. E: J. Sci Instrum. 3, 214-218 (1970).
[CrossRef]

Exp. Mech. (1)

K. A. Stetson, "The use of an image derotator in hologram interferometry and speckle photography of rotating objects," Exp. Mech. 18, 67-73 (1978).
[CrossRef]

J. Nondestruct. Eval. (1)

Y. Y. Hung, "Shearography: a novel and practical approach for nondestructive inspection," J. Nondestruct. Eval. 8, 55-67 (1989).
[CrossRef]

J. Opt. Soc. Am. (1)

Nature (1)

A. E. Ennos, J. M. Burch, E. Archbold and P. A. Taylor, "Visual observation of surface vibration nodal patterns," Nature 222, 263-265 (1969).
[CrossRef]

Opt. Commun. (1)

S. Waldner, "Removing the image-doubling in shearography by reconstruction of the displacement field," Opt. Commun. 27, 117-126 (1996).
[CrossRef]

Proc. SPIE (1)

J. M. Huntley, "Random phase measurement errors in digital speckle pattern interferometry," Proc. SPIE 2544, 246-257 (1995).

Other (2)

J. W. Goodman, Speckle Phenomena in Optics, (Roberts & Company Publisher, 2007).

J. W. Goodman, Introduction to Fourier Optics, (Roberts & Company Publisher, 2005).

Supplementary Material (1)

» Media 1: AVI (1842 KB)     

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Figures (10)

Fig. 1.
Fig. 1.

Speckle interferometers adopting an external reference beam realized by a beam-splitter located between: a) the lens and the light sensor; b) the object and the lens.

Fig. 2.
Fig. 2.

Self-referenced interferometer based on: a) double-illumination and b) double-image principle.

Fig. 3.
Fig. 3.

Focusing and defocusing geometry: a) perfect imaging; b) light gathered at a point of the image plane for f’<f; c) defocusing of a point at the image plane for f’<f; d) light gathered at a point of the image plane for f’’>f; c) defocusing of a point at the image plane for f’’>f.

Fig. 4.
Fig. 4.

Simulation of an “ideal” speckle interferometer neglecting the electronic noise and the decorrelation of the speckle pattern: a) the deformed specimen; b) the phase map c) the correlation fringes.

Fig. 5.
Fig. 5.

Degradation process of the reference beam.

Fig. 6.
Fig. 6.

Effect of the dimension of the reference convolving area: a) D equal to the minimum dimension of the object against a dark background; b) phase map relative to the illumination condition depicted in a); c) fringe pattern relative to the illumination condition depicted in a); d) D equal to the double of the maximum dimension of the object against a dark background; e) phase map relative to the illumination condition depicted in d); f) fringe pattern relative to the illumination condition depicted in d); g) D equal to the double of the maximum dimension of the object against a bright background; h) phase map relative to the illumination condition depicted in g); i) fringe pattern relative to the illumination condition depicted in g). The object is the small rectangle inside the bigger one in a), d) and g).

Fig. 7.
Fig. 7.

(1842 KB) Effect of the dimension of the reference convolving area for the typical deformation field of a debonding when the ratio between its diameter D and the diameter of the defect and is equal to: a) 1/2; b) 1; c) 2; d) 4. [Media 1]

Fig. 8.
Fig. 8.

A double-focus Michelson interferometer: a) the balanced version; b) the unbalanced version. In figure: Sf, surface under investigation; ID, illumination direction; Ob, objective; BS, beamsplitter; FMr, flat mirror; CMr, curved mirror; CCD, CCD camera.

Fig. 9.
Fig. 9.

A double-focus Mach-Zender interferometer. In figure: Sf, surface under investigation; ID, illumination direction; Ob, objective; BS, beamsplitter; Ls, lens; FMr, flat mirror; CCD, CCD camera.

Fig. 10.
Fig. 10.

(a). The layout of a full in-line implementation of a double-focus interferometer. The double-focus device can be obtained by adding in front of the objective: (b) a smaller lens; (c) a smaller lens designed for compensating the optical paths; (d) a Fresnel lens. In figure: Sf, surface under investigation; ID, illumination direction; DF, double-focus device; CCD, CCD camera. In b), c) and d) the upper row refers to the use of a smaller positive lens, the lower row to the use of a smaller negative lens.

Equations (5)

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1 s o + 1 s i = 1 f
s o = f ( 1 + 1 m )
s i = f ( 1 + m )
D = D [ f f ( 1 + 1 m ) ( 1 + 1 m ) ] for f < f
D = D [ ( 1 + 1 m ) f f ′′ ( 1 + 1 m ) ] for f ′′ > f

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