Abstract

Theoretical background along with experimental results are given for a simple method for in-plane fringe enhancement in dual-beam illumination holographic interferometry. In this method, the fringes representing in-plane displacements arise as a moiré pattern between two interferograms. To distinguish the in-plane displacement, a sequence of images is recorded while the reference mirror is continuously tilted at random. The in-plane fringes are then found as the maximum contrast of the out-of-plane fringes in the image sequence. The resulting fringe quality is close to the quality of the out-of-plane fringes.

© 1998 Optical Society of America

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References

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  1. N. H. Abramson, The Making and Evaluation of Holograms (Academic, London, 1981), pp. 156–205.
  2. A. E. Ennos, “Measurement of in-plane surface strain by hologram interferometry,” J. Phys. E 1, 731–734 (1968).
    [CrossRef]
  3. J. N. Butters, “Application of holography to instrument diaphragm deformations and associated topics,” in The Engineering Uses of Holography (Cambridge U. Press, London, 1970), pp. 151–172.
  4. P. M. Boone, “Holographic determination of in-plane deformation,” Opt. Technol. 2, 94–98 (1970).
    [CrossRef]
  5. M. Schlüter, A. Nowatzyk, “In-plane deformation measurement by video-electronic hologram interferometry,” Opt. Acta 27, 799–808 (1980).
    [CrossRef]
  6. T. Kreis, “Digital holographic interference-phase measurement using the Fourier-transform method,” J. Opt. Soc. Am. A 3, 847–855 (1986).
    [CrossRef]
  7. T. Kreis, Holographic Interferometry (Akademie, Berlin, 1996), pp. 138–149.

1986 (1)

1980 (1)

M. Schlüter, A. Nowatzyk, “In-plane deformation measurement by video-electronic hologram interferometry,” Opt. Acta 27, 799–808 (1980).
[CrossRef]

1970 (1)

P. M. Boone, “Holographic determination of in-plane deformation,” Opt. Technol. 2, 94–98 (1970).
[CrossRef]

1968 (1)

A. E. Ennos, “Measurement of in-plane surface strain by hologram interferometry,” J. Phys. E 1, 731–734 (1968).
[CrossRef]

Abramson, N. H.

N. H. Abramson, The Making and Evaluation of Holograms (Academic, London, 1981), pp. 156–205.

Boone, P. M.

P. M. Boone, “Holographic determination of in-plane deformation,” Opt. Technol. 2, 94–98 (1970).
[CrossRef]

Butters, J. N.

J. N. Butters, “Application of holography to instrument diaphragm deformations and associated topics,” in The Engineering Uses of Holography (Cambridge U. Press, London, 1970), pp. 151–172.

Ennos, A. E.

A. E. Ennos, “Measurement of in-plane surface strain by hologram interferometry,” J. Phys. E 1, 731–734 (1968).
[CrossRef]

Kreis, T.

Nowatzyk, A.

M. Schlüter, A. Nowatzyk, “In-plane deformation measurement by video-electronic hologram interferometry,” Opt. Acta 27, 799–808 (1980).
[CrossRef]

Schlüter, M.

M. Schlüter, A. Nowatzyk, “In-plane deformation measurement by video-electronic hologram interferometry,” Opt. Acta 27, 799–808 (1980).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Phys. E (1)

A. E. Ennos, “Measurement of in-plane surface strain by hologram interferometry,” J. Phys. E 1, 731–734 (1968).
[CrossRef]

Opt. Acta (1)

M. Schlüter, A. Nowatzyk, “In-plane deformation measurement by video-electronic hologram interferometry,” Opt. Acta 27, 799–808 (1980).
[CrossRef]

Opt. Technol. (1)

P. M. Boone, “Holographic determination of in-plane deformation,” Opt. Technol. 2, 94–98 (1970).
[CrossRef]

Other (3)

N. H. Abramson, The Making and Evaluation of Holograms (Academic, London, 1981), pp. 156–205.

J. N. Butters, “Application of holography to instrument diaphragm deformations and associated topics,” in The Engineering Uses of Holography (Cambridge U. Press, London, 1970), pp. 151–172.

T. Kreis, Holographic Interferometry (Akademie, Berlin, 1996), pp. 138–149.

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Figures (4)

Fig. 1
Fig. 1

Optical configuration for recording a dual-beam holographic interferogram for the detection of in-plane displacements.

Fig. 2
Fig. 2

Geometric relations.

Fig. 3
Fig. 3

Left: A detail of the fringe pattern produced by a real-time dual-beam illumination holographic interferogram of an electronic wafer board during heating. The temperature of the board is the highest for test 1 at the bottom and the lowest for test 3 at the top. The moiré patterns showing the in-plane displacements are very hard to distinguish among the fringes owing to out-of-plane movement. Right: The same moiré patterns, now enhanced by image processing while the phase of the reconstruction beam is changed. The in-plane displacements are easily detected.

Fig. 4
Fig. 4

Evaluated in-line displacements and strains for the tests of Fig. 3 as a function of the actual distance on the electronic wafer board.

Equations (4)

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k Δ r 1 = k V - k 1 Δ r = - k   sin   α Δ x       + k 1 + cos   α Δ y = - k x Δ x + k y Δ y k Δ r 2 = k V - k 2 Δ r = k   sin   α Δ x       + k 1 + cos   α Δ y = k x Δ x + k y Δ y ,
u 11 = u 11 0 × ν 1 * × ν 2 = a 11 exp ik r 1 + Δ ρ , u 12 = u 12 0 × ν 1 * × ν 2 = a 12 exp ik r 2 + Δ ρ , u 21 = a 21 exp ik r 1 + Δ r 1 , u 22 = a 22 exp ik r 2 + Δ r 2 ,
I = u 11 + u 12 + u 21 + u 22 × u 11 + u 12 + u 21 + u 22 * = 2 I 1 + 2 I 2 + 4 I 12 cos k x Δ x × cos k y Δ y + k Δ ρ .
I max = 2 I 1 + 2 I 2 + 4 I 12 cos k x Δ x , I min = 2 I 1 + 2 I 2 - 4 I 12 cos k x Δ x , I max - I min = 8 I 12 cos k x Δ x = 8 I 12 cos 2 π   sin   α λ   Δ x .

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