Abstract

The fundamentals of digital recording and mathematical reconstruction of Fresnel holograms are described. The object is recorded in two different states, and the holograms are stored electronically with a charge-coupled-device detector. In the process of reconstruction the digitally sampled holograms are applied to the different coherent optical methods as hologram interferometry and shearography. If the holograms are superimposed and reconstructed jointly, a holographic interferogram results. If a shearing is introduced in the reconstruction process, a shearogram results. This means that the evaluation technique, e.g., hologram interferometry or shearography, can be influenced by numerical methods.

© 1994 Optical Society of America

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References

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  1. Y. I. Ostrovsky, M. M. Butusov, G. V. Ostrovskaya, Interferometry by Holography (Springer-Verlag, New York, 1980), Chap. 1, p. 11.
  2. W. Jüptner, “Holographic techniques,” in Sensors and Sensory Systems for Advanced Robots, P. Dario, ed., Vol. 43 of North Atlantic Treaty Organization ASI Series (Springer-Verlag, New York, 1988), pp. 273–293.
  3. U. Schnars, W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
    [CrossRef] [PubMed]
  4. L. P. Yaroslavskii, N. S. Merzylakov, Methods of Digital Holography (Consultants Bureau, New York, 1980), Chap. 1, p. 14.
  5. J. A. Leendertz, J. N. Butters, “An image shearing-speckle pattern interferometer for measuring bending moments,” J. Phys. E 6, 1107 (1973).
    [CrossRef]
  6. Y. Y. Hung, C. Y. Liang, “Image-shearing camera for direct measurement of surface strains,” Appl. Opt. 18, 1046–1051 (1979).
    [CrossRef] [PubMed]

1994 (1)

1979 (1)

1973 (1)

J. A. Leendertz, J. N. Butters, “An image shearing-speckle pattern interferometer for measuring bending moments,” J. Phys. E 6, 1107 (1973).
[CrossRef]

Butters, J. N.

J. A. Leendertz, J. N. Butters, “An image shearing-speckle pattern interferometer for measuring bending moments,” J. Phys. E 6, 1107 (1973).
[CrossRef]

Butusov, M. M.

Y. I. Ostrovsky, M. M. Butusov, G. V. Ostrovskaya, Interferometry by Holography (Springer-Verlag, New York, 1980), Chap. 1, p. 11.

Hung, Y. Y.

Jüptner, W.

U. Schnars, W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
[CrossRef] [PubMed]

W. Jüptner, “Holographic techniques,” in Sensors and Sensory Systems for Advanced Robots, P. Dario, ed., Vol. 43 of North Atlantic Treaty Organization ASI Series (Springer-Verlag, New York, 1988), pp. 273–293.

Leendertz, J. A.

J. A. Leendertz, J. N. Butters, “An image shearing-speckle pattern interferometer for measuring bending moments,” J. Phys. E 6, 1107 (1973).
[CrossRef]

Liang, C. Y.

Merzylakov, N. S.

L. P. Yaroslavskii, N. S. Merzylakov, Methods of Digital Holography (Consultants Bureau, New York, 1980), Chap. 1, p. 14.

Ostrovskaya, G. V.

Y. I. Ostrovsky, M. M. Butusov, G. V. Ostrovskaya, Interferometry by Holography (Springer-Verlag, New York, 1980), Chap. 1, p. 11.

Ostrovsky, Y. I.

Y. I. Ostrovsky, M. M. Butusov, G. V. Ostrovskaya, Interferometry by Holography (Springer-Verlag, New York, 1980), Chap. 1, p. 11.

Schnars, U.

Yaroslavskii, L. P.

L. P. Yaroslavskii, N. S. Merzylakov, Methods of Digital Holography (Consultants Bureau, New York, 1980), Chap. 1, p. 14.

Appl. Opt. (2)

J. Phys. E (1)

J. A. Leendertz, J. N. Butters, “An image shearing-speckle pattern interferometer for measuring bending moments,” J. Phys. E 6, 1107 (1973).
[CrossRef]

Other (3)

L. P. Yaroslavskii, N. S. Merzylakov, Methods of Digital Holography (Consultants Bureau, New York, 1980), Chap. 1, p. 14.

Y. I. Ostrovsky, M. M. Butusov, G. V. Ostrovskaya, Interferometry by Holography (Springer-Verlag, New York, 1980), Chap. 1, p. 11.

W. Jüptner, “Holographic techniques,” in Sensors and Sensory Systems for Advanced Robots, P. Dario, ed., Vol. 43 of North Atlantic Treaty Organization ASI Series (Springer-Verlag, New York, 1988), pp. 273–293.

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Figures (11)

Fig. 1
Fig. 1

Off-axis holography with a plane reference (ref.) wave: (a) recording, (b) reconstruction.

Fig. 2
Fig. 2

Principle of shearography.

Fig. 3
Fig. 3

Graphical representation of the reconstruction process for hologram interferometry and for shearography: FRT’s, Fresnel transformations; compl. ampl., complex amplitude.

Fig. 4
Fig. 4

Experimental setup: BS, beam splitter; M’s, mirrors; L, lenses.

Fig. 5
Fig. 5

Digitally sampled hologram.

Fig. 6
Fig. 6

Numerical reconstruction; the letters are the initials of the authors’ institution.

Fig. 7
Fig. 7

Digitally sampled hologram of an aluminum plate.

Fig. 8
Fig. 8

Digitally sampled hologram of a deformed plate.

Fig. 9
Fig. 9

Numerically reconstructed holographic interferogram.

Fig. 10
Fig. 10

Numerically reconstructed shearogram; shearing δ = 2 mm.

Fig. 11
Fig. 11

Numerically reconstructed shearogram; shearing δ = 0.8 mm.

Equations (8)

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f max = 2 λ sin ( θ max 2 ) ,
Γ ( m , n ) = exp [ i π λ d ( m 2 Δ ξ 2 + n 2 Δ η 2 ) ] × k = 0 N 1 l = 0 N 1 t ( k , l ) exp [ i π λ d ( k 2 Δ x 2 + l 2 Δ y 2 ) ] × exp [ i 2 π ( k m N + ln N ) ] , m = 0 , 1 , , N 1 , n = 0 , 1 , , N 1 .
I ( m , n ) = | Γ ( m , n ) | 2 .
t ( k , l ) = t 1 ( k , l ) + t 2 ( k , l ) ,
I shear ( m , n ) = | Γ ( m , n ) + Γ ( m + δ , n ) | 2 .
Δ I shear = | I shear 1 I shear 2 | .
f max = 2 ( 6 . 8 μ m ) 1 .
θ max = 2 arcsin ( λ f max 2 ) = 47 mrad .

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