Abstract

TV holograms for spatial phase stepping are formed with a small angular offset between the object and the reference beams to give a spatial frequency bias to the pattern recorded by the TV camera. It is common to set the bias so that there is a 90° or 120° phase shift between adjacent pixels and to use the irradiance of three or more adjacent pixels to evaluate the phase of the interference. We report the Fourier-transform evaluation of such recordings to obtain their phase data. We also demonstrate the direct calculation of the phase difference between successive recordings without intermediate calculation of the random phase of each hologram. This technique is proposed as an approach to pulsed TV holography.

© 1996 Optical Society of America

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References

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  1. D. M. Sough, O. Y. Kwon, “High-speed interferometric measurement of aerodynamic phenomena,” in Propagation of High-Energy Laser Beams Through the Earth's Atmosphere, P. B. Ulrich, L. E. Wilson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1221, 394–403 (1990).
  2. M. Kujawinska, J. Wójciak, “Spatial phase-shifting techniques in fringe pattern analysis in photomechanics,” in Moiré Techniques, Holographic Interferometry, Optical NDT, and Applications to Fluid Mechanics, F. Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554B, 503–513 (1991).
  3. G. Pedrini, B. Pfister, H. Tiziani, “Double pulse electronic speckle interferometry,” J. Mod. Opt. 40, 89–96 (1993).
    [CrossRef]
  4. L. Mertz, “Real-time fringe pattern analysis,” Appl. Opt. 22, 1535–1539 (1983).
    [CrossRef] [PubMed]
  5. T. Kreis, “Computer-aided evaluation of holographic interferograms,” in Holographic Interferometry (Springer-Verlag, New York, 1994) Chap. 6, pp. 184–193.
  6. M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1981).
    [CrossRef]
  7. U. Schnars, W. P. O. Jüptner, “Digital recording and reconstruction of holograms in hologram interferometry and shearography,”Appl. Opt. 33, 4373–4377 (1994).
    [CrossRef] [PubMed]
  8. Y. Ichioka, M. Inuiya, “Direct phase detecting system,” Appl. Opt. 11, 1507–1514 (1972).
    [CrossRef] [PubMed]
  9. K. Biedermann, L. Ek, “A recording and display system for hologram interferometry with low resolution imaging devices,” J. Phys. E 8, 571–591 (1975).
    [CrossRef]
  10. K. A. Stetson, W. R. Brohinsky, “Electro-optic holography and its application to hologram interferometry,” Appl. Opt. 24, 3631–3637 (1985).
    [CrossRef] [PubMed]
  11. K. A. Stetson, “Theory and applications of electronic holography,” in Proceedings SEM on Hologram Interferometry and Speckle Metrology, (Society for Experimental Mechanics, Bethel, Conn., 1990), pp. 294–300.
  12. J. M. Huntley, “Noise immune phase unwrapping algorithm,” Appl. Opt. 28, 3268–3270 (1989).
    [CrossRef] [PubMed]

1994 (1)

1993 (1)

G. Pedrini, B. Pfister, H. Tiziani, “Double pulse electronic speckle interferometry,” J. Mod. Opt. 40, 89–96 (1993).
[CrossRef]

1989 (1)

1985 (1)

1983 (1)

1981 (1)

1975 (1)

K. Biedermann, L. Ek, “A recording and display system for hologram interferometry with low resolution imaging devices,” J. Phys. E 8, 571–591 (1975).
[CrossRef]

1972 (1)

Biedermann, K.

K. Biedermann, L. Ek, “A recording and display system for hologram interferometry with low resolution imaging devices,” J. Phys. E 8, 571–591 (1975).
[CrossRef]

Brohinsky, W. R.

Ek, L.

K. Biedermann, L. Ek, “A recording and display system for hologram interferometry with low resolution imaging devices,” J. Phys. E 8, 571–591 (1975).
[CrossRef]

Huntley, J. M.

Ichioka, Y.

Ina, H.

Inuiya, M.

Jüptner, W. P. O.

Kobayashi, S.

Kreis, T.

T. Kreis, “Computer-aided evaluation of holographic interferograms,” in Holographic Interferometry (Springer-Verlag, New York, 1994) Chap. 6, pp. 184–193.

Kujawinska, M.

M. Kujawinska, J. Wójciak, “Spatial phase-shifting techniques in fringe pattern analysis in photomechanics,” in Moiré Techniques, Holographic Interferometry, Optical NDT, and Applications to Fluid Mechanics, F. Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554B, 503–513 (1991).

Kwon, O. Y.

D. M. Sough, O. Y. Kwon, “High-speed interferometric measurement of aerodynamic phenomena,” in Propagation of High-Energy Laser Beams Through the Earth's Atmosphere, P. B. Ulrich, L. E. Wilson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1221, 394–403 (1990).

Mertz, L.

Pedrini, G.

G. Pedrini, B. Pfister, H. Tiziani, “Double pulse electronic speckle interferometry,” J. Mod. Opt. 40, 89–96 (1993).
[CrossRef]

Pfister, B.

G. Pedrini, B. Pfister, H. Tiziani, “Double pulse electronic speckle interferometry,” J. Mod. Opt. 40, 89–96 (1993).
[CrossRef]

Schnars, U.

Sough, D. M.

D. M. Sough, O. Y. Kwon, “High-speed interferometric measurement of aerodynamic phenomena,” in Propagation of High-Energy Laser Beams Through the Earth's Atmosphere, P. B. Ulrich, L. E. Wilson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1221, 394–403 (1990).

Stetson, K. A.

K. A. Stetson, W. R. Brohinsky, “Electro-optic holography and its application to hologram interferometry,” Appl. Opt. 24, 3631–3637 (1985).
[CrossRef] [PubMed]

K. A. Stetson, “Theory and applications of electronic holography,” in Proceedings SEM on Hologram Interferometry and Speckle Metrology, (Society for Experimental Mechanics, Bethel, Conn., 1990), pp. 294–300.

Takeda, M.

Tiziani, H.

G. Pedrini, B. Pfister, H. Tiziani, “Double pulse electronic speckle interferometry,” J. Mod. Opt. 40, 89–96 (1993).
[CrossRef]

Wójciak, J.

M. Kujawinska, J. Wójciak, “Spatial phase-shifting techniques in fringe pattern analysis in photomechanics,” in Moiré Techniques, Holographic Interferometry, Optical NDT, and Applications to Fluid Mechanics, F. Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554B, 503–513 (1991).

Appl. Opt. (5)

J. Mod. Opt. (1)

G. Pedrini, B. Pfister, H. Tiziani, “Double pulse electronic speckle interferometry,” J. Mod. Opt. 40, 89–96 (1993).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. E (1)

K. Biedermann, L. Ek, “A recording and display system for hologram interferometry with low resolution imaging devices,” J. Phys. E 8, 571–591 (1975).
[CrossRef]

Other (4)

T. Kreis, “Computer-aided evaluation of holographic interferograms,” in Holographic Interferometry (Springer-Verlag, New York, 1994) Chap. 6, pp. 184–193.

D. M. Sough, O. Y. Kwon, “High-speed interferometric measurement of aerodynamic phenomena,” in Propagation of High-Energy Laser Beams Through the Earth's Atmosphere, P. B. Ulrich, L. E. Wilson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1221, 394–403 (1990).

M. Kujawinska, J. Wójciak, “Spatial phase-shifting techniques in fringe pattern analysis in photomechanics,” in Moiré Techniques, Holographic Interferometry, Optical NDT, and Applications to Fluid Mechanics, F. Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554B, 503–513 (1991).

K. A. Stetson, “Theory and applications of electronic holography,” in Proceedings SEM on Hologram Interferometry and Speckle Metrology, (Society for Experimental Mechanics, Bethel, Conn., 1990), pp. 294–300.

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Figures (7)

Fig. 1
Fig. 1

Aperture with a pair of vertical slots with the reference beam positioned symmetrically between them as proposed in Ref. 9.

Fig. 2
Fig. 2

Fourier spectrum of the hologram obtained by the two-slit aperture as in Fig. 1.

Fig. 3
Fig. 3

Interferometer of the TV-holography system used to record the spatially phase-biased TV holograms. The single-slot aperture is placed inside the video lens. BE, beam expander; M, mirror; R, relay lens; BS, beam splitter; CCD, charge-coupled-device camera.

Fig. 4
Fig. 4

Part (50 × 50 pixels) of a recorded hologram as seen by the CCD camera with approximately 4 to 5 pixels between the carrier fringes.

Fig. 5
Fig. 5

Fourier spectrum of the recorded hologram for a single-slot aperture and a smooth off-axis reference beam. The area within the white frame was used for the inverse FFT transformation.

Fig. 6
Fig. 6

Deformation field of the object displacement shown as a wrapped phase map calculated by use of Eq. (4).

Fig. 7
Fig. 7

Unwrapped phase map showing the out-of-plane deformation field of the object. The circular area in the lower left is a mask used in the phase unwrapping to remove areas with too high a fringe density and too much noise.

Equations (9)

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I ( x , y ) = A 2 + A S ( x , y ) exp ( ikx ) + A S * ( x , y ) exp ( ikx ) + | S ( x , y ) | 2 ,
I ( x , y ) I ( ξ , ψ ) , S ( x , y ) S ( ξ , ψ ) .
I ( ξ , ψ ) = A 2 δ ( ξ , ψ ) + A S ( ξ + k , ψ ) + A S * ( k ξ , ψ ) + S ( ξ , ψ ) * S * ( ξ , ψ ) ,
S ( ξ , ψ ) S ( x , y ) ,
ϕ = arctan { Im [ S ( x , y ) ] / Re [ S ( x , y ) ] }
ϕ = arctan { Im [ S ( x , y ) ] / Re [ S ( x , y ) ] } + π sgn { Im [ S ( x , y ) ] }
Δ ϕ = arctan { [ Re ( S ) Im ( S ) Im ( S ) Re ( S ) ] / [ Im ( S ) Im ( S ) + Re ( S ) Re ( S ) ] } .
H = z λ / 2 p υ .
W = z λ / 4 p h .

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