Abstract

A concept called fringe compensation was first presented in phase-shifting electronic speckle-pattern interferometry. We apply a similar principle to digital holographic interferometry; here the phase of a wave front is known and can be manipulated. The basic mathematical formulation of fringe compensation and some experimental results are shown with relatively large, simple rigid-body rotation and circular membrane deformation.

© 2004 Optical Society of America

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References

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  1. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  2. J. W. Goodman, R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
    [CrossRef]
  3. M. Jacquot, P. Sandoz, G. Tribillon, “High resolution digital holography,” Opt. Commun. 190, 87–94 (2001).
    [CrossRef]
  4. S. Grilli, P. Ferraro, S. de Nicola, A. Finizio, G. Pierattini, R. Meucci, “Whole optical wavefields reconstruction by digital holography,” Opt. Express 9, 294–302 (2001), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  5. N. Bokor, Zs. Papp, “Monte Carlo method in computer holography,” Opt. Eng. 36, 1014–1020 (1997).
    [CrossRef]
  6. I. Yamaguchi, T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
    [CrossRef] [PubMed]
  7. S. Lai, B. King, M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155–160 (2000).
    [CrossRef]
  8. B. Gombkötő, J. Kornis, Z. Füzessy, “Difference displacement measurement using digital holography,” Opt. Commun. 214, 115–121 (2002).
    [CrossRef]
  9. C. Wagner, W. Osten, S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring,” Opt. Eng. 39, 79–85 (2000).
    [CrossRef]
  10. G. Pedrini, P. Fröning, H. J. Tiziani, M. E. Gusev, “Pulsed digital holography for high-speed contouring that uses a two-wavelength method,” Appl. Opt. 38, 3460–3467 (1999).
    [CrossRef]
  11. G. Pedrini, P. Fröning, H. J. Tiziani, F. M. Santoyo, “Shape measurement of microscopic structures using digital holograms,” Opt. Commun. 164, 257–268 (1999).
    [CrossRef]
  12. U. Schnars, “Direct phase determination in hologram interferometry with use of digitally recorded holograms,” J. Opt. Soc. Am. A 11, 2011–2015 (1994).
    [CrossRef]
  13. A. Németh, J. Kornis, Z. Füzessy, “Fringe compensation measurement in holographic interferometry using phase-shifted interferograms,” Opt. Eng. 39, 3196–3200 (2000).
    [CrossRef]
  14. J. Kornis, A. Németh, “Fringe compensation displacement measurement using synthesized reference beam TV holography,” Opt. Commun. 167, 203–210 (1999).
    [CrossRef]

2002 (1)

B. Gombkötő, J. Kornis, Z. Füzessy, “Difference displacement measurement using digital holography,” Opt. Commun. 214, 115–121 (2002).
[CrossRef]

2001 (2)

2000 (3)

S. Lai, B. King, M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155–160 (2000).
[CrossRef]

C. Wagner, W. Osten, S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring,” Opt. Eng. 39, 79–85 (2000).
[CrossRef]

A. Németh, J. Kornis, Z. Füzessy, “Fringe compensation measurement in holographic interferometry using phase-shifted interferograms,” Opt. Eng. 39, 3196–3200 (2000).
[CrossRef]

1999 (3)

J. Kornis, A. Németh, “Fringe compensation displacement measurement using synthesized reference beam TV holography,” Opt. Commun. 167, 203–210 (1999).
[CrossRef]

G. Pedrini, P. Fröning, H. J. Tiziani, F. M. Santoyo, “Shape measurement of microscopic structures using digital holograms,” Opt. Commun. 164, 257–268 (1999).
[CrossRef]

G. Pedrini, P. Fröning, H. J. Tiziani, M. E. Gusev, “Pulsed digital holography for high-speed contouring that uses a two-wavelength method,” Appl. Opt. 38, 3460–3467 (1999).
[CrossRef]

1997 (2)

I. Yamaguchi, T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
[CrossRef] [PubMed]

N. Bokor, Zs. Papp, “Monte Carlo method in computer holography,” Opt. Eng. 36, 1014–1020 (1997).
[CrossRef]

1994 (1)

1967 (1)

J. W. Goodman, R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

Bokor, N.

N. Bokor, Zs. Papp, “Monte Carlo method in computer holography,” Opt. Eng. 36, 1014–1020 (1997).
[CrossRef]

de Nicola, S.

Ferraro, P.

Finizio, A.

Fröning, P.

G. Pedrini, P. Fröning, H. J. Tiziani, M. E. Gusev, “Pulsed digital holography for high-speed contouring that uses a two-wavelength method,” Appl. Opt. 38, 3460–3467 (1999).
[CrossRef]

G. Pedrini, P. Fröning, H. J. Tiziani, F. M. Santoyo, “Shape measurement of microscopic structures using digital holograms,” Opt. Commun. 164, 257–268 (1999).
[CrossRef]

Füzessy, Z.

B. Gombkötő, J. Kornis, Z. Füzessy, “Difference displacement measurement using digital holography,” Opt. Commun. 214, 115–121 (2002).
[CrossRef]

A. Németh, J. Kornis, Z. Füzessy, “Fringe compensation measurement in holographic interferometry using phase-shifted interferograms,” Opt. Eng. 39, 3196–3200 (2000).
[CrossRef]

Gombköto, B.

B. Gombkötő, J. Kornis, Z. Füzessy, “Difference displacement measurement using digital holography,” Opt. Commun. 214, 115–121 (2002).
[CrossRef]

Goodman, J. W.

J. W. Goodman, R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Grilli, S.

Gusev, M. E.

Jacquot, M.

M. Jacquot, P. Sandoz, G. Tribillon, “High resolution digital holography,” Opt. Commun. 190, 87–94 (2001).
[CrossRef]

King, B.

S. Lai, B. King, M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155–160 (2000).
[CrossRef]

Kornis, J.

B. Gombkötő, J. Kornis, Z. Füzessy, “Difference displacement measurement using digital holography,” Opt. Commun. 214, 115–121 (2002).
[CrossRef]

A. Németh, J. Kornis, Z. Füzessy, “Fringe compensation measurement in holographic interferometry using phase-shifted interferograms,” Opt. Eng. 39, 3196–3200 (2000).
[CrossRef]

J. Kornis, A. Németh, “Fringe compensation displacement measurement using synthesized reference beam TV holography,” Opt. Commun. 167, 203–210 (1999).
[CrossRef]

Lai, S.

S. Lai, B. King, M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155–160 (2000).
[CrossRef]

Lawrence, R. W.

J. W. Goodman, R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

Meucci, R.

Neifeld, M. A.

S. Lai, B. King, M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155–160 (2000).
[CrossRef]

Németh, A.

A. Németh, J. Kornis, Z. Füzessy, “Fringe compensation measurement in holographic interferometry using phase-shifted interferograms,” Opt. Eng. 39, 3196–3200 (2000).
[CrossRef]

J. Kornis, A. Németh, “Fringe compensation displacement measurement using synthesized reference beam TV holography,” Opt. Commun. 167, 203–210 (1999).
[CrossRef]

Osten, W.

C. Wagner, W. Osten, S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring,” Opt. Eng. 39, 79–85 (2000).
[CrossRef]

Papp, Zs.

N. Bokor, Zs. Papp, “Monte Carlo method in computer holography,” Opt. Eng. 36, 1014–1020 (1997).
[CrossRef]

Pedrini, G.

G. Pedrini, P. Fröning, H. J. Tiziani, M. E. Gusev, “Pulsed digital holography for high-speed contouring that uses a two-wavelength method,” Appl. Opt. 38, 3460–3467 (1999).
[CrossRef]

G. Pedrini, P. Fröning, H. J. Tiziani, F. M. Santoyo, “Shape measurement of microscopic structures using digital holograms,” Opt. Commun. 164, 257–268 (1999).
[CrossRef]

Pierattini, G.

Sandoz, P.

M. Jacquot, P. Sandoz, G. Tribillon, “High resolution digital holography,” Opt. Commun. 190, 87–94 (2001).
[CrossRef]

Santoyo, F. M.

G. Pedrini, P. Fröning, H. J. Tiziani, F. M. Santoyo, “Shape measurement of microscopic structures using digital holograms,” Opt. Commun. 164, 257–268 (1999).
[CrossRef]

Schnars, U.

Seebacher, S.

C. Wagner, W. Osten, S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring,” Opt. Eng. 39, 79–85 (2000).
[CrossRef]

Tiziani, H. J.

G. Pedrini, P. Fröning, H. J. Tiziani, F. M. Santoyo, “Shape measurement of microscopic structures using digital holograms,” Opt. Commun. 164, 257–268 (1999).
[CrossRef]

G. Pedrini, P. Fröning, H. J. Tiziani, M. E. Gusev, “Pulsed digital holography for high-speed contouring that uses a two-wavelength method,” Appl. Opt. 38, 3460–3467 (1999).
[CrossRef]

Tribillon, G.

M. Jacquot, P. Sandoz, G. Tribillon, “High resolution digital holography,” Opt. Commun. 190, 87–94 (2001).
[CrossRef]

Wagner, C.

C. Wagner, W. Osten, S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring,” Opt. Eng. 39, 79–85 (2000).
[CrossRef]

Yamaguchi, I.

Zhang, T.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. W. Goodman, R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

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

Opt. Commun. (5)

M. Jacquot, P. Sandoz, G. Tribillon, “High resolution digital holography,” Opt. Commun. 190, 87–94 (2001).
[CrossRef]

S. Lai, B. King, M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155–160 (2000).
[CrossRef]

B. Gombkötő, J. Kornis, Z. Füzessy, “Difference displacement measurement using digital holography,” Opt. Commun. 214, 115–121 (2002).
[CrossRef]

G. Pedrini, P. Fröning, H. J. Tiziani, F. M. Santoyo, “Shape measurement of microscopic structures using digital holograms,” Opt. Commun. 164, 257–268 (1999).
[CrossRef]

J. Kornis, A. Németh, “Fringe compensation displacement measurement using synthesized reference beam TV holography,” Opt. Commun. 167, 203–210 (1999).
[CrossRef]

Opt. Eng. (3)

A. Németh, J. Kornis, Z. Füzessy, “Fringe compensation measurement in holographic interferometry using phase-shifted interferograms,” Opt. Eng. 39, 3196–3200 (2000).
[CrossRef]

C. Wagner, W. Osten, S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring,” Opt. Eng. 39, 79–85 (2000).
[CrossRef]

N. Bokor, Zs. Papp, “Monte Carlo method in computer holography,” Opt. Eng. 36, 1014–1020 (1997).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Other (1)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

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Figures (3)

Fig. 1
Fig. 1

Calculated correlation of object wave amplitudes before and after rotation.

Fig. 2
Fig. 2

(a) Uncompensated rotational intensity fringes at 0.041 deg and (b) compensated rotational intensity and (c) phase fringes at 0.156 deg. (Image size: 330 by 330 pixels, 34.4-mm by 34.4-mm area.)

Fig. 3
Fig. 3

(a) Uncompensated intensity and (b) compensated intensity and (c) phase displacement fringes of a circular membrane plate at a 25-μm load. (Image size: 673 by 673 pixels.)

Equations (5)

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Ak, l=ainitk, l-adispk, l,
Δϕk, l=arcainitk, l-arcadispk, l.
Acompk, l=ainitk, l -adispk, lexpj2π/λ)gLk, l,
Acompk, l=ainitk, lasim,initk, l-adispk, lasim,dispk, l
Δx=λD/NΔx=λD/2NΔx/2.

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