Abstract

When a digital holographic reconstruction is performed, digital diffraction effects occur at the borders when the hologram amplitudes at the two opposite border points are different on each vertical or horizontal line. We propose a method of digital hologram extension to reduce such diffraction effects. The method consists of extending the size of the digital hologram and of filling the extended part by complex values that minimize, according to a numerical criterion, the highest spatial frequencies. The theoretical aspects of the method are given and the results from a demonstration are provided.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. U. Schnars, W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
    [CrossRef] [PubMed]
  2. Katherine Creath, “Temporal phase measurement methods,” in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, D. W. Robinson, ed. ReidygG. T.,(IOP Publishing Ltd, Middlesex, UK, 1993), pp. 94–140.
  3. I. Yamaguchi, T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
    [CrossRef] [PubMed]
  4. B. Skarman, K. Wozniac, J. Becker, “Simultaneous 3D-PIV and temperature measurement using a New CCD based holographic interferometer,” Flow Meas. Instrum. 7, 1–6 (1996).
    [CrossRef]
  5. T. M. Kreis, W. P. O. Jüptner, “Principle of digital holography,” Proceedings of the 3rd International Workshop on Automatic Processing of Fringe Patterns (Fringe ’97), W. Jüptner, W. Osten, eds., (Akademie Verlag Series in Optical Metrology, Vol. 3, Berlin, 1997), pp. 353–363.
  6. B. Nilsson, T. E. Carlsson, “Direct three-dimensional shape measurement by digital light-in-flight holography,” Appl. Opt. 37, 7954–7959 (1998).
    [CrossRef]
  7. E. Cuche, F. Bevilacqua, C. Depeursinge, “Digital holography for quantitative phase contrast imaging,” Opt. Lett. 24, 291–293 (1999).
    [CrossRef]
  8. D. O. Hogenboom, C. A. Dimarzio, T. J. Gaudette, A. J. Devaney, S. C. Lindberg, “Three-dimensional images generated by quadrature interferometry,” Opt. Lett. 23, 783–785 (1998).
    [CrossRef]
  9. M. Adams, T. M. Kreis, W. P. O. Jüptner, “Particle size and position measurement with digital holography,” in Proc. SPIE3098, Optical Inspection and Micromeasurements II, C. Govecki, ed., 234–240 (1997).
    [CrossRef]
  10. B. Javidi, E. Tajahuerce, “Three-dimensional recognition by use of digital holography,” Opt. Lett. 25, 610–612 (2000).
    [CrossRef]
  11. B. Javidi, E. Tajahuerce, “Encrypting three-dimensional information with digital holography,” Opt. Lett. 39, 6595–6601 (2000).
  12. F. Dubois, L. Joannes, O. Dupont, J. L. Dewandel, J. C. Legros, “An integrated optical set-up for fluid-physics experiments under microgravity conditions,” Meas. Sci. Technol. 10, 934–945 (1999).
    [CrossRef]
  13. T. Zhang, I. Yamaguchi, “Three-dimensional microscopy with phase-shifting digital holography,” Opt. Lett. 23, 1221–1223 (1998).
    [CrossRef]
  14. F. Dubois, L. Joannes, J.-C. Legros, “Improved three-dimensional imaging with digital holography microscope using a partial spatial coherent source,” Appl. Opt. 38, 7085–7094 (1999).
    [CrossRef]
  15. Y. Takaki, H. Ohzu, “Hybrid holographic microscopy: Visualization of three-dimensional object information by use of viewing angles,” Appl. Opt. 39, 5302–5308 (2000).
    [CrossRef]
  16. E. Cuche, P. Marquet, C. Despeuringe, “Aperture apodization using cubic spline interpolation: application in digital holography microscopy,” Opt. Commun. 182, 59–69 (2000).
    [CrossRef]

2000

B. Javidi, E. Tajahuerce, “Three-dimensional recognition by use of digital holography,” Opt. Lett. 25, 610–612 (2000).
[CrossRef]

B. Javidi, E. Tajahuerce, “Encrypting three-dimensional information with digital holography,” Opt. Lett. 39, 6595–6601 (2000).

Y. Takaki, H. Ohzu, “Hybrid holographic microscopy: Visualization of three-dimensional object information by use of viewing angles,” Appl. Opt. 39, 5302–5308 (2000).
[CrossRef]

E. Cuche, P. Marquet, C. Despeuringe, “Aperture apodization using cubic spline interpolation: application in digital holography microscopy,” Opt. Commun. 182, 59–69 (2000).
[CrossRef]

1999

1998

1997

1996

B. Skarman, K. Wozniac, J. Becker, “Simultaneous 3D-PIV and temperature measurement using a New CCD based holographic interferometer,” Flow Meas. Instrum. 7, 1–6 (1996).
[CrossRef]

1994

Adams, M.

M. Adams, T. M. Kreis, W. P. O. Jüptner, “Particle size and position measurement with digital holography,” in Proc. SPIE3098, Optical Inspection and Micromeasurements II, C. Govecki, ed., 234–240 (1997).
[CrossRef]

Becker, J.

B. Skarman, K. Wozniac, J. Becker, “Simultaneous 3D-PIV and temperature measurement using a New CCD based holographic interferometer,” Flow Meas. Instrum. 7, 1–6 (1996).
[CrossRef]

Bevilacqua, F.

Carlsson, T. E.

Creath, Katherine

Katherine Creath, “Temporal phase measurement methods,” in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, D. W. Robinson, ed. ReidygG. T.,(IOP Publishing Ltd, Middlesex, UK, 1993), pp. 94–140.

Cuche, E.

E. Cuche, P. Marquet, C. Despeuringe, “Aperture apodization using cubic spline interpolation: application in digital holography microscopy,” Opt. Commun. 182, 59–69 (2000).
[CrossRef]

E. Cuche, F. Bevilacqua, C. Depeursinge, “Digital holography for quantitative phase contrast imaging,” Opt. Lett. 24, 291–293 (1999).
[CrossRef]

Depeursinge, C.

Despeuringe, C.

E. Cuche, P. Marquet, C. Despeuringe, “Aperture apodization using cubic spline interpolation: application in digital holography microscopy,” Opt. Commun. 182, 59–69 (2000).
[CrossRef]

Devaney, A. J.

Dewandel, J. L.

F. Dubois, L. Joannes, O. Dupont, J. L. Dewandel, J. C. Legros, “An integrated optical set-up for fluid-physics experiments under microgravity conditions,” Meas. Sci. Technol. 10, 934–945 (1999).
[CrossRef]

Dimarzio, C. A.

Dubois, F.

F. Dubois, L. Joannes, O. Dupont, J. L. Dewandel, J. C. Legros, “An integrated optical set-up for fluid-physics experiments under microgravity conditions,” Meas. Sci. Technol. 10, 934–945 (1999).
[CrossRef]

F. Dubois, L. Joannes, J.-C. Legros, “Improved three-dimensional imaging with digital holography microscope using a partial spatial coherent source,” Appl. Opt. 38, 7085–7094 (1999).
[CrossRef]

Dupont, O.

F. Dubois, L. Joannes, O. Dupont, J. L. Dewandel, J. C. Legros, “An integrated optical set-up for fluid-physics experiments under microgravity conditions,” Meas. Sci. Technol. 10, 934–945 (1999).
[CrossRef]

Gaudette, T. J.

Hogenboom, D. O.

Javidi, B.

B. Javidi, E. Tajahuerce, “Three-dimensional recognition by use of digital holography,” Opt. Lett. 25, 610–612 (2000).
[CrossRef]

B. Javidi, E. Tajahuerce, “Encrypting three-dimensional information with digital holography,” Opt. Lett. 39, 6595–6601 (2000).

Joannes, L.

F. Dubois, L. Joannes, O. Dupont, J. L. Dewandel, J. C. Legros, “An integrated optical set-up for fluid-physics experiments under microgravity conditions,” Meas. Sci. Technol. 10, 934–945 (1999).
[CrossRef]

F. Dubois, L. Joannes, J.-C. Legros, “Improved three-dimensional imaging with digital holography microscope using a partial spatial coherent source,” Appl. Opt. 38, 7085–7094 (1999).
[CrossRef]

Jüptner, W.

Jüptner, W. P. O.

T. M. Kreis, W. P. O. Jüptner, “Principle of digital holography,” Proceedings of the 3rd International Workshop on Automatic Processing of Fringe Patterns (Fringe ’97), W. Jüptner, W. Osten, eds., (Akademie Verlag Series in Optical Metrology, Vol. 3, Berlin, 1997), pp. 353–363.

M. Adams, T. M. Kreis, W. P. O. Jüptner, “Particle size and position measurement with digital holography,” in Proc. SPIE3098, Optical Inspection and Micromeasurements II, C. Govecki, ed., 234–240 (1997).
[CrossRef]

Kreis, T. M.

M. Adams, T. M. Kreis, W. P. O. Jüptner, “Particle size and position measurement with digital holography,” in Proc. SPIE3098, Optical Inspection and Micromeasurements II, C. Govecki, ed., 234–240 (1997).
[CrossRef]

T. M. Kreis, W. P. O. Jüptner, “Principle of digital holography,” Proceedings of the 3rd International Workshop on Automatic Processing of Fringe Patterns (Fringe ’97), W. Jüptner, W. Osten, eds., (Akademie Verlag Series in Optical Metrology, Vol. 3, Berlin, 1997), pp. 353–363.

Legros, J. C.

F. Dubois, L. Joannes, O. Dupont, J. L. Dewandel, J. C. Legros, “An integrated optical set-up for fluid-physics experiments under microgravity conditions,” Meas. Sci. Technol. 10, 934–945 (1999).
[CrossRef]

Legros, J.-C.

Lindberg, S. C.

Marquet, P.

E. Cuche, P. Marquet, C. Despeuringe, “Aperture apodization using cubic spline interpolation: application in digital holography microscopy,” Opt. Commun. 182, 59–69 (2000).
[CrossRef]

Nilsson, B.

Ohzu, H.

Schnars, U.

Skarman, B.

B. Skarman, K. Wozniac, J. Becker, “Simultaneous 3D-PIV and temperature measurement using a New CCD based holographic interferometer,” Flow Meas. Instrum. 7, 1–6 (1996).
[CrossRef]

Tajahuerce, E.

B. Javidi, E. Tajahuerce, “Encrypting three-dimensional information with digital holography,” Opt. Lett. 39, 6595–6601 (2000).

B. Javidi, E. Tajahuerce, “Three-dimensional recognition by use of digital holography,” Opt. Lett. 25, 610–612 (2000).
[CrossRef]

Takaki, Y.

Wozniac, K.

B. Skarman, K. Wozniac, J. Becker, “Simultaneous 3D-PIV and temperature measurement using a New CCD based holographic interferometer,” Flow Meas. Instrum. 7, 1–6 (1996).
[CrossRef]

Yamaguchi, I.

Zhang, T.

Appl. Opt.

Flow Meas. Instrum.

B. Skarman, K. Wozniac, J. Becker, “Simultaneous 3D-PIV and temperature measurement using a New CCD based holographic interferometer,” Flow Meas. Instrum. 7, 1–6 (1996).
[CrossRef]

Meas. Sci. Technol.

F. Dubois, L. Joannes, O. Dupont, J. L. Dewandel, J. C. Legros, “An integrated optical set-up for fluid-physics experiments under microgravity conditions,” Meas. Sci. Technol. 10, 934–945 (1999).
[CrossRef]

Opt. Commun.

E. Cuche, P. Marquet, C. Despeuringe, “Aperture apodization using cubic spline interpolation: application in digital holography microscopy,” Opt. Commun. 182, 59–69 (2000).
[CrossRef]

Opt. Lett.

Other

M. Adams, T. M. Kreis, W. P. O. Jüptner, “Particle size and position measurement with digital holography,” in Proc. SPIE3098, Optical Inspection and Micromeasurements II, C. Govecki, ed., 234–240 (1997).
[CrossRef]

T. M. Kreis, W. P. O. Jüptner, “Principle of digital holography,” Proceedings of the 3rd International Workshop on Automatic Processing of Fringe Patterns (Fringe ’97), W. Jüptner, W. Osten, eds., (Akademie Verlag Series in Optical Metrology, Vol. 3, Berlin, 1997), pp. 353–363.

Katherine Creath, “Temporal phase measurement methods,” in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, D. W. Robinson, ed. ReidygG. T.,(IOP Publishing Ltd, Middlesex, UK, 1993), pp. 94–140.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Input amplitude x i (sΔ, tΔ) of 512 × 512 pixels for the simulated example. The optical phase is constant.

Fig. 2
Fig. 2

Intensity after a propagation over a distance d = 100 µm without border processing.

Fig. 3
Fig. 3

Module of the extended amplitude of Fig. 1 by the border-processing method. The internal part of the added white square frame is the amplitude of Fig. 1 and the external part is the extension by the border-processing method.

Fig. 4
Fig. 4

Intensity after a propagation over a distance d = 100 µm with border processing.

Fig. 5
Fig. 5

Onion peel inserted in an interferometric microscope under partially coherent illumination. The global defocus distance is 150 µm. Field of view: 512 µm × 512 µm, sampling distance, 1 µm.

Fig. 6
Fig. 6

Digital holographic reconstruction of the image of Fig. 5 with a distance d = 150 µm without border processing.

Fig. 7
Fig. 7

Digital-holographic reconstruction of the image of Fig. 5 with a distance d = 150 µm with border processing.

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

xiq+N2Δ, r+N2Δ=xiqΔ, rΔ.
x0sΔ, tΔ=expjkdEU, V-1 exp-jkλ2d8N2Δ2×U2+V2Es, t+1xisΔ, tΔ,
Eαβ±1gα, β=12Nα,β2N-1exp2πj2N×αα+ββgα, β.
w=w+g,
gz=0,
z=N2 ,, 3N2-1.
U=02N-1 H*U, zGU=0
z=N2 ,, 3N2-1,
F+G=0,
Φ=a|W0|2+U=1N-1 U2|WU|2+U=N2N-12N-U2|WU|2,
M0, 0=a, MU, U=U2, for U=0,, N-1, MU, U=2N-U2, for U=N,, 2N-1.
Φ=W+MW,
W=W+G.
Crz=U=02N-1FrU, zGrU+FjU, zGjU=0, Cjz=U=02N-1FrU, zGjU-FjU, zGrU=0,
T=W+MW-z=02N-1γrzCrz+γjzCjz.
TGrU=2MU, UWrU+GrU-zγrzFrU, z-γjzFjU, z=0, TGjU=2MU, UWjU+GjU-zγrzFjU, z+γjzFrU, z=0,
2MW+2MG-FΓ=0,
G=12 M-1F Γ-W.
G=M-1FF+M-1F-1F+W-W.

Metrics