Abstract

We present a new method for numerically reconstructing digital holograms on tilted planes. The method is based on the angular spectrum of plane waves. Fast Fourier transform algorithm is used twice and coordinate rotation in the Fourier domain enables to reconstruct the object field on the tilted planes. Correction of the anamorphism resulting from the coordinate transformation is performed by suitable interpolation of the spectral data. Experimental results are presented to demonstrate the method for a single-axis rotation. The algorithm is especially useful for tomographic image reconstruction.

© 2005 Optical Society of America

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References

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  1. L. Yaroslavsky and M. Eden, Fundamentals of Digital Optics, (BirkhŠuser, Boston, 1996).
  2. O. Schnars andW. Juptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179-181 (1994).
    [CrossRef] [PubMed]
  3. T. M. Kreis, “Frequency analysis of digital holography,” Opt. Eng. 41, 771-778 (2002).
    [CrossRef]
  4. M. Kim, "Tomographic three-dimensional imaging of a biological specimen using wavelength-scanning digital interference holography," Opt. Express 7, 305-310 (2000).
    [CrossRef] [PubMed]
  5. Y. Takaki and H. Ohzu, “Hybrid holographic microscopy: visualization of three-dimensional object information by use of viewing angles,” Appl. Opt. 39, 5302-5308 (2000).
    [CrossRef]
  6. T.C. Poon, K.B. Doh, B.W. Schilling, "Three-dimensional microscopy by optical scanning holography," Opt. Eng. 34, 1338-44 (1995).
    [CrossRef]
  7. P. Ferraro, S. De Nicola, G. Coppola, A. Finizio, D. Alfieri,G. Pierattini, ”Controlling image size as a function of distance and wavelength in Fresnel-transform reconstruction of digital hologram,” Opt. Lett. 29, 854-856 (2004).
    [CrossRef] [PubMed]
  8. T. Zhang and I. Yamaguchi, "Three-dimensional microscopy with phase-shifting digital holography," Opt. Lett. 23, 1221-3 (1998).
    [CrossRef]
  9. D. Leserberg and C. Frère, “Computer generated holograms of 3-D objects composed of tilted planar segments,” Appl. Opt. 27, 3020-2024 (1988)
    [CrossRef]
  10. N. Delen and B. Hooker, “Free-space beam propagation between arbitrarily oriented planes based on full diffraction theory: a fast Fourier approach,” J. Opt. Soc. A. 15, 857-867 (1998).
    [CrossRef]
  11. L. Yu, Y. An and L. Cai, ”Numerical reconstruction of digital holograms with variable viewing angles,” Opt. Express 10, 1250-1257 (2002).
    [PubMed]
  12. K. Matsushima, H. Schimmel, F. Wyrowski, “Fast calculation method for optical diffraction on tilted planes by use of the angular spectrum of plane waves,” J. Opt. Soc. Am. A 20, 1755-1762 (2003).
    [CrossRef]
  13. E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. 24, 291-293 (1999).
    [CrossRef]
  14. P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, G. Coppola, “Recovering image resolution in reconstructing digital off-axis holograms by Fresnel-transform method,” Appl. Phys. Lett. 85, 2709-2711 (2004).
    [CrossRef]

2003 (1)

Appl. Opt. (3)

Appl. Phys. Lett. (1)

P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, G. Coppola, “Recovering image resolution in reconstructing digital off-axis holograms by Fresnel-transform method,” Appl. Phys. Lett. 85, 2709-2711 (2004).
[CrossRef]

J. Opt. Soc. A. (1)

N. Delen and B. Hooker, “Free-space beam propagation between arbitrarily oriented planes based on full diffraction theory: a fast Fourier approach,” J. Opt. Soc. A. 15, 857-867 (1998).
[CrossRef]

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

Opt. Eng. (2)

T. M. Kreis, “Frequency analysis of digital holography,” Opt. Eng. 41, 771-778 (2002).
[CrossRef]

T.C. Poon, K.B. Doh, B.W. Schilling, "Three-dimensional microscopy by optical scanning holography," Opt. Eng. 34, 1338-44 (1995).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Other (1)

L. Yaroslavsky and M. Eden, Fundamentals of Digital Optics, (BirkhŠuser, Boston, 1996).

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Figures (3)

Fig. 1.
Fig. 1.

Experimental set-up fro recording off-axis digital holograms. PBS polarizing beam splitter; BS beam splitter; SF’s spatial filters; MO microscope objective. The hologram are recorded by the CCD camera.

Fig. 2.
Fig. 2.

Schematic illustration of the ASA algorithm for reconstructing digital holograms on tilted planes.

Fig. 3.
Fig. 3.

(a) digitized hologram of the logo “MEMS”; (b) amplitude image reconstruction at 240 mm; (c) amplitude image reconstruction at 265 mm; (d) amplitude image reconstruction at 290 mm; (e) reconstruction by the angular spectrum-based algorithm; (e)compensation of the anamorphism.

Equations (3)

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O ̂ ( d ; u , v ) = O ( u , v ) exp i 2 πd ( λ 2 u 2 v 2 )
O ( u , v ) = o ( x , y ) exp [ i 2 π ( ux + vy ) ] dxdy
o ( x ̂ , y ̂ ) = 1 [ O ̂ ( d ; u ̂ cos θ ) + w ̂ sin θ , v ̂ ) ]

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