Abstract

A method for numerical reconstruction of digitally recorded holograms with variable magnification is presented. The proposed strategy allows for smaller, equal, or larger magnification than that achieved with Fresnel transform by introducing the Bluestein substitution into the Fresnel kernel. The magnification is obtained independent of distance, wavelength, and number of pixels, which enables the method to be applied in color digital holography and metrological applications. The approach is supported by experimental and simulation results in digital holography of objects of comparable dimensions with the recording device and in the reconstruction of holograms from digital in-line holographic microscopy.

© 2010 Optical Society of America

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References

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  1. P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital a noninvasive contrast holographic microscopy: imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. 30, 468–470 (2005).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. L. Yu and M. K. Kim, “Wavelength-scanning digital interference holography for tomographic three-dimensional imaging by use of the angular spectrum method,” Opt. Lett. 30, 2092–2094 (2005).
    [CrossRef] [PubMed]
  4. Th. Kreis, M. Adams, and W. Jüptner, “Methods of digital holography: a comparison,” Proc. SPIE 3098, 224–233(1997).
    [CrossRef]
  5. I. Yamaguchi, T. Matsumura, and J. Kato, “Phase-shifting colour digital holography,” Opt. Lett. 27, 1108–1110 (2002).
    [CrossRef]
  6. J. Li, P. Tankam, Z. Peng, and P. Picart, “Digital holographic reconstruction of large objects using a convolution approach and adjustable magnification,” Opt. Lett. 34, 572–574(2009).
    [CrossRef] [PubMed]
  7. L. Yu and M. K. Kim, “Pixel resolution control in numerical reconstruction of digital holography,” Opt. Lett. 31, 897–899(2006).
    [CrossRef] [PubMed]
  8. U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).
  9. M. Sypeck, C. Prokopowicz, and M. Gorecki, “Image multiplying and high-frequency oscillations effects in the Fresnel region light propagation simulation,” Opt. Eng. 42, 3158–3164 (2003).
    [CrossRef]
  10. J. Gass, A. Dakoff, and M. K. Kim, “Phase imaging without 2π ambiguity by multiwavelength digital holography,” Opt. Lett. 28, 1141–1143 (2003).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  12. F. Zhang, I. Yamaguchi, and L. P. Yaroslavsky, “Algorithm for reconstruction of digital holograms with adjustable magnification,” Opt. Lett. 29, 1668–1670 (2004).
    [CrossRef] [PubMed]
  13. L. Bluestein, “Linear filtering approach to the computation of the discrete Fourier transform,” IEEE Trans. Audio Electroacoust. 18, 451–455 (1970).
    [CrossRef]
  14. H. J. Kreuzer, “Holographic microscope and method of hologram reconstruction,” U. S. patent 6411406 B1 (25 June 2002).
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    [CrossRef]
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    [CrossRef] [PubMed]
  19. S. K. Jericho, J. Garcia-Sucerquia, W. Xu, M. H. Jericho, and H. J. Kreuzer, “Submersible digital in-line holographic microscope,” Rev. Sci. Instrum. 77, 043706 (2006).
    [CrossRef]

2009 (1)

2008 (1)

2006 (5)

2005 (2)

2004 (2)

2003 (2)

J. Gass, A. Dakoff, and M. K. Kim, “Phase imaging without 2π ambiguity by multiwavelength digital holography,” Opt. Lett. 28, 1141–1143 (2003).
[CrossRef] [PubMed]

M. Sypeck, C. Prokopowicz, and M. Gorecki, “Image multiplying and high-frequency oscillations effects in the Fresnel region light propagation simulation,” Opt. Eng. 42, 3158–3164 (2003).
[CrossRef]

2002 (1)

1997 (1)

Th. Kreis, M. Adams, and W. Jüptner, “Methods of digital holography: a comparison,” Proc. SPIE 3098, 224–233(1997).
[CrossRef]

1970 (1)

L. Bluestein, “Linear filtering approach to the computation of the discrete Fourier transform,” IEEE Trans. Audio Electroacoust. 18, 451–455 (1970).
[CrossRef]

Adams, M.

Th. Kreis, M. Adams, and W. Jüptner, “Methods of digital holography: a comparison,” Proc. SPIE 3098, 224–233(1997).
[CrossRef]

Alfieri, D.

Baumbach, T.

Bluestein, L.

L. Bluestein, “Linear filtering approach to the computation of the discrete Fourier transform,” IEEE Trans. Audio Electroacoust. 18, 451–455 (1970).
[CrossRef]

Castañeda, R.

J. Garcia-Sucerquia, J. Herrera, and R. Castañeda, “Incoherent recovering of the spatial resolution in digital holography,” Opt. Commun. 260, 62–67 (2006).
[CrossRef]

Colomb, T.

Coppola, G.

Cuche, E.

Dakoff, A.

De Nicola, S.

Depeursinge, C.

Desse, J.

Emery, Y.

Ferraro, P.

Finizio, A.

Garcia-Sucerquia, J.

J. Garcia-Sucerquia, J. Herrera, and R. Castañeda, “Incoherent recovering of the spatial resolution in digital holography,” Opt. Commun. 260, 62–67 (2006).
[CrossRef]

J. Garcia-Sucerquia, W. Xu, P. Kagles, S. M. Jericho, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45, 836–850 (2006).
[CrossRef] [PubMed]

S. K. Jericho, J. Garcia-Sucerquia, W. Xu, M. H. Jericho, and H. J. Kreuzer, “Submersible digital in-line holographic microscope,” Rev. Sci. Instrum. 77, 043706 (2006).
[CrossRef]

Gass, J.

Goodman, J. W.

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

Gorecki, M.

M. Sypeck, C. Prokopowicz, and M. Gorecki, “Image multiplying and high-frequency oscillations effects in the Fresnel region light propagation simulation,” Opt. Eng. 42, 3158–3164 (2003).
[CrossRef]

Herrera, J.

J. Garcia-Sucerquia, J. Herrera, and R. Castañeda, “Incoherent recovering of the spatial resolution in digital holography,” Opt. Commun. 260, 62–67 (2006).
[CrossRef]

Jericho, M. H.

J. Garcia-Sucerquia, W. Xu, P. Kagles, S. M. Jericho, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45, 836–850 (2006).
[CrossRef] [PubMed]

S. K. Jericho, J. Garcia-Sucerquia, W. Xu, M. H. Jericho, and H. J. Kreuzer, “Submersible digital in-line holographic microscope,” Rev. Sci. Instrum. 77, 043706 (2006).
[CrossRef]

Jericho, S. K.

S. K. Jericho, J. Garcia-Sucerquia, W. Xu, M. H. Jericho, and H. J. Kreuzer, “Submersible digital in-line holographic microscope,” Rev. Sci. Instrum. 77, 043706 (2006).
[CrossRef]

Jericho, S. M.

Jueptner, W.

U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

Juptner, W.

Jüptner, W.

Th. Kreis, M. Adams, and W. Jüptner, “Methods of digital holography: a comparison,” Proc. SPIE 3098, 224–233(1997).
[CrossRef]

Kagles, P.

Kato, J.

Kebbel, V.

Kim, M. K.

Kolenovic, E.

Kreis, Th.

Th. Kreis, M. Adams, and W. Jüptner, “Methods of digital holography: a comparison,” Proc. SPIE 3098, 224–233(1997).
[CrossRef]

Kreuzer, H. J.

J. Garcia-Sucerquia, W. Xu, P. Kagles, S. M. Jericho, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45, 836–850 (2006).
[CrossRef] [PubMed]

S. K. Jericho, J. Garcia-Sucerquia, W. Xu, M. H. Jericho, and H. J. Kreuzer, “Submersible digital in-line holographic microscope,” Rev. Sci. Instrum. 77, 043706 (2006).
[CrossRef]

H. J. Kreuzer, “Holographic microscope and method of hologram reconstruction,” U. S. patent 6411406 B1 (25 June 2002).

Li, J.

Magistretti, P. J.

Marquet, P.

Matsumura, T.

Peng, Z.

Picart, P.

Pierattini, G.

Prokopowicz, C.

M. Sypeck, C. Prokopowicz, and M. Gorecki, “Image multiplying and high-frequency oscillations effects in the Fresnel region light propagation simulation,” Opt. Eng. 42, 3158–3164 (2003).
[CrossRef]

Rappaz, B.

Schnars, U.

U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

Sypeck, M.

M. Sypeck, C. Prokopowicz, and M. Gorecki, “Image multiplying and high-frequency oscillations effects in the Fresnel region light propagation simulation,” Opt. Eng. 42, 3158–3164 (2003).
[CrossRef]

Tankam, P.

Xu, W.

J. Garcia-Sucerquia, W. Xu, P. Kagles, S. M. Jericho, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45, 836–850 (2006).
[CrossRef] [PubMed]

S. K. Jericho, J. Garcia-Sucerquia, W. Xu, M. H. Jericho, and H. J. Kreuzer, “Submersible digital in-line holographic microscope,” Rev. Sci. Instrum. 77, 043706 (2006).
[CrossRef]

Yamaguchi, I.

Yaroslavsky, L. P.

Yu, L.

Zhang, F.

Appl. Opt. (2)

IEEE Trans. Audio Electroacoust. (1)

L. Bluestein, “Linear filtering approach to the computation of the discrete Fourier transform,” IEEE Trans. Audio Electroacoust. 18, 451–455 (1970).
[CrossRef]

Opt. Commun. (1)

J. Garcia-Sucerquia, J. Herrera, and R. Castañeda, “Incoherent recovering of the spatial resolution in digital holography,” Opt. Commun. 260, 62–67 (2006).
[CrossRef]

Opt. Eng. (1)

M. Sypeck, C. Prokopowicz, and M. Gorecki, “Image multiplying and high-frequency oscillations effects in the Fresnel region light propagation simulation,” Opt. Eng. 42, 3158–3164 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (8)

L. Yu and M. K. Kim, “Wavelength-scanning digital interference holography for tomographic three-dimensional imaging by use of the angular spectrum method,” Opt. Lett. 30, 2092–2094 (2005).
[CrossRef] [PubMed]

J. Gass, A. Dakoff, and M. K. Kim, “Phase imaging without 2π ambiguity by multiwavelength digital holography,” Opt. Lett. 28, 1141–1143 (2003).
[CrossRef] [PubMed]

P. Ferraro, S. De Nicola, G. Coppola, A. Finizio, D. Alfieri, and G. Pierattini, “Controlling image size as a function of distance and wavelength in Fresnel-transform reconstruction of digital holograms,” Opt. Lett. 29, 854–856 (2004).
[CrossRef] [PubMed]

F. Zhang, I. Yamaguchi, and L. P. Yaroslavsky, “Algorithm for reconstruction of digital holograms with adjustable magnification,” Opt. Lett. 29, 1668–1670 (2004).
[CrossRef] [PubMed]

I. Yamaguchi, T. Matsumura, and J. Kato, “Phase-shifting colour digital holography,” Opt. Lett. 27, 1108–1110 (2002).
[CrossRef]

J. Li, P. Tankam, Z. Peng, and P. Picart, “Digital holographic reconstruction of large objects using a convolution approach and adjustable magnification,” Opt. Lett. 34, 572–574(2009).
[CrossRef] [PubMed]

L. Yu and M. K. Kim, “Pixel resolution control in numerical reconstruction of digital holography,” Opt. Lett. 31, 897–899(2006).
[CrossRef] [PubMed]

P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital a noninvasive contrast holographic microscopy: imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. 30, 468–470 (2005).
[CrossRef] [PubMed]

Proc. SPIE (1)

Th. Kreis, M. Adams, and W. Jüptner, “Methods of digital holography: a comparison,” Proc. SPIE 3098, 224–233(1997).
[CrossRef]

Rev. Sci. Instrum. (1)

S. K. Jericho, J. Garcia-Sucerquia, W. Xu, M. H. Jericho, and H. J. Kreuzer, “Submersible digital in-line holographic microscope,” Rev. Sci. Instrum. 77, 043706 (2006).
[CrossRef]

Other (3)

H. J. Kreuzer, “Holographic microscope and method of hologram reconstruction,” U. S. patent 6411406 B1 (25 June 2002).

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

U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

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Figures (5)

Fig. 1
Fig. 1

Digital holography setup.

Fig. 2
Fig. 2

Reconstruction of the digitally recorded holograms using the Fresnel transform presented in Eq. (2). The image has 1024 × 1024 pixels and covers an area of 34.2 mm × 34.2   mm . The magnification achieved is m FT = Δ ξ / Δ x = λ z / ( M Δ x 2 ) = 4.5 .

Fig. 3
Fig. 3

Reconstruction of the digitally recorded holograms using the Fresnel–Bluestein transform presented in Eq. (3). The image has 1024 × 1024 pixels but now covers different areas according to magnification; see the text for details. For comparison, the magnification is expressed in terms of m FT in (a)–(d).

Fig. 4
Fig. 4

Schematic setup for lensless digital in-line holographic microscopy (DIHM).

Fig. 5
Fig. 5

Fresnel–Bluestein transform applied to DIHM. (a) Modeled in-line hologram of two particles separated by 2 µm . (b) Reconstruction for the magnification dictated by the experimental setup. (c), (d) Reconstructions for optimized magnifications. See text for further details.

Equations (5)

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U p ( z ) = exp ( i k z ) i λ z exp ( i k 2 z Δ ξ 2 p 2 ) n = 0 M 1 I n exp ( i k 2 z Δ x 2 n 2 ) exp ( i k z Δ x n Δ ξ p ) ,
U p ( z ) = exp ( i k z ) i λ z exp ( i π λ z p 2 M 2 Δ x 2 ) n = 0 M 1 I n exp ( i k 2 z Δ x 2 n 2 ) exp ( i 2 π n p M ) .
U p ( z ) = exp ( i k z ) i λ z exp ( i π λ z Δ ξ ( Δ x Δ ξ ) p 2 ) n = 0 M 1 I n exp ( i π λ z Δ x ( Δ x Δ ξ ) n 2 ) exp ( i π λ z Δ x Δ ξ ( p n ) 2 ) .
f 1 n = I n exp ( i π λ z Δ x ( Δ x Δ ξ ) n 2 )
f 2 n = exp ( i π λ z Δ x Δ ξ n 2 ) .

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