Abstract

This paper presents a reconstruction algorithm based on the convolution formula of diffraction which uses the Fresnel impulse response of free space propagation. The bandwidth of the reconstructing convolution kernel is extended to the one of the object in order to allow the direct reconstruction of objects with size quite larger than the recording area. The spatial bandwidth extension is made possible by the use of a numerical spherical wave as a virtual reconstructing wave, thus modifying the virtual reconstruction distance and increasing the kernel bandwidth. Experimental results confirm the suitability of the proposed method in the case of the simultaneous recording of two-color digital holograms by using a spatial color multiplexing scheme.

© 2009 Optical Society of America

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  1. U. Schnars and W. Jüptner, ‘‘Direct recording of holograms by a CCD target and numerical reconstruction,’’ Appl. Opt. 33, 179-181 (1994).
    [CrossRef]
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    [CrossRef] [PubMed]
  3. T. Nomura, B. Javidi, S. Murata, E. Nitanai, and T. Numata, ‘‘Polarization imaging of a 3D object by use of on-axis phase-shifting digital holography,’’ Opt. Lett. 32, 481-483 (2007).
    [CrossRef] [PubMed]
  4. P. Picart, B. Diouf, E. Lolive, and J.-M. Berthelot, "Investigation of fracture mechanisms in resin concrete using spatially multiplexed digital Fresnel holograms," Opt. Eng. 43, 1169-1176 (2004).
    [CrossRef]
  5. I. Yamaguchi, J. Kato, and S. Ohta, ‘‘Surface shape measurement by phase shifting digital holography," Opt. Rev. 8, 85-89 (2001).
    [CrossRef]
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    [CrossRef]
  7. P. Picart, J. Leval, D. Mounier, and S. Gougeon, "Time averaged digital holography," Opt. Lett. 28, 1900-1902 (2003).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  11. B. Javidi, P. Ferraro, S. Hong, S. De Nicola, A. Finizio, D. Alfieri, and G. Pierattini, "Three-dimensional image fusion by use of multiwavelength digital holography," Opt. Lett. 30, 144-146 (2005).
    [CrossRef] [PubMed]
  12. D. Alfieri, G. Coppola, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, and B. Javidi, "Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength," Opt. Commun. 260, 113-116 (2006).
    [CrossRef]
  13. J. Zhao, H. Jiang, and J. Di, "Recording and reconstruction of a color holographic image by using digital lensless Fourier transform holography," Opt. Express 16, 2514-2519 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-4-2514
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    [CrossRef]
  16. P. Picart, D. Mounier, and J. M. Desse, "High resolution digital two-color holographic metrology," Opt. Lett. 33, 276-278 (2008).
    [CrossRef] [PubMed]
  17. J.M. Desse, P. Picart, and P. Tankam, "Digital three-color holographic interferometry for flow analysis," Opt. Express 16, 5471-5480 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-8-5471
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  18. Th. Kreis, M. Adams, and W. Jüptner, ‘‘Methods of digital holography: a comparison,’’ Proc. SPIE 3098, 224-233 (1997).
    [CrossRef]
  19. 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]
  20. J. W. Goodman, Introduction to Fourier Optics (second edition, McGraw-Hill Editions, New York, 1996).
  21. P. Picart and J. Leval, "General theoretical formulation of image formation in digital Fresnel holography," J. Opt. Soc. Am. A 25, 1744-1761 (2008).
    [CrossRef]
  22. I. Yamaguchi, J. Kato, S. Ohta, and J. Mizuno, ‘‘Image formation in phase shifting digital holography and application to microscopy,’’ Appl. Opt. 40, 6177-6186 (2001).
    [CrossRef]
  23. U. Schnars and W. Jüptner, ‘‘Digital recording and numerical reconstruction of holograms,’’ Meas. Sci. Technol. 13, R85-R101 (2002).
    [CrossRef]

2008

2007

2006

P. Ferraro, D. Alferi, S. De Nicola, L. De Petrocellis, A. Finizio, and G. Pierattini, ‘‘Quantitative phase-contrast microscopy by a lateral shear approach to digital holographic image reconstruction,’’ Opt. Lett. 31, 1405-1407 (2006).
[CrossRef] [PubMed]

D. Alfieri, G. Coppola, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, and B. Javidi, "Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength," Opt. Commun. 260, 113-116 (2006).
[CrossRef]

2005

2004

2003

2002

2001

I. Yamaguchi, J. Kato, S. Ohta, and J. Mizuno, ‘‘Image formation in phase shifting digital holography and application to microscopy,’’ Appl. Opt. 40, 6177-6186 (2001).
[CrossRef]

I. Yamaguchi, J. Kato, and S. Ohta, ‘‘Surface shape measurement by phase shifting digital holography," Opt. Rev. 8, 85-89 (2001).
[CrossRef]

1997

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

1994

Adams, M.

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

Alferi, D.

Alfieri, D.

Berthelot, J.-M.

P. Picart, B. Diouf, E. Lolive, and J.-M. Berthelot, "Investigation of fracture mechanisms in resin concrete using spatially multiplexed digital Fresnel holograms," Opt. Eng. 43, 1169-1176 (2004).
[CrossRef]

Charriere, F.

Coetmellec, S.

Colomb, T.

Coppola, G.

D. Alfieri, G. Coppola, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, and B. Javidi, "Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength," Opt. Commun. 260, 113-116 (2006).
[CrossRef]

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]

Cuche, E.

De Nicola, S.

De Petrocellis, L.

Demoli, N.

Depeursinge, C.

Desse, J. M.

Desse, J.M.

Di, J.

Diouf, B.

P. Picart, B. Diouf, E. Lolive, and J.-M. Berthelot, "Investigation of fracture mechanisms in resin concrete using spatially multiplexed digital Fresnel holograms," Opt. Eng. 43, 1169-1176 (2004).
[CrossRef]

Emery, Y.

Ferraro, P.

Finizio, A.

Gougeon, S.

Hong, S.

Javidi, B.

Jiang, H.

Jüptner, W.

U. Schnars and W. Jüptner, ‘‘Digital recording and numerical reconstruction of holograms,’’ Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

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

U. Schnars and W. Jüptner, ‘‘Direct recording of holograms by a CCD target and numerical reconstruction,’’ Appl. Opt. 33, 179-181 (1994).
[CrossRef]

Kato, J.

Kreis, Th.

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

Kuhn, J.

Lebrun, D.

Leval, J.

Lolive, E.

P. Picart, B. Diouf, E. Lolive, and J.-M. Berthelot, "Investigation of fracture mechanisms in resin concrete using spatially multiplexed digital Fresnel holograms," Opt. Eng. 43, 1169-1176 (2004).
[CrossRef]

Marquet, P.

Matsumura, T.

Mizuno, J.

Moisson, E.

Montfort, F.

Mounier, D.

Murata, S.

Nitanai, E.

Nomura, T.

Numata, T.

Ohta, S.

I. Yamaguchi, J. Kato, and S. Ohta, ‘‘Surface shape measurement by phase shifting digital holography," Opt. Rev. 8, 85-89 (2001).
[CrossRef]

I. Yamaguchi, J. Kato, S. Ohta, and J. Mizuno, ‘‘Image formation in phase shifting digital holography and application to microscopy,’’ Appl. Opt. 40, 6177-6186 (2001).
[CrossRef]

Oskul, C.

Picart, P.

Pierattini, G.

Schnars, U.

U. Schnars and W. Jüptner, ‘‘Digital recording and numerical reconstruction of holograms,’’ Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

U. Schnars and W. Jüptner, ‘‘Direct recording of holograms by a CCD target and numerical reconstruction,’’ Appl. Opt. 33, 179-181 (1994).
[CrossRef]

Tankam, P.

Torzynski, M.

Vukicevic, D.

Yamaguchi, I.

Yaroslavsky, L. P.

Zhang, F.

Zhao, J.

Appl. Opt.

J. Opt. Soc. Am. A

Meas. Sci. Technol.

U. Schnars and W. Jüptner, ‘‘Digital recording and numerical reconstruction of holograms,’’ Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

Opt. Commun.

D. Alfieri, G. Coppola, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, and B. Javidi, "Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength," Opt. Commun. 260, 113-116 (2006).
[CrossRef]

Opt. Eng.

P. Picart, B. Diouf, E. Lolive, and J.-M. Berthelot, "Investigation of fracture mechanisms in resin concrete using spatially multiplexed digital Fresnel holograms," Opt. Eng. 43, 1169-1176 (2004).
[CrossRef]

Opt. Express

Opt. Lett.

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]

P. Picart, D. Mounier, and J. M. Desse, "High resolution digital two-color holographic metrology," Opt. Lett. 33, 276-278 (2008).
[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]

B. Javidi, P. Ferraro, S. Hong, S. De Nicola, A. Finizio, D. Alfieri, and G. Pierattini, "Three-dimensional image fusion by use of multiwavelength digital holography," Opt. Lett. 30, 144-146 (2005).
[CrossRef] [PubMed]

P. Picart, J. Leval, D. Mounier, and S. Gougeon, "Time averaged digital holography," Opt. Lett. 28, 1900-1902 (2003).
[CrossRef] [PubMed]

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

P. Ferraro, D. Alferi, S. De Nicola, L. De Petrocellis, A. Finizio, and G. Pierattini, ‘‘Quantitative phase-contrast microscopy by a lateral shear approach to digital holographic image reconstruction,’’ Opt. Lett. 31, 1405-1407 (2006).
[CrossRef] [PubMed]

T. Nomura, B. Javidi, S. Murata, E. Nitanai, and T. Numata, ‘‘Polarization imaging of a 3D object by use of on-axis phase-shifting digital holography,’’ Opt. Lett. 32, 481-483 (2007).
[CrossRef] [PubMed]

Opt. Rev.

I. Yamaguchi, J. Kato, and S. Ohta, ‘‘Surface shape measurement by phase shifting digital holography," Opt. Rev. 8, 85-89 (2001).
[CrossRef]

Proc. SPIE

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

Other

J. W. Goodman, Introduction to Fourier Optics (second edition, McGraw-Hill Editions, New York, 1996).

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Figures (8)

Fig. 1.
Fig. 1.

Synoptic of the convolution algorithm

Fig. 2.
Fig. 2.

Optical setup for the simultaneous recording of two-color digital holograms (PBS: polarizing beam splitter, SF: spatial filter, λG =0.532μm, λR =0.6328μm, θG =25°, θR =45°)

Fig. 3.
Fig. 3.

Reconstruction of the red object, a) real part of the impulse response, b) transfer function corresponding to the spatially modulated impulse response, c) spatial frequency spectrum of the recorded hologram, d) red object reconstructed with a magnification of 0.17

Fig. 4.
Fig. 4.

Reconstruction of the green object, (a) real part of the impulse response, (b) transfer function corresponding to the spatially modulated impulse response, (c) spatial frequency spectrum of the recorded hologram, (d) green object reconstructed with a magnification of 0.17

Fig. 5.
Fig. 5.

Comparison between the digital two-color object reconstruction and a two-color image obtained with a classical color camera, (a) color image resulting from the weighted superposition, (b) CCD image of the object illuminated in the same conditions with the two lasers.

Fig. 6.
Fig. 6.

Reconstruction of the circular red object, (a) real part of the impulse response, (b) transfer function corresponding to the spatially modulated impulse response, (c) spatial frequency spectrum of the recorded hologram, (d) red object reconstructed with a magnification of 0.17

Fig. 7.
Fig. 7.

Reconstruction of the circular green object, (a) real part of the impulse response, (b) transfer function corresponding to the spatially modulated impulse response, (c) spatial frequency spectrum of the recorded hologram, (d) green object reconstructed with a magnification of 0.17

Fig. 8.
Fig. 8.

Comparison of the two color images of the spot medal, (a) color image resulting from the weighted superposition, (b) CCD image of the object illuminated in the same conditions with the two lasers.

Equations (14)

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

A(x,y)=A0(x,y) exp [iψ0(x,y)] ,
O(x,y,z+d0)=A(x,y)*h(x,y,d0),
h(x,y,d0)=iλd0 exp [2iπd0λ] exp [iπλd0(x2+y2)] .
H(x,y,d0)=O(x,y,d0)2+r(x,y)2
+r*(x,y)O(x,y,d0)+r(x,y)O*(x,y,d0).
Δukernel×Δvkernel=Lpxλd0×Kpyλd0.
w(x,y,Rc) =exp[iπλRc(x2+y2)].
1dR=1Rc1d0.
γ=dRd0,
{Δvobject,Δvobject}={γΔAxλdR,γΔAyλdR} ,
H˜(u,v,d0)=O˜0(u,v)+a0λO˜(uu0λ,vv0λ,d0)+a0λO˜*(u+u0λ,v+v0λ,d0),
hm(x,y,dR)=iλdRexp[2iπdRλ]exp[iπλdR(x2+y2)+2iπ(u0λx+v0λy)].
h(x,y,dR)={iλdRexp[2iπdRλ]exp[iπλdR(x2+y2)]ifx2+y2γ2ΔA20elsewhere .
h(x,y,dR)={iλdRexp[2iπdRλ]exp[iπλdR(x2+y2)]ifxγΔAx/2andyγΔAy/20elsewhere .

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