Abstract

In the research of digital holography, this paper presents a numerical method using an adjustable magnification for local object field reconstruction together with experiment verification. The method first designs a spherical wave according to the given magnification to illuminate the digital hologram, then through a Fourier transform of diffraction, it calculates the reconstructed image plane. Afterward, a filtering window is set in the image plane to extract the image of the local object field, and then the object field reached hologram plane is formed using diffraction’s inverse operation. Finally, the object field is reconstructed through diffraction’s angular spectrum theory.

© 2011 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2010 (1)

J.-c. Li, Z.-j. Peng, P. Tankam, and P. Picart, “Design of the spatial filter window for digital holographic convolution reconstruction of object beam field,” Opt. Commun. 283, 4166–4170 (2010).
[CrossRef]

2009 (2)

2008 (3)

2006 (2)

D. Alfieri, G. Coppola, S. D. 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]

T. Colomb, F. Montfort, J. Kühn, N. Aspert, E. Cuche, A. Marian, F. Charrière, S. Bourquin, P. Marquet, and C. Depeursinge, “Numerical parametric lens for shifting, magnification and complete aberration compensation in digital holographic microscopy,” J. Opt. Soc. Am. A 23, 3177–3190(2006).
[CrossRef]

2004 (1)

2002 (1)

2000 (1)

1999 (1)

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).
[CrossRef]

1971 (1)

T. Huang, Digital holography, Proc. IEEE 59, 1335–1346 (1971).
[CrossRef]

1967 (1)

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

Alfieri, D.

P. Ferraro, S. Grilli, L. Miccio, D. Alfieri, S. D. Nicola, A. Finizio, and B. Javidi, “Full color 3-D imaging by digital holography and removal of chromatic aberrations,” J. Display Technology 4, 97–100 (2008).
[CrossRef]

D. Alfieri, G. Coppola, S. D. 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]

Aspert, N.

Bernardo, L. M.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).
[CrossRef]

Bourquin, S.

Charrière, F.

Colomb, T.

Coppola, G.

D. Alfieri, G. Coppola, S. D. 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]

Cuche, E.

Denis, M.

Depeursinge, C.

Desse, J. M.

Ferraro, P.

P. Ferraro, S. Grilli, L. Miccio, D. Alfieri, S. D. Nicola, A. Finizio, and B. Javidi, “Full color 3-D imaging by digital holography and removal of chromatic aberrations,” J. Display Technology 4, 97–100 (2008).
[CrossRef]

D. Alfieri, G. Coppola, S. D. 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]

Ferreira, C.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).
[CrossRef]

Finizio, A.

P. Ferraro, S. Grilli, L. Miccio, D. Alfieri, S. D. Nicola, A. Finizio, and B. Javidi, “Full color 3-D imaging by digital holography and removal of chromatic aberrations,” J. Display Technology 4, 97–100 (2008).
[CrossRef]

D. Alfieri, G. Coppola, S. D. 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]

Garcia, J.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).
[CrossRef]

Goodman, J. W.

J. W. Goodman and 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, 1996).

Grilli, S.

P. Ferraro, S. Grilli, L. Miccio, D. Alfieri, S. D. Nicola, A. Finizio, and B. Javidi, “Full color 3-D imaging by digital holography and removal of chromatic aberrations,” J. Display Technology 4, 97–100 (2008).
[CrossRef]

Huang, T.

T. Huang, Digital holography, Proc. IEEE 59, 1335–1346 (1971).
[CrossRef]

Javidi, B.

P. Ferraro, S. Grilli, L. Miccio, D. Alfieri, S. D. Nicola, A. Finizio, and B. Javidi, “Full color 3-D imaging by digital holography and removal of chromatic aberrations,” J. Display Technology 4, 97–100 (2008).
[CrossRef]

D. Alfieri, G. Coppola, S. D. 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]

Jueptner, W.

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

Kato, J.

Kreis, T.

T. Kreis, Handbook of holographic interferometry: optical and digital methods (Wiley, 2004), p. 10.

Kühn, J.

Lawrence, R. W.

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

Leval, J.

Li, J. C.

Li, J.-c.

J.-c. Li, Z.-j. Peng, P. Tankam, and P. Picart, “Design of the spatial filter window for digital holographic convolution reconstruction of object beam field,” Opt. Commun. 283, 4166–4170 (2010).
[CrossRef]

Marian, A.

Marinho, F.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).
[CrossRef]

Marquet, P.

Mas, D.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).
[CrossRef]

Matsumura, T.

Miccio, L.

P. Ferraro, S. Grilli, L. Miccio, D. Alfieri, S. D. Nicola, A. Finizio, and B. Javidi, “Full color 3-D imaging by digital holography and removal of chromatic aberrations,” J. Display Technology 4, 97–100 (2008).
[CrossRef]

Montfort, F.

Nicola, S. D.

P. Ferraro, S. Grilli, L. Miccio, D. Alfieri, S. D. Nicola, A. Finizio, and B. Javidi, “Full color 3-D imaging by digital holography and removal of chromatic aberrations,” J. Display Technology 4, 97–100 (2008).
[CrossRef]

D. Alfieri, G. Coppola, S. D. 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]

Pascal, P.

Patrice, T

Patrice, T.

Peng, Z. J.

Peng, Z.-j.

J.-c. Li, Z.-j. Peng, P. Tankam, and P. Picart, “Design of the spatial filter window for digital holographic convolution reconstruction of object beam field,” Opt. Commun. 283, 4166–4170 (2010).
[CrossRef]

Picart, P.

Pierattini, G.

D. Alfieri, G. Coppola, S. D. 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]

Schnars, U.

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

Tankam, P.

J.-c. Li, Z.-j. Peng, P. Tankam, and P. Picart, “Design of the spatial filter window for digital holographic convolution reconstruction of object beam field,” Opt. Commun. 283, 4166–4170 (2010).
[CrossRef]

J. M. Desse, P. Picart, and P. Tankam, “Digital three-color holographic interferometry for flow analysis,” Opt. Express 16, 5471–5480 (2008).
[CrossRef] [PubMed]

P. Tankam, “Méthodes d’holographie numérique couleur pour la métrologie sans contact en acoustique et mécanique,” Ph.D. dissertation (Universite du Maine, 2010).

Yamaguchi, I.

Yaroslavsky, L. P.

Zhang, F.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

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

J. Display Technology (1)

P. Ferraro, S. Grilli, L. Miccio, D. Alfieri, S. D. Nicola, A. Finizio, and B. Javidi, “Full color 3-D imaging by digital holography and removal of chromatic aberrations,” J. Display Technology 4, 97–100 (2008).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Commun. (3)

J.-c. Li, Z.-j. Peng, P. Tankam, and P. Picart, “Design of the spatial filter window for digital holographic convolution reconstruction of object beam field,” Opt. Commun. 283, 4166–4170 (2010).
[CrossRef]

D. Alfieri, G. Coppola, S. D. 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]

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Proc. IEEE (1)

T. Huang, Digital holography, Proc. IEEE 59, 1335–1346 (1971).
[CrossRef]

Other (4)

T. Kreis, Handbook of holographic interferometry: optical and digital methods (Wiley, 2004), p. 10.

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

P. Tankam, “Méthodes d’holographie numérique couleur pour la métrologie sans contact en acoustique et mécanique,” Ph.D. dissertation (Universite du Maine, 2010).

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

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Figures (6)

Fig. 1
Fig. 1

Coordinate definition for theoretical study.

Fig. 2
Fig. 2

FIMG4FFT reconstructed process when M = 0.08 . (a) The 1-FFT image plane of z = z i , (b) the filtered pattern of the 1-FFT image plane, (c) digital filtered hologram in the plane of z = 0 , and (d) the FIMG4FFT reconstructed image in the plane of z = z i .

Fig. 3
Fig. 3

2-FFT reconstructed image when M = 0.08 . (a) The object light frequency spectrum in the plane of z = 0 and the filtering window. (b) The 2-FFT reconstructed image.

Fig. 4
Fig. 4

Frequency distribution of four periods in the hologram discrete Fourier transform plane when M = 0.08 .

Fig. 5
Fig. 5

Reconstruction example of the object local area ( 1024 × 1024 pixels) for (a)  M = 0.16 and (b)  M = 0.23 .

Fig. 6
Fig. 6

FIMG4FFT reconstructed image and its frequency of differ ent M. (a) the object field intensity image when M = 0.08 and its frequency spectrum (b), (c) the object field intensity image when M = 0.06 and its frequency spectrum (d), (e) object field intensity image when M = 0.04 and its frequency spectrum (f).

Equations (6)

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R ( x , y ) = A r exp { j k 2 z r [ ( x a ) 2 + ( y b ) 2 ] } ,
R ( x , y ) = R r ( x , y ) exp [ j 2 π ( a λ z r x + b λ z r y ) ] .
R c ( x , y ) w ( x , y ) I ( x , y ) = R c ( x , y ) w ( x , y ) [ | U ( x , y ) | 2 + A r 2 ] + R c ( x , y ) w ( x , y ) R ( x , y ) U * ( x , y ) + R c ( x , y ) w ( x , y ) R * ( x , y ) U ( x , y ) ,
z i = ( 1 z 0 1 z c 1 z r ) 1 .
U i ( x , y ) = F 1 { F { R c ( x , y ) w ( x , y ) R r ( x , y ) U * ( x , y ) } exp [ j k z i 1 λ 2 ( u 2 + v 2 ) ] } ,
F { R c ( x , y ) w ( x , y ) R r ( x , y ) U * ( x , y ) } exp [ j k z i 1 λ 2 ( u 2 + v 2 ) ] .

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