Abstract

In-line digital holography based on two-intensity measurements [Zhang et al. Opt. Lett. 29, 1787 (2004)], is modified by introducing a π shifting in the reference phase. Such an improvement avoids the assumption that the object beam must be much weaker than the reference beam in strength and results in a simplified experimental implementation. Computer simulations and optical experiments are carried out to validate the method, which we refer to as position-phase-shifting digital holography.

© 2008 Optical Society of America

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2006 (4)

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[CrossRef]

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[CrossRef]

S. Lai, B. Kemper, and G. von Bally, “Off-axis reconstruction of in-line holograms for twin-image elimination,” Opt. Commun. 169, 37-43 (1999).
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1998 (2)

S. Seebacher, W. Osten, and W. Jüptner, “Measuring shape and deformation of small objects using digital holography,” Proc. SPIE 3479, 104-115 (1998).
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I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268-1270 (1997).
[CrossRef] [PubMed]

1994 (2)

1992 (1)

1987 (1)

1983 (1)

1968 (1)

1951 (1)

W. L. Bragg and G. L. Rogers, “Elimination of the unwanted image in diffraction microscopy,” Nature 167, 190-191 (1951).
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Adams, M.

M. Adams, T. Kreis, and W. Jüptner, “Particle size and position measurement with digital holography,” Proc. SPIE 3098, 234-240 (1997).
[CrossRef]

Alfieri, D.

L. Miccio, D. Alfieri, S. Grilli, P. Ferraro, A. Finizio, L. De Petrocellis, and S. D. Nicola, “Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram,” Appl. Phys. Lett. 90, 041104 (2007).
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Bernardo, L. M.

D. Mas, J. Carcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithm for free-space diffraction patterns calculation,” Opt. Commun. 164, 233-245 (1999).
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Burow, R.

Cai, L. Z.

Carcia, J.

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

Charriére, F.

Chen, J. W.

T. Q. Xiao, H. J. Xu, Y. J. Zhang, J. W. Chen, and Z. Z. Xu, “Digital image decoding for in-line X-ray holography using two holograms,” J. Mod. Opt. 45, 343-353 (1998).
[CrossRef]

Colomb, T.

Cuche, E.

Cullen, D.

Darakis, E.

De Petrocellis, L.

L. Miccio, D. Alfieri, S. Grilli, P. Ferraro, A. Finizio, L. De Petrocellis, and S. D. Nicola, “Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram,” Appl. Phys. Lett. 90, 041104 (2007).
[CrossRef]

Depeursinge, C.

Dong, G. Y.

Elssner, K.-E.

Ferraro, P.

L. Miccio, D. Alfieri, S. Grilli, P. Ferraro, A. Finizio, L. De Petrocellis, and S. D. Nicola, “Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram,” Appl. Phys. Lett. 90, 041104 (2007).
[CrossRef]

Ferreira, C.

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

Finizio, A.

L. Miccio, D. Alfieri, S. Grilli, P. Ferraro, A. Finizio, L. De Petrocellis, and S. D. Nicola, “Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram,” Appl. Phys. Lett. 90, 041104 (2007).
[CrossRef]

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G. Pedrini, P. Fröning, H. Tiziani, and F. M. Santoyo, “Shape measurement of microscopic structures using digital holograms,” Opt. Commun. 164, 257-268 (1999).
[CrossRef]

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Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2004).

Gopinathan, U.

A. Nelleri, U. Gopinathan, J. Joseph, and K. Singh, “Three dimensional object recognition from digital Fresnel hologram by wavelength matched filtering,” Opt. Commun. 259, 499-506 (2006).
[CrossRef]

Grilli, S.

L. Miccio, D. Alfieri, S. Grilli, P. Ferraro, A. Finizio, L. De Petrocellis, and S. D. Nicola, “Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram,” Appl. Phys. Lett. 90, 041104 (2007).
[CrossRef]

Gross, M.

Grzanna, J.

Guo, C. S.

Haddad, W.

Hayashi, K.

Y. Nishino, T. Ishikawa, K. Hayashi, Y. Takahashi, and E. Matsubara, “Two-energy twin image removal in atomic-resolution x-ray holography,” Phys. Rev. B 66, 092105 (2002).
[CrossRef]

Hennelly, B. M.

Ishikawa, T.

Y. Nishino, T. Ishikawa, K. Hayashi, Y. Takahashi, and E. Matsubara, “Two-energy twin image removal in atomic-resolution x-ray holography,” Phys. Rev. B 66, 092105 (2002).
[CrossRef]

Javidi, B.

Jericho, M. H.

Jericho, S. K.

Joseph, J.

A. Nelleri, U. Gopinathan, J. Joseph, and K. Singh, “Three dimensional object recognition from digital Fresnel hologram by wavelength matched filtering,” Opt. Commun. 259, 499-506 (2006).
[CrossRef]

Jüptner, W.

S. Seebacher, W. Osten, and W. Jüptner, “Measuring shape and deformation of small objects using digital holography,” Proc. SPIE 3479, 104-115 (1998).
[CrossRef]

M. Adams, T. Kreis, and W. Jüptner, “Particle size and position measurement with digital holography,” Proc. SPIE 3098, 234-240 (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] [PubMed]

Kato, J.

Kemper, B.

S. Lai, B. Kemper, and G. von Bally, “Off-axis reconstruction of in-line holograms for twin-image elimination,” Opt. Commun. 169, 37-43 (1999).
[CrossRef]

King, B.

S. Lai, B. King, and M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155-160 (2000).
[CrossRef]

Klages, P.

Konforti, N.

D. Mendlovic, Z. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407-414 (1997).
[CrossRef]

Kreis, T.

M. Adams, T. Kreis, and W. Jüptner, “Particle size and position measurement with digital holography,” Proc. SPIE 3098, 234-240 (1997).
[CrossRef]

Kreuzer, H. J.

Lai, S.

S. Lai, B. King, and M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155-160 (2000).
[CrossRef]

S. Lai, B. Kemper, and G. von Bally, “Off-axis reconstruction of in-line holograms for twin-image elimination,” Opt. Commun. 169, 37-43 (1999).
[CrossRef]

Lalor, Ê.

Liao, J.

Liu, G.

Longworth, J. M.

Marinho, F.

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

Marquet, P.

Mas, D.

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

Massig, J. H.

Matsubara, E.

Y. Nishino, T. Ishikawa, K. Hayashi, Y. Takahashi, and E. Matsubara, “Two-energy twin image removal in atomic-resolution x-ray holography,” Phys. Rev. B 66, 092105 (2002).
[CrossRef]

McPherson, A.

Mendlovic, D.

D. Mendlovic, Z. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407-414 (1997).
[CrossRef]

Meng, X. F.

Merkel, K.

Miccio, L.

L. Miccio, D. Alfieri, S. Grilli, P. Ferraro, A. Finizio, L. De Petrocellis, and S. D. Nicola, “Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram,” Appl. Phys. Lett. 90, 041104 (2007).
[CrossRef]

Mizuno, J.

Montfort, F.

Naughton, T. J.

Neifeld, M. A.

S. Lai, B. King, and M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155-160 (2000).
[CrossRef]

Nelleri, A.

A. Nelleri, U. Gopinathan, J. Joseph, and K. Singh, “Three dimensional object recognition from digital Fresnel hologram by wavelength matched filtering,” Opt. Commun. 259, 499-506 (2006).
[CrossRef]

Nicola, S. D.

L. Miccio, D. Alfieri, S. Grilli, P. Ferraro, A. Finizio, L. De Petrocellis, and S. D. Nicola, “Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram,” Appl. Phys. Lett. 90, 041104 (2007).
[CrossRef]

Nishino, Y.

Y. Nishino, T. Ishikawa, K. Hayashi, Y. Takahashi, and E. Matsubara, “Two-energy twin image removal in atomic-resolution x-ray holography,” Phys. Rev. B 66, 092105 (2002).
[CrossRef]

Nomura, T.

Ohta, S.

Osten, W.

Pedrini, G.

Rhodes, C. K.

Rogers, G. L.

G. L. Rogers, “In-line soft-x-ray holography: the unwanted image,” Opt. Lett. 19, 67-67 (1994).
[CrossRef] [PubMed]

W. L. Bragg and G. L. Rogers, “Elimination of the unwanted image in diffraction microscopy,” Nature 167, 190-191 (1951).
[CrossRef] [PubMed]

Santoyo, F. M.

G. Pedrini, P. Fröning, H. Tiziani, and F. M. Santoyo, “Shape measurement of microscopic structures using digital holograms,” Opt. Commun. 164, 257-268 (1999).
[CrossRef]

Schnars, U.

Schwider, J.

Scott, P. D.

Seebacher, S.

S. Seebacher, W. Osten, and W. Jüptner, “Measuring shape and deformation of small objects using digital holography,” Proc. SPIE 3479, 104-115 (1998).
[CrossRef]

Shen, X. X.

Sheridan, J. T.

B. M. Hennelly and J. T. Sheridan, “Generalizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transforms,” J. Opt. Soc. Am. A 22, 917-927 (2005).
[CrossRef]

B. M. Hennelly and J. T. Sheridan, “Fast numerical algorithm for the linear canonical transform,” J. Opt. Soc. Am. A 22, 928-937 (2005).
[CrossRef]

G. Situ and J. T. Sheridan, “A new reconstruction algorithm for in-line digital holography,” in European Conference on Lasers and Electro-Optics, 2007 and the International Quantum Electronics, Conference (CLEOE-IQEC 2007) (IEEE, 2007), digital OID: 4386033.
[CrossRef] [PubMed]

Singh, K.

A. Nelleri, U. Gopinathan, J. Joseph, and K. Singh, “Three dimensional object recognition from digital Fresnel hologram by wavelength matched filtering,” Opt. Commun. 259, 499-506 (2006).
[CrossRef]

Situ, G.

G. Situ and J. T. Sheridan, “A new reconstruction algorithm for in-line digital holography,” in European Conference on Lasers and Electro-Optics, 2007 and the International Quantum Electronics, Conference (CLEOE-IQEC 2007) (IEEE, 2007), digital OID: 4386033.
[CrossRef] [PubMed]

Solem, J. C.

Soraghan, J. J.

Spolaczyk, R.

Stadelmaier, A.

Tajahuerce, E.

Takahashi, Y.

Y. Nishino, T. Ishikawa, K. Hayashi, Y. Takahashi, and E. Matsubara, “Two-energy twin image removal in atomic-resolution x-ray holography,” Phys. Rev. B 66, 092105 (2002).
[CrossRef]

Tiziani, H.

G. Pedrini, P. Fröning, H. Tiziani, and F. M. Santoyo, “Shape measurement of microscopic structures using digital holograms,” Opt. Commun. 164, 257-268 (1999).
[CrossRef]

Tiziani, H. J.

von Bally, G.

S. Lai, B. Kemper, and G. von Bally, “Off-axis reconstruction of in-line holograms for twin-image elimination,” Opt. Commun. 169, 37-43 (1999).
[CrossRef]

Wang, H. T.

Xiao, T. Q.

T. Q. Xiao, H. J. Xu, Y. J. Zhang, J. W. Chen, and Z. Z. Xu, “Digital image decoding for in-line X-ray holography using two holograms,” J. Mod. Opt. 45, 343-353 (1998).
[CrossRef]

Xu, H. J.

T. Q. Xiao, H. J. Xu, Y. J. Zhang, J. W. Chen, and Z. Z. Xu, “Digital image decoding for in-line X-ray holography using two holograms,” J. Mod. Opt. 45, 343-353 (1998).
[CrossRef]

Xu, W.

Xu, X. F.

Xu, Z. Z.

T. Q. Xiao, H. J. Xu, Y. J. Zhang, J. W. Chen, and Z. Z. Xu, “Digital image decoding for in-line X-ray holography using two holograms,” J. Mod. Opt. 45, 343-353 (1998).
[CrossRef]

Yamaguchi, I.

Zalevsky, Z.

D. Mendlovic, Z. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407-414 (1997).
[CrossRef]

Zhang, L.

Zhang, T.

Zhang, Y.

Zhang, Y. J.

T. Q. Xiao, H. J. Xu, Y. J. Zhang, J. W. Chen, and Z. Z. Xu, “Digital image decoding for in-line X-ray holography using two holograms,” J. Mod. Opt. 45, 343-353 (1998).
[CrossRef]

Zhu, Y. Y.

Appl. Opt. (7)

Appl. Phys. Lett. (1)

L. Miccio, D. Alfieri, S. Grilli, P. Ferraro, A. Finizio, L. De Petrocellis, and S. D. Nicola, “Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram,” Appl. Phys. Lett. 90, 041104 (2007).
[CrossRef]

J. Mod. Opt. (2)

T. Q. Xiao, H. J. Xu, Y. J. Zhang, J. W. Chen, and Z. Z. Xu, “Digital image decoding for in-line X-ray holography using two holograms,” J. Mod. Opt. 45, 343-353 (1998).
[CrossRef]

D. Mendlovic, Z. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407-414 (1997).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

Nature (1)

W. L. Bragg and G. L. Rogers, “Elimination of the unwanted image in diffraction microscopy,” Nature 167, 190-191 (1951).
[CrossRef] [PubMed]

Opt. Commun. (5)

S. Lai, B. King, and M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155-160 (2000).
[CrossRef]

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

A. Nelleri, U. Gopinathan, J. Joseph, and K. Singh, “Three dimensional object recognition from digital Fresnel hologram by wavelength matched filtering,” Opt. Commun. 259, 499-506 (2006).
[CrossRef]

S. Lai, B. Kemper, and G. von Bally, “Off-axis reconstruction of in-line holograms for twin-image elimination,” Opt. Commun. 169, 37-43 (1999).
[CrossRef]

G. Pedrini, P. Fröning, H. Tiziani, and F. M. Santoyo, “Shape measurement of microscopic structures using digital holograms,” Opt. Commun. 164, 257-268 (1999).
[CrossRef]

Opt. Lett. (9)

Phys. Rev. B (1)

Y. Nishino, T. Ishikawa, K. Hayashi, Y. Takahashi, and E. Matsubara, “Two-energy twin image removal in atomic-resolution x-ray holography,” Phys. Rev. B 66, 092105 (2002).
[CrossRef]

Proc. SPIE (2)

M. Adams, T. Kreis, and W. Jüptner, “Particle size and position measurement with digital holography,” Proc. SPIE 3098, 234-240 (1997).
[CrossRef]

S. Seebacher, W. Osten, and W. Jüptner, “Measuring shape and deformation of small objects using digital holography,” Proc. SPIE 3479, 104-115 (1998).
[CrossRef]

Other (3)

G. Situ and J. T. Sheridan, “A new reconstruction algorithm for in-line digital holography,” in European Conference on Lasers and Electro-Optics, 2007 and the International Quantum Electronics, Conference (CLEOE-IQEC 2007) (IEEE, 2007), digital OID: 4386033.
[CrossRef] [PubMed]

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2004).

http://www.edmundoptics.com/onlinecatalog/displayproduct.cfm?productID=1790.

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Figures (6)

Fig. 1
Fig. 1

(Color online) Setup of the in-line DH recording system. HWP, half-wave plate; BS, beam splitter.

Fig. 2
Fig. 2

(Color online) Schematic for computer simulations. BS, beam splitter; reference, reference beam. The object volume is used to simulate a 3D object.

Fig. 3
Fig. 3

Simulation results of the reconstruction of the three letters at the best focus distance of (a) U, 140   mm ; (b) C, 120   mm ; (c) D, 100   mm from the CCD plane.

Fig. 4
Fig. 4

(Color online) Experimental setup of the proposed technique. BS, beam splitter; LP, linear polarizer.

Fig. 5
Fig. 5

Experimental results of the reconstruction image with the proposed technique: (a) magnitude, (b) phase, and (c) the cross section of the phase map as indicated with a dot–dash cross line in (b). Note that those marked with dot ellipses are associating the transparent area.

Fig. 6
Fig. 6

Reconstruction with a twin image superposition: (a) amplitude, (b) phase component.

Tables (1)

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Table 1 Statistic Properties of the Phase Patterns (in Radians)

Equations (18)

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I 11 ( x 1 , y 1 ) = | r + u 1 ( x 1 , y 1 ) | 2 ,
I 21 ( x 2 , y 2 ) = | r + u 2 ( x 2 , y 2 ) | 2 ,
u i ( x i , y i ) = P { u 0 ( x 0 , y 0 ) ; z i } , = 1 2 π u 0 ( x 0 , y 0 ) z i [ exp [ j k r i ] r i ] d x 0 d y 0 ,
I 12 ( x 1 , y 1 ) = | r + u 1 ( x 1 , y 1 ) | 2 ,
I 22 ( x 2 , y 2 ) = | r + u 2 ( x 2 , y 2 ) | 2 .
Δ I 1 ( x 1 , y 1 ) = u 1 ( x 1 , y 1 ) + u 1 * ( x 1 , y 1 ) ,
Δ I 2 ( x 2 , y 2 ) = u 2 ( x 2 , y 2 ) + u 2 * ( x 2 , y 2 ) .
u 1 * ( x 1 , y 1 ) = P { u 2 * ( x 2 , y 2 ) ; Δ z } .
δ I ( x 1 , y 1 ) = Δ I 1 ( x 1 , y 1 ) P { Δ I 2 ( x 2 , y 2 ) ; Δ z } = u 1 ( x 1 , y 1 ) + u 1 * ( x 1 , y 1 ) P { u 2 ( x 2 , y 2 ) ; Δ z } P { u 2 * ( x 2 , y 2 ) ; Δ z } = u 1 ( x 1 , y 1 ) P { u 2 ( x 2 , y 2 ) ; Δ z } = u 1 ( x 1 , y 1 ) P { u 1 ( x 1 , y 1 ) ; 2 Δ z } .
δ ( ξ , η ) = U 1 ( ξ , η ) [ 1 ( ξ , η ; 2 Δ z ) ] ,
u 1 ( x 1 , y 1 ) = 1 { δ ( ξ , η ) 1 ( ξ , η ; 2 Δ z ) } ,
h ( x 0 , y 0 ; x i , y i ; z i ) = 1 2 π z i [ exp [ j k r i ] r i ] .
( ξ , η ; z i ) = { h ( x 0 , y 0 ; x i , y i ; z i ) } = exp { j k z i [ 1 ( λ ξ ) 2 ( λ η ) 2 ] 1 / 2 } .
( m , n ; z i ) = exp { j k z i [ 1 ( λ m M δ x ) 2 ( λ n N δ y ) 2 ] 1 / 2 } ,
1 ( ξ , η , 2 Δ z ) 0 .
k 2 Δ z [ 1 λ 2 ( ξ 2 + η 2 ) ] 1 / 2 2 l π ,
Δ z λ 2 l 1 λ 2 ( ξ 2 + η 2 ) .
Δ z λ 2 l N δ N 2 δ 2 λ 2 ( m 2 + n 2 ) ,

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