Abstract

We propose a method to suppress the so-called zero-order term in a hologram, based on an iterative principle. During the hologram acquisition process, the encoded information includes the intensities of the two beams creating the interference pattern, which do not contain information about the recorded complex wavefront, and that can disrupt the reconstructed signal. The proposed method selectively suppresses the zero-order term by employing the information obtained during wavefront reconstruction in an iterative procedure, thus enabling its suppression without any a priori knowledge about the object. The method is analyzed analytically and its convergence is studied. Then, its performance is shown experimentally. Its robustness is assessed by applying the procedure on various types of holograms, such as topographic images of microscopic specimens or speckle holograms.

© 2010 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] [PubMed]
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    [CrossRef]
  29. U. Schnars, and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
    [CrossRef]
  30. F. Montfort, F. Charrière, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Purely numerical compensation for microscope objective phase curvature in digital holographic microscopy: Influence of digital phase mask position,” J. Opt. Soc. Am. A 23, 2944–2953 (2006).
    [CrossRef]
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2009 (1)

2008 (6)

B. Kemper, and G. von Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt. 47, A52–A61 (2008).
[CrossRef] [PubMed]

B. Rappaz, F. Charrière, C. Depeursinge, P. Magistretti, and P. Marquet, “Simultaneous cell morphometry and refractive index measurement with dual-wavelength digital holographic microscopy and dye–enhanced dispersion of perfusion medium,” Opt. Lett. 33, 744–746 (2008).
[CrossRef] [PubMed]

J. Weng, J. Zhong, and C. Hu, “Digital reconstruction based on angular spectrum diffraction with the ridge of wavelet transform in holographic phase-contrast microscopy,” Opt. Express 16, 21971–21981 (2008).
[CrossRef] [PubMed]

J. Kühn, F. Charrière, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, “Axial sub-nanometer accuracy in digital holographic microscopy,” Meas. Sci. Technol. 19, 074007 (2008).
[CrossRef]

P. Jacquot, “Speckle interferometry: a review of the principal methods in use for experimental mechanics applications,” Strain 44, 57–69 (2008).
[CrossRef]

M. L. Cruz, A. Castro, and V. Arrizon, “Phase retrieval in digital holographic microscopy using a Gerchberg-Saxton algorithm,” Proc. SPIE 7072, 70721C (2008).
[CrossRef]

2007 (2)

2006 (3)

2005 (2)

2004 (3)

2003 (1)

2002 (1)

U. Schnars, and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

2001 (1)

2000 (1)

1999 (2)

1997 (2)

I. Yamaguchi, and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
[CrossRef] [PubMed]

T. Kreis, and W. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[CrossRef]

1996 (1)

1982 (2)

1962 (1)

Arrizon, V.

M. L. Cruz, A. Castro, and V. Arrizon, “Phase retrieval in digital holographic microscopy using a Gerchberg-Saxton algorithm,” Proc. SPIE 7072, 70721C (2008).
[CrossRef]

Aspert, N.

Badizadegan, K.

Bourquin, S.

Cai, L.

Castro, A.

M. L. Cruz, A. Castro, and V. Arrizon, “Phase retrieval in digital holographic microscopy using a Gerchberg-Saxton algorithm,” Proc. SPIE 7072, 70721C (2008).
[CrossRef]

Chang, C.-C.

Charrière, F.

Chen, G.-L.

Colomb, T.

Cruz, M. L.

M. L. Cruz, A. Castro, and V. Arrizon, “Phase retrieval in digital holographic microscopy using a Gerchberg-Saxton algorithm,” Proc. SPIE 7072, 70721C (2008).
[CrossRef]

Cuche, E.

Dasari, R. R.

de Lega, X. C.

Deflores, L. P.

Depeursinge, C.

N. Pavillon, C. Seelamantula, J. Kühn, M. Unser, and C. Depeursinge, “Suppression of the zero-order term in off-axis digital holography through nonlinear filtering,” Appl. Opt. 48, H186–H195 (2009).
[CrossRef] [PubMed]

B. Rappaz, F. Charrière, C. Depeursinge, P. Magistretti, and P. Marquet, “Simultaneous cell morphometry and refractive index measurement with dual-wavelength digital holographic microscopy and dye–enhanced dispersion of perfusion medium,” Opt. Lett. 33, 744–746 (2008).
[CrossRef] [PubMed]

J. Kühn, F. Charrière, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, “Axial sub-nanometer accuracy in digital holographic microscopy,” Meas. Sci. Technol. 19, 074007 (2008).
[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]

F. Montfort, F. Charrière, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Purely numerical compensation for microscope objective phase curvature in digital holographic microscopy: Influence of digital phase mask position,” J. Opt. Soc. Am. A 23, 2944–2953 (2006).
[CrossRef]

T. Colomb, J. Kühn, F. Charrière, C. Depeursinge, P. Marquet, and N. Aspert, “Total aberrations compensation in digital holographic microscopy with a reference conjugated hologram,” Opt. Express 14, 4300–4306 (2006).
[CrossRef] [PubMed]

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

E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994–7001 (1999).
[CrossRef]

Devaney, A.

Duan, Z.

Emery, Y.

J. Kühn, F. Charrière, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, “Axial sub-nanometer accuracy in digital holographic microscopy,” Meas. Sci. Technol. 19, 074007 (2008).
[CrossRef]

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

Feld, M. S.

Fienup, J.

Fu, Y.

Guo, P.

Han, B.

Hu, C.

Ina, H.

Indebetouw, G.

Iwai, H.

Jacquot, P.

P. Jacquot, “Speckle interferometry: a review of the principal methods in use for experimental mechanics applications,” Strain 44, 57–69 (2008).
[CrossRef]

X. C. de Lega, and P. Jacquot, “Deformation measurement with object-induced dynamic phase shifting,” Appl. Opt. 35, 5115–5121 (1996).
[CrossRef]

Jüptner, W.

T. Kreis, and W. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[CrossRef]

Jüptner, W. P. O.

U. Schnars, and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Kawai, H.

Kemper, B.

Kim, T.

Klysubun, P.

Kobayashi, S.

Kreis, T.

T. Kreis, and W. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[CrossRef]

Kühn, J.

Kuo, M.-K.

Leith, E. N.

Lin, C.-Y.

Liu, Q.

Magistretti, P.

Magistretti, P. J.

Marian, A.

Marquet, P.

J. Kühn, F. Charrière, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, “Axial sub-nanometer accuracy in digital holographic microscopy,” Meas. Sci. Technol. 19, 074007 (2008).
[CrossRef]

B. Rappaz, F. Charrière, C. Depeursinge, P. Magistretti, and P. Marquet, “Simultaneous cell morphometry and refractive index measurement with dual-wavelength digital holographic microscopy and dye–enhanced dispersion of perfusion medium,” Opt. Lett. 33, 744–746 (2008).
[CrossRef] [PubMed]

T. Colomb, J. Kühn, F. Charrière, C. Depeursinge, P. Marquet, and N. Aspert, “Total aberrations compensation in digital holographic microscopy with a reference conjugated hologram,” Opt. Express 14, 4300–4306 (2006).
[CrossRef] [PubMed]

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]

F. Montfort, F. Charrière, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Purely numerical compensation for microscope objective phase curvature in digital holographic microscopy: Influence of digital phase mask position,” J. Opt. Soc. Am. A 23, 2944–2953 (2006).
[CrossRef]

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

E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994–7001 (1999).
[CrossRef]

Miyamoto, Y.

Montfort, F.

Ohzu, H.

Osten, W.

Pavillon, N.

Pedrini, G.

Poon, T.-C.

Popescu, G.

Rappaz, B.

Schnars, U.

U. Schnars, and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Seelamantula, C.

Takaki, Y.

Takeda, M.

Unser, M.

Upatnieks, J.

Vaughan, J. C.

von Bally, G.

Wang, W.

Wang, Z.

Weng, J.

Yamaguchi, I.

Yang, X.

Zhang, T.

Zhong, J.

Appl. Opt. (7)

J. Opt. Soc. Am. (2)

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

Meas. Sci. Technol. (2)

U. Schnars, and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

J. Kühn, F. Charrière, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, “Axial sub-nanometer accuracy in digital holographic microscopy,” Meas. Sci. Technol. 19, 074007 (2008).
[CrossRef]

Opt. Eng. (1)

T. Kreis, and W. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[CrossRef]

Opt. Express (4)

Opt. Lett. (7)

B. Rappaz, F. Charrière, C. Depeursinge, P. Magistretti, and P. Marquet, “Simultaneous cell morphometry and refractive index measurement with dual-wavelength digital holographic microscopy and dye–enhanced dispersion of perfusion medium,” Opt. Lett. 33, 744–746 (2008).
[CrossRef] [PubMed]

I. Yamaguchi, and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
[CrossRef] [PubMed]

L. Cai, Q. Liu, and X. Yang, “Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps,” Opt. Lett. 28, 1808–1810 (2003).
[CrossRef] [PubMed]

P. Guo, and A. Devaney, “Digital microscopy using phase-shifting digital holography with two reference waves,” Opt. Lett. 29, 857–859 (2004).
[CrossRef] [PubMed]

Z. Wang, and B. Han, “Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms,” Opt. Lett. 29, 1671–1673 (2004).
[CrossRef] [PubMed]

G. Popescu, L. P. Deflores, J. C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, “Fourier phase microscopy for investigation of biological structures and dynamics,” Opt. Lett. 29, 2503–2505 (2004).
[CrossRef] [PubMed]

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

Proc. SPIE (1)

M. L. Cruz, A. Castro, and V. Arrizon, “Phase retrieval in digital holographic microscopy using a Gerchberg-Saxton algorithm,” Proc. SPIE 7072, 70721C (2008).
[CrossRef]

Strain (1)

P. Jacquot, “Speckle interferometry: a review of the principal methods in use for experimental mechanics applications,” Strain 44, 57–69 (2008).
[CrossRef]

Other (2)

T. Kreis, “Digital Recording and Numerical Reconstruction of Wave Fields,” in Handbook of Holographic Interferometry, T. Kreis, ed. (Wiley-VCH Verlag, 2005), pp. 81–183.

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

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Figures (8)

Fig. 1.
Fig. 1.

(a) Simulated hologram representing a structure similar to a USAF test target and (b) its corresponding spectrum, where some overlap between the zero-order and the imaging order can be identified, especially on the directional frequencies.

Fig. 2.
Fig. 2.

Representation of the terms of Eq. (7) at the first iteration for the hologram of Fig. 1, showing (a) the object autocorrelation estimator, |o|2, (b) the O W 2 R 2 error term and (c), (d) the modulated error terms o R O W , j * e i φ . On each figure, the multiplicative factor to make the term visible is given.

Fig. 3.
Fig. 3.

Reconstruction of the hologram of Fig. 1 with (a) standard reconstruction and (b) the iterative method. The spectrum of the iterative reconstruction (c) shows no zero-order in the wavefield.

Fig. 4.
Fig. 4.

Convergence of the sum of the error estimator for the object intensity as defined in Eq. (8), normalized by the object intensity.

Fig. 5.
Fig. 5.

(a) Spectrum of the simulated speckle hologram, clearly showing the zero-order with twice the size compared to the imaging orders. (b) Spectrum of the wavefield after iterative reconstruction and (c) amplitude of the object where the zero-order has been suppressed by the iterative procedure.

Fig. 6.
Fig. 6.

Reconstruction of the hologram of a USAF test target. Amplitude reconstructed with (a) the standard method and (b) the iterative method. (c) Phase image reconstructed with the iterative procedure.

Fig. 7.
Fig. 7.

Topographic phase profile along the dashed line of Fig. 6(c) for the standard and iterative techniques, where a strong artifacts can be identified in the case of the standard technique, due to the zero-order term.

Fig. 8.
Fig. 8.

(a) Spectrum of a reflection hologram on a Swiss coin containing the letter “A”, along with (b) its reconstruction performed with standard method and (c) spectrum and (d) amplitude after employing the iterative method.

Equations (11)

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I ( x , y ) = o + r 2 = o 2 + r 2 + or * + o * r ,
{ I } ( ω x , ω y ) = I ̂ ( ω x , ω y ) = o ̂ o ̂ * ( ω x , ω y ) + R 2 δ ( ω x , ω y ) +
o ̂ R δ ( ω x + ω 0 , x , ω y + ω 0 , y ) + o ̂ * R δ ( ω x ω 0 , x , ω y ω 0 , y ) ,
or * ( x , y ) = o ( x , y ) Re i φ ( x , y ) = 1 { I ̂ ( ω x , ω y ) W ̂ ( ω x , ω y ) } ,
o est 2 ( x , y ) = 1 r exp 2 ( oRe i φ ) ( oRe i φ ) * o 2 ,
I = I ( x , y ) r exp 2 o est 2 or * + o * r .
1 { I ̂ ( ω x , ω y ) W ̂ ( ω x , ω y ) } = oRe i φ + o 2 W ( x , y ) .
o est , 1 2 = 1 r exp 2 ( oRe i φ + O W ( x , y ) ) ( oRe i φ + O W ( x , y ) ) *
= R 2 r exp 2 ( o 2 + O W 2 R 2 + o R O W * e i φ + o * R O W e i φ ) .
ε k ( x , y ) = o 2 o est , k 2 = ( 1 R 2 r exp 2 ) o 2 + R 2 j = 3 2 k + 1 O ( o j R j ) ,
S = E iter , zero E iter , noise E std , zero E std , noise .

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