Abstract

Digital Holographic Microscopy (DHM) is a single shot interferometric technique, which provides quantitative phase images with subwavelength axial accuracy. A short hologram acquisition time (down to microseconds), allows DHM to offer a reduced sensitivity to vibrations, and real time observation is achievable thanks to present performances of personal computers and charge coupled devices (CCDs). Fast dynamic imaging at low-light level involves few photons, requiring proper camera settings (integration time and gain of the CCD; power of the light source) to minimize the influence of shot noise on the hologram when the highest phase accuracy is aimed. With simulated and experimental data, a systematic analysis of the fundamental shot noise influence on phase accuracy in DHM is presented.

© 2007 Optical Society of America

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  1. J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
    [CrossRef]
  2. M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavskii, "Reconstruction of a hologram with a computer," Sov. Phys. Tech. Phys. 17, 333-334 (1972).
  3. 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]
  4. U. Schnars and W. P. O. Jüptner, "Digital recording and numerical reconstruction of holograms," Meas. Sci. Technol. 13, R85-R101 (2002).
    [CrossRef]
  5. P. Ferraro, S. De Nicola, A. Finizio, G. Coppola, S. Grilli, C. Magro, and G. Pierattini, "Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging," Appl. Opt. 42, 1938-1946 (2003).
    [CrossRef] [PubMed]
  6. C. Liu, Z. G. Liu, F. Bo, Y. Wang, and J. Q. Zhu, "Digital holographic aberration compensation in electron holography," Opt. Eng. 42, 651-655 (2003).
    [CrossRef]
  7. 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]
  8. V. Kebbel, J. Muller, and W. P. O. Jüptner, "Characterization of aspherical micro-optics using digital holography: improvement of accuracy," in Interferometry XI: Applications, Proc. SPIE 4778, 188-197 (2002).
    [CrossRef]
  9. F. Charrière, J. Kühn, T. Colomb, F. Monfort, E. Cuche, Y. Emery, K. Weible, P. Marquet, and C. Depeursinge, "Characterization of microlenses by digital holographic microscopy," Appl. Opt. 45, 829-835 (2006).
    [CrossRef] [PubMed]
  10. S. Grilli, P. Ferraro, M. Paturzo, D. Alfieri, and P. De Natale, "In-situ visualization, monitoring and analysis of electric field domain reversal process in ferroelectric crystals by digital holography," Opt. Express 12, 1832-1842 (2004).
    [CrossRef] [PubMed]
  11. 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]
  12. B. Rappaz, P. Marquet, E. Cuche, Y. Emery, C. Depeursinge, and P. Magistretti, "Measurement of the integral refractive index and dynamic cell morphometry of living cells with digital holographic microscopy," Opt. Express 13, 9361-9373 (2005).
    [CrossRef] [PubMed]
  13. G. N. Vishnyakov, G. G. Levin, A. V. Likhachev, V. V. Pikalov, "Phase Tomography of 3D Biological Microobjects: numerical simulation and experimental results," Opt. Spectrosc. 87, 413-419 (1999).
  14. M. K. Kim, "Tomographic three-dimensional imaging of a biological specimen using wavelength-scanning digital interference holography," Opt. Express 7, 305-310 (2000).
    [CrossRef] [PubMed]
  15. V.  Lauer, "New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope," J. Microsc. 205, 165-176 (2002).
    [CrossRef] [PubMed]
  16. F. Charrière, N. Pavillon, T. Colomb, Ch. Depeursinge, T. Heger, E. A. D. Mitchell, P. Marquet and B. Rappaz, "Living specimen tomography by digital holographic microscopy: morphometry of testate amoeba," Opt. Express 14, 7005-7013 (2006).
    [CrossRef] [PubMed]
  17. T. Colomb, F. Dürr, E. Cuche, P. Marquet, H. Limberger, R.-P. Salathé, and Ch. Depeursinge, "Polarization microscopy by use of digital holography: application to optical fiber birefringence measurements," Appl. Opt. 44, 4461-4469 (2005).
    [CrossRef] [PubMed]
  18. J. W. Goodman, Statistical Optics (John Wiley & Sons, New York, 1985).
  19. O. Monnom, F. Dubois, C. Yourassowsky, and J. C. Legros, "Improvement in visibility of an in-focus reconstructed image in digital holography by reduction of the influence of out-of-focus objects," Appl. Opt. 44, 3827-3832 (2005).
    [CrossRef] [PubMed]
  20. D. Paganin, A. Barty, P. J. McMahon and K. A. Nugent, "Quantitative phase-amplitude microscopy. III. The effects of noise," J. Microsc. 214, 51-61 (2004).
    [CrossRef] [PubMed]
  21. W. J. De Ruijter and J. K. Weiss, "Detection limits in quantitative off-axis electron holography," Ultramicroscopy 50, 269-283 (1993).
    [CrossRef]
  22. G. A. Mills, and I. Yamaguchi, "Effects of quantization in phase-shifting digital holography," Appl. Opt. 44, 1216-1225 (2005).
    [CrossRef] [PubMed]
  23. T. Baumbach, E. Kolenovic, V. Kebbel, and W. Jüptner, "Improvement of accuracy in digital holography by use of multiple holograms," Appl. Opt. 45, 6077-6085 (2006).
    [CrossRef] [PubMed]
  24. R. F. Wagner and D. G. Brown, "Unified SNR Analysis of Medical Imaging-Systems," Phys. Med. Biol. 30, 489-518 (1985).
    [CrossRef]
  25. F. Charrière, T. Colomb, F. Montfort, E. Cuche, P. Marquet and Ch. Depeursinge, "Shot noise influence in reconstructed phase image SNR in digital holographic microscopy," Appl. Opt. 45, 7667-7673 (2006).
    [CrossRef] [PubMed]
  26. G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Observation of dynamic subdomains in red blood cells," J. Biomed. Opt. 11, 040503-3 (2006).
  27. E. Cuche, P. Marquet, and C. Depeursinge, "Aperture apodization using cubic spline interpolation: application in digital holographic microscopy," Opt. Commun. 182, 59-69 (2000).
    [CrossRef]

2006 (6)

2005 (4)

2004 (3)

2003 (2)

2002 (3)

V. Kebbel, J. Muller, and W. P. O. Jüptner, "Characterization of aspherical micro-optics using digital holography: improvement of accuracy," in Interferometry XI: Applications, Proc. SPIE 4778, 188-197 (2002).
[CrossRef]

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

V.  Lauer, "New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope," J. Microsc. 205, 165-176 (2002).
[CrossRef] [PubMed]

2000 (2)

M. K. Kim, "Tomographic three-dimensional imaging of a biological specimen using wavelength-scanning digital interference holography," Opt. Express 7, 305-310 (2000).
[CrossRef] [PubMed]

E. Cuche, P. Marquet, and C. Depeursinge, "Aperture apodization using cubic spline interpolation: application in digital holographic microscopy," Opt. Commun. 182, 59-69 (2000).
[CrossRef]

1999 (2)

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]

G. N. Vishnyakov, G. G. Levin, A. V. Likhachev, V. V. Pikalov, "Phase Tomography of 3D Biological Microobjects: numerical simulation and experimental results," Opt. Spectrosc. 87, 413-419 (1999).

1993 (1)

W. J. De Ruijter and J. K. Weiss, "Detection limits in quantitative off-axis electron holography," Ultramicroscopy 50, 269-283 (1993).
[CrossRef]

1985 (1)

R. F. Wagner and D. G. Brown, "Unified SNR Analysis of Medical Imaging-Systems," Phys. Med. Biol. 30, 489-518 (1985).
[CrossRef]

1972 (1)

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavskii, "Reconstruction of a hologram with a computer," Sov. Phys. Tech. Phys. 17, 333-334 (1972).

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.

Aspert, N.

Badizadegan, K.

Barty, A.

D. Paganin, A. Barty, P. J. McMahon and K. A. Nugent, "Quantitative phase-amplitude microscopy. III. The effects of noise," J. Microsc. 214, 51-61 (2004).
[CrossRef] [PubMed]

Baumbach, T.

Bo, F.

C. Liu, Z. G. Liu, F. Bo, Y. Wang, and J. Q. Zhu, "Digital holographic aberration compensation in electron holography," Opt. Eng. 42, 651-655 (2003).
[CrossRef]

Bourquin, S.

Brown, D. G.

R. F. Wagner and D. G. Brown, "Unified SNR Analysis of Medical Imaging-Systems," Phys. Med. Biol. 30, 489-518 (1985).
[CrossRef]

Charrière, F.

Colomb, T.

Coppola, G.

Cuche, E.

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. Charrière, J. Kühn, T. Colomb, F. Monfort, E. Cuche, Y. Emery, K. Weible, P. Marquet, and C. Depeursinge, "Characterization of microlenses by digital holographic microscopy," Appl. Opt. 45, 829-835 (2006).
[CrossRef] [PubMed]

F. Charrière, T. Colomb, F. Montfort, E. Cuche, P. Marquet and Ch. Depeursinge, "Shot noise influence in reconstructed phase image SNR in digital holographic microscopy," Appl. Opt. 45, 7667-7673 (2006).
[CrossRef] [PubMed]

T. Colomb, F. Dürr, E. Cuche, P. Marquet, H. Limberger, R.-P. Salathé, and Ch. Depeursinge, "Polarization microscopy by use of digital holography: application to optical fiber birefringence measurements," Appl. Opt. 44, 4461-4469 (2005).
[CrossRef] [PubMed]

B. Rappaz, P. Marquet, E. Cuche, Y. Emery, C. Depeursinge, and P. Magistretti, "Measurement of the integral refractive index and dynamic cell morphometry of living cells with digital holographic microscopy," Opt. Express 13, 9361-9373 (2005).
[CrossRef] [PubMed]

E. Cuche, P. Marquet, and C. Depeursinge, "Aperture apodization using cubic spline interpolation: application in digital holographic microscopy," Opt. Commun. 182, 59-69 (2000).
[CrossRef]

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]

Dasari, R. R.

De Natale, P.

De Nicola, S.

De Ruijter, W. J.

W. J. De Ruijter and J. K. Weiss, "Detection limits in quantitative off-axis electron holography," Ultramicroscopy 50, 269-283 (1993).
[CrossRef]

Deflores, L. P.

Depeursinge, C.

Depeursinge, Ch.

Dubois, F.

Dürr, F.

Emery, Y.

Feld, M. S.

Ferraro, P.

Finizio, A.

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]

Grilli, S.

Heger, T.

Iwai, H.

Jüptner, W.

Jüptner, W. P. O.

V. Kebbel, J. Muller, and W. P. O. Jüptner, "Characterization of aspherical micro-optics using digital holography: improvement of accuracy," in Interferometry XI: Applications, Proc. SPIE 4778, 188-197 (2002).
[CrossRef]

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

Kebbel, V.

T. Baumbach, E. Kolenovic, V. Kebbel, and W. Jüptner, "Improvement of accuracy in digital holography by use of multiple holograms," Appl. Opt. 45, 6077-6085 (2006).
[CrossRef] [PubMed]

V. Kebbel, J. Muller, and W. P. O. Jüptner, "Characterization of aspherical micro-optics using digital holography: improvement of accuracy," in Interferometry XI: Applications, Proc. SPIE 4778, 188-197 (2002).
[CrossRef]

Kim, M. K.

Kolenovic, E.

Kronrod, M. A.

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavskii, "Reconstruction of a hologram with a computer," Sov. Phys. Tech. Phys. 17, 333-334 (1972).

Kühn, J.

Lauer, V.

V.  Lauer, "New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope," J. Microsc. 205, 165-176 (2002).
[CrossRef] [PubMed]

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]

Legros, J. C.

Levin, G. G.

G. N. Vishnyakov, G. G. Levin, A. V. Likhachev, V. V. Pikalov, "Phase Tomography of 3D Biological Microobjects: numerical simulation and experimental results," Opt. Spectrosc. 87, 413-419 (1999).

Likhachev, A. V.

G. N. Vishnyakov, G. G. Levin, A. V. Likhachev, V. V. Pikalov, "Phase Tomography of 3D Biological Microobjects: numerical simulation and experimental results," Opt. Spectrosc. 87, 413-419 (1999).

Limberger, H.

Liu, C.

C. Liu, Z. G. Liu, F. Bo, Y. Wang, and J. Q. Zhu, "Digital holographic aberration compensation in electron holography," Opt. Eng. 42, 651-655 (2003).
[CrossRef]

Liu, Z. G.

C. Liu, Z. G. Liu, F. Bo, Y. Wang, and J. Q. Zhu, "Digital holographic aberration compensation in electron holography," Opt. Eng. 42, 651-655 (2003).
[CrossRef]

Magistretti, P.

Magro, C.

Marian, A.

Marquet, P.

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. Charrière, J. Kühn, T. Colomb, F. Monfort, E. Cuche, Y. Emery, K. Weible, P. Marquet, and C. Depeursinge, "Characterization of microlenses by digital holographic microscopy," Appl. Opt. 45, 829-835 (2006).
[CrossRef] [PubMed]

F. Charrière, N. Pavillon, T. Colomb, Ch. Depeursinge, T. Heger, E. A. D. Mitchell, P. Marquet and B. Rappaz, "Living specimen tomography by digital holographic microscopy: morphometry of testate amoeba," Opt. Express 14, 7005-7013 (2006).
[CrossRef] [PubMed]

F. Charrière, T. Colomb, F. Montfort, E. Cuche, P. Marquet and Ch. Depeursinge, "Shot noise influence in reconstructed phase image SNR in digital holographic microscopy," Appl. Opt. 45, 7667-7673 (2006).
[CrossRef] [PubMed]

B. Rappaz, P. Marquet, E. Cuche, Y. Emery, C. Depeursinge, and P. Magistretti, "Measurement of the integral refractive index and dynamic cell morphometry of living cells with digital holographic microscopy," Opt. Express 13, 9361-9373 (2005).
[CrossRef] [PubMed]

T. Colomb, F. Dürr, E. Cuche, P. Marquet, H. Limberger, R.-P. Salathé, and Ch. Depeursinge, "Polarization microscopy by use of digital holography: application to optical fiber birefringence measurements," Appl. Opt. 44, 4461-4469 (2005).
[CrossRef] [PubMed]

E. Cuche, P. Marquet, and C. Depeursinge, "Aperture apodization using cubic spline interpolation: application in digital holographic microscopy," Opt. Commun. 182, 59-69 (2000).
[CrossRef]

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]

McMahon, P. J.

D. Paganin, A. Barty, P. J. McMahon and K. A. Nugent, "Quantitative phase-amplitude microscopy. III. The effects of noise," J. Microsc. 214, 51-61 (2004).
[CrossRef] [PubMed]

Merzlyakov, N. S.

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavskii, "Reconstruction of a hologram with a computer," Sov. Phys. Tech. Phys. 17, 333-334 (1972).

Mills, G. A.

Mitchell, E. A. D.

Monfort, F.

Monnom, O.

Montfort, F.

Muller, J.

V. Kebbel, J. Muller, and W. P. O. Jüptner, "Characterization of aspherical micro-optics using digital holography: improvement of accuracy," in Interferometry XI: Applications, Proc. SPIE 4778, 188-197 (2002).
[CrossRef]

Nugent, K. A.

D. Paganin, A. Barty, P. J. McMahon and K. A. Nugent, "Quantitative phase-amplitude microscopy. III. The effects of noise," J. Microsc. 214, 51-61 (2004).
[CrossRef] [PubMed]

Paganin, D.

D. Paganin, A. Barty, P. J. McMahon and K. A. Nugent, "Quantitative phase-amplitude microscopy. III. The effects of noise," J. Microsc. 214, 51-61 (2004).
[CrossRef] [PubMed]

Paturzo, M.

Pavillon, N.

Pierattini, G.

Pikalov, V. V.

G. N. Vishnyakov, G. G. Levin, A. V. Likhachev, V. V. Pikalov, "Phase Tomography of 3D Biological Microobjects: numerical simulation and experimental results," Opt. Spectrosc. 87, 413-419 (1999).

Popescu, G.

Rappaz, B.

Salathé, R.-P.

Schnars, U.

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

Vaughan, J. C.

Vishnyakov, G. N.

G. N. Vishnyakov, G. G. Levin, A. V. Likhachev, V. V. Pikalov, "Phase Tomography of 3D Biological Microobjects: numerical simulation and experimental results," Opt. Spectrosc. 87, 413-419 (1999).

Wagner, R. F.

R. F. Wagner and D. G. Brown, "Unified SNR Analysis of Medical Imaging-Systems," Phys. Med. Biol. 30, 489-518 (1985).
[CrossRef]

Wang, Y.

C. Liu, Z. G. Liu, F. Bo, Y. Wang, and J. Q. Zhu, "Digital holographic aberration compensation in electron holography," Opt. Eng. 42, 651-655 (2003).
[CrossRef]

Weible, K.

Weiss, J. K.

W. J. De Ruijter and J. K. Weiss, "Detection limits in quantitative off-axis electron holography," Ultramicroscopy 50, 269-283 (1993).
[CrossRef]

Yamaguchi, I.

Yaroslavskii, L. P.

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavskii, "Reconstruction of a hologram with a computer," Sov. Phys. Tech. Phys. 17, 333-334 (1972).

Yourassowsky, C.

Zhu, J. Q.

C. Liu, Z. G. Liu, F. Bo, Y. Wang, and J. Q. Zhu, "Digital holographic aberration compensation in electron holography," Opt. Eng. 42, 651-655 (2003).
[CrossRef]

Appl. Opt. (8)

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]

P. Ferraro, S. De Nicola, A. Finizio, G. Coppola, S. Grilli, C. Magro, and G. Pierattini, "Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging," Appl. Opt. 42, 1938-1946 (2003).
[CrossRef] [PubMed]

F. Charrière, J. Kühn, T. Colomb, F. Monfort, E. Cuche, Y. Emery, K. Weible, P. Marquet, and C. Depeursinge, "Characterization of microlenses by digital holographic microscopy," Appl. Opt. 45, 829-835 (2006).
[CrossRef] [PubMed]

T. Colomb, F. Dürr, E. Cuche, P. Marquet, H. Limberger, R.-P. Salathé, and Ch. Depeursinge, "Polarization microscopy by use of digital holography: application to optical fiber birefringence measurements," Appl. Opt. 44, 4461-4469 (2005).
[CrossRef] [PubMed]

O. Monnom, F. Dubois, C. Yourassowsky, and J. C. Legros, "Improvement in visibility of an in-focus reconstructed image in digital holography by reduction of the influence of out-of-focus objects," Appl. Opt. 44, 3827-3832 (2005).
[CrossRef] [PubMed]

G. A. Mills, and I. Yamaguchi, "Effects of quantization in phase-shifting digital holography," Appl. Opt. 44, 1216-1225 (2005).
[CrossRef] [PubMed]

T. Baumbach, E. Kolenovic, V. Kebbel, and W. Jüptner, "Improvement of accuracy in digital holography by use of multiple holograms," Appl. Opt. 45, 6077-6085 (2006).
[CrossRef] [PubMed]

F. Charrière, T. Colomb, F. Montfort, E. Cuche, P. Marquet and Ch. Depeursinge, "Shot noise influence in reconstructed phase image SNR in digital holographic microscopy," Appl. Opt. 45, 7667-7673 (2006).
[CrossRef] [PubMed]

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. Biomed. Opt. (1)

G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Observation of dynamic subdomains in red blood cells," J. Biomed. Opt. 11, 040503-3 (2006).

J. Microsc. (2)

D. Paganin, A. Barty, P. J. McMahon and K. A. Nugent, "Quantitative phase-amplitude microscopy. III. The effects of noise," J. Microsc. 214, 51-61 (2004).
[CrossRef] [PubMed]

V.  Lauer, "New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope," J. Microsc. 205, 165-176 (2002).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

Meas. Sci. Technol. (1)

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

Opt. Commun. (1)

E. Cuche, P. Marquet, and C. Depeursinge, "Aperture apodization using cubic spline interpolation: application in digital holographic microscopy," Opt. Commun. 182, 59-69 (2000).
[CrossRef]

Opt. Eng. (1)

C. Liu, Z. G. Liu, F. Bo, Y. Wang, and J. Q. Zhu, "Digital holographic aberration compensation in electron holography," Opt. Eng. 42, 651-655 (2003).
[CrossRef]

Opt. Express (4)

Opt. Lett. (1)

Opt. Spectrosc. (1)

G. N. Vishnyakov, G. G. Levin, A. V. Likhachev, V. V. Pikalov, "Phase Tomography of 3D Biological Microobjects: numerical simulation and experimental results," Opt. Spectrosc. 87, 413-419 (1999).

Phys. Med. Biol. (1)

R. F. Wagner and D. G. Brown, "Unified SNR Analysis of Medical Imaging-Systems," Phys. Med. Biol. 30, 489-518 (1985).
[CrossRef]

Proc. SPIE (1)

V. Kebbel, J. Muller, and W. P. O. Jüptner, "Characterization of aspherical micro-optics using digital holography: improvement of accuracy," in Interferometry XI: Applications, Proc. SPIE 4778, 188-197 (2002).
[CrossRef]

Sov. Phys. Tech. Phys. (1)

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavskii, "Reconstruction of a hologram with a computer," Sov. Phys. Tech. Phys. 17, 333-334 (1972).

Ultramicroscopy (1)

W. J. De Ruijter and J. K. Weiss, "Detection limits in quantitative off-axis electron holography," Ultramicroscopy 50, 269-283 (1993).
[CrossRef]

Other (1)

J. W. Goodman, Statistical Optics (John Wiley & Sons, New York, 1985).

Supplementary Material (2)

» Media 1: AVI (2351 KB)     
» Media 2: AVI (2049 KB)     

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Figures (8)

Fig. 1.
Fig. 1.

Holographic microscope for transmission imaging: NF neutral density filter; PBS polarizing beam splitter; BE beam expander with spatial filter; λ/2 half-wave plate; MO microscope objective; RL field lens; M mirror; BS beam splitter; O object wave; R reference wave; PC perfusion chamber; S specimen. Inset: a detail showing the off-axis geometry at the incidence on the CCD.

Fig. 2.
Fig. 2.

Effect of hologram quantization on the standard deviation of the reconstructed phase a) for a noise-free hologram, inset exhibits a zoom on the high quantization values, and b) for a hologram with an average number of photons per pixel of 500, 1500, 8’000 and 50’000 with the corresponding shot noise.

Fig. 3.
Fig. 3.

Standard deviation of the phase value in the reconstructed images as a function of the optical power, expressed by the average number of photons per pixels for simulated holograms with shot noise; inset shows a zoom on the high optical power values.

Fig. 4.
Fig. 4.

Phase image (central zone of 256×256 pixels) showing the shot noise structure for simulated holograms with a mean number of photons per pixel of respectively 500 (a), 1’500 (b), 8’000 (c) and 50’000 (d); insets: the phase STD s calculated on the phase images are indicated. A movie comprising 50 phase images illustrates the noise fluctuation [2.0 Mb]. [Media 1]

Fig. 5.
Fig. 5.

Effect of averaging demonstrated on a series of simulated holograms for a mean number of photons per pixel of 1500: STD value of the reconstructed phase image as a function of the number of phase images N used in the averaging procedure with a fitted curve, which equation shows clearly the N-1/2 tendency; R is the parameter fitter value.

Fig. 6
Fig. 6

(a). Reconstructed phase image (512×512 pixels, field of view 250 μm × 250 μm) from an experimentally recorded blank hologram with an average photon numbers of 1’500 per pixel; the dashed zone in the image shows the 256×256 pixels square on which the phase STD was calculated. (b) Simulated (shot noise only) and experimental standard deviation of the phase in the reconstructed images as a function of the optical level, expressed as the average number of photons per pixels; the dotted curve corresponds to the experimental dataset after subtraction of the fixed phase pattern from all the reconstructed phase images; inset shows a zoom on the high optical power values.

Fig. 7.
Fig. 7.

Acquired frames (256×256 pixels) under homogenous illumination for extremes configurations of the CCD: (a) high gain (25dB) with short acquisition time (5μs) and (b) no gain with a long acquisition time (670 μs). For each frame, its Fourier transform is also displayed in inset.

Fig. 8.
Fig. 8.

Phase images (260×340 pixels) of 7-days old mouse neurons in culture, with a mean number of photons of 500 (a), 1’500 (b) and 8’000 (c): insets in images have been displayed on a 2x-reduced phase range to appreciate the reduction of the phase fluctuation caused by the shot noise in the case of non-optimal vs optimal imaging conditions. Movie [2.4Mb] presenting the fluctuating noise in (a), (b) and (c) along 50 phase images. [Media 2]

Equations (4)

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I H x y = OO * + RR * zero order + OR * real image + R * O virtual image ,
R D k l = A R exp [ i ( k Dx kΔx + k Dy lΔy ) ] ,
Ψ = mΔξ nΔη = m n FFT 1 { FFT { R D k l I H k l } p , q exp [ i πλd ( p 2 + q 2 ) ] } m , n ,
Ψ = R D R * O , with R D = exp [ i ( k Dx kΔx + k Dy lΔy ) ] ,

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