Abstract

In digital holographic microscopy, shot noise is an intrinsic part of the recording process with the digital camera. We present a study based on simulations and real measurements describing the shot-noise influence in the quality of the reconstructed phase images. Different configurations of the reference wave and the object wave intensities will be discussed, illustrating the detection limit and the coherent amplification of the object wave. The signal-to-noise ratio (SNR) calculation of the reconstructed phase images based on the decision statistical theory is derived from a model for image quality estimation proposed by Wagner and Brown [Phys. Med. Biol. 30, 489 (1985)]. It will be shown that a phase image with a SNR above 10 can be obtained with a mean intensity lower than 10 photons per pixel and per hologram coming from the observed object. Experimental measurements on a glass–chrome probe will be presented to illustrate the main results of the simulations.

© 2006 Optical Society of America

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References

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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 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. 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).
  6. F. Charrière, J. Kühn, T. Colomb, F. Montfort, 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]
  7. 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]
  8. 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]
  9. 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]
  10. F. Charrière, F. Montfort, J. Kühn, T. Colomb, A. Marian, E. Cuche, P. Marquet, and C. Depeursinge, "Cell refractive index tomography by digital holographic microscopy," Opt. Lett. 31, 178-180 (2006).
    [CrossRef] [PubMed]
  11. 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]
  12. T. Colomb, E. Cuche, F. Montfort, P. Marquet, and C. Depeursinge, "Jones vector imaging by use of digital holography: simulation and experimentation," Opt. Commun. 231, 137-147 (2004).
    [CrossRef]
  13. 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]
  14. 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]
  15. T. Colomb, E. Cuche, F. Charrière, J. Kühn, N. Aspert, F. Montfort, P. Marquet, and C. Depeursinge, "Automatic procedure for aberrations compensation in digital holographic microscopy and applications to specimen shape compensation," Appl. Opt. 45, 851-863 (2006).
    [CrossRef] [PubMed]
  16. J. W. Goodman, Statistical Optics (Wiley, 1985).
  17. 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]
  18. 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]
  19. W. J. De Ruijter and J. K. Weiss, "Detection limits in quantitative off-axis electron holography," Ultramicroscopy 50, 269-283 (1993).
    [CrossRef]
  20. R. F. Wagner and D. G. Brown, "Unified SNR analysis of medical imaging-systems," Phys. Med. Biol. 30, 489-518 (1985).
    [CrossRef]
  21. E. Cuche, P. Marquet, and C. Depeursinge, "Spatial filtering for zero-order and twin-image elimination in digital off-axis holography," Appl. Opt. 39, 4070-4075 (2000).
    [CrossRef]
  22. H. Takajo and T. Takahashi, "Noniterative method for obtaining the exact solution for the normal equation in least-squares phase estimation from the phase difference," J. Opt. Soc. Am. A 5, 1818-1827 (1988).
    [CrossRef]

2006 (3)

2005 (2)

2004 (4)

2003 (2)

2002 (1)

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

2000 (2)

1999 (1)

1993 (1)

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

1988 (1)

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]

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]

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, E. Cuche, F. Charrière, J. Kühn, N. Aspert, F. Montfort, P. Marquet, and C. Depeursinge, "Automatic procedure for aberrations compensation in digital holographic microscopy and applications to specimen shape compensation," Appl. Opt. 45, 851-863 (2006).
[CrossRef] [PubMed]

F. Charrière, F. Montfort, J. Kühn, T. Colomb, A. Marian, E. Cuche, P. Marquet, and C. Depeursinge, "Cell refractive index tomography by digital holographic microscopy," Opt. Lett. 31, 178-180 (2006).
[CrossRef] [PubMed]

F. Charrière, J. Kühn, T. Colomb, F. Montfort, 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]

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]

T. Colomb, E. Cuche, F. Montfort, P. Marquet, and C. Depeursinge, "Jones vector imaging by use of digital holography: simulation and experimentation," Opt. Commun. 231, 137-147 (2004).
[CrossRef]

E. Cuche, P. Marquet, and C. Depeursinge, "Spatial filtering for zero-order and twin-image elimination in digital off-axis holography," Appl. Opt. 39, 4070-4075 (2000).
[CrossRef]

E. Cuche, P. Marquet, and C. Depeursinge, "Simultaneous amplitude 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.

F. Charrière, J. Kühn, T. Colomb, F. Montfort, 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, F. Montfort, J. Kühn, T. Colomb, A. Marian, E. Cuche, P. Marquet, and C. Depeursinge, "Cell refractive index tomography by digital holographic microscopy," Opt. Lett. 31, 178-180 (2006).
[CrossRef] [PubMed]

T. Colomb, E. Cuche, F. Charrière, J. Kühn, N. Aspert, F. Montfort, P. Marquet, and C. Depeursinge, "Automatic procedure for aberrations compensation in digital holographic microscopy and applications to specimen shape compensation," Appl. Opt. 45, 851-863 (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]

T. Colomb, E. Cuche, F. Montfort, P. Marquet, and C. Depeursinge, "Jones vector imaging by use of digital holography: simulation and experimentation," Opt. Commun. 231, 137-147 (2004).
[CrossRef]

E. Cuche, P. Marquet, and C. Depeursinge, "Spatial filtering for zero-order and twin-image elimination in digital off-axis holography," Appl. Opt. 39, 4070-4075 (2000).
[CrossRef]

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

Dubois, 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]

J. W. Goodman, Statistical Optics (Wiley, 1985).

Grilli, S.

Iwai, H.

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]

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).

Kebbel, V.

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).

Kim, M. K.

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.

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.

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. J.

Magro, C.

Marian, A.

Marquet, P.

F. Charrière, F. Montfort, J. Kühn, T. Colomb, A. Marian, E. Cuche, P. Marquet, and C. Depeursinge, "Cell refractive index tomography by digital holographic microscopy," Opt. Lett. 31, 178-180 (2006).
[CrossRef] [PubMed]

F. Charrière, J. Kühn, T. Colomb, F. Montfort, 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, E. Cuche, F. Charrière, J. Kühn, N. Aspert, F. Montfort, P. Marquet, and C. Depeursinge, "Automatic procedure for aberrations compensation in digital holographic microscopy and applications to specimen shape compensation," Appl. Opt. 45, 851-863 (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]

T. Colomb, E. Cuche, F. Montfort, P. Marquet, and C. Depeursinge, "Jones vector imaging by use of digital holography: simulation and experimentation," Opt. Commun. 231, 137-147 (2004).
[CrossRef]

E. Cuche, P. Marquet, and C. Depeursinge, "Spatial filtering for zero-order and twin-image elimination in digital off-axis holography," Appl. Opt. 39, 4070-4075 (2000).
[CrossRef]

E. Cuche, P. Marquet, and C. Depeursinge, "Simultaneous amplitude 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).

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).

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.

Pierattini, G.

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]

Takahashi, T.

Takajo, H.

Vaughan, J. C.

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]

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. (6)

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. Microsc. (1)

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]

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)

T. Colomb, E. Cuche, F. Montfort, P. Marquet, and C. Depeursinge, "Jones vector imaging by use of digital holography: simulation and experimentation," Opt. Commun. 231, 137-147 (2004).
[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 (2)

Opt. Lett. (3)

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]

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 (2)

J. W. Goodman, Statistical Optics (Wiley, 1985).

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).

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Figures (6)

Fig. 1
Fig. 1

(a) Real neuron phase image registered with DHM, (b) virtual neuron phase image, (c) virtual neuron characteristics summary, and (c) schematic of the off-axis hologram simulation (propagation of the wavefront on a distance d via the Fresnel integral): O, object wave; R, reference wave.

Fig. 2
Fig. 2

(a) SNR on the neuron phase image as a function of the repartition of the total intensity between the two beams for different total intensities, (b) SNR on Gaussian objects as a function of the repartition of the total intensity between the two beams for a different object radius, and (c) SNR on the neuron phase image as a function of the object intensity for different reference intensities.

Fig. 3
Fig. 3

Degradation of the reconstructed neuron phase image for different SNR values.

Fig. 4
Fig. 4

Schematic of the holographic microscope for reflection imaging. NF, neutral-density filter; PBS, polarizing beam splitter; BE, beam expander with spatial filter; λ / 2 , half-wave plate; M, mirror; BS, beam splitter; O, object wave; R, reference wave.

Fig. 5
Fig. 5

(a) Glass–chrome specimen reflection DHM phase image perspective, (b) specimen characteristics summary, and (c) specimen phase image for an average illumination intensity of 2.9 nW / cm 2 .

Fig. 6
Fig. 6

SNR of the glass–chrome probe phase image as a function of the repartition of the total intensity between the two beams.

Equations (11)

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

I H ( x , y ) = O O * + R R * zero order + O R * real image + R * O virtual image ,
R D ( k , l ) = A R exp [ i ( k D x k x ¯ + k D y l y ¯ ) ] ,
Ψ ( m Δ ξ , n Δ η ) = A Φ ( m , n ) FFT - 1 { FFT [ R D ( k , l ) × I H ( k , l ) ] p , q exp [ − i πλ d ( p 2 + q 2 ) ] } m , n ,
Ψ = R D R * O ,  with R D = exp [ i ( k D x k x ¯ + k D y l y ¯ ) ] ,
SNR = d f x d f y | F [ S ( x , y ) ] | 2 d f x d f y | F [ S ( x , y ) ] | 2 W ( f x , f y ) ,
W ( f x , f y ) = lim L x , L y 1 4 L x L y | - L x L x d x - L y L y d y Δ S ( x , y ) × exp [ - 2 π i ( x f x + y f y ) ] | 2 ,
I interference = I Obj + I Ref + I Obj I Ref cos ( φ ) ,
SNR holo = 2 I Obj I Ref I Obj + I Ref ,
lim I Obj 0 SNR holo = 2 I Obj I Ref I Obj + I Ref = 0 I Ref = 0 ,
lim I Ref 0 SNR holo = 2 I Obj I Ref I Obj + I Ref = 0 I Obj = 0.
lim I Ref SNR holo = 2 I Obj I Ref I Obj + I Ref = 2 I Ref I Obj I Ref I Obj I Ref + 1 = 2 I Obj .

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