Abstract

We have compared the respective efficiencies of off-axis and phase-shifting holography in terms of noise and aliases removal. The comparison is made by analyzing holograms of a USAF target backlit with laser illumination, recorded with a charge-coupled device camera. We show that it is essential to remove the local oscillator beam noise, especially at low illumination levels.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  10. E. Cuche, F. Belivacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. 24, 291-293 (1999).
  11. J. H. Massig, “Digital off-axis holography with a synthetic aperture,” Opt. Lett. 27, 2179-2181 (2005).
    [CrossRef]
  12. Z. Ansari, Y. Gu, M. Tziraki, R. Jones, P. M. W. French, D. D. Nolte, and M. R. Melloch, “Elimination of beam walk-off in low-coherence off-axis photorefractive holography,” Opt. Lett. 26, 334-336 (2001).
    [CrossRef]
  13. P. Massatsch, F. Charrire, E. Cuche, P. Marquet, and C. D. Depeursinge, “Time-domain optical coherence tomography with digital holographic microscopy,” Appl. Opt. 44, 1806-1812 (2005).
    [CrossRef]
  14. 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]
  15. K. Creath, “Phase-shifting speckle interferometry,” Appl. Opt. 24, 3053-3058 (1985).
  16. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 18, 31-33 (1997).
  17. T. Zhang and I. Yamaguchi, “Three-dimensional microscopy with phase-shifting digital holography,” Opt. Lett. 23, 1221-1223 (1998).
  18. T. Nomura, B. Javidi, S. Murata, E. Nitanai, and T. Numata, “Polarization imaging of a 3D object by use of on-axis phase-shifting digital holography,” Opt. Lett. 32, 481-483(2007).
    [CrossRef]
  19. I. Yamaguchi, T. Matsumura, and J.-I. Kato, “Phase-shifting color digital holography,” Opt. Lett. 27, 1108-1110 (2002).
    [CrossRef]
  20. J. Kato, I. Yamaguchi, and T. Matsumura, “Multicolor digital holography with an achromatic phase shifter,” Opt. Lett. 27, 1403-1405 (2002).
    [CrossRef]
  21. F. LeClerc, L. Collot, and M. Gross, “Synthetic-aperture experiment in visible with on-axis digital heterodyne holography,” Opt. Lett. 26 (2001).
    [CrossRef]
  22. S. Tamano, Y. Hayasaki, and N. Nishida, “Phase-shifting digital holography with a low-coherence light source for reconstruction of a digital relief object hidden behind a light-scattering medium,” Appl. Opt. 45, 953-959 (2006).
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  24. P. Guo and A. J. Devaney, “Multicolor digital holography with an achromatic phase shifter,” Opt. Lett. 29, 857-859(2004).
    [CrossRef]
  25. F. LeClerc, L. Collot, and M. Gross, “Numerical heterodyne holography using 2D photodetector arrays,” Opt. Lett. 25, 716-718 (2000).
    [CrossRef]
  26. M. Gross and M. Atlan, “Digital holography with ultimate sensitivity,” Opt. Lett. 32, 909-911 (2007).
    [CrossRef]
  27. M. Atlan, M. Gross, and E. Absil, “Accurate phase-shifting digital interferometry,” Opt. Lett. submitted Feb 2007 ID: 79800.
  28. T. Kreis, “Digital holography for metrologic applications,” in Interferometry in Speckle Light, P. Jacquot and J. -M. Fournier, eds. (Springer Verlag, 2000), pp. 205-212.
  29. F. Zhang, I. Yamaguchi, and L. P. Yaroslavsky, “Algorithm for reconstruction of digital holograms with adjustable magnification,” Opt. Lett. 29, 1668-1670 (2004).
    [CrossRef]
  30. I. Yamaguchi, J. I. Kato, S. Ohta, and J. Mizuno, “Image formation in phase-shifting digital holography and applications to microscopy,” Appl. Opt. 40, 6177-6186 (2001).
    [CrossRef]

2007

2006

2005

2004

2002

2001

2000

1999

1998

1997

1994

U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179-181 (1994).

U. Schnars, “Direct phase determination in hologram interferometry with use of digitally recorded holograms,” J. Opt. Soc. Am. A. 11, 977 (1994).

1988

T. M. Kreis, W. P. O. Juptner, and J. Geldmacher, “Principles of digital holographic interferometry,” Proc. SPIE 3478, 45-54(1988).

1985

1967

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

1965

1949

D. Gabor, “Microscopy by reconstructed wave-fronts,” Proc. Royal Soc. London, Ser. A. 197, 454-487 (1949).

Absil, E.

M. Atlan, M. Gross, and E. Absil, “Accurate phase-shifting digital interferometry,” Opt. Lett. submitted Feb 2007 ID: 79800.

Ansari, Z.

Atlan, M.

M. Gross and M. Atlan, “Digital holography with ultimate sensitivity,” Opt. Lett. 32, 909-911 (2007).
[CrossRef]

M. Atlan, M. Gross, and E. Absil, “Accurate phase-shifting digital interferometry,” Opt. Lett. submitted Feb 2007 ID: 79800.

Beghuin, D.

Belivacqua, F.

Charrire, F.

Collot, L.

F. LeClerc, L. Collot, and M. Gross, “Synthetic-aperture experiment in visible with on-axis digital heterodyne holography,” Opt. Lett. 26 (2001).
[CrossRef]

F. LeClerc, L. Collot, and M. Gross, “Numerical heterodyne holography using 2D photodetector arrays,” Opt. Lett. 25, 716-718 (2000).
[CrossRef]

Colomb, T.

Creath, K.

Cuche, E.

Dahlgren, P.

Depeursinge, C.

Depeursinge, C. D.

Devaney, A. J.

Emery, Y.

French, P. M. W.

Gabor, D.

D. Gabor, “Microscopy by reconstructed wave-fronts,” Proc. Royal Soc. London, Ser. A. 197, 454-487 (1949).

Geldmacher, J.

T. M. Kreis, W. P. O. Juptner, and J. Geldmacher, “Principles of digital holographic interferometry,” Proc. SPIE 3478, 45-54(1988).

Goodmann, J. W.

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

Gross, M.

M. Gross and M. Atlan, “Digital holography with ultimate sensitivity,” Opt. Lett. 32, 909-911 (2007).
[CrossRef]

F. LeClerc, L. Collot, and M. Gross, “Synthetic-aperture experiment in visible with on-axis digital heterodyne holography,” Opt. Lett. 26 (2001).
[CrossRef]

F. LeClerc, L. Collot, and M. Gross, “Numerical heterodyne holography using 2D photodetector arrays,” Opt. Lett. 25, 716-718 (2000).
[CrossRef]

M. Atlan, M. Gross, and E. Absil, “Accurate phase-shifting digital interferometry,” Opt. Lett. submitted Feb 2007 ID: 79800.

Gu, Y.

Guo, P.

Haines, K. A.

Hayasaki, Y.

Ida, T.

Javidi, B.

Jones, R.

Juptner, W. P. O.

T. M. Kreis, W. P. O. Juptner, and J. Geldmacher, “Principles of digital holographic interferometry,” Proc. SPIE 3478, 45-54(1988).

Jüptner, W.

Kato, J.

Kato, J. I.

Kato, J.-I.

Kreis, T.

T. Kreis, “Digital holography for metrologic applications,” in Interferometry in Speckle Light, P. Jacquot and J. -M. Fournier, eds. (Springer Verlag, 2000), pp. 205-212.

Kreis, T. M.

T. M. Kreis, W. P. O. Juptner, and J. Geldmacher, “Principles of digital holographic interferometry,” Proc. SPIE 3478, 45-54(1988).

Lawrence, R. W.

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

LeClerc, F.

F. LeClerc, L. Collot, and M. Gross, “Synthetic-aperture experiment in visible with on-axis digital heterodyne holography,” Opt. Lett. 26 (2001).
[CrossRef]

F. LeClerc, L. Collot, and M. Gross, “Numerical heterodyne holography using 2D photodetector arrays,” Opt. Lett. 25, 716-718 (2000).
[CrossRef]

Leith, E. N.

Magistretti, P. J.

Marquet, P.

Massatsch, P.

Massig, J. H.

Matsumura, T.

Melloch, M. R.

Meng, H.

Mizuno, J.

Murata, S.

Nishida, N.

Nitanai, E.

Nolte, D. D.

Nomura, T.

Numata, T.

Ohta, S.

Pu, Y.

Rappaz, B.

Schnars, U.

U. Schnars, “Direct phase determination in hologram interferometry with use of digitally recorded holograms,” J. Opt. Soc. Am. A. 11, 977 (1994).

U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179-181 (1994).

Tamano, S.

Tziraki, M.

Upatnieks, J.

Yamaguchi, I.

Yamashita, K.

Yaroslavsky, L. P.

Yokota, M.

Zhang, F.

Zhang, T.

Appl. Opt.

Appl. Phys. Lett.

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

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. A.

U. Schnars, “Direct phase determination in hologram interferometry with use of digitally recorded holograms,” J. Opt. Soc. Am. A. 11, 977 (1994).

Opt. Lett.

E. Cuche, F. Belivacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. 24, 291-293 (1999).

J. H. Massig, “Digital off-axis holography with a synthetic aperture,” Opt. Lett. 27, 2179-2181 (2005).
[CrossRef]

Z. Ansari, Y. Gu, M. Tziraki, R. Jones, P. M. W. French, D. D. Nolte, and M. R. Melloch, “Elimination of beam walk-off in low-coherence off-axis photorefractive holography,” Opt. Lett. 26, 334-336 (2001).
[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]

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 18, 31-33 (1997).

T. Zhang and I. Yamaguchi, “Three-dimensional microscopy with phase-shifting digital holography,” Opt. Lett. 23, 1221-1223 (1998).

T. Nomura, B. Javidi, S. Murata, E. Nitanai, and T. Numata, “Polarization imaging of a 3D object by use of on-axis phase-shifting digital holography,” Opt. Lett. 32, 481-483(2007).
[CrossRef]

I. Yamaguchi, T. Matsumura, and J.-I. Kato, “Phase-shifting color digital holography,” Opt. Lett. 27, 1108-1110 (2002).
[CrossRef]

J. Kato, I. Yamaguchi, and T. Matsumura, “Multicolor digital holography with an achromatic phase shifter,” Opt. Lett. 27, 1403-1405 (2002).
[CrossRef]

F. LeClerc, L. Collot, and M. Gross, “Synthetic-aperture experiment in visible with on-axis digital heterodyne holography,” Opt. Lett. 26 (2001).
[CrossRef]

F. Zhang, I. Yamaguchi, and L. P. Yaroslavsky, “Algorithm for reconstruction of digital holograms with adjustable magnification,” Opt. Lett. 29, 1668-1670 (2004).
[CrossRef]

P. Guo and A. J. Devaney, “Multicolor digital holography with an achromatic phase shifter,” Opt. Lett. 29, 857-859(2004).
[CrossRef]

F. LeClerc, L. Collot, and M. Gross, “Numerical heterodyne holography using 2D photodetector arrays,” Opt. Lett. 25, 716-718 (2000).
[CrossRef]

M. Gross and M. Atlan, “Digital holography with ultimate sensitivity,” Opt. Lett. 32, 909-911 (2007).
[CrossRef]

Proc. Royal Soc. London, Ser. A.

D. Gabor, “Microscopy by reconstructed wave-fronts,” Proc. Royal Soc. London, Ser. A. 197, 454-487 (1949).

Proc. SPIE

T. M. Kreis, W. P. O. Juptner, and J. Geldmacher, “Principles of digital holographic interferometry,” Proc. SPIE 3478, 45-54(1988).

Other

M. Atlan, M. Gross, and E. Absil, “Accurate phase-shifting digital interferometry,” Opt. Lett. submitted Feb 2007 ID: 79800.

T. Kreis, “Digital holography for metrologic applications,” in Interferometry in Speckle Light, P. Jacquot and J. -M. Fournier, eds. (Springer Verlag, 2000), pp. 205-212.

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Figures (12)

Fig. 1
Fig. 1

Off-axis dynamic phase-shifting digital holography setup. L, main laser; BS, beam splitter; AOM1 and AOM2, acousto-optic modulators (Bragg cells); BE, beam expander; M, mirror; A, light attenuator; USAF, transmission USAF 1951 resolution target; E L , E LO , and E are illumination, local oscillator, and object field, respectively; and CCD, charge-coupled device array detector.

Fig. 2
Fig. 2

Off-axis single-phase reconstruction of the target image. (a) Hologram H ( x , y , 0 ) that corresponds to the 1280 × 1024 CCD image padded in a 2048 × 2048 zero matrix (linear gray scale display). (b) k space field ( 2048 × 2048 matrix, logarithmic gray scale for the intensity | H ˜ | 2 ). (c) Image calculated on the 2048 × 2048 matrix with logarithmic gray scale display for the intensity | H | 2 . (d) Enlargement of the k space true image region [dashed square in Fig. 2b]. The 400 × 400   pixels wide true image region is copied within a 512 × 512 zero matrix. The resulting 512 × 512 | H | 2 intensity image is displayed in logarithmic scale. (a), (d) Images corresponding to a total signal of 4.3 × 10 8 photoelectrons for the sequence of three images.

Fig. 3
Fig. 3

Horizontal cut ( y 1196 ) of the reconstructed field intensity | H ˜ | 2 of Fig. 2c. Vertical axis is | H ˜ | 2 in arb. units. Horizontal axis is pixel index x = 0 2047 . Vertical display is logarithmic.

Fig. 4
Fig. 4

Off-axis reconstructed image of a USAF target in transmission with low light illumination. Images are obtained with k space filtering with ≃ (a) 4.3 × 10 8 , (b) 8.7 × 10 6 , (c) 8.7 × 10 4 , and (d) 1.2 × 10 4 photoelectrons, respectively, for the sequence of three images. | H | 2 intensity is displayed in linear gray scale.

Fig. 5
Fig. 5

Horizontal cuts ( y 264 ) of the reconstructed field intensity | H ˜ | 2 corresponding to the images in Fig. 4. (a)–(d) Curves correspond to (a)–(d) images. Vertical axis is | H ˜ | 2 in arb units. Horizontal axis is pixel index x = 0 512 . Vertical display is logarithmic. The total signal is ≃ (a) 4.3 × 10 8 , (b) 8.7 × 10 6 , (c) 8.7 × 10 4 , and (d) 1.2 × 10 4 photoelectrons, respectively, for the sequence of three images.

Fig. 6
Fig. 6

Four-phase reconstructed image of a USAF target in transmission with low light illumination without k space filtering. Images are reconstructed with (a) 1.7 × 10 9 , (b) 3.5 × 10 7 , (c) 3.5 × 10 5 , and (d) 5 × 10 4 photoelectrons, respectively, for all the pixels of the whole sequence of 12 images. | H | 2 intensity is displayed in linear gray scale.

Fig. 7
Fig. 7

Horizontal cuts ( y 1196 ) of the reconstructed field intensity | H ˜ | 2 corresponding to the four phase images of Fig. 6. (a)–(d) Curves correspond to (a)–(d) images. Vertical axis is | H ˜ | 2 in arb. units. Horizontal axis is pixel index x = 0 2048 . Vertical display is logarithmic. The total signal is ≃ (a) 1.7 × 10 9 , (b) 3.5 × 10 7 , (c) 3.5 × 10 5 , and (d) 5 × 10 4 photoelectrons, respectively, for all the pixels of the whole sequence of 12 images.

Fig. 8
Fig. 8

Four-phase reconstructed image of a USAF target in transmission at low light illumination with k space filtering. Images are reconstructed with ≃ (a) 1.7 × 10 9 , (b) 3.5 × 10 7 , (c) 3.5 × 10 5 , and (d) 5 × 10 4 photoelectrons, respectively, for all the pixels of the whole sequence of 12 images. | H | 2 intensity is displayed in linear gray scale.

Fig. 9
Fig. 9

Horizontal cuts ( y 264 ) of the reconstructed field intensity | H ˜ | 2 corresponding to the images in Fig. 8. (a)–(d) Curves correspond to (a)–(d) images. Vertical axis is | H ˜ | 2 in arb. units. Horizontal axis is pixel index x = 0 512 . Vertical display is logarithmic. The total signal is ≃ (a) 1.7 × 10 9 , (b) 3.5 × 10 7 , (c) 3.5 × 10 5 , and (d) 5 × 10 4 photoelectrons, respectively, for all the pixels of the whole sequence of 12 images.

Fig. 10
Fig. 10

(a), (b) k space field intensity | H ˜ | 2 and | H ˜ | 2 reconstructed from (a) one-phase and (b) four-phase holograms obtained without signal (i.e., without illumination of the USAF target). (c), (d) Cut along the white dashed diagonal lines for (c) one-phase and (d) four-phase holograms. Vertical axis is the k space intensity | H ˜ | 2 and | H ˜ | 2 along the cut. Vertical axis is the pixel index. Intensity is averaged over 11   pixels , i.e., in the interval ( i , i 5 ) ( i , + 5 ) , where i = 0 2047 is the pixel index.

Fig. 11
Fig. 11

One-phase reconstructed images of a USAF target in transmission with substraction of the average LO beam signal. Images are obtained with k space filtering with ≃ (a) 4.3 × 10 8 , (b) 8.7 × 10 6 , (c) 8.7 × 10 4 , and (d) 1.2 × 10 4 photoelectrons, respectively, for the sequence of three images.

Fig. 12
Fig. 12

Cuts of the one-phase reconstructed images of the USAF target in transmission with substraction of the LO beam signal. Images are obtained with k space filtering with ≃ (a) 4.3 × 10 8 , (b) 8.7 × 10 6 , (c) 8.7 × 10 4 , and (d) 1.2 × 10 4 photoelectrons, respectively, for the sequence of three images.

Equations (16)

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ω L ω LO = ω AOM 2 ω AOM 1 ω CCD / 4.
t m = 2 π m / ω CCD .
E ( t ) = ε e j ω t + ε * e j ω t ,
E LO ( t ) = ε LO e j ω t + ε LO * e j ω t ,
I m = | ε e j ω t m + ε LO e j ω LO t m | 2 ,
I m = | ε | 2 + | ε LO | 2 + ε ε LO * e j ω CCD t m / 4 + cc ,
e j ω CCD t m / 4 e j m π / 2 = j m .
H ( x , y , 0 ) = I 0 ( x , y ) + I 4 ( x , y ) + I 8 ( x , y ) .
H ˜ ( k x , k y , 0 ) = FT [ H ( x , y , 0 ) ] .
H ˜ ( k x , k y , z ) = H ˜ ( k x , k y , 0 ) exp ( j z ( k x 2 + k y 2 ) / k ) ,
H ( x , y , D ) = FT 1 [ H ˜ ( k x , k y , D ) ] .
H ( x , y ) = m = 0 11 ( j ) m I m ( x , y ) ,
H = m = 0 11 ( j ) m ( | ε | 2 + | ε LO | 2 ) + m = 0 11 ( j ) m e + ω CCD t m / 4 ε ε LO * + m = 0 11 ( j ) m e ω CCD t m / 4 ε * ε LO .
I LO ( x , y ) = 1 12 m = 0 11 I m ( x , y ) .
H ( x , y , 0 ) = I 0 ( x , y ) + I 4 ( x , y ) + I 8 ( x , y ) 3 I LO ( x , y ) ,
H = ( m = 0 , 4 , 8 + 3 12 m = 0 11 ) ( | ε | 2 + | ε LO | 2 ) + m = 0 , 4 , 8 e + ω CCD t m / 4 ε ε LO * + cc .

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