Abstract

An optimal setup in the sense of imaging resolution for the Fresnel incoherent correlation holography (FINCH) system is proposed and analyzed. Experimental results of the proposed setup in reflection mode suffer from low signal-to-noise ratio (SNR) due to a granular noise. SNR improvement is achieved by two methods that rely on increasing the initial amount of phase-shifted recorded holograms. In the first method, we average over several independent complex-valued digital holograms obtained by recording different sets of three digital phase-shifted holograms. In the second method, the least-squares solution for solving a system of an overdetermined set of linear equations is approximated by utilizing the Moore–Penrose pseudoinverse. These methods improve the resolution of the reconstructed image due to their ability to reveal fine and weak details of the observed object.

© 2010 Optical Society of America

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References

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  1. J. Rosen and G. Brooker, “Digital spatially incoherent Fresnel holography,” Opt. Lett. 32, 912–914 (2007).
    [CrossRef] [PubMed]
  2. J. Rosen and G. Brooker, “Fluorescence incoherent color holography,” Opt. Express 15, 2244–2250 (2007).
    [CrossRef] [PubMed]
  3. J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photon. 2, 190–195 (2008).
    [CrossRef]
  4. B. Katz and J. Rosen, “Super-resolution in incoherent optical imaging using synthetic aperture with Fresnel elements,” Opt. Express 18, 962–972 (2010).
    [CrossRef] [PubMed]
  5. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J.C.Dainty, ed., Vol. 9 of Topics in Applied Physics (Springer–Verlag, 1975), pp. 9–75.
    [CrossRef]
  6. P. Lancaster and M. Tismenetsky, The Theory of Matrices, 2nd ed. (Academic, 1985), pp. 432–438.
  7. J. P. Huignard, J. P. Herriau, L. Pichon, and A. Marrakchi, “Speckle-free imaging in four-wave mixing experiments with Bi12SiO20 crystals,” Opt. Lett. 5, 436–437 (1980).
    [CrossRef] [PubMed]
  8. F. Wyrowski and O. Bryngdahl, “Speckle-free reconstruction in digital holography,” J. Opt. Soc. Am. A 6, 1171–1174 (1989).
    [CrossRef]
  9. A. Capanni, L. Pezzati, D. Bertani, M. Cetica, and F. Francini, “Phase-shifting speckle interferometry: a noise reduction filter for phase unwrapping,” Opt. Eng. 36, 2466–2472(1997).
    [CrossRef]
  10. A. Brozeit, J. Burke, H. Helmers, H. Sagehorn, and R. Schuh, “Noise reduction in electronic speckle pattern interferometry fringes by merging orthogonally polarized speckle fields,” Opt. Laser Technol. 30, 325–329 (1998).
    [CrossRef]
  11. S.-H. Shin and B. Javidi, “Speckle-reduced three-dimensional volume holographic display by use of integral imaging,” Appl. Opt. 41, 2644–2649 (2002).
    [CrossRef] [PubMed]
  12. J. Kauffmann, M. Gahr, and H. J. Tiziani, “Noise reduction in speckle pattern interferometry,” Proc. SPIE 4933, 9–14 (2003).
    [CrossRef]
  13. Y. Morimoto, T. Nomura, M. Fujigaki, S. Yoneyama, and I. Takahashi, “Deformation measurement by phase-shifting digital holography,” Exp. Mech. 45, 65–70 (2005).
    [CrossRef]
  14. T. Nomura, M. Okamura, E. Nitanai, and T. Numata, “Speckles removal in digital holography using multiple wavelengths/distances from an object,” in LEOS 2006. 19th Annual Meeting of the IEEE (Lasers and Electro-Optics Society, 2006), pp. 74–75..
    [CrossRef]
  15. 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]
  16. L. Rong, W. Xiao, and F. Pan, “Reduction of speckle noise in digital holography by multiple holograms,” Proc. SPIE 7382, 73823T (2009).
    [CrossRef]
  17. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw–Hill, 1996), pp. 314–317.

2010 (1)

2009 (1)

L. Rong, W. Xiao, and F. Pan, “Reduction of speckle noise in digital holography by multiple holograms,” Proc. SPIE 7382, 73823T (2009).
[CrossRef]

2008 (1)

J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photon. 2, 190–195 (2008).
[CrossRef]

2007 (2)

2006 (1)

2005 (1)

Y. Morimoto, T. Nomura, M. Fujigaki, S. Yoneyama, and I. Takahashi, “Deformation measurement by phase-shifting digital holography,” Exp. Mech. 45, 65–70 (2005).
[CrossRef]

2003 (1)

J. Kauffmann, M. Gahr, and H. J. Tiziani, “Noise reduction in speckle pattern interferometry,” Proc. SPIE 4933, 9–14 (2003).
[CrossRef]

2002 (1)

1998 (1)

A. Brozeit, J. Burke, H. Helmers, H. Sagehorn, and R. Schuh, “Noise reduction in electronic speckle pattern interferometry fringes by merging orthogonally polarized speckle fields,” Opt. Laser Technol. 30, 325–329 (1998).
[CrossRef]

1997 (1)

A. Capanni, L. Pezzati, D. Bertani, M. Cetica, and F. Francini, “Phase-shifting speckle interferometry: a noise reduction filter for phase unwrapping,” Opt. Eng. 36, 2466–2472(1997).
[CrossRef]

1989 (1)

1980 (1)

Baumbach, T.

Bertani, D.

A. Capanni, L. Pezzati, D. Bertani, M. Cetica, and F. Francini, “Phase-shifting speckle interferometry: a noise reduction filter for phase unwrapping,” Opt. Eng. 36, 2466–2472(1997).
[CrossRef]

Brooker, G.

Brozeit, A.

A. Brozeit, J. Burke, H. Helmers, H. Sagehorn, and R. Schuh, “Noise reduction in electronic speckle pattern interferometry fringes by merging orthogonally polarized speckle fields,” Opt. Laser Technol. 30, 325–329 (1998).
[CrossRef]

Bryngdahl, O.

Burke, J.

A. Brozeit, J. Burke, H. Helmers, H. Sagehorn, and R. Schuh, “Noise reduction in electronic speckle pattern interferometry fringes by merging orthogonally polarized speckle fields,” Opt. Laser Technol. 30, 325–329 (1998).
[CrossRef]

Capanni, A.

A. Capanni, L. Pezzati, D. Bertani, M. Cetica, and F. Francini, “Phase-shifting speckle interferometry: a noise reduction filter for phase unwrapping,” Opt. Eng. 36, 2466–2472(1997).
[CrossRef]

Cetica, M.

A. Capanni, L. Pezzati, D. Bertani, M. Cetica, and F. Francini, “Phase-shifting speckle interferometry: a noise reduction filter for phase unwrapping,” Opt. Eng. 36, 2466–2472(1997).
[CrossRef]

Francini, F.

A. Capanni, L. Pezzati, D. Bertani, M. Cetica, and F. Francini, “Phase-shifting speckle interferometry: a noise reduction filter for phase unwrapping,” Opt. Eng. 36, 2466–2472(1997).
[CrossRef]

Fujigaki, M.

Y. Morimoto, T. Nomura, M. Fujigaki, S. Yoneyama, and I. Takahashi, “Deformation measurement by phase-shifting digital holography,” Exp. Mech. 45, 65–70 (2005).
[CrossRef]

Gahr, M.

J. Kauffmann, M. Gahr, and H. J. Tiziani, “Noise reduction in speckle pattern interferometry,” Proc. SPIE 4933, 9–14 (2003).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw–Hill, 1996), pp. 314–317.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J.C.Dainty, ed., Vol. 9 of Topics in Applied Physics (Springer–Verlag, 1975), pp. 9–75.
[CrossRef]

Helmers, H.

A. Brozeit, J. Burke, H. Helmers, H. Sagehorn, and R. Schuh, “Noise reduction in electronic speckle pattern interferometry fringes by merging orthogonally polarized speckle fields,” Opt. Laser Technol. 30, 325–329 (1998).
[CrossRef]

Herriau, J. P.

Huignard, J. P.

Javidi, B.

Jüptner, W.

Katz, B.

Kauffmann, J.

J. Kauffmann, M. Gahr, and H. J. Tiziani, “Noise reduction in speckle pattern interferometry,” Proc. SPIE 4933, 9–14 (2003).
[CrossRef]

Kebbel, V.

Kolenovic, E.

Lancaster, P.

P. Lancaster and M. Tismenetsky, The Theory of Matrices, 2nd ed. (Academic, 1985), pp. 432–438.

Marrakchi, A.

Morimoto, Y.

Y. Morimoto, T. Nomura, M. Fujigaki, S. Yoneyama, and I. Takahashi, “Deformation measurement by phase-shifting digital holography,” Exp. Mech. 45, 65–70 (2005).
[CrossRef]

Nitanai, E.

T. Nomura, M. Okamura, E. Nitanai, and T. Numata, “Speckles removal in digital holography using multiple wavelengths/distances from an object,” in LEOS 2006. 19th Annual Meeting of the IEEE (Lasers and Electro-Optics Society, 2006), pp. 74–75..
[CrossRef]

Nomura, T.

Y. Morimoto, T. Nomura, M. Fujigaki, S. Yoneyama, and I. Takahashi, “Deformation measurement by phase-shifting digital holography,” Exp. Mech. 45, 65–70 (2005).
[CrossRef]

T. Nomura, M. Okamura, E. Nitanai, and T. Numata, “Speckles removal in digital holography using multiple wavelengths/distances from an object,” in LEOS 2006. 19th Annual Meeting of the IEEE (Lasers and Electro-Optics Society, 2006), pp. 74–75..
[CrossRef]

Numata, T.

T. Nomura, M. Okamura, E. Nitanai, and T. Numata, “Speckles removal in digital holography using multiple wavelengths/distances from an object,” in LEOS 2006. 19th Annual Meeting of the IEEE (Lasers and Electro-Optics Society, 2006), pp. 74–75..
[CrossRef]

Okamura, M.

T. Nomura, M. Okamura, E. Nitanai, and T. Numata, “Speckles removal in digital holography using multiple wavelengths/distances from an object,” in LEOS 2006. 19th Annual Meeting of the IEEE (Lasers and Electro-Optics Society, 2006), pp. 74–75..
[CrossRef]

Pan, F.

L. Rong, W. Xiao, and F. Pan, “Reduction of speckle noise in digital holography by multiple holograms,” Proc. SPIE 7382, 73823T (2009).
[CrossRef]

Pezzati, L.

A. Capanni, L. Pezzati, D. Bertani, M. Cetica, and F. Francini, “Phase-shifting speckle interferometry: a noise reduction filter for phase unwrapping,” Opt. Eng. 36, 2466–2472(1997).
[CrossRef]

Pichon, L.

Rong, L.

L. Rong, W. Xiao, and F. Pan, “Reduction of speckle noise in digital holography by multiple holograms,” Proc. SPIE 7382, 73823T (2009).
[CrossRef]

Rosen, J.

Sagehorn, H.

A. Brozeit, J. Burke, H. Helmers, H. Sagehorn, and R. Schuh, “Noise reduction in electronic speckle pattern interferometry fringes by merging orthogonally polarized speckle fields,” Opt. Laser Technol. 30, 325–329 (1998).
[CrossRef]

Schuh, R.

A. Brozeit, J. Burke, H. Helmers, H. Sagehorn, and R. Schuh, “Noise reduction in electronic speckle pattern interferometry fringes by merging orthogonally polarized speckle fields,” Opt. Laser Technol. 30, 325–329 (1998).
[CrossRef]

Shin, S.-H.

Takahashi, I.

Y. Morimoto, T. Nomura, M. Fujigaki, S. Yoneyama, and I. Takahashi, “Deformation measurement by phase-shifting digital holography,” Exp. Mech. 45, 65–70 (2005).
[CrossRef]

Tismenetsky, M.

P. Lancaster and M. Tismenetsky, The Theory of Matrices, 2nd ed. (Academic, 1985), pp. 432–438.

Tiziani, H. J.

J. Kauffmann, M. Gahr, and H. J. Tiziani, “Noise reduction in speckle pattern interferometry,” Proc. SPIE 4933, 9–14 (2003).
[CrossRef]

Wyrowski, F.

Xiao, W.

L. Rong, W. Xiao, and F. Pan, “Reduction of speckle noise in digital holography by multiple holograms,” Proc. SPIE 7382, 73823T (2009).
[CrossRef]

Yoneyama, S.

Y. Morimoto, T. Nomura, M. Fujigaki, S. Yoneyama, and I. Takahashi, “Deformation measurement by phase-shifting digital holography,” Exp. Mech. 45, 65–70 (2005).
[CrossRef]

Appl. Opt. (2)

Exp. Mech. (1)

Y. Morimoto, T. Nomura, M. Fujigaki, S. Yoneyama, and I. Takahashi, “Deformation measurement by phase-shifting digital holography,” Exp. Mech. 45, 65–70 (2005).
[CrossRef]

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

Nat. Photon. (1)

J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photon. 2, 190–195 (2008).
[CrossRef]

Opt. Eng. (1)

A. Capanni, L. Pezzati, D. Bertani, M. Cetica, and F. Francini, “Phase-shifting speckle interferometry: a noise reduction filter for phase unwrapping,” Opt. Eng. 36, 2466–2472(1997).
[CrossRef]

Opt. Express (2)

Opt. Laser Technol. (1)

A. Brozeit, J. Burke, H. Helmers, H. Sagehorn, and R. Schuh, “Noise reduction in electronic speckle pattern interferometry fringes by merging orthogonally polarized speckle fields,” Opt. Laser Technol. 30, 325–329 (1998).
[CrossRef]

Opt. Lett. (2)

Proc. SPIE (2)

L. Rong, W. Xiao, and F. Pan, “Reduction of speckle noise in digital holography by multiple holograms,” Proc. SPIE 7382, 73823T (2009).
[CrossRef]

J. Kauffmann, M. Gahr, and H. J. Tiziani, “Noise reduction in speckle pattern interferometry,” Proc. SPIE 4933, 9–14 (2003).
[CrossRef]

Other (4)

T. Nomura, M. Okamura, E. Nitanai, and T. Numata, “Speckles removal in digital holography using multiple wavelengths/distances from an object,” in LEOS 2006. 19th Annual Meeting of the IEEE (Lasers and Electro-Optics Society, 2006), pp. 74–75..
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw–Hill, 1996), pp. 314–317.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J.C.Dainty, ed., Vol. 9 of Topics in Applied Physics (Springer–Verlag, 1975), pp. 9–75.
[CrossRef]

P. Lancaster and M. Tismenetsky, The Theory of Matrices, 2nd ed. (Academic, 1985), pp. 432–438.

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Figures (5)

Fig. 1
Fig. 1

Possible experimental setups: (a) Lensless FINCH, (b) FINCH with a positive refractive lens. BS—beam splitter. BPF—bandpass filter. CCD—charge-coupled device. SLM—spatial light modulator.

Fig. 2
Fig. 2

Results of the proposed noise suppression method. (a)–(c) are the three masks displayed on the SLM during the recording process of the raw holograms presented in (d)–(f), (g)–(h) are the magnitude and phase of the noisy CVH generated from three raw holograms, and (i) and (j) are the noise-suppressed CVH generated from 36 raw holograms. (k) and (l) are the corresponding best in-focus reconstructed planes from the holograms (g), (h) and (i), (j), respectively.

Fig. 3
Fig. 3

Comparative results of the SNR obtained by the averaging approach and by the pseudoinverse approach versus the theoretical graph M SNR ( 1 ) .

Fig. 4
Fig. 4

Evaluation of the optimal resolution setup. The magnitude of noise-suppressed holograms is shown with (a) f d = 2 z h , (b) f d = 3 z h , (c) f d = 4 z h , and (d) lensless FINCH. The phase of noise-suppressed holograms is shown with (e) f d = 2 z h , (f) f d = 3 z h , (g) f d = 4 z h , and (h) lensless FINCH. The best in-focus reconstructed plane from the noise-suppressed holograms is shown with (i) f d = 2 z h , (j) f d = 3 z h , (k) f d = 4 z h , and (l) lensless FINCH.

Fig. 5
Fig. 5

Set of the best in-focus reconstructed planes from holograms recorded with diffractive lenses ranging between f d = 3 z h to 3 z h .

Equations (13)

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I h ( r ¯ o ; r ¯ s ) = | { C 1 ( r ¯ s ) L [ r ¯ s f 1 ] Q [ 1 f 1 ] × ( Q [ 1 f 1 ] + Q [ 1 f 2 ] ) } * Q [ 1 z h ] | 2 = ( C 2 + C 3 ( r ¯ s ) Q [ 1 z r ] L [ r ¯ r z r ] + C 3 * ( r ¯ s ) Q [ 1 z r ] L [ r ¯ r z r ] ) ,
z r = ± ( f e + z h ) , where f e = f 1 f 2 / ( f 2 f 1 )
r ¯ r = r ¯ s z h / f 1 , where r ¯ r = ( x r , y r ) .
M T = r ¯ r / r ¯ s = z h / f 1 .
Δ min = max { λ / NA in , λ / ( M T NA out ) } = max { 2 λ f 1 / D SLM , 2 λ | z r | / ( M T D CCD ) } ,
2 λ f 1 / D SLM 2 λ | z r | / ( M T D CCD ) .
2 z h f e < 0.
I h ( r ¯ o ; r ¯ s ) = | { C 1 ( r ¯ s ) L [ r ¯ s f r ] Q [ 1 f r ] Q [ 1 f r ] × ( 1 + Q [ 1 f d ] ) } * Q [ 1 z h ] | 2 = ( C 2 + C 3 ( r ¯ s ) Q [ 1 z r ] L [ r ¯ r z r ] + C 3 * ( r ¯ s ) Q [ 1 z r ] L [ r ¯ r z r ] ) ,
f min f d 2 z h ,
H ( x o , y o ) = I s ( x s , y s , z s ) I h ( x o , y o ; x s , y s , z s ) d x s d y s d z s .
{ H 1 ( x , y ; t 1 ) = B + H f exp ( i α 1 ) + H f * exp ( i α 1 ) H 2 ( x , y ; t 2 ) = B + H f exp ( i α 2 ) + H f * exp ( i α 2 ) H 3 ( x , y ; t 3 ) = B + H f exp ( i α 3 ) + H f * exp ( i α 3 ) } ,
H f ( x , y ) = H 1 ( x , y ; t 1 ) [ exp ( i α 3 ) exp ( i α 2 ) ] + H 2 ( x , y ; t 2 ) [ exp ( i α 1 ) exp ( i α 3 ) ] + H 3 ( x , y ; t 3 ) [ exp ( i α 2 ) exp ( i α 1 ) ] .
A ˜ = ( A T A ) 1 A T .

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