Abstract

Several automatic approaches have been proposed in the past to compute the refocus distance in digital holography (DH). However most of them are based on a maximization or minimization of a suitable amplitude image contrast measure, regarded as a function of the reconstruction distance parameter. Here we show that, by using the sparsity measure coefficient regarded as a refocusing criterion in the holographic reconstruction, it is possible to recover the focus plane and, at the same time, establish the degree of sparsity of digital holograms, when samples of the diffraction Fresnel propagation integral are used as a sparse signal representation. We employ a sparsity measurement coefficient known as Gini’s index thus showing for the first time, to the best of our knowledge, its application in DH, as an effective refocusing criterion. Demonstration is provided for different holographic configurations (i.e., lens and lensless apparatus) and for completely different objects (i.e., a thin pure phase microscopic object as an in vitro cell, and macroscopic puppets) preparation.

© 2014 Optical Society of America

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References

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  1. M. U. Schnars and W. Juptner, Appl. Opt. 33, 179 (1994).
    [CrossRef]
  2. L. Miccio, P. Memmolo, F. Merola, S. Fusco, V. Embrione, A. Paciello, M. Ventre, P. A. Netti, and P. Ferraro, Lab Chip 14, 1129 (2014).
    [CrossRef]
  3. P. Memmolo, M. Iannone, M. Ventre, P. A. Netti, A. Finizio, M. Paturzo, and P. Ferraro, Opt. Express 20, 28485 (2012).
    [CrossRef]
  4. T. W. Sua, L. Xuea, and A. Ozcan, Proc. Natl. Acad. Sci. 109, 16018 (2012).
  5. M. Paturzo, P. Memmolo, A. Finizio, R. Nsnen, T. J. Naughton, and P. Ferraro, Opt. Express 18, 8806 (2010).
    [CrossRef]
  6. Y. S. Kim, T. Kim, S. S. Woo, H. Kang, T. C. Poon, and C. Zhou, Opt. Express 21, 8183 (2013).
    [CrossRef]
  7. M. Paturzo, A. Finizio, P. Memmolo, R. Puglisi, D. Balduzzi, A. Galli, and P. Ferraro, Lab Chip 12, 3073 (2012).
    [CrossRef]
  8. F. Merola, L. Miccio, P. Memmolo, G. Di Caprio, A. Galli, R. Puglisi, D. Balduzzi, G. Coppola, P. A. Netti, and P. Ferraro, Lab Chip 13, 4512 (2013).
    [CrossRef]
  9. Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, Nat. Photonics 7, 113 (2013).
    [CrossRef]
  10. P. Memmolo, C. Distante, M. Paturzo, A. Finizio, P. Ferraro, and B. Javidi, Opt. Lett. 36, 1945 (2011).
    [CrossRef]
  11. T. Kim and T. C. Poon, Appl. Opt. 48, H153 (2009).
    [CrossRef]
  12. M. Liebling and M. Unser, J. Opt. Soc. Am. A 21, 2424 (2004).
    [CrossRef]
  13. C. A. Trujillo and J. Garcia-Sucerquia, Opt. Lett. 39, 2569 (2014).
    [CrossRef]
  14. M. F. Toy, J. Kühn, S. Richard, J. Parent, M. Egli, and C. Depeursinge, Opt. Lett. 37, 5094 (2012).
    [CrossRef]
  15. P. Gao, B. Yao, R. Rupp, J. Min, R. Guo, B. Ma, J. Zheng, M. Lei, S. Yan, D. Dan, and T. Ye, Opt. Lett. 37, 1172 (2012).
    [CrossRef]
  16. P. Gao, B. Yao, J. Min, R. Guo, B. Ma, J. Zheng, M. Lei, S. Yan, D. Dan, and T. Ye, Opt. Lett. 37, 3630 (2012).
    [CrossRef]
  17. P. Langehanenberg, B. Kemper, D. Dirksen, and G. von Bally, Appl. Opt. 47, D176 (2008).
    [CrossRef]
  18. F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, Opt. Express 14, 5895 (2006).
    [CrossRef]
  19. A. El Mallahi and F. Dubois, Opt. Express 19, 6684 (2011).
    [CrossRef]
  20. W. Li, N. C. Loomis, Q. Hu, and C. S. Davis, J. Opt. Soc. Am. A 24, 3054 (2007).
    [CrossRef]
  21. D. Zonoobi, A. A. Kassim, and Y. V. Venkatesh, IEEE J. Sel. Topics Signal Process. 5, 927 (2011).
  22. D. Donoho, IEEE Trans. Inf. Theory 52, 1289 (2006).
    [CrossRef]
  23. E. Candes, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 1289 (2006).
    [CrossRef]
  24. P. Memmolo, I. Esnaola, A. Finizio, M. Paturzo, P. Ferraro, and A. M. Tulino, Opt. Express 20, 17250 (2012).
    [CrossRef]
  25. D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, Opt. Express 17, 13040 (2009).
    [CrossRef]
  26. Y. Rivenson, A. Stern, and B. Javidi, J. Disp. Technol. 6, 506 (2010).
    [CrossRef]
  27. Y. Rivenson, A. Stern, and B. Javidi, Appl. Opt. 52, A423 (2013).
    [CrossRef]
  28. Y. Rivenson, A. Stern, J. Rosen, and B. Javidi, eds. Multi-Dimensional Imaging (Wiley, 2014).
  29. M. Paturzo, P. Memmolo, L. Miccio, A. Finizio, P. Ferraro, A. Tulino, and B. Javidi, Opt. Lett. 33, 2629 (2008).
    [CrossRef]
  30. M. Paturzo, P. Memmolo, A. Tulino, A. Finizio, and P. Ferraro, Opt. Express 17, 8709 (2009).
    [CrossRef]
  31. P. Memmolo, M. Paturzo, A. Pelagotti, A. Finizio, P. Ferraro, and B. Javidi, Opt. Lett. 35, 3883 (2010).
    [CrossRef]

2014

L. Miccio, P. Memmolo, F. Merola, S. Fusco, V. Embrione, A. Paciello, M. Ventre, P. A. Netti, and P. Ferraro, Lab Chip 14, 1129 (2014).
[CrossRef]

C. A. Trujillo and J. Garcia-Sucerquia, Opt. Lett. 39, 2569 (2014).
[CrossRef]

2013

Y. Rivenson, A. Stern, and B. Javidi, Appl. Opt. 52, A423 (2013).
[CrossRef]

Y. S. Kim, T. Kim, S. S. Woo, H. Kang, T. C. Poon, and C. Zhou, Opt. Express 21, 8183 (2013).
[CrossRef]

F. Merola, L. Miccio, P. Memmolo, G. Di Caprio, A. Galli, R. Puglisi, D. Balduzzi, G. Coppola, P. A. Netti, and P. Ferraro, Lab Chip 13, 4512 (2013).
[CrossRef]

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, Nat. Photonics 7, 113 (2013).
[CrossRef]

2012

2011

2010

2009

2008

2007

2006

F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, Opt. Express 14, 5895 (2006).
[CrossRef]

D. Donoho, IEEE Trans. Inf. Theory 52, 1289 (2006).
[CrossRef]

E. Candes, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 1289 (2006).
[CrossRef]

2004

1994

Balduzzi, D.

F. Merola, L. Miccio, P. Memmolo, G. Di Caprio, A. Galli, R. Puglisi, D. Balduzzi, G. Coppola, P. A. Netti, and P. Ferraro, Lab Chip 13, 4512 (2013).
[CrossRef]

M. Paturzo, A. Finizio, P. Memmolo, R. Puglisi, D. Balduzzi, A. Galli, and P. Ferraro, Lab Chip 12, 3073 (2012).
[CrossRef]

Boss, D.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, Nat. Photonics 7, 113 (2013).
[CrossRef]

Brady, D. J.

Callens, N.

Candes, E.

E. Candes, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 1289 (2006).
[CrossRef]

Choi, K.

Coppola, G.

F. Merola, L. Miccio, P. Memmolo, G. Di Caprio, A. Galli, R. Puglisi, D. Balduzzi, G. Coppola, P. A. Netti, and P. Ferraro, Lab Chip 13, 4512 (2013).
[CrossRef]

Cotte, Y.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, Nat. Photonics 7, 113 (2013).
[CrossRef]

Dan, D.

Davis, C. S.

Depeursinge, C.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, Nat. Photonics 7, 113 (2013).
[CrossRef]

M. F. Toy, J. Kühn, S. Richard, J. Parent, M. Egli, and C. Depeursinge, Opt. Lett. 37, 5094 (2012).
[CrossRef]

Di Caprio, G.

F. Merola, L. Miccio, P. Memmolo, G. Di Caprio, A. Galli, R. Puglisi, D. Balduzzi, G. Coppola, P. A. Netti, and P. Ferraro, Lab Chip 13, 4512 (2013).
[CrossRef]

Dirksen, D.

Distante, C.

Donoho, D.

D. Donoho, IEEE Trans. Inf. Theory 52, 1289 (2006).
[CrossRef]

Dubois, F.

Egli, M.

El Mallahi, A.

Embrione, V.

L. Miccio, P. Memmolo, F. Merola, S. Fusco, V. Embrione, A. Paciello, M. Ventre, P. A. Netti, and P. Ferraro, Lab Chip 14, 1129 (2014).
[CrossRef]

Esnaola, I.

Ferraro, P.

Finizio, A.

Fusco, S.

L. Miccio, P. Memmolo, F. Merola, S. Fusco, V. Embrione, A. Paciello, M. Ventre, P. A. Netti, and P. Ferraro, Lab Chip 14, 1129 (2014).
[CrossRef]

Galli, A.

F. Merola, L. Miccio, P. Memmolo, G. Di Caprio, A. Galli, R. Puglisi, D. Balduzzi, G. Coppola, P. A. Netti, and P. Ferraro, Lab Chip 13, 4512 (2013).
[CrossRef]

M. Paturzo, A. Finizio, P. Memmolo, R. Puglisi, D. Balduzzi, A. Galli, and P. Ferraro, Lab Chip 12, 3073 (2012).
[CrossRef]

Gao, P.

Garcia-Sucerquia, J.

Guo, R.

Horisaki, R.

Hu, Q.

Iannone, M.

Javidi, B.

Jourdain, P.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, Nat. Photonics 7, 113 (2013).
[CrossRef]

Juptner, W.

Kang, H.

Kassim, A. A.

D. Zonoobi, A. A. Kassim, and Y. V. Venkatesh, IEEE J. Sel. Topics Signal Process. 5, 927 (2011).

Kemper, B.

Kim, T.

Kim, Y. S.

Kühn, J.

Langehanenberg, P.

Lei, M.

Li, W.

Liebling, M.

Lim, S.

Loomis, N. C.

Ma, B.

Magistretti, P.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, Nat. Photonics 7, 113 (2013).
[CrossRef]

Marks, D. L.

Marquet, P.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, Nat. Photonics 7, 113 (2013).
[CrossRef]

Memmolo, P.

Merola, F.

L. Miccio, P. Memmolo, F. Merola, S. Fusco, V. Embrione, A. Paciello, M. Ventre, P. A. Netti, and P. Ferraro, Lab Chip 14, 1129 (2014).
[CrossRef]

F. Merola, L. Miccio, P. Memmolo, G. Di Caprio, A. Galli, R. Puglisi, D. Balduzzi, G. Coppola, P. A. Netti, and P. Ferraro, Lab Chip 13, 4512 (2013).
[CrossRef]

Miccio, L.

L. Miccio, P. Memmolo, F. Merola, S. Fusco, V. Embrione, A. Paciello, M. Ventre, P. A. Netti, and P. Ferraro, Lab Chip 14, 1129 (2014).
[CrossRef]

F. Merola, L. Miccio, P. Memmolo, G. Di Caprio, A. Galli, R. Puglisi, D. Balduzzi, G. Coppola, P. A. Netti, and P. Ferraro, Lab Chip 13, 4512 (2013).
[CrossRef]

M. Paturzo, P. Memmolo, L. Miccio, A. Finizio, P. Ferraro, A. Tulino, and B. Javidi, Opt. Lett. 33, 2629 (2008).
[CrossRef]

Min, J.

Naughton, T. J.

Netti, P. A.

L. Miccio, P. Memmolo, F. Merola, S. Fusco, V. Embrione, A. Paciello, M. Ventre, P. A. Netti, and P. Ferraro, Lab Chip 14, 1129 (2014).
[CrossRef]

F. Merola, L. Miccio, P. Memmolo, G. Di Caprio, A. Galli, R. Puglisi, D. Balduzzi, G. Coppola, P. A. Netti, and P. Ferraro, Lab Chip 13, 4512 (2013).
[CrossRef]

P. Memmolo, M. Iannone, M. Ventre, P. A. Netti, A. Finizio, M. Paturzo, and P. Ferraro, Opt. Express 20, 28485 (2012).
[CrossRef]

Nsnen, R.

Ozcan, A.

T. W. Sua, L. Xuea, and A. Ozcan, Proc. Natl. Acad. Sci. 109, 16018 (2012).

Paciello, A.

L. Miccio, P. Memmolo, F. Merola, S. Fusco, V. Embrione, A. Paciello, M. Ventre, P. A. Netti, and P. Ferraro, Lab Chip 14, 1129 (2014).
[CrossRef]

Parent, J.

Paturzo, M.

Pavillon, N.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, Nat. Photonics 7, 113 (2013).
[CrossRef]

Pelagotti, A.

Poon, T. C.

Puglisi, R.

F. Merola, L. Miccio, P. Memmolo, G. Di Caprio, A. Galli, R. Puglisi, D. Balduzzi, G. Coppola, P. A. Netti, and P. Ferraro, Lab Chip 13, 4512 (2013).
[CrossRef]

M. Paturzo, A. Finizio, P. Memmolo, R. Puglisi, D. Balduzzi, A. Galli, and P. Ferraro, Lab Chip 12, 3073 (2012).
[CrossRef]

Richard, S.

Rivenson, Y.

Y. Rivenson, A. Stern, and B. Javidi, Appl. Opt. 52, A423 (2013).
[CrossRef]

Y. Rivenson, A. Stern, and B. Javidi, J. Disp. Technol. 6, 506 (2010).
[CrossRef]

Romberg, J.

E. Candes, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 1289 (2006).
[CrossRef]

Rupp, R.

Schnars, M. U.

Schockaert, C.

Stern, A.

Y. Rivenson, A. Stern, and B. Javidi, Appl. Opt. 52, A423 (2013).
[CrossRef]

Y. Rivenson, A. Stern, and B. Javidi, J. Disp. Technol. 6, 506 (2010).
[CrossRef]

Sua, T. W.

T. W. Sua, L. Xuea, and A. Ozcan, Proc. Natl. Acad. Sci. 109, 16018 (2012).

Tao, T.

E. Candes, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 1289 (2006).
[CrossRef]

Toy, F.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, Nat. Photonics 7, 113 (2013).
[CrossRef]

Toy, M. F.

Trujillo, C. A.

Tulino, A.

Tulino, A. M.

Unser, M.

Venkatesh, Y. V.

D. Zonoobi, A. A. Kassim, and Y. V. Venkatesh, IEEE J. Sel. Topics Signal Process. 5, 927 (2011).

Ventre, M.

L. Miccio, P. Memmolo, F. Merola, S. Fusco, V. Embrione, A. Paciello, M. Ventre, P. A. Netti, and P. Ferraro, Lab Chip 14, 1129 (2014).
[CrossRef]

P. Memmolo, M. Iannone, M. Ventre, P. A. Netti, A. Finizio, M. Paturzo, and P. Ferraro, Opt. Express 20, 28485 (2012).
[CrossRef]

von Bally, G.

Woo, S. S.

Xuea, L.

T. W. Sua, L. Xuea, and A. Ozcan, Proc. Natl. Acad. Sci. 109, 16018 (2012).

Yan, S.

Yao, B.

Ye, T.

Yourassowsky, C.

Zheng, J.

Zhou, C.

Zonoobi, D.

D. Zonoobi, A. A. Kassim, and Y. V. Venkatesh, IEEE J. Sel. Topics Signal Process. 5, 927 (2011).

Appl. Opt.

IEEE J. Sel. Topics Signal Process.

D. Zonoobi, A. A. Kassim, and Y. V. Venkatesh, IEEE J. Sel. Topics Signal Process. 5, 927 (2011).

IEEE Trans. Inf. Theory

D. Donoho, IEEE Trans. Inf. Theory 52, 1289 (2006).
[CrossRef]

E. Candes, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 1289 (2006).
[CrossRef]

J. Disp. Technol.

Y. Rivenson, A. Stern, and B. Javidi, J. Disp. Technol. 6, 506 (2010).
[CrossRef]

J. Opt. Soc. Am. A

Lab Chip

L. Miccio, P. Memmolo, F. Merola, S. Fusco, V. Embrione, A. Paciello, M. Ventre, P. A. Netti, and P. Ferraro, Lab Chip 14, 1129 (2014).
[CrossRef]

M. Paturzo, A. Finizio, P. Memmolo, R. Puglisi, D. Balduzzi, A. Galli, and P. Ferraro, Lab Chip 12, 3073 (2012).
[CrossRef]

F. Merola, L. Miccio, P. Memmolo, G. Di Caprio, A. Galli, R. Puglisi, D. Balduzzi, G. Coppola, P. A. Netti, and P. Ferraro, Lab Chip 13, 4512 (2013).
[CrossRef]

Nat. Photonics

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, Nat. Photonics 7, 113 (2013).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. Natl. Acad. Sci.

T. W. Sua, L. Xuea, and A. Ozcan, Proc. Natl. Acad. Sci. 109, 16018 (2012).

Other

Y. Rivenson, A. Stern, J. Rosen, and B. Javidi, eds. Multi-Dimensional Imaging (Wiley, 2014).

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Figures (3)

Fig. 1.
Fig. 1.

Comparing GI, TC, and energy metrics for the astronaut’s hologram. In (a) we show the values assumed by the three metrics for different values of the reconstruction distance. The TC and the energy metrics are properly normalized to be compared with GI. In (b) and (c) we present the retrieved amplitude reconstruction, calculated at a distance corresponding to the extreme point of the GI, and the amplitude of the Fourier transform, respectively (see the dotted black circles).

Fig. 2.
Fig. 2.

Comparing GI, TC, and energy metrics for the hologram of a mouse’s cell. In (a) we show the values given by the three metrics for different values of reconstruction distance. In (b) we show the amplitude reconstruction, calculated at a distance corresponding to the extreme point of GI (black circles), while in (c) the corresponding phase reconstruction is reported.

Fig. 3.
Fig. 3.

Comparing among GI, TC, and energy metrics for the hologram of a mouse’s cell in the case of long reconstruction distances. In (a) we show the values given by the three metrics. In (b) we show the amplitude reconstruction calculated at a distance retrieved by the extreme point of GI (black circles), which in this case corresponds to the BFP of microscope objective, while in (c) we show the Fourier transform amplitude.

Equations (4)

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

C(x,y,δ)=1iλδH(ξ,η)R(ξ,η)×exp{i2πδλ[1+(xξ)2+(yη)22δ2]}dξdη,
A(δ)=|C(δ)|=|FT{H(ξ,η)exp{iπλδ(ξ2+η2)}}|
GI{c(δ)}=12k=1Na[k](δ)c(δ)1(Nk+0.5N),
|C|=limδA(δ)=|FT{H(ξ,η)}|.

Metrics