Abstract

We propose a generalized framework for single-shot acquisition of multidimensional objects using compressive Fresnel holography. A multidimensional object with spatial, spectral, and polarimetric information is propagated with the Fresnel diffraction, and the propagated signal of each channel is observed by an image sensor with randomly arranged optical elements for filtering. The object data are reconstructed using a compressive sensing algorithm. This scheme is verified with numerical experiments. The proposed framework can be applied to imageries for spectrum, polarization, and so on.

© 2012 Optical Society of America

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References

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  1. D. L. Donoho, IEEE Trans. Inf. Theory 52, 1289 (2006).
    [CrossRef]
  2. J. W. Goodman and R. W. Lawrence, Appl. Phys. Lett. 11, 77 (1967).
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  5. P. Ferraro, S. D. Nicola, G. Coppola, A. Finizio, D. Alfieri, and G. Pierattini, Opt. Lett. 29, 854 (2004).
    [CrossRef]
  6. C. Fournier, L. Denis, and T. Fournel, J. Opt. Soc. Am. A 27, 1856 (2010).
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  8. Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, Proc. IEEE 94, 636 (2006).
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  9. P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, Opt. Lett. 30, 468 (2005).
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  12. D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, Opt. Express 17, 13040 (2009).
    [CrossRef]
  13. Y. Rivenson and A. Stern, IEEE Signal Process. Lett. 16, 449 (2009).
    [CrossRef]
  14. J. M. Bioucas-Dias and M. A. T. Figueiredo, IEEE Trans. Image Process. 16, 2992 (2007).
    [CrossRef]
  15. L. I. Rudin, S. Osher, and E. Fatemi, Phys. D 60, 259 (1992).
    [CrossRef]
  16. Y. Rivenson and A. Stern, Opt. Lett. 36, 3365 (2011).
    [CrossRef]
  17. A. Mahalanobis and R. Muise, IEEE Trans. Aerosp. Electron. Syst. 45, 1167 (2009).
    [CrossRef]
  18. O. Matoba and B. Javidi, Opt. Lett. 24, 762 (1999).
    [CrossRef]

2011 (1)

2010 (2)

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

C. Fournier, L. Denis, and T. Fournel, J. Opt. Soc. Am. A 27, 1856 (2010).
[CrossRef]

2009 (4)

L. Granero, V. Micó, Z. Zalevsky, and J. García, Opt. Express 17, 15008 (2009).
[CrossRef]

D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, Opt. Express 17, 13040 (2009).
[CrossRef]

Y. Rivenson and A. Stern, IEEE Signal Process. Lett. 16, 449 (2009).
[CrossRef]

A. Mahalanobis and R. Muise, IEEE Trans. Aerosp. Electron. Syst. 45, 1167 (2009).
[CrossRef]

2007 (1)

J. M. Bioucas-Dias and M. A. T. Figueiredo, IEEE Trans. Image Process. 16, 2992 (2007).
[CrossRef]

2006 (2)

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, Proc. IEEE 94, 636 (2006).
[CrossRef]

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

2005 (1)

2004 (2)

1999 (1)

1992 (1)

L. I. Rudin, S. Osher, and E. Fatemi, Phys. D 60, 259 (1992).
[CrossRef]

1967 (1)

J. W. Goodman and R. W. Lawrence, Appl. Phys. Lett. 11, 77 (1967).
[CrossRef]

Alfieri, D.

Bioucas-Dias, J. M.

J. M. Bioucas-Dias and M. A. T. Figueiredo, IEEE Trans. Image Process. 16, 2992 (2007).
[CrossRef]

Brady, D. J.

Choi, K.

Colomb, T.

Coppola, G.

Cuche, E.

Denis, L.

Depeursinge, C.

Donoho, D. L.

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

Emery, Y.

Fatemi, E.

L. I. Rudin, S. Osher, and E. Fatemi, Phys. D 60, 259 (1992).
[CrossRef]

Ferraro, P.

Figueiredo, M. A. T.

J. M. Bioucas-Dias and M. A. T. Figueiredo, IEEE Trans. Image Process. 16, 2992 (2007).
[CrossRef]

Finizio, A.

Fournel, T.

Fournier, C.

Frauel, Y.

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, Proc. IEEE 94, 636 (2006).
[CrossRef]

García, J.

Goodman, J. W.

J. W. Goodman and R. W. Lawrence, Appl. Phys. Lett. 11, 77 (1967).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Granero, L.

Horisaki, R.

Javidi, B.

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

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, Proc. IEEE 94, 636 (2006).
[CrossRef]

O. Matoba and B. Javidi, Opt. Lett. 24, 762 (1999).
[CrossRef]

Jueptner, W.

U. Schnars and W. Jueptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2005).

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, Appl. Phys. Lett. 11, 77 (1967).
[CrossRef]

Lim, S.

Magistretti, P. J.

Mahalanobis, A.

A. Mahalanobis and R. Muise, IEEE Trans. Aerosp. Electron. Syst. 45, 1167 (2009).
[CrossRef]

Marks, D. L.

Marquet, P.

Matoba, O.

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, Proc. IEEE 94, 636 (2006).
[CrossRef]

O. Matoba and B. Javidi, Opt. Lett. 24, 762 (1999).
[CrossRef]

Micó, V.

Muise, R.

A. Mahalanobis and R. Muise, IEEE Trans. Aerosp. Electron. Syst. 45, 1167 (2009).
[CrossRef]

Naughton, T.

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, Proc. IEEE 94, 636 (2006).
[CrossRef]

Nicola, S. D.

Osher, S.

L. I. Rudin, S. Osher, and E. Fatemi, Phys. D 60, 259 (1992).
[CrossRef]

Osten, W.

Pedrini, G.

Pierattini, G.

Rappaz, B.

Rivenson, Y.

Y. Rivenson and A. Stern, Opt. Lett. 36, 3365 (2011).
[CrossRef]

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

Y. Rivenson and A. Stern, IEEE Signal Process. Lett. 16, 449 (2009).
[CrossRef]

Rudin, L. I.

L. I. Rudin, S. Osher, and E. Fatemi, Phys. D 60, 259 (1992).
[CrossRef]

Schnars, U.

U. Schnars and W. Jueptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2005).

Stern, A.

Y. Rivenson and A. Stern, Opt. Lett. 36, 3365 (2011).
[CrossRef]

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

Y. Rivenson and A. Stern, IEEE Signal Process. Lett. 16, 449 (2009).
[CrossRef]

Tahajuerce, E.

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, Proc. IEEE 94, 636 (2006).
[CrossRef]

Tiziani, H. J.

Zalevsky, Z.

Zhang, Y.

Appl. Phys. Lett. (1)

J. W. Goodman and R. W. Lawrence, Appl. Phys. Lett. 11, 77 (1967).
[CrossRef]

IEEE Signal Process. Lett. (1)

Y. Rivenson and A. Stern, IEEE Signal Process. Lett. 16, 449 (2009).
[CrossRef]

IEEE Trans. Aerosp. Electron. Syst. (1)

A. Mahalanobis and R. Muise, IEEE Trans. Aerosp. Electron. Syst. 45, 1167 (2009).
[CrossRef]

IEEE Trans. Image Process. (1)

J. M. Bioucas-Dias and M. A. T. Figueiredo, IEEE Trans. Image Process. 16, 2992 (2007).
[CrossRef]

IEEE Trans. Inf. Theory (1)

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

J. Disp. Technol. (1)

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

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

Opt. Express (2)

Opt. Lett. (5)

Phys. D (1)

L. I. Rudin, S. Osher, and E. Fatemi, Phys. D 60, 259 (1992).
[CrossRef]

Proc. IEEE (1)

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, Proc. IEEE 94, 636 (2006).
[CrossRef]

Other (2)

U. Schnars and W. Jueptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2005).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

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Figures (4)

Fig. 1.
Fig. 1.

Multidimensional imaging using CFH.

Fig. 2.
Fig. 2.

Simulation with an object with five channels: (a) object, (b) filter pattern, (c) captured image, and the reconstructed result (d) without and (e) with the regularization.

Fig. 3.
Fig. 3.

(a)–(c), (f) Simulation with an object with ten channels: (a) object, (b) representative filter pattern of one channel, (c) captured image, and (f) reconstructed result. (d),(e),(g) Simulation with filters passing multiple channels: (d) representative filter pattern of one channel, (e) captured image, and (g) reconstructed result.

Fig. 4.
Fig. 4.

Simulation with an object with RGB channels at three distances: (a) object, (b) filter pattern, (c) captured image, and (d) reconstructed result.

Tables (1)

Tables Icon

Table 1. Applications of the Proposed Scheme

Equations (6)

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G(u)=CQ(u,C)P(ux,z)F(x,z,C)dxdz,
g=Hf=QPf,
Q=[Q1Q2QNC],
P=[P000P000P],
P=[P1P2PNZ],
f^=argminfgHf2+τR(f),

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