Abstract

Efficient storage and transmission of digital holograms (DHs) requires the development of appropriate compression techniques for such a special class of images. In this Letter, we investigate a method to compress DHs using a sparse matrix representation. Using digital holography to numerically manage complex wave fields, we are able to apply an adaptive mask, based on a threshold filter, to the object wave field. From there, we store the result of this filtering by sparse representation. In this Letter, we demonstrate that using sparse representation allows for a high compres sion factor with minimal loss in the quality of the reconstructed image. This technique is efficient for storage and transmission of DHs.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. W. Goodman and R. W. Lawrence, Appl. Phys. Lett. 11, 77 (1967).
    [CrossRef]
  2. M. A. Kronod, N. S. Merzlyakov, and L. P. Yaroslavskii, Sov. Phys. Tech. Phys. 17, 333 (1972).
  3. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, Appl. Opt. 13, 2693 (1974).
    [CrossRef] [PubMed]
  4. L. Onural and P. D. Scott, Opt. Eng. 26, 1124 (1987).
  5. U. Schnars and W. P. O. Jüptner, Appl. Opt. 33, 179 (1994).
    [CrossRef] [PubMed]
  6. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  7. I. Yamaguchi and T. Zhang, Opt. Lett. 22, 1268 (1997).
    [CrossRef] [PubMed]
  8. E. Cuche, F. Bevilacqua, and C. Depeursinge, Opt. Lett. 24, 291 (1999).
    [CrossRef]
  9. A. Shortt, T. J. Naughton, and B. Javidi, Opt. Express 14, 2625 (2006).
    [CrossRef] [PubMed]
  10. T. J. Naughton, Y. Frauel, B. Javidi, and E. Tajahuerce, Appl. Opt. 41, 4124 (2002).
    [CrossRef] [PubMed]
  11. T. J. Naughton, J. B. McDonald, and B. Javidi, Appl. Opt. 42, 4758 (2003).
    [CrossRef] [PubMed]
  12. E. Darakis and J. J. Soraghan, Appl. Opt. 46, 351 (2007).
    [CrossRef] [PubMed]
  13. Md. M. Hossain, D. S. Mehta, and C. Shakher, Opt. Laser Technol. 40, 120 (2008).
    [CrossRef]
  14. J. Widjaja, Opt. Lasers Eng. 44, 1239 (2006).
    [CrossRef]
  15. A. Shortt, T. J. Naughton, and B. Javidi, J. Display Technol. 2, 401 (2006).
    [CrossRef]
  16. T. Colomb, F. Dürr, E. Cuche, P. Marquet, H. G. Limberger, R.-P. Salathé, and C. Depeursinge, Appl. Opt. 44, 4461 (2005).
    [CrossRef] [PubMed]
  17. P. Picart, E. Moisson, and D. Mounier, Appl. Opt. 42, 1947 (2003).
    [CrossRef] [PubMed]
  18. M. Paturzo, P. Memmolo, A. Tulino, A. Finizio, and P. Ferraro, Opt. Express 17, 8709 (2009).
    [CrossRef] [PubMed]
  19. M. Paturzo, P. Memmolo, L. Miccio, A. Finizio, P. Ferraro, A. Tulino, and B. Javidi, Opt. Lett. 33, 2629 (2008).
    [CrossRef] [PubMed]
  20. Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, Proc. IEEE 94, 636 (2006).
    [CrossRef]
  21. G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins, 1996).
  22. J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, 3rd ed. (Springer-Verlag, 2002).
  23. G. Coppola, V. Striano, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and P. Maccagnani, J. Microelectromech. Syst. 16, 659 (2007).
    [CrossRef]
  24. P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and G. Coppola, Appl. Phys. Lett. 85, 2709 (2004).
    [CrossRef]

2009 (1)

2008 (2)

2007 (2)

G. Coppola, V. Striano, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and P. Maccagnani, J. Microelectromech. Syst. 16, 659 (2007).
[CrossRef]

E. Darakis and J. J. Soraghan, Appl. Opt. 46, 351 (2007).
[CrossRef] [PubMed]

2006 (4)

J. Widjaja, Opt. Lasers Eng. 44, 1239 (2006).
[CrossRef]

A. Shortt, T. J. Naughton, and B. Javidi, J. Display Technol. 2, 401 (2006).
[CrossRef]

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

A. Shortt, T. J. Naughton, and B. Javidi, Opt. Express 14, 2625 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (1)

P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and G. Coppola, Appl. Phys. Lett. 85, 2709 (2004).
[CrossRef]

2003 (2)

2002 (1)

1999 (1)

1997 (1)

1994 (1)

1987 (1)

L. Onural and P. D. Scott, Opt. Eng. 26, 1124 (1987).

1974 (1)

1972 (1)

M. A. Kronod, N. S. Merzlyakov, and L. P. Yaroslavskii, Sov. Phys. Tech. Phys. 17, 333 (1972).

1967 (1)

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

Bevilacqua, F.

Brangaccio, D. J.

Bruning, J. H.

Bulirsch, R.

J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, 3rd ed. (Springer-Verlag, 2002).

Colomb, T.

Coppola, G.

G. Coppola, V. Striano, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and P. Maccagnani, J. Microelectromech. Syst. 16, 659 (2007).
[CrossRef]

P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and G. Coppola, Appl. Phys. Lett. 85, 2709 (2004).
[CrossRef]

Cuche, E.

Darakis, E.

De Nicola, S.

G. Coppola, V. Striano, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and P. Maccagnani, J. Microelectromech. Syst. 16, 659 (2007).
[CrossRef]

P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and G. Coppola, Appl. Phys. Lett. 85, 2709 (2004).
[CrossRef]

Depeursinge, C.

Dürr, F.

Ferraro, P.

M. Paturzo, P. Memmolo, A. Tulino, A. Finizio, and P. Ferraro, Opt. Express 17, 8709 (2009).
[CrossRef] [PubMed]

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

G. Coppola, V. Striano, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and P. Maccagnani, J. Microelectromech. Syst. 16, 659 (2007).
[CrossRef]

P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and G. Coppola, Appl. Phys. Lett. 85, 2709 (2004).
[CrossRef]

Finizio, A.

M. Paturzo, P. Memmolo, A. Tulino, A. Finizio, and P. Ferraro, Opt. Express 17, 8709 (2009).
[CrossRef] [PubMed]

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

G. Coppola, V. Striano, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and P. Maccagnani, J. Microelectromech. Syst. 16, 659 (2007).
[CrossRef]

P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and G. Coppola, Appl. Phys. Lett. 85, 2709 (2004).
[CrossRef]

Frauel, Y.

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

T. J. Naughton, Y. Frauel, B. Javidi, and E. Tajahuerce, Appl. Opt. 41, 4124 (2002).
[CrossRef] [PubMed]

Gallagher, J. E.

Golub, G. H.

G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins, 1996).

Goodman, J. W.

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

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Herriott, D. R.

Hossain, Md. M.

Md. M. Hossain, D. S. Mehta, and C. Shakher, Opt. Laser Technol. 40, 120 (2008).
[CrossRef]

Javidi, B.

Jüptner, W. P. O.

Kronod, M. A.

M. A. Kronod, N. S. Merzlyakov, and L. P. Yaroslavskii, Sov. Phys. Tech. Phys. 17, 333 (1972).

Lawrence, R. W.

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

Limberger, H. G.

Maccagnani, P.

G. Coppola, V. Striano, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and P. Maccagnani, J. Microelectromech. Syst. 16, 659 (2007).
[CrossRef]

Marquet, P.

Matoba, O.

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

McDonald, J. B.

Mehta, D. S.

Md. M. Hossain, D. S. Mehta, and C. Shakher, Opt. Laser Technol. 40, 120 (2008).
[CrossRef]

Memmolo, P.

Merzlyakov, N. S.

M. A. Kronod, N. S. Merzlyakov, and L. P. Yaroslavskii, Sov. Phys. Tech. Phys. 17, 333 (1972).

Miccio, L.

Moisson, E.

Mounier, D.

Naughton, T.

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

Naughton, T. J.

Onural, L.

L. Onural and P. D. Scott, Opt. Eng. 26, 1124 (1987).

Paturzo, M.

Picart, P.

Pierattini, G.

G. Coppola, V. Striano, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and P. Maccagnani, J. Microelectromech. Syst. 16, 659 (2007).
[CrossRef]

P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and G. Coppola, Appl. Phys. Lett. 85, 2709 (2004).
[CrossRef]

Rosenfeld, D. P.

Salathé, R.-P.

Schnars, U.

Scott, P. D.

L. Onural and P. D. Scott, Opt. Eng. 26, 1124 (1987).

Shakher, C.

Md. M. Hossain, D. S. Mehta, and C. Shakher, Opt. Laser Technol. 40, 120 (2008).
[CrossRef]

Shortt, A.

Soraghan, J. J.

Stoer, J.

J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, 3rd ed. (Springer-Verlag, 2002).

Striano, V.

G. Coppola, V. Striano, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and P. Maccagnani, J. Microelectromech. Syst. 16, 659 (2007).
[CrossRef]

Tahajuerce, E.

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

Tajahuerce, E.

Tulino, A.

Van Loan, C. F.

G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins, 1996).

White, A. D.

Widjaja, J.

J. Widjaja, Opt. Lasers Eng. 44, 1239 (2006).
[CrossRef]

Yamaguchi, I.

Yaroslavskii, L. P.

M. A. Kronod, N. S. Merzlyakov, and L. P. Yaroslavskii, Sov. Phys. Tech. Phys. 17, 333 (1972).

Zhang, T.

Appl. Opt. (7)

Appl. Phys. Lett. (2)

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

P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and G. Coppola, Appl. Phys. Lett. 85, 2709 (2004).
[CrossRef]

J. Display Technol. (1)

J. Microelectromech. Syst. (1)

G. Coppola, V. Striano, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and P. Maccagnani, J. Microelectromech. Syst. 16, 659 (2007).
[CrossRef]

Opt. Eng. (1)

L. Onural and P. D. Scott, Opt. Eng. 26, 1124 (1987).

Opt. Express (2)

Opt. Laser Technol. (1)

Md. M. Hossain, D. S. Mehta, and C. Shakher, Opt. Laser Technol. 40, 120 (2008).
[CrossRef]

Opt. Lasers Eng. (1)

J. Widjaja, Opt. Lasers Eng. 44, 1239 (2006).
[CrossRef]

Opt. Lett. (3)

Proc. IEEE (1)

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

Sov. Phys. Tech. Phys. (1)

M. A. Kronod, N. S. Merzlyakov, and L. P. Yaroslavskii, Sov. Phys. Tech. Phys. 17, 333 (1972).

Other (3)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins, 1996).

J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, 3rd ed. (Springer-Verlag, 2002).

Supplementary Material (1)

» Media 1: MOV (2319 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

(a) Plot of K versus the threshold value S; (b) plot of the compression factor 1 / K versus the threshold S; (c) plot of the correlation coefficient η versus the threshold S.

Fig. 2
Fig. 2

(a) Microheater hologram and (b) its amplitude reconstruction in the BFP; inset, the profile of object spectrum: the variable threshold level is indicated.

Fig. 3
Fig. 3

Amplitude reconstruction of the hologram in the BFP, for a threshold value (a) S = 0 (Media 1), (b) S = M * 0.11 , (c) S = M * 0.17 , and (d) M = S * 0.29 .

Fig. 4
Fig. 4

Reconstructed images in the in-focus image plane obtained by the filtered spectrum using threshold value (a) S = 0 (Media 1), (b) S = M * 0.11 , (c) S = M * 0.17 , and (d) M = S * 0.29 .

Tables (1)

Tables Icon

Table 1 Performance of Compression Algorithm

Equations (5)

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

M ( ν x , ν y ) = { 1 | O ( ν x , ν y ) | S 0 otherwise ,
O ^ = O M ,
O ^ O ^ s , r , c ,
K = 3 N n m .
C = corr ( | O | , | O ^ | ) = ( 1 η η 1 ) .

Metrics