Abstract

We consider the problem of representation of a finite-energy optical field, with a finite number of bits. The optical field is represented with a finite number of uniformly spaced finite-accuracy samples (there is a finite number of amplitude levels that can be reliably distinguished for each sample). The total number of bits required to encode all samples constitutes the cost of the representation. We investigate the optimal number and spacing of these samples under a total cost budget. Our framework reveals the trade-off between the number, spacing, and accuracy of the samples. When we vary the cost budget, we obtain trade-off curves between the representation error and the cost budget. We also discuss the effect of degree of coherence of the field.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Toraldo Di Francia, J. Opt. Soc. Am. 59, 799 (1969).
    [CrossRef]
  2. F. Gori and G. Guattari, J. Opt. Soc. Am. 61, 36 (1971).
    [CrossRef]
  3. M. J. Bastiaans, J. Opt. Soc. Am. A 3, 1243 (1986).
    [CrossRef]
  4. A. Lohmann, R. Dorsch, D. Mendlovic, Z. Zalevsky, and C. Ferreira, J. Opt. Soc. Am. A 13, 470 (1996).
    [CrossRef]
  5. F. T. Yu, Entropy and Information Optics (Marcel Dekker, 2000).
  6. A. Burvall, P. Martinsson, and A. T. Friberg, Opt. Lett. 32, 611 (2007).
    [CrossRef]
  7. J. J. Healy, B. M. Hennelly, and J. T. Sheridan, Opt. Lett. 33, 2599 (2008).
    [CrossRef]
  8. E. D. Micheli and G. A. Viano, J. Opt. Soc. Am. A 26, 1393 (2009).
    [CrossRef]
  9. A. Kumar, S. Prabhakar, P. Vaity, and R. P. Singh, Opt. Lett. 36, 1161 (2011).
    [CrossRef]
  10. H. M. Ozaktas, S. O. Arik, and T. Coşkun, Opt. Lett. 37, 103 (2012).
    [CrossRef]
  11. A. Özçelikkale, H. M. Ozaktas, and E. Arıkan, IEEE Trans. Signal Process. 58, 3607 (2010).
    [CrossRef]
  12. H. L. Van Trees, Detection, Estimation and Modulation Theory, Part I (Wiley, 2001).
  13. A. Starikov and E. Wolf, J. Opt. Soc. Am. A 72, 923 (1982).
    [CrossRef]
  14. A. T. Friberg and J. Turunen, J. Opt. Soc. Am. A 5, 713 (1988).
    [CrossRef]
  15. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ., 1995).

2012 (1)

2011 (1)

2010 (1)

A. Özçelikkale, H. M. Ozaktas, and E. Arıkan, IEEE Trans. Signal Process. 58, 3607 (2010).
[CrossRef]

2009 (1)

2008 (1)

2007 (1)

1996 (1)

1988 (1)

1986 (1)

1982 (1)

A. Starikov and E. Wolf, J. Opt. Soc. Am. A 72, 923 (1982).
[CrossRef]

1971 (1)

1969 (1)

Arik, S. O.

Arikan, E.

A. Özçelikkale, H. M. Ozaktas, and E. Arıkan, IEEE Trans. Signal Process. 58, 3607 (2010).
[CrossRef]

Bastiaans, M. J.

Burvall, A.

Coskun, T.

Dorsch, R.

Ferreira, C.

Friberg, A. T.

Gori, F.

Guattari, G.

Healy, J. J.

Hennelly, B. M.

Kumar, A.

Lohmann, A.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ., 1995).

Martinsson, P.

Mendlovic, D.

Micheli, E. D.

Ozaktas, H. M.

H. M. Ozaktas, S. O. Arik, and T. Coşkun, Opt. Lett. 37, 103 (2012).
[CrossRef]

A. Özçelikkale, H. M. Ozaktas, and E. Arıkan, IEEE Trans. Signal Process. 58, 3607 (2010).
[CrossRef]

Özçelikkale, A.

A. Özçelikkale, H. M. Ozaktas, and E. Arıkan, IEEE Trans. Signal Process. 58, 3607 (2010).
[CrossRef]

Prabhakar, S.

Sheridan, J. T.

Singh, R. P.

Starikov, A.

A. Starikov and E. Wolf, J. Opt. Soc. Am. A 72, 923 (1982).
[CrossRef]

Toraldo Di Francia, G.

Turunen, J.

Vaity, P.

Van Trees, H. L.

H. L. Van Trees, Detection, Estimation and Modulation Theory, Part I (Wiley, 2001).

Viano, G. A.

Wolf, E.

A. Starikov and E. Wolf, J. Opt. Soc. Am. A 72, 923 (1982).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ., 1995).

Yu, F. T.

F. T. Yu, Entropy and Information Optics (Marcel Dekker, 2000).

Zalevsky, Z.

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 (3)

Fig. 1.
Fig. 1.

Error versus cost budget CB (varying β).

Fig. 2.
Fig. 2.

Optimum sampling interval versus number of samples for different cost budgets CB=Ci, β=1/16.

Fig. 3.
Fig. 3.

Optimum sampling interval versus number of samples for different cost budgets CB=Ci, β=1.

Equations (3)

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

si=f(ξi)+mi,
ε(CB)=minΔx,x0,ME[Df(x)f^(xs)2dx],
Kf(x1,x2)=Afexp(x12+x224σI2)exp((x1x2)22σν2).

Metrics