Abstract

We analyze photon-noise effects on target detection performance in low-flux coherent active imagery systems. We show that when photon noise is expected, the performance of classical detection techniques designed for pure and fully developed speckle images can be improved with no increase in algorithm complexity. Furthermore, the mean photon number under which photon noise becomes sensitive is higher when the target and background mean values are unknown than in the idealized case, where they are assumed to be known, and when the reflectivity ratio between the target and the background is low.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), pp. 347–356.
  2. F. Goudail, N. Roux, and Ph. Réfrégier, Opt. Lett. 28, 81 (2003).
    [CrossRef] [PubMed]
  3. J. W. Goodman, Proc. IEEE 53, 1688 (1965).
    [CrossRef]
  4. H. V. Poor, An Introduction to Signal Detection and Estimation (Springer-Verlag, New York, 1994), pp. 5–39.
    [CrossRef]
  5. V. Pagé, F. Goudail, and Ph. Réfrégier, Opt. Lett. 24, 1383 (1999).
    [CrossRef]
  6. H. H. Barrett, C. K. Abbey, and E. Clarkson, J. Opt. Soc. Am. A 15, 1520 (1998).
    [CrossRef]
  7. C. J. Oliver, D. Blacknell, and R. G. White, IEEE Proc. Radar Sonar Navigat. 143, 31 (1996).
    [CrossRef]

2003 (1)

1999 (1)

1998 (1)

1996 (1)

C. J. Oliver, D. Blacknell, and R. G. White, IEEE Proc. Radar Sonar Navigat. 143, 31 (1996).
[CrossRef]

1965 (1)

J. W. Goodman, Proc. IEEE 53, 1688 (1965).
[CrossRef]

Abbey, C. K.

Barrett, H. H.

Blacknell, D.

C. J. Oliver, D. Blacknell, and R. G. White, IEEE Proc. Radar Sonar Navigat. 143, 31 (1996).
[CrossRef]

Clarkson, E.

Goodman, J. W.

J. W. Goodman, Proc. IEEE 53, 1688 (1965).
[CrossRef]

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), pp. 347–356.

Goudail, F.

Oliver, C. J.

C. J. Oliver, D. Blacknell, and R. G. White, IEEE Proc. Radar Sonar Navigat. 143, 31 (1996).
[CrossRef]

Pagé, V.

Poor, H. V.

H. V. Poor, An Introduction to Signal Detection and Estimation (Springer-Verlag, New York, 1994), pp. 5–39.
[CrossRef]

Réfrégier, Ph.

Roux, N.

White, R. G.

C. J. Oliver, D. Blacknell, and R. G. White, IEEE Proc. Radar Sonar Navigat. 143, 31 (1996).
[CrossRef]

IEEE Proc. Radar Sonar Navigat. (1)

C. J. Oliver, D. Blacknell, and R. G. White, IEEE Proc. Radar Sonar Navigat. 143, 31 (1996).
[CrossRef]

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

Opt. Lett. (2)

Proc. IEEE (1)

J. W. Goodman, Proc. IEEE 53, 1688 (1965).
[CrossRef]

Other (2)

H. V. Poor, An Introduction to Signal Detection and Estimation (Springer-Verlag, New York, 1994), pp. 5–39.
[CrossRef]

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), pp. 347–356.

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

AUC as a function of Bhattacharyya distance for the ideal observer and the GLRT lPHOT in the presence of speckle and photon noise. The curves correspond to expression (2) for the ideal observer and Eq. (5) for the GLRT (for two values of Na/Nb). The symbols fitted to each curve correspond to Monte Carlo simulations with three different target sizes Na=3,10,50, where each ROC was estimated from 104 random experiments.

Fig. 2
Fig. 2

AUC as a function of the mean flux I for the ideal observer and the GLRT for Na/Nb=1. The curves correspond to AUC obtained with expression (2) for the ideal observer and with Eq. (5) for the GLRT. The symbols fitted to each curve correspond to Monte Carlo simulations from 104 random experiments: r=λa/λb=2 ×, and 5 +,*.

Fig. 3
Fig. 3

Mean flux Ic required for an AUC equal to α times the AUC without the photon-noise effect for two values of α, 0.999 and 0.99, as a function of reflectivity ratio r=λa/λb.

Fig. 4
Fig. 4

AUC as a function of mean flux I for the detector adapted to pure speckle lSPEC, with Na/Nb=1, r=2+, and r=5×. Each ROC was estimated from 104 random experiments. The solid and dashed curves were obtained with Eq. (5) and correspond to the performance obtained with the detector adapted to speckle with photon noise lPHOT (see Fig. 2). The dashed–dotted (dashed) lines represent the AUC obtained when lSPEC lPHOT is applied to pure fully developed speckle noise.

Equations (7)

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

pλn=11+λλ1+λ2,
AUCHIOdB=12+12erf2dB,
dB=Na ln1+λa1+λb-λaλb.
lPHOT=Nafλaˆ+Nbfλbˆ-Na+Nbfλcˆ,
HudB=1-12exp-budBβu
Ic=4r-ρα,r21+r28rρα,r-1,
lSPEC=-Na logλaˆ-Nb logλbˆ+Na+Nblogλcˆ,

Metrics