Abstract

We analyze the optimization of low-flux coherent active imagery systems for target detection. We demonstrate that, unlike the Fisher ratio, the Bhattacharyya distance is an efficient figure of merit when one uses detection algorithms based on the generalized likelihood ratio test for realistic situations when the target and the background mean values are unknown. For example, we show that detection capabilities can be better if the pulse energy is divided into four shots, whereas using more than ten shots does not significantly improve the results.

© 2003 Optical Society of America

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References

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  1. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), pp. 347–356.
  2. J. W. Goodman, Proc. IEEE 53, 1688 (1965).
    [CrossRef]
  3. H. V. Poor, An Introduction to Signal Detection and Estimation (Springer-Verlag, New York, 1994), pp. 5–39.
    [CrossRef]
  4. V. Pagé, F. Goudail, and Ph. Réfrégier, Opt. Lett. 24, 1383 (1999).
    [CrossRef]
  5. T. S. Ferguson, Mathematical Statistics, A Decision Theoretic Approach (Academic, New York, 1967), pp. 125–132.
  6. R. O. Duda and P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).
  7. T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley Interscience, New York, 1991).
    [CrossRef]
  8. H. H. Barrett, C. K. Abbey, and E. Clarkson, J. Opt. Soc. Am. A 15, 1520 (1998).
    [CrossRef]

1999 (1)

1998 (1)

1965 (1)

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

Abbey, C. K.

Barrett, H. H.

Clarkson, E.

Cover, T. M.

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley Interscience, New York, 1991).
[CrossRef]

Duda, R. O.

R. O. Duda and P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).

Ferguson, T. S.

T. S. Ferguson, Mathematical Statistics, A Decision Theoretic Approach (Academic, New York, 1967), pp. 125–132.

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.

Hart, P. E.

R. O. Duda and P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).

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.

Thomas, J. A.

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley Interscience, New York, 1991).
[CrossRef]

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

Opt. Lett. (1)

Proc. IEEE (1)

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

Other (5)

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

T. S. Ferguson, Mathematical Statistics, A Decision Theoretic Approach (Academic, New York, 1967), pp. 125–132.

R. O. Duda and P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley Interscience, New York, 1991).
[CrossRef]

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

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Figures (3)

Fig. 1
Fig. 1

AUC obtained from the GLRT in Eq. (4) as a function of the Fisher ratio for several values of λa, λb, and L and for two combinations of the target pixel number, Na, and the background pixel number, Nb, Na=1,Nb=16 and Na=4,Nb=36. Each ROC has been estimated from 104 random experiments.

Fig. 2
Fig. 2

AUC obtained from the GLRT in Eq. (4) as a function of the Bhattacharyya distance for the same parameter combinations as in Fig. 1. Inset, AUC obtained with the GLRT as a function of the Bhattacharyya distance for several values of the ratio Na/Nb; solid curve, approximation of the AUC of the ideal observer [relation (6)].

Fig. 3
Fig. 3

Contrast ratio λa/λb required for obtaining a Bhattacharyya distance of 1.2 as a function of L for several values of background photon flux λb. The target size is Na=4.

Equations (11)

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pn=0Ppoisson(n|I)PspeckleIdI,
PspeckleI=LμLIL-1ΓLexp-LμI, I>0,
pλn=ΓL+nΓLΓn+111+Lλn11+λLL,
L=iWlogpλani+iW¯logpλbni
=-iFlogpλbni.
lGLRT=Nafλaˆ+Nbfλbˆ-Ncfλcˆ,
fx=x ln x-L+xlnL+x.
AUC½+½ erf2dB,
dB=-Na lnn=0pλanpλbn1/2.
dB=NaL ln1+λa/L1/21+λb/L1/2-λa/L1/2λb/L1/2.
AUCHNa/NbdB.

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