Abstract

Fisher-information-based optimization of a conventional phase diversity speckle imaging system is presented. I demonstrate how Fisher information can be used to determine the optimum value of defocus in the diversity channel for estimating the mid-frequency integrated object power spectrum. This approach is likely to be useful in optimizing the design and performance of a general imaging system.

© 2004 Optical Society of America

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References

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  1. R. A. Gonsalves, Opt. Eng. 21, 829 (1982).
    [Crossref]
  2. R. G. Paxman, T. J. Schulz, and J. R. Fienup, J. Opt. Soc. Am. A 9, 1072 (1992).
    [Crossref]
  3. C. R. Vogel, T. Chan, and R. J. Plemmons, Proc. SPIE 3353, 994 (1998).
    [Crossref]
  4. B. H. Dean and C. W. Bowers, J. Opt. Soc. Am. A 20, 1490 (2003).
    [Crossref]
  5. J. R. Fienup, J. C. Marron, T. J. Schulz, and J. H. Seldin, Appl. Opt. 32, 1747 (1993).
    [Crossref] [PubMed]
  6. D. J. Lee, M. C. Roggemann, and B. M. Welsh, J. Opt. Soc. Am. A 16, 1005 (1999).
    [Crossref]
  7. S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, Englewood Cliffs, N.J., 1993).
  8. S. Prasad, “Fisher information based analysis of a phase diversity speckle imaging system,” J. Opt. Soc. Am. A (to be published).
  9. M. C. Roggemann, Imaging Through Turbulence (CRC Press, Boca Raton, Fla., 1996).

2003 (1)

1999 (1)

1998 (1)

C. R. Vogel, T. Chan, and R. J. Plemmons, Proc. SPIE 3353, 994 (1998).
[Crossref]

1993 (1)

1992 (1)

1982 (1)

R. A. Gonsalves, Opt. Eng. 21, 829 (1982).
[Crossref]

Bowers, C. W.

Chan, T.

C. R. Vogel, T. Chan, and R. J. Plemmons, Proc. SPIE 3353, 994 (1998).
[Crossref]

Dean, B. H.

Fienup, J. R.

Gonsalves, R. A.

R. A. Gonsalves, Opt. Eng. 21, 829 (1982).
[Crossref]

Kay, S. M.

S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, Englewood Cliffs, N.J., 1993).

Lee, D. J.

Marron, J. C.

Paxman, R. G.

Plemmons, R. J.

C. R. Vogel, T. Chan, and R. J. Plemmons, Proc. SPIE 3353, 994 (1998).
[Crossref]

Prasad, S.

S. Prasad, “Fisher information based analysis of a phase diversity speckle imaging system,” J. Opt. Soc. Am. A (to be published).

Roggemann, M. C.

D. J. Lee, M. C. Roggemann, and B. M. Welsh, J. Opt. Soc. Am. A 16, 1005 (1999).
[Crossref]

M. C. Roggemann, Imaging Through Turbulence (CRC Press, Boca Raton, Fla., 1996).

Schulz, T. J.

Seldin, J. H.

Vogel, C. R.

C. R. Vogel, T. Chan, and R. J. Plemmons, Proc. SPIE 3353, 994 (1998).
[Crossref]

Welsh, B. M.

Appl. Opt. (1)

J. Opt. Soc. Am. A (3)

Opt. Eng. (1)

R. A. Gonsalves, Opt. Eng. 21, 829 (1982).
[Crossref]

Proc. SPIE (1)

C. R. Vogel, T. Chan, and R. J. Plemmons, Proc. SPIE 3353, 994 (1998).
[Crossref]

Other (3)

S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, Englewood Cliffs, N.J., 1993).

S. Prasad, “Fisher information based analysis of a phase diversity speckle imaging system,” J. Opt. Soc. Am. A (to be published).

M. C. Roggemann, Imaging Through Turbulence (CRC Press, Boca Raton, Fla., 1996).

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Figures (3)

Fig. 1
Fig. 1

Surface plot of joint FI.

Fig. 2
Fig. 2

Fractional integrated (a) FI increase and (b) CRLB reduction for three different dc SNR values of 10, 100, and 1000.

Fig. 3
Fig. 3

Fractional integrated (a) FI increase and (b) CRLB reduction for three different detector noise ratios of χ=0.1,1,10.

Equations (8)

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h˜iuh˜j*uc˜ijhuδ2u-u,    i,j=0,1.
c˜00huηr04λFD2h˜diffu,
g˜iu=f˜uh˜iu+n˜iu.
J0,1f˜u1,f˜u2δ ln P˜0,1g˜0,g˜1δf˜*u1δ ln P˜0,1g˜0,g˜1δf˜u2=i,jh˜iu1k˜ijg*u1h˜j*u1+δ0f˜u12αu12-2 det c˜hu1det c˜gu1×δu1-u2,
αu=2f˜u2 det c˜hu+σ02c˜11hu+σ12c˜00hudet c˜gu,
J0f˜u1,f˜u2=δu1-u2h˜0u12c˜00gu1+δ0f˜u12β0u12,
β0u=c˜00huc˜00gu.
σeff2=σ02σ12σ02+σ12,

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