Abstract

To focus a synthetic-aperture radar image that is suffering from phase errors, a phase-error estimate is found that, when it is applied, maximizes the sharpness of the image. Closed-form expressions are derived for the gradients of a sharpness metric with respect to phase-error parameters, including both a point-by-point (nonparametric) phase function and coefficients of a polynomial expansion. Use of these expressions allows for a highly efficient gradient-search algorithm for high-order phase errors. The effectiveness of the algorithm is demonstrated with an example.

© 2000 Optical Society of America

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References

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1996

F. Berizzi and G. Corsini, IEEE Trans. Aerospace Electron. Syst. 32, 1185 (1996).
[CrossRef]

1993

1989

1988

R. G. Paxman and J. C. Marron, Proc. SPIE 976, 37 (1988).
[CrossRef]

1980

C. C. Chen and H. C. Andrews, IEEE Trans. Aerosp. Electron Syst. AES-16, 2 (1980).
[CrossRef]

1974

Andrews, H. C.

C. C. Chen and H. C. Andrews, IEEE Trans. Aerosp. Electron Syst. AES-16, 2 (1980).
[CrossRef]

Berizzi, F.

F. Berizzi and G. Corsini, IEEE Trans. Aerospace Electron. Syst. 32, 1185 (1996).
[CrossRef]

Buffington, A.

Chen, C. C.

C. C. Chen and H. C. Andrews, IEEE Trans. Aerosp. Electron Syst. AES-16, 2 (1980).
[CrossRef]

Corsini, G.

F. Berizzi and G. Corsini, IEEE Trans. Aerospace Electron. Syst. 32, 1185 (1996).
[CrossRef]

Eichel, P. H.

Fienup, J. R.

Ghiglia, D. C.

Jakowatz, C. V.

Marron, J. C.

R. G. Paxman and J. C. Marron, Proc. SPIE 976, 37 (1988).
[CrossRef]

Muller, R. A.

Paxman, R. G.

R. G. Paxman and J. C. Marron, Proc. SPIE 976, 37 (1988).
[CrossRef]

Appl. Opt.

IEEE Trans. Aerosp. Electron Syst.

C. C. Chen and H. C. Andrews, IEEE Trans. Aerosp. Electron Syst. AES-16, 2 (1980).
[CrossRef]

IEEE Trans. Aerospace Electron. Syst.

F. Berizzi and G. Corsini, IEEE Trans. Aerospace Electron. Syst. 32, 1185 (1996).
[CrossRef]

J. Opt. Soc. Am.

Opt. Lett.

Proc. SPIE

R. G. Paxman and J. C. Marron, Proc. SPIE 976, 37 (1988).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Simulation example. (a) Original image, (b) image smeared in the azimuth (vertical) direction by random phase errors, (c) image after 50 iterations, (d) final focused image, with recentering.

Fig. 2
Fig. 2

Sharpness as a function of number of interations (sharpness evaluations).

Equations (13)

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Gdx,v=Fx,vexpiϕev,
Gdkx,v=Fgdkx,y=y=0N-1gdkx,yexp-i2πvy/N.
Gdkx,v=Fkx,vexpiϕev,
Gkx,v=Gdkx,vexp-iϕv,
gkx,y=F-1Gkx,v.
S1=kx,ywkx,ygkx,y4=kx,ywkx,ygkx,y22,
wkx=wkoygkx,y22,
S1n=kx,ywkx,ygkx,y4kx,ywkx,ygkx,y22,
S1ϕv=2kx,ywkx,y×gkx,y2gkx,y2ϕv.
gkx,y2ϕv=-iN-1gk*x,yGkx,v×expi2πvy/N+c.c.,
S1ϕv=4N-1kx,ywkx,y×ImGkx,vFgkx,ygkx,y2*,
ϕv=j=1JajLjv,
S1aj=vLjvS1ϕv,

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