Abstract

Previous studies have shown that the isoplanatic distortion due to turbulence and the image of a remote object may be jointly estimated from the 4D mutual intensity across an aperture. This Letter shows that decompressive inference on a 2D slice of the 4D mutual intensity, as measured by a rotational shear interferometer, is sufficient for estimation of sparse objects imaged through turbulence. The 2D slice is processed using an iterative algorithm that alternates between estimating the sparse objects and estimating the turbulence-induced phase screen. This approach may enable new systems that infer object properties through turbulence without exhaustive sampling of coherence functions.

© 2010 Optical Society of America

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References

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J. M. Bioucas-Dias and M. A. T. Figueiredo, IEEE Trans. Image Process. 16, 2992 (2007).
[CrossRef]

2006

E. J. Candes, J. K. Romberg, and T. Tao, Commun. Pure Appl. Math. 59, 1207 (2006).
[CrossRef]

2005

2003

S. Basty, M. Neifeld, D. Brady, and S. Kraut, Opt. Commun. 228, 249 (2003).
[CrossRef]

2002

1992

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Basty, S.

S. Basty, M. Neifeld, D. Brady, and S. Kraut, Opt. Commun. 228, 249 (2003).
[CrossRef]

Bioucas-Dias, J. M.

J. M. Bioucas-Dias and M. A. T. Figueiredo, IEEE Trans. Image Process. 16, 2992 (2007).
[CrossRef]

Boyd, S.

S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge U. Press, 2004).

Brady, D.

Candes, E. J.

E. J. Candes, J. K. Romberg, and T. Tao, Commun. Pure Appl. Math. 59, 1207 (2006).
[CrossRef]

Dimotakis, P.

Fienup, J. R.

Figueiredo, M. A. T.

J. M. Bioucas-Dias and M. A. T. Figueiredo, IEEE Trans. Image Process. 16, 2992 (2007).
[CrossRef]

Fontanella, J.

Kern, B.

Kraut, S.

S. Basty, M. Neifeld, D. Brady, and S. Kraut, Opt. Commun. 228, 249 (2003).
[CrossRef]

Lane, R.

Lang, D.

Marks, D.

Martin, C.

Neifeld, M.

S. Basty, M. Neifeld, D. Brady, and S. Kraut, Opt. Commun. 228, 249 (2003).
[CrossRef]

Paxman, R. G.

Primot, J.

Romberg, J. K.

E. J. Candes, J. K. Romberg, and T. Tao, Commun. Pure Appl. Math. 59, 1207 (2006).
[CrossRef]

Rousset, G.

Schulz, T. J.

Stack, R.

Tallon, M.

Tao, T.

E. J. Candes, J. K. Romberg, and T. Tao, Commun. Pure Appl. Math. 59, 1207 (2006).
[CrossRef]

Thessin, R.

Vandenberghe, L.

S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge U. Press, 2004).

Appl. Opt.

Commun. Pure Appl. Math.

E. J. Candes, J. K. Romberg, and T. Tao, Commun. Pure Appl. Math. 59, 1207 (2006).
[CrossRef]

IEEE Trans. Image Process.

J. M. Bioucas-Dias and M. A. T. Figueiredo, IEEE Trans. Image Process. 16, 2992 (2007).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

S. Basty, M. Neifeld, D. Brady, and S. Kraut, Opt. Commun. 228, 249 (2003).
[CrossRef]

Other

S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge U. Press, 2004).

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Figures (3)

Fig. 1
Fig. 1

Experimental setup to measure the mutual intensity from LEDs with a phase distortion.

Fig. 2
Fig. 2

Results of using approach in Eqs. (7) to image three LEDs aberrated by turbulence.

Fig. 3
Fig. 3

Results of a control experiment for the reconstruction of three LEDs not aberrated by turbulence.

Equations (8)

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J ( r ¯ Δ r 2 , r ¯ + Δ r 2 ) = E ( r ¯ Δ r 2 ) * E ( r ¯ + Δ r 2 ) ,
J ( Δ r ) = S ( r ) z 2 e i ω c z ( Δ r r ) d 2 r .
J ( r ¯ Δ r 2 , r ¯ + Δ r 2 ) = [ S ( r ) z 2 e i ω c z [ ( Δ r ) r ] d 2 r ] × e i ω c [ d ( r ¯ Δ r 2 ) d ( r ¯ + Δ r 2 ) ] .
J ( x , y ) = [ S ( x , y ) z 2 e 2 i ω c z ( y x + x y ) sin ( 2 θ ) d x d y ] × e i φ ( x , y ) ,
[ x e , P e ] = arg min x , P g A P F x 2 2 ,
f e = arg min f f 1 s.t. g = Φ x e = Φ Ψ f e = H f e ,
x e i = arg min x 1 2 g Φ x 2 2 + λ x 1 = arg min x 1 2 g A P e i 1 F x 2 2 + λ x 1
P e i = sgn [ ( A F x e i ) * g ] ,

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