Abstract

Spatial speckle intensity correlations are used to determine the spatial Fourier magnitude of a field incident on a random scattering medium. The patterned beam is scanned across the scattering medium, and the speckle pattern on the opposite side is imaged at each beam position. A theory based on a Green’s function representation is used to reconstruct the spatial Fourier magnitude of the patterned incident field.

© 2012 Optical Society of America

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References

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2010 (1)

2007 (1)

2006 (1)

2002 (1)

M. A. Webster, K. J. Webb, and A. M. Weiner, Phys. Rev. Lett. 88, 033901 (2002).
[CrossRef]

2001 (1)

A. Dunn, H. Bolay, M. Moskowitz, and D. Boas, J. Cereb. Blood Flow Metab. 21, 195 (2001).

2000 (2)

1999 (1)

J. Schmitt, S. Xiang, and K. Yung, J. Biomed. Opt. 4, 95 (1999).
[CrossRef]

1995 (1)

A. Yodh and B. Chance, Phys. Today 48, 34 (1995).
[CrossRef]

1993 (1)

1991 (1)

1982 (1)

1963 (1)

B. Oliver, Proc. IEEE 51, 220 (1963).
[CrossRef]

1962 (1)

I. S. Reed, IRE Trans. Inf. Theory 8, 194 (1962).

Alfano, R. R.

Bashkansky, M.

Boas, D.

A. Dunn, H. Bolay, M. Moskowitz, and D. Boas, J. Cereb. Blood Flow Metab. 21, 195 (2001).

Bolay, H.

A. Dunn, H. Bolay, M. Moskowitz, and D. Boas, J. Cereb. Blood Flow Metab. 21, 195 (2001).

Chance, B.

A. Yodh and B. Chance, Phys. Today 48, 34 (1995).
[CrossRef]

Chang, W.-S.

Chiang, H.-P.

Dunn, A.

A. Dunn, H. Bolay, M. Moskowitz, and D. Boas, J. Cereb. Blood Flow Metab. 21, 195 (2001).

Fienup, J. R.

Goodman, J.

J. Goodman, Statistical Optics (Wiley-Interscience, 1985).

McKinney, J. D.

Moskowitz, M.

A. Dunn, H. Bolay, M. Moskowitz, and D. Boas, J. Cereb. Blood Flow Metab. 21, 195 (2001).

Oliver, B.

B. Oliver, Proc. IEEE 51, 220 (1963).
[CrossRef]

Reed, I. S.

I. S. Reed, IRE Trans. Inf. Theory 8, 194 (1962).

Reintjes, J.

Schmitt, J.

J. Schmitt, S. Xiang, and K. Yung, J. Biomed. Opt. 4, 95 (1999).
[CrossRef]

Wang, J.

Wang, Z.

Webb, K. J.

Webster, M. A.

Weiner, A. M.

Xiang, S.

J. Schmitt, S. Xiang, and K. Yung, J. Biomed. Opt. 4, 95 (1999).
[CrossRef]

Xing, Q.

Yodh, A.

A. Yodh and B. Chance, Phys. Today 48, 34 (1995).
[CrossRef]

Yoo, K. M.

Yung, K.

J. Schmitt, S. Xiang, and K. Yung, J. Biomed. Opt. 4, 95 (1999).
[CrossRef]

Appl. Opt. (2)

IRE Trans. Inf. Theory (1)

I. S. Reed, IRE Trans. Inf. Theory 8, 194 (1962).

J. Biomed. Opt. (1)

J. Schmitt, S. Xiang, and K. Yung, J. Biomed. Opt. 4, 95 (1999).
[CrossRef]

J. Cereb. Blood Flow Metab. (1)

A. Dunn, H. Bolay, M. Moskowitz, and D. Boas, J. Cereb. Blood Flow Metab. 21, 195 (2001).

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

Opt. Lett. (5)

Phys. Rev. Lett. (1)

M. A. Webster, K. J. Webb, and A. M. Weiner, Phys. Rev. Lett. 88, 033901 (2002).
[CrossRef]

Phys. Today (1)

A. Yodh and B. Chance, Phys. Today 48, 34 (1995).
[CrossRef]

Proc. IEEE (1)

B. Oliver, Proc. IEEE 51, 220 (1963).
[CrossRef]

Other (1)

J. Goodman, Statistical Optics (Wiley-Interscience, 1985).

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Figures (3)

Fig. 1.
Fig. 1.

Experimental setup. The source was an 850 nm laser diode with a line-width of less than 10 MHz. A commercially available acrylic plastic, 9 mm thick, with embedded TiO2 spheres of average diameter 50 nm and reduced scattering coefficient μs=4cm1 was used as the scattering sample. A mirror and apertures with separation ds were scanned together across the sample. A spatial filter, magnifying lens, polarizer, and CCD camera imaged an 1mm2 area on the back surface of the scattering sample.

Fig. 2.
Fig. 2.

Spatial speckle intensity correlations over incident field position for patterned incident beams with varying degrees of spatial Fourier spectrum support. Experimental data are shown as symbols and simulated data, using (7), are shown as solid lines. The incident beam is patterned using two circular apertures separated by a distance, ds, as shown in Fig. 1. As ds increases, the spatial Fourier support decreases, leading directly to an increase in the spatial speckle intensity correlation length.

Fig. 3.
Fig. 3.

Comparison between the magnitudes of the simulated incident field Fourier spectrum, shown as solid lines, and the reconstructed spectrum using experimental speckle intensity data, as dashed lines, for aperture spacings, ds, of 23 mm, 35 mm, 53 mm, and 65 mm.

Equations (8)

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E[U(r)]E*[U(r+Δr)]=drU(r)G(rd,r)×dr′′U*(r′′+Δr)G*(rd,r′′+Δr),
E[U(r)]E*[U(r+Δr)]=drU(r)U*(r+Δr)|G(rd,r)|2.
E˜[U(r)]E˜*[U(r+Δr)]1(2π)4drdk×ejk·rU(k)dkejk·(r+Δr)U*(k),
E˜[U(r)]E˜*[U(r+Δr)]1(2π)4dkU(k)×dkU*(k)ejk·Δrdrej(kk)·r.
E˜[U(r)]E˜*[U(r+Δr)]1(2π)2dk|U(k)|2×ejk·Δr.
E˜[U(r)]E˜*[U(r+Δr)]{F1[|U(k)|2]}*.
I˜[U(r)]I˜[U(r+Δr)]|F1{|U(k)|2}|2.
|U(k)||[F{[I˜[U(r)]I˜[U(r+Δr)]]12ejϕ(Δr)}]12|,

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