Imaging Optical Fields Through Heavily Scattering Media

Jason A. Newman and Kevin J. Webb

Phys. Rev. Lett. 113, 263903 – Published 30 December 2014

Abstract

Coherent imaging and communication through or within heavily scattering random media has been considered impossible due to the randomization of the information contained in the scattered electromagnetic field. We report a remarkable result based on speckle correlations over incident field position that demonstrates that the field incident on a heavily scattering random medium can be obtained using a method that is not restricted to weak scatter and is, in principle, independent of the thickness of the scattering medium. Natural motion can be exploited, and the approach can be extended to other geometries. The near-infrared optical results presented indicate that the approach is applicable to other frequency regimes, as well as other wave types. This work presents opportunities to enhance communication channel capacity in the large source and detector number regime, for a new method to view binary stars from Earth, and in biomedical applications.

Received 12 February 2014

DOI:https://doi.org/10.1103/PhysRevLett.113.263903

Authors & Affiliations

Jason A. Newman and Kevin J. Webb^*

School of Electrical and Computer Engineering, Purdue University 465 Northwestern Avenue, West Lafayette, Indiana 47907-1285, USA

^*Corresponding author. webb@purdue.edu

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Issue

Vol. 113, Iss. 26 — 31 December 2014

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Images

Figure 1
Experimental setup. Scattering slabs with reduced scattering coefficients of $4$ or $14 {cm}^{- 1}$ and thicknesses of 3, 6, and 9 mm were illuminated by an 850 nm laser which was shaped by an aperture arrangement. The patterned beam, the object of interest, was scanned across the slab. The speckle imaging arrangement was composed of a CCD camera, a spatial filter, a magnification lens, and a polarizer. The measurement imaged a small spot on the back of the scattering slab, resulting in a mean intensity that was independent of position within the camera image. With heavy scatter, this mean is independent of the object position over sufficiently small scan distances, the case in this Letter.
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Figure 2
Speckle spatial intensity correlation comparisons between our theory, the autocorrelation of the incident intensity, and experimental data, for scattering samples with a reduced scattering coefficient of $μ_{s}^{'} = 4 {cm}^{- 1}$ and thicknesses of 3, 6, and 9 mm, and $μ_{s}^{'} = 14 {cm}^{- 1}$ samples with thicknesses of 3 and 6 mm. As the scattering in the slab increases, the spatial speckle intensity correlation approaches the theory in (4).
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Figure 3
Field reconstruction results for a $500 μ m$ circular aperture. The circular aperture was illuminated with a quasispherical wave generated by a $50 μ m$ circular aperture placed 65 mm in front of it. The scattering slab was 9 mm thick and had a reduced scattering coefficient of $μ_{s}^{'} = 4 {cm}^{- 1}$ . (a) Estimated aperture field magnitude. (b) Estimated aperture field phase. (c) Reconstructed field magnitude. (d) Reconstructed field phase. The phase images have been truncated to only show the phase where the magnitude is significant.
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Figure 4
Reconstructed field for a two-hole illumination pattern. The scattering slab was 9 mm thick and had a reduced scattering coefficient of $μ_{s}^{'} = 4 {cm}^{- 1}$ . (a) Estimated aperture field magnitude. (b) Estimated aperture field phase. (c) Reconstructed field magnitude. (d) Reconstructed field phase. The phase images have been truncated to only show the phase where the magnitude is significant.
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Figure 5
Speckle image cross-correlation as a function of pixel shift for four different object positions. The illuminating object was a two hole aperture, aligned in the $x$ direction. The maximum correlation is centered at zero, indicating that the speckle pattern is not translating in response to changes in the object position.
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Figure 6
Ensemble average power spectral density, averaged over 100 speckle images, shown on a log scale. The power spectral density, in this case, is practically circular, as shown by the cross sections at $k_{x, y} = 0$ . The illuminating object was a two hole aperture, aligned in the $x$ direction. The speckle image power spectral density clearly does not contain information about the object. In our experiments, the speckle image power spectrum is determined by the imaging optics; i.e., the detection optics dictate the speckle size and shape.
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