Abstract

In this Letter, we describe an easy to implement technique to measure the spatial backscattering impulse-response at length scales shorter than a transport mean free path with resolution of better than 10 μm using the enhanced backscattering phenomenon. This technique enables spectroscopic measurements throughout the visible range and sensitivity to all polarization channels. Through a combination of Monte Carlo simulations and experimental measurements of latex microspheres, we explore the various sensitivities of our technique to both intrinsic sample properties and extrinsic instrumental properties. We conclude by demonstrating the extraordinary sensitivity of our technique to the shape of the scattering phase function, including higher order shape parameters than the anisotropy factor (or first moment).

© 2011 Optical Society of America

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References

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  1. A. Hielscher, A. Eick, J. Mourant, D. Shen, J. Freyer, and I. Bigio, Opt. Express 1, 441 (1997).
    [CrossRef]
  2. R. Lenke and G. Maret, in Scattering in Polymeric and Colloidal Systems (2000).
  3. V. Turzhitsky, J. D. Rogers, N. N. Mutyal, H. K. Roy, and V. Backman, IEEE J. Sel. Top. Quantum Electron. 16, 619 (2010).
    [CrossRef]
  4. A. J. Radosevich, J. D. Rogers, V. Turzhitsky, N. N. Mutyal, J. Yi, H. K. Roy, and V. Backman, “Polarized enhanced backscattering spectroscopy for characterization of biological tissues at subdiffusion length scales,” IEEE J. Sel. Top. Quantum Elect., to be published.
  5. M. Ospeck and S. Fraden, Phys. Rev. E 49, 4578 (1994).
    [CrossRef]
  6. R. Lenke and G. Maret, Eur. Phys. J. B 17, 171 (2000).
    [CrossRef]

2010 (1)

V. Turzhitsky, J. D. Rogers, N. N. Mutyal, H. K. Roy, and V. Backman, IEEE J. Sel. Top. Quantum Electron. 16, 619 (2010).
[CrossRef]

2000 (1)

R. Lenke and G. Maret, Eur. Phys. J. B 17, 171 (2000).
[CrossRef]

1997 (1)

1994 (1)

M. Ospeck and S. Fraden, Phys. Rev. E 49, 4578 (1994).
[CrossRef]

Backman, V.

V. Turzhitsky, J. D. Rogers, N. N. Mutyal, H. K. Roy, and V. Backman, IEEE J. Sel. Top. Quantum Electron. 16, 619 (2010).
[CrossRef]

A. J. Radosevich, J. D. Rogers, V. Turzhitsky, N. N. Mutyal, J. Yi, H. K. Roy, and V. Backman, “Polarized enhanced backscattering spectroscopy for characterization of biological tissues at subdiffusion length scales,” IEEE J. Sel. Top. Quantum Elect., to be published.

Bigio, I.

Eick, A.

Fraden, S.

M. Ospeck and S. Fraden, Phys. Rev. E 49, 4578 (1994).
[CrossRef]

Freyer, J.

Hielscher, A.

Lenke, R.

R. Lenke and G. Maret, Eur. Phys. J. B 17, 171 (2000).
[CrossRef]

R. Lenke and G. Maret, in Scattering in Polymeric and Colloidal Systems (2000).

Maret, G.

R. Lenke and G. Maret, Eur. Phys. J. B 17, 171 (2000).
[CrossRef]

R. Lenke and G. Maret, in Scattering in Polymeric and Colloidal Systems (2000).

Mourant, J.

Mutyal, N. N.

V. Turzhitsky, J. D. Rogers, N. N. Mutyal, H. K. Roy, and V. Backman, IEEE J. Sel. Top. Quantum Electron. 16, 619 (2010).
[CrossRef]

A. J. Radosevich, J. D. Rogers, V. Turzhitsky, N. N. Mutyal, J. Yi, H. K. Roy, and V. Backman, “Polarized enhanced backscattering spectroscopy for characterization of biological tissues at subdiffusion length scales,” IEEE J. Sel. Top. Quantum Elect., to be published.

Ospeck, M.

M. Ospeck and S. Fraden, Phys. Rev. E 49, 4578 (1994).
[CrossRef]

Radosevich, A. J.

A. J. Radosevich, J. D. Rogers, V. Turzhitsky, N. N. Mutyal, J. Yi, H. K. Roy, and V. Backman, “Polarized enhanced backscattering spectroscopy for characterization of biological tissues at subdiffusion length scales,” IEEE J. Sel. Top. Quantum Elect., to be published.

Rogers, J. D.

V. Turzhitsky, J. D. Rogers, N. N. Mutyal, H. K. Roy, and V. Backman, IEEE J. Sel. Top. Quantum Electron. 16, 619 (2010).
[CrossRef]

A. J. Radosevich, J. D. Rogers, V. Turzhitsky, N. N. Mutyal, J. Yi, H. K. Roy, and V. Backman, “Polarized enhanced backscattering spectroscopy for characterization of biological tissues at subdiffusion length scales,” IEEE J. Sel. Top. Quantum Elect., to be published.

Roy, H. K.

V. Turzhitsky, J. D. Rogers, N. N. Mutyal, H. K. Roy, and V. Backman, IEEE J. Sel. Top. Quantum Electron. 16, 619 (2010).
[CrossRef]

A. J. Radosevich, J. D. Rogers, V. Turzhitsky, N. N. Mutyal, J. Yi, H. K. Roy, and V. Backman, “Polarized enhanced backscattering spectroscopy for characterization of biological tissues at subdiffusion length scales,” IEEE J. Sel. Top. Quantum Elect., to be published.

Shen, D.

Turzhitsky, V.

V. Turzhitsky, J. D. Rogers, N. N. Mutyal, H. K. Roy, and V. Backman, IEEE J. Sel. Top. Quantum Electron. 16, 619 (2010).
[CrossRef]

A. J. Radosevich, J. D. Rogers, V. Turzhitsky, N. N. Mutyal, J. Yi, H. K. Roy, and V. Backman, “Polarized enhanced backscattering spectroscopy for characterization of biological tissues at subdiffusion length scales,” IEEE J. Sel. Top. Quantum Elect., to be published.

Yi, J.

A. J. Radosevich, J. D. Rogers, V. Turzhitsky, N. N. Mutyal, J. Yi, H. K. Roy, and V. Backman, “Polarized enhanced backscattering spectroscopy for characterization of biological tissues at subdiffusion length scales,” IEEE J. Sel. Top. Quantum Elect., to be published.

Eur. Phys. J. B (1)

R. Lenke and G. Maret, Eur. Phys. J. B 17, 171 (2000).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

V. Turzhitsky, J. D. Rogers, N. N. Mutyal, H. K. Roy, and V. Backman, IEEE J. Sel. Top. Quantum Electron. 16, 619 (2010).
[CrossRef]

Opt. Express (1)

Phys. Rev. E (1)

M. Ospeck and S. Fraden, Phys. Rev. E 49, 4578 (1994).
[CrossRef]

Other (2)

R. Lenke and G. Maret, in Scattering in Polymeric and Colloidal Systems (2000).

A. J. Radosevich, J. D. Rogers, V. Turzhitsky, N. N. Mutyal, J. Yi, H. K. Roy, and V. Backman, “Polarized enhanced backscattering spectroscopy for characterization of biological tissues at subdiffusion length scales,” IEEE J. Sel. Top. Quantum Elect., to be published.

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Figures (5)

Fig. 1.
Fig. 1.

EBS instrument. Collimating lens L1 (f=200mm), linear polarizer P, mirror M, beam splitter B, quarter wave plate QWP, linear analyzer A, Fourier lens L2 (f=100mm), liquid crystal tunable filter LCTF.

Fig. 2.
Fig. 2.

Polarization sensitivities. (a) Function pc for the four measured polarization channels as a function of exit radius. (b) Experimental (symbols) and simulation (lines) peff. Sample: 0.65 μm diameter sphere with ls*=205μm at 633 nm. Spot size=6000μm and Lsc=. Simulation scaled by 0.65 to obtain match with experiment.

Fig. 3.
Fig. 3.

Illumination beam spot size sensitivities. (a) s as a function of exit radius for two beam spot sizes. (b) Comparison between experiment (symbols) and simulation (lines) for the different beam spot sizes using ++ polarization. Sample: 0.65 μm diameter sphere with ls*=950μm at 633 nm. Lsc=. Simulation scaled by 0.65.

Fig. 4.
Fig. 4.

Sensitivities to the spatial coherence of the illumination. (a) Function c for different Lsc. (b) Comparison between experiment (symbols) and simulation (lines) for different Lsc using ++ polarization. Sample: 0.65 μm diameter sphere with ls*=205μm at 633 nm. Spot size=6000μm and Lsc=. Simulation scaled by 0.65.

Fig. 5.
Fig. 5.

Sensitivity of EBS to the phase function. (a) Phase function for two microsphere samples with the same g but different ka. (b) Corresponding peff for ++ polarization shows a large difference in shape at short length-scales. ka4: 0.65 μm diameter sphere at 633 nm. ka16: 2.1 μm diameter sphere at 558 nm. Spot size=2000μm and Lsc=. Simulation scaled by 0.65.

Equations (6)

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IEBS(θx,θy)=F{p(x,y)·pc(x,y)·s(x,y)·c(x,y)·mtf(x,y)},
peff=F-1{IEBS(θx,θy)}.
Δs=λn·Δθ,
pcxy(r)=dlp(r)+dcp(r)1-dlp(r)pc+(r)=2·dlp(r)1-dcp(r).
s(x,y)=ACF{A(x,y)}.
c(r)=2J1(r/Lsc)r/Lsc.

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