Beyond the Diffusing-Wave Spectroscopy Model for the Temporal Fluctuations of Scattered Light

We extend the theory of diffusing-wave spectroscopy using a random-walk approach and a numerical solution of the radiative transfer equation. The theory is not restricted to the diffusive regime and allows one to describe the crossover between the single-scattering and the diffusive regimes, which has been observed experimentally. It also predicts a lower bound of the scattered-field correlation time at long paths. This extended theory should have broad experimental applications in the field of imaging through biological tissues.

Figure 1

Linewidth of the PSD of the scattered field fluctuations versus the path length $s$. Solid line: extended DWS theory. Dashed line: QELS prediction (short paths) and standard DWS prediction (long paths). The system is a thick slab (width $L=5\mathrm{mm}$) in a reflection geometry, containing polystyrene spheres with radius $110\mathrm{nm}$ in water. $D_B=1.99\times {10}^{-12}{\mathrm{m}}^2{\mathrm{s}}^{-1}$. Illumination wavelength: $\lambda =850\mathrm{nm}$. Effective index: $n_{\mathrm{eff}}=1.339$. $l_s=111.4\mu \mathrm{m}$, $l^{*}=140.2\mu \mathrm{m}$, albedo $a=0.993$. Inset: experimental result, after 13.

Figure 2

Amplitude of the PSD versus the path length $s$. The system is similar to that in Fig. 1, with $D_B=1.7\times {10}^{-12}{\mathrm{m}}^2{\mathrm{s}}^{-1}$, $\lambda =845\mathrm{nm}$, and effective index $n_{\mathrm{eff}}=1.333$. $l_s=175\mu \mathrm{m}$, $l^{*}=247\mu \mathrm{m}$, albedo $a=0.995$. Inset: experimental result, after 15.

Figure 3

Linewidth of the PSD versus the path length $s$. Solid line: extended DWS theory. Dashed line: standard DWS theory. Parameters: same as in Fig. 2. Inset: experimental result, after 15.