Characterization of light transport in scattering media at sub-diffusion length scales with Low-coherence Enhanced Backscattering

Abstract

Low-coherence enhanced backscattering (LEBS) is a technique that has recently shown promise for tissue characterization and the detection of early pre-cancer. Although several Monte Carlo models of LEBS have been described, these models have not been accurate enough to predict all of the experimentally observed LEBS features. We present an appropriate Monte Carlo model to simulate LEBS peak properties from polystyrene microsphere suspensions in water. Results show that the choice of the phase function greatly impacts the accuracy of the simulation when the transport mean free path (ls*) is much greater than the spatial coherence length (L(SC)). When ls* < L(SC), a diffusion approximation based model of LEBS is sufficiently accurate. We also use the Monte Carlo model to validate that LEBS can be used to measure the radial scattering probability distribution (radial point spread function), p(r), at small length scales and demonstrate LEBS measurements of p(r) from biological tissue. In particular, we show that pre-cancerous and benign mucosal tissues have different small length scale light transport properties.

Figure. 1

Schematic of LEBS experimental instrument. A broadbaned 450 W Xenon source (S) is imaged onto an aperture of variable size which serves as a secondary source (SS). The size of the aperture is selected by appropriately positioning the aperture wheel. The beam is collimated with lens L₂ and passed through polarizer P₁. A beam splitter (B) allows collection of backscattered light from the sample. The co-polarized light is selected with polarized P₂. Lens L₃ then maps the angular distribution of the backscattered light onto the CCD camera detection chip. A liquid crystal tunable filter (LCTF) attached to the camera is used to select the wavelength of collection.

Figure 2

Demonstration of speckle reduction in LEBS from a dried paint sample (ls* ~ 4μm). Panel a: EBS measurement obtained with Helium Neon (HeNe) laser. Panel b: average of 30 ensembles of EBS measurements collected with HeNe laser. The EBS signal begins to be visible over the speckle noise. Panel c: a single measurement with partial coherence illumination (L_SC = 160μm). Panel d: a sinlge measurement with partial coherence measurement (L_SC = 20μm).

Figure. 3

Enhancement factor as a function of μ_s* for varying L_SC (g=0.86). In panel a, the enhancement factor is shown to have three distinct dependencies on μ_s* for three values of L_SC. In panel b, the three dependencies coincide when enhancement factor is plotted against L_SCμ_s*. The Monte Carlo results (lines) show the same dependencies as the experimental results (symbols).

Figure. 4

LEBS width relationship with ls* and L_SC. Panel a shows the inverse width dependence on spatial coherence length (g=0.86) for Monte Carlo (lines) and experiment (symbols). Panel b shows the data from panel a when the width is scaled by the angular extent of the source and ls* is scaled by the spatial coherence length.

Figure. 5

Dependence of LEBS enhancement factor and width on ls* for phase functions with varying values of the anisotropy coefficient (g). The dependence of the enhancement factor (panel a) is approximately described through the value of L_SC·μ_s. On the other hand the LEBS width (panel b) has a more complicated relationship on the phase function when ls*>>L_SC. The relationships of both the enhancement factor and peak width are well modeled with the Monte Carlo simulation.

Figure. 6

Comparison of diffusion approximation of LEBS with Monte Carlo simulations utilizing various phase functions. In panel a, the LEBS peak width agrees with the diffusion approximation for ls* < L_SC. At ls* >> L_SC, the diffusion approximation is no longer accurate because it is not a good model for p(r) for r<ls*. A comparison between the Mie and Henyey Greenstein phase function for the same value of g indicates that the accuracy of the phase function is important for modeling the LEBS peak width. In panel b, the same data are shown as in panel a, but simulated for a spectrometer based LEBS measurement where the spectrometer slit is of angular width 1.3α. In this case, the sensitivity due to varying phase functions at ls*>>L_SC becomes more pronounced.

Figure. 7

Experimental measurements of p(r) compared with Monte Carlo Simulation. In panel a, a comparison for two different values of g and similar values of ls* is made between Monte Carlo and Experimentally collected data. In panel b, three values of ls* are shown for g = 0.86. In all cases experimentally calculated p(r) curves agree well with Monte Carlo simulation.

Figure 8

Measurement of p(r) from normal and AOM-treated pre-cancerous rat tissue for (L_SC= 86μm). Alterations in p(r) at small length scales indicate that pre-cancerous structural changes are present in the epithelial tissue of AOM-treated rats.