Structural length-scale sensitivities of reflectance measurements in continuous random media under the Born approximation

Abstract

Which range of structures contributes to light scattering in a continuous random media, such as biological tissue? In this Letter, we present a model to study the structural length-scale sensitivity of scattering in continuous random media under the Born approximation. The scattering coefficient μs, backscattering coefficient μb, anisotropy factor g, and reduced scattering coefficient μs* as well as the shape of the spatial reflectance profile are calculated under this model. For media with a biologically relevant Henyey-Greenstein phase function with g∼0.93 at wavelength λ=633 nm, we report that μs* is sensitive to structural length-scales from 46.9 nm to 2.07 μm (i.e., λ/13 to 3λ), μb is sensitive from 26.7 to 320 nm (i.e., λ/24 to λ/2), and the spatial reflectance profile is sensitive from 30.8 nm to 2.71 μm (i.e., λ/21 to 4λ).

Fig. 1

Lower length-scale analysis for W_l = 0, 10, 50, and 100 nm with D = 3, l_c = 1 μm, and λ = 633 nm. The normalized (a) $B_n^l(r_d)$ and (b) ${\mathrm{\Phi }}_s^l(k_s)$. In each panel the arrow indicates increasing W_l.

Fig. 2

Upper length-scale analysis for W_h = ∞, 10, 5, and 1 μm with D = 3, l_c = 1 μm, and λ = 633 nm. (a) $B_n^h(r_d)$ where the dashed lines indicate locations in which the curve is negative. (b) ${\mathrm{\Phi }}_s^h(k_s)$. In each panel the arrow indicates decreasing W_h.

Fig. 3

Example media with D = 3 and l_c = 1 μm. (a) n_Δ(r⃗). (b) $n_{\mathrm{\Delta }}^l(\overrightarrow{r})$ and (c) $n_{\mathrm{\Delta }}^h(\overrightarrow{r})$ for W_l = W_h = 100 nm.

Fig. 4

Percent change in scattering parameters with varying values of W_l and W_h for D = 3, l_c = 1 μm, and λ = 633 nm. (a) Lower and (b) upper length-scale percent changes. The dotted line indicates the ± 5 % threshold.

Fig. 5

Monte Carlo simulations of P_oo with D = 3, l_c = 1 μm, and λ = 633 nm. (a) Lower length-scale analysis for W_l = 0, 30, 60, and 90 nmm. Arrow indicates increasing W_l. (b) Upper length-scale analysis for W_h = ∞, 10, 2, 0.5 μm. Arrows indicate decreasing W_h.

Fig. 6

(a) r_min and (b) r_max for ${\mu }_s^{\ast }$ with different shapes of B_n(r_d) and λ = 633 nm.