Subramanian Hariharan, Pradhan Prabhakar, Kim Young L, Liu Yang, Li Xu, Backman Vadim
Department of Biomedical Engineering, Northwestern University, Evanston, Illinois 60208, USA.
Appl Opt. 2006 Aug 20;45(24):6292-300. doi: 10.1364/ao.45.006292.
Constructive interference between coherent waves traveling time-reversed paths in a random medium gives rise to the enhancement of light scattering observed in directions close to backscattering. This phenomenon is known as enhanced backscattering (EBS). According to diffusion theory, the angular width of an EBS cone is proportional to the ratio of the wavelength of light lambda to the transport mean-free-path length l(s)* of a random medium. In biological media a large l(s)* approximately 0.5-2 mm >> lambda results in an extremely small (approximately 0.001 degrees ) angular width of the EBS cone, making the experimental observation of such narrow peaks difficult. Recently, the feasibility of observing EBS under low spatial coherence illumination (spatial coherence length Lsc << l(s)*) was demonstrated. Low spatial coherence behaves as a spatial filter rejecting longer path lengths and thus resulting in an increase of more than 100 times in the angular width of low coherence EBS (LEBS) cones. However, a conventional diffusion approximation-based model of EBS has not been able to explain such a dramatic increase in LEBS width. We present a photon random walk model of LEBS by using Monte Carlo simulation to elucidate the mechanism accounting for the unprecedented broadening of the LEBS peaks. Typically, the exit angles of the scattered photons are not considered in modeling EBS in the diffusion regime. We show that small exit angles are highly sensitive to low-order scattering, which is crucial for accurate modeling of LEBS. Our results show that the predictions of the model are in excellent agreement with the experimental data.
在随机介质中沿时间反演路径传播的相干波之间的相长干涉，会导致在接近后向散射的方向上观察到光散射增强。这种现象被称为增强后向散射（EBS）。根据扩散理论，EBS锥的角宽度与光的波长λ与随机介质的输运平均自由程长度l(s)*的比值成正比。在生物介质中，较大的l(s)约为0.5 - 2毫米 >> λ，会导致EBS锥的角宽度极小（约为0.001度），使得对如此窄的峰值进行实验观测变得困难。最近，有人证明了在低空间相干照明（空间相干长度Lsc << l(s)）下观测EBS的可行性。低空间相干起到空间滤波器的作用，拒绝较长的路径长度，从而导致低相干EBS（LEBS）锥的角宽度增加超过100倍。然而，基于传统扩散近似的EBS模型一直无法解释LEBS宽度如此显著的增加。我们通过蒙特卡罗模拟提出了一个LEBS的光子随机游走模型，以阐明导致LEBS峰值前所未有的展宽的机制。通常，在扩散区域对EBS进行建模时不考虑散射光子的出射角。我们表明，小出射角对低阶散射高度敏感，这对于准确建模LEBS至关重要。我们的结果表明，该模型的预测与实验数据非常吻合。
