Enhanced backscattering (EBS) is one of the two self-interference phenomena observed when a sample is illuminated with a coherent light source. The enhanced backscattering effect, also known as coherent backscattering, manifests as an enhancement of intensity in the backward direction of the incident light. This effect was initially tied with weak localization of electrons, and later extended to optical waves[1
]. Further theoretical and experimental work uncovered that EBS can be used to measure the optical properties of diffusely scattering media[2
]. The width of the coherent backscattering peak was found to be proportional to λ/ls*, where λ is the wavelength and ls* is the transport mean free path. However, due to the inherent challenges in this method, the utilization of this phenomenon for characterizing biological tissue has been hampered until recent years.
The second self-interference phenomenon, known as speckle, is one of the primary impediments to measuring the enhanced backscattering in tissue. The large amplitude and ubiquity of the speckle pattern overwhelms the coherent backscattering signal in solid samples. This is why early studies primarily utilized liquid suspensions of particles such that the Brownian motion inside the sample provides a large number of ensembles, all of which are averaged within a single acquisition of the detector. The lack of Brownian motion in biological tissue requires the averaging of many ensembles by moving the entire sample. Furthermore, the narrow line shape of the coherent backscattering peak from tissue requires high angular resolution detection capable of resolving signals on the order of 0.001 degrees.
The extension of enhanced backscattering into the partial spatial coherence regime was first explored by Kim et al
] and provides several advantages which make the technique amenable for tissue characterization. The technique overcomes the difficulties of measuring enhanced backscattering from tissue by broadening the coherent backscattering peak by several orders of magnitude and virtually eliminating the speckle noise.
The new method also offers further advantages that are essential for the biomedical application of enhanced backscattering. The reduced spatial coherence results in a depth selective signal by removing the contribution of light at longer scattered radii[5
]. The addition of spectrally-resolved detection allows for obtaining the interference phenomenon from a range of wavelengths, adding an extra dimension for more complete characterization of tissue properties[7
]. Thus far, Low-coherence Enhanced Backscattering (LEBS) has shown promise for the early detection of colorectal cancer[8
] and pancreatic cancer[9
] by the quantification of superficial tissue layer changes that are unapparent from conventional histology.
Earlier work in characterizing LEBS has revealed that the dependencies of the peak width and enhancement factor on sample properties are more complicated than the those of EBS[4
]. For example, the LEBS peak width was found to have three ls* dependent regimes with distinctly different behaviors for varying values of the anisotropy factor (g) [7
], this being very different from the λ/ls* relationship seen in EBS. The enhancement factor, defined as the relative height of the peak, was also found to be dependent on the mean free path of the medium. On the other hand, the enhancement factor of EBS has no dependence on the mean free path of the sample.
These experimental findings combined with the demonstrated diagnostic potential of the LEBS measurement have motivated several groups to develop Monte Carlo[11
] and theoretical[6
] models for the simulation and understanding of LEBS. Although these Monte Carlo models have given insight into important properties such as the penetration depth of the LEBS signal [6
], a good correspondence between the experimental peak properties, including peak width and enhancement factor, with a simulated result has not been demonstrated until now.
In the following sections, this paper will discuss the experimental and modeling methodologies required to obtain agreement between simulated and experimental peak properties. We will present experimental and Monte Carlo results that illustrate the dependence of the LEBS peak width and enhancement factor on optical properties and the spatial coherence length. We will then present a diffusion based model for LEBS, which can be accurate in certain conditions. Finally, we will apply LEBS as a technique for measuring the scattering probability distribution, p(r), at small length scales.