Enhancement of the backscattered intensity from fractal aggregates

Holey random walks: optics of heterogeneous turbid composites

We present a probabilistic theory of random walks in turbid media with nonscattering regions. It is shown that important characteristics such as diffusion constants, average step lengths, crossing statistics, and void spacings can be analytically predicted. The theory is validated using Monte Carlo simulations of light transport in heterogeneous systems in the form of random sphere packings and good agreement is found. The role of step correlations is discussed and differences between unbounded and bounded systems are investigated. Our results are relevant to the optics of heterogeneous systems in general and represent an important step forward in the understanding of media with strong (fractal) heterogeneity in particular.

Modeling low-coherence enhanced backscattering using Monte Carlo simulation

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.

Low-coherent backscattering spectroscopy for tissue characterization

Although the phenomenon of coherent backscattering (CBS) in nonbiological media has generated substantial research interest, observing CBS in biological tissue has been extremely difficult. Here we show that the combination of low-spatial-coherence, broadband illumination, and low-temporal-coherence, spectrally resolved detection significantly facilitates CBS observation in biological tissue and other random media with long-transport mean-free path lengths, which have been previously beyond the reach of conventional CBS investigations. Furthermore, we demonstrate that depth-selective, speckle-free, low-coherent backscattering spectroscopy has the potential to diagnose the earliest, previously undetectable, precancerous alterations in the colon by means of probing short light paths.

Effective Mie scattering of a spherical fractal aggregate and its application in turbid media

An effective Mie-scattering model is developed to deal with the scattering property of a spherical fractal aggregate consisting of scattering particles. In this model the scattered field of a scattering particle is given by the classical Mie-scattering theory. On the basis of the Monte Carlo simulation method, we determine the physical parameters of a scattering aggregate, the scattering efficiency Q, and the anisotropy value g, as well as their dependence on the size and the effective mean-free-path length of a scattering aggregate. Accordingly, photon migration through a microscope objective focused into a turbid medium including scattering aggregates is simulated to understand the effect of complex tissue on image quality.

Laboratory experiments on backscattering from regolith samples

The investigation of the backscattering peak has applications in the surface texture characterization of asteroids and planetary surfaces. Laboratory experiments are important because they give an opportunity for systematic variation and comparison of samples. A backscattering experiment from regolith samples, which uses a laser light source and a beam splitter to reach the smallest phase angles, is presented. Measurements at zero and small phase angles for Sahara sand and meteorite rocks are made, and the preliminary results are presented in comparison with the phase curve observed for asteroid 69 Hesperia. The results are applicable to the further interpretation of the coherent backscattering opposition effect.

Optical free-path-length distribution in a fractal aggregate and its effect on enhanced backscattering

A free-path-length distribution function (FPDF) of multiply backscattered light is theoretically derived for a fractal aggregate of particles. An effective mean-free path-length l(D) is newly introduced as a measure of randomness analogous with a homogeneously random medium. We confirm the validity of the FPDF by demonstrating agreement between the dimensions designed for a particle distribution generated by a random walk based on the derived FPDF and estimated by the radius of gyration method. The FPDF is applied to Monte Carlo simulations for copolarized multiply backscattered light from the fractal aggregate of particles. It is shown that a copolarized intensity peak of enhanced backscattering in the far field decreases in accordance with theta(2-D) and has an angular width of lambda/l(D). This spatial feature of the backscattering enhancement corresponds to that of the copolarized intensity peak produced from a homogeneously random medium with a dimension of D = 3. As a result, the validity of the model for the fractal structure of particle aggregates and the applicability of the derived FPDF are confirmed by the numerical results.