Experimental and Numerical Studies of Short Pulse Propagation in Model Systems

In this paper experimental and numerical studies of shortpulsed lasers propagation through scattering and absorbing media are investigated. Experimental results of a 60 ps pulse laser transmission in tissue phantoms are presented and compared with Monte Carlo simulation. Good agreement between the Monte Carlo simulation and experimental measurement is found. Three models are developed for the simulation of short pulse transport. Benchmark comparisons among the Monte Carlo, transient discrete ordinates method and transient radiation element method are conducted. INTRODUCTION The study of short pulse laser propagation through highly scattering media has received considerable recent interest mainly due to its applications in biomedical imaging such as optical tomography, remote sensing of oceans and atmospheres, laser material processing of microstructures, etc. The unique features of short pulses of radiation and the characteristics of their interaction with participating medium make them a valuable research tool. Firstly, short pulse monochromatic radiation can be easily created and accurately detected with high spatial, temporal, and signal resolution. Secondly, the distinct feature of the technique is the multiple scattering induced temporal signature that persists for time periods greater than the source pulse duration and is a function of the scattering-absorbing properties of the medium and the location in the medium where the properties undergo changes. This temporal variation of reflected and transmitted signals is of significance in visualization, imaging and modeling. The modeling of multi-dimensional radiative transfer is usually a formidable task even in steady state since it involves solving integro-differential equations. The addition of the transient term in transfer equation further increases the complexity of modeling. There are mainly two categories in the modeling of transient radiative transfer, i.e., the stochastic method and the deterministic method. The stochastic Monte Carlo (MC) method is usually adopted for the simulation of short pulse laser propagation since it avoids the handling of the complicated integro-differential relationship, is flexible to deal with realistic physical conditions, and is algorithmically simple (Flock et al., 1989; Hasegwa et al., 1991; Guo et al., 2000). The shortcomings of the Monte Carlo method are that it is time-consuming and that the results are subject to statistical error due to practical finite samplings. In brain tumor diagnosis, for example, the nondimensional optical thickness of the tissue is usually over 100, the ballistic component of the laser beam passing through the tissue is then in the order of 1 Copyright © 2002by ASME exp(-100), which is very small to be captured precisely by the Monte Carlo method even with the use of a huge number of samplings. In contrast, the deterministic method does not suffer such defects. The most commonly used model in biomedical field is the diffusion theory, in which the light is assumed to be multiply scattered and the radiative transfer equation is simplified into a diffusion or parabolic equation for the solidangle independent fluence (Yamada, 1995; Madsen et al., 1992; Ishimaru, 1987). Time-resolved experiments on tissues have shown that such diffusion-based analyses are accurate for thick samples but fail to match experimental data for thin samples (Yoo et al., 1990; Yodh and Chance, 1995). In addition, it fails to predict adequately the radiative transport in the region near light incidence and near surface boundaries. In the solution of complete time-dependent radiative transfer equation (RTE), some previous studies have solved the one-dimensional hyperbolic transient RTE, but with a constant strength at the boundaries for a conservative medium using adding-doubling method (Rackmil and Buckius,1983). Hyperbolic formulation using P1 model was proposed by Ishimaru (1987). Kumar et al. (1996) employed the P1 model to solve the hyperbolic one-dimensional transient transfer equation. Mitra et al. (1997) further developed the P1 model to two-dimensional rectangular enclosure. More recently, Mitra and Kumar (1998) examined discrete ordinates method, P1 and P3 models, diffuse approximation, and two-flux method for short pulse laser transport in one-dimensional planar medium, and found that the discrete ordinates method predicts more accurate transient results. After that, Tan and Hsu (2000) and Wu and Wu (2000) separately developed integral formulation for transient radiative transfer in oneand two-dimensional geometries, but it has not yet been applied to short pulse laser transport. Guo and Kumar (2001a) developed transient radiation element method for 1D plane-parallel systems. Few studies are addressed to multi-dimensional short pulse radiation transport through turbid media. Guo and Kumar (2001b, 2001c) have formulated transient discrete ordinates method for multi-dimensional geometries. Guo (2001) developed 3D transient radiation element method. The objective of the work is to study the characteristics of ultrashort laser pulses radiation transport in multi-dimensional geometries containing scattering and absorbing turbid medium. The research goal is to develop adequate transient radiative transfer models for utilization as tools in simulation based engineering and biomedical applications. Experimental study of short pulse laser transport through scattering media is performed for the validation of the numerical models. Comparisons between experimental measurement and numerical modeling are given. Benchmark comparisons among the models are also made. NOMENCLATURE c = speed of light g = asymmetric factor G = incident radiation I = radiation intensity = spatial location vector r = unit vector of direction ŝ t = time tp = pulse width x,y,z = coordinates μ = direction cosine q = polar angle