Mathematical modeling of light transfer in low-coherence reflectometry of random media

Background and Objectives: The mathematical model of stochastic interference of spectrally selected fluorescence radiation in multiple scattering random media is considered. The expressions for the normalized second- and third-order moments of spatial intensity fluctuations of detected probe light are derived. The developed model establishes the relationships between the normalized second- and third-order statistical moments of the intensity fluctuations of detected probe light and the probability density function of the pathlength differences of fluorescence radiation in probed media. The obtained theoretical results are compared with the experimental data on the reference-free low-coherence reflectometry of dye-saturated model random media pumped with a continuous-wave laser radiation. Materials and Methods: The discrete scattering model is applied to derive the basic relationships between the normalized statistical moments of intensity fluctuations and the probability density function of the pathlength differences. The Monte-Carlo technique is applied to obtain the pathlength distributions in probed media for used illumination and detection conditions. The experimental data used for verification of the developed model are obtained using model scattering systems on the base of densely packed silica grains, which are saturated by a water solution of Rhodamine 6G and pumped by continuous-wave laser radiation at the wavelength of 532 nm. Results: The adequacy of the developed mathematical model is confirmed by the obtained experimental data. The universal relationship is established between the integral parameters dependent on the probability density function of the pathlength differences and the coherence function of spectrally selected probe radiation is established. Conclusion: The obtained results can be used as the physical base for the development of novel low-coherence probes for applications in biomedical optics and material science.