OP: Complex Media Optics and Imaging

University Of California-Irvine, Irvine CA

Investigators

Abstract

Scintillation of the stars is a physical phenomenon that everyone observes and most appreciate as a fascinating and beautiful phenomenon. Albeit well understood from a physical perspective, the phenomenon still is not rigorously described from a precise quantitative perspective. This project concerns an analogous phenomenon that arises in biomedical applications, where one needs to describe how the optical field "scintillates" and is affected by tissue microstructure in imaging studies. High-resolution biomedical imaging is fundamentally important for early cancer detection, monitoring of drug efficiency, computer assisted surgery, and for the evaluation of health of tissue, organs, and bones in general. Monitoring of glucose level, heart rate, blood pressure, and other medical indicators may in the future be optically based, and new drugs that are activated by focusing of optical energy may significantly reduce potential side effects in the treatment of cancer or diabetes. Biological tissue is typically so complicated that one can only describe the microstructure in a statistical fashion. In this project the complex multiscale propagation environment will be modeled as a heterogeneous multiscale random field varying in both space and time. The project will support the development of new optically based techniques in biomedical imaging by enhancing our understanding of how the optical field is affected by the microstructure. The project will also support the development of new techniques in other areas of imaging and wave propagation, such as remote sensing and communication through the atmosphere and in geophysical imaging. In the project, specific scaling relations will used to derive asymptotic descriptions of wave field statistics. The descriptions will be used in the development of optimal filtering and imaging techniques that can exploit the vast amount of data that new optical technology provides. Such a description of the wave field will have important applications in a range of areas in optics and imaging, while the focus here is on quantitative biomedical imaging. The project aims at developing new results that allow one to model optical wave propagation in complicated media. This will concern propagation both for paraxial waves and propagation in the sub-diffusive regime, moreover, propagation in the radiative transfer and diffusion regimes. The development is based on stochastic modeling of the multiscale medium and using scaling limits that allow one to characterize the statistics of the wave field. A main technical challenge in this work is the fact that in the context of waves, information flows in all directions due to wave scattering, rather than being an evolution problem as in the classic context of stochastic processes. This situation leads to an infinite family of imbedding problems that couple statistically. Novel imaging and filtering techniques that exploit spectral wave information for multi-point observations of the optical field will be analyzed and developed in the project, using the scaling limit results developed together with random matrix theory and statistical estimation techniques.