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Book and Book Chapters: Abstracts

[5] Yang Pu, Wubao Wang, Min Xu, James A. Eastham, and Robert R. Alfano. Deep Tissue Imaging with Linear and Non-linear Optics, chapter Deep Imaging of Prostate Cancer Using Diffusion Reconstruction of Banana Paths with Near Infrared Prostatoscope Analyzer. Pan Stanford Publishing Pte. Ltd., 2017.
[4] Min Xu, Wei Cai, and Robert R. Alfano. Deep Tissue Imaging with Linear and Non-linear Optics, chapter Overview of the Cumulant Solution to Light Propagation Inside a Turbid Medium and Its Applications in Deep Imaging Beyond the Diffusion Approximation. Pan Stanford Publishing Pte. Ltd., 2017.
[3] W. Cai and M. Xu. Light Scattering Reviews, volume XI, chapter Analytical solution of radiative transfer using cumulant expansion. Springer, 2016.
[2] M. Xu and A. Katz. Light Scattering Reviews, volume III, chapter Statistical Interpretation of Light Anomalous Diffraction by Small Particles and its Applications in Bio-agent Detection and Monitoring, pages 27--68. Springer, 2008.
Anomalous diffraction theory (ADT) for light extinction and scattering is one of the simplest and most powerful approximations of electro-magnetic radiation interaction with spherical and non-spherical soft particles. Such approximate theories have been widely used to solve the inverse problem in the areas of remote sensing and particle sizing. They also fill the gap in cases, such as computation of the optical efficiencies of particles of large size parameters and aspect ratios, where the exact numerical methods fail due to the limitation of current computational resources and floating point accuracy. In this study, we review some latest developments of ADT and its applications in bio-agent detection and monitoring. The statistical interpretation of light anomalous diffraction is first presented. The optical efficiencies in ADT are shown to be determined by the probability distribution of the geometrical paths of the rays inside the particles. The optical efficiencies of spheroids and finite circular cylinders are studied in detail with this approach. One important consequence of this statistical view is that the main feature of optical efficiencies of soft particles is characterized by the mean and mean-squared-root geometrical paths of the rays. A Gaussian ray approximation in ADT is then proposed based on this observation. This Gaussian ray approximation is successfully applied in detection of bio-agents and in situ monitoring of changes in the refractive index and size of spores during spore germination.
[1] M. Lax, W. Cai, and M. Xu. Random Processes in Physics and Finance. Oxford University Press, USA, 2006.

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