## Illinois iOptics Lecture 3: A tissue scattering-phase theorem

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During the past two-three decades, tissue light scattering has evolved as a dynamic area of study and attracted extensive research interest, especially due to the potential it offers for in-vivo diagnosis. The refractive index distribution of biological structures, which governs the light-tissue interaction, has been modeled both as discrete particle distribution and continuous or even fractal. Upon propagation in tissues, light changes its properties in terms of polarization, amplitude, phase, spectrum, direction of propagation, and coherence. Thus, quantifying these modifications, reports upon the tissue properties and, potentially, on disease-induced alterations.

Mathematically, the strong light-tissue interaction can be described by a radiative transport equation, in complete analogy to the problem of neutron transport in nuclear reactors. With further simplifying assumptions, a diffusion model can be applied to describe the steady state and time-resolved light transport in tissues. Light propagation in bulk tissue is described by two statistical parameters: the scattering mean free path, ls, which provides the characteristic length scale of the scattering process, and the anisotropy factor, g, which scales ls to higher values, ls/(1-g), to account for forward scattering. The direct measurement of these scattering parameters is extremely challenging and, often, simulations such as Monte Carlo or finite difference time domain, are used iteratively instead.

Recently, we have derived two mathematical relationships between quantitative phase images of thin tissue slices and the scattering parameters of the bulk, i.e. scattering mean free path, ls, and anisotropy factor, g. The ls turns out to be inversely proportional to the mean-squared phase shift and g is related to the phase gradient. These formulas, referred collectively to as the scattering-phase theorem, allow for mapping large cross-sections of tissues in terms of scattering properties and may offer a straight forward experimental alternative to simulations of tissue scattering. Experimentally, we demonstrated this new approach via experiments on mouse organ tissue slices and human cancer biopsies.

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1000 MNTL, University of Illinois, Urbana-Champaign, IL