Maxwell's equations based 3D model of light scattering in the retina

Abstract

The goal of this work is to develop a computational model of the human retina and simulate light scattering through its structure aiming to shed light on data obtained by optical coherence tomography in human retinas. Currently, light propagation in scattering media is often described by Mie's solution to Maxwell's equations, which only describes the scattering patterns for homogeneous spheres, thus limiting its application for scatterers of more complex shapes. In this work, we propose a discontinuous Galerkin method combined with a low-storage Runge-Kutta method as an accurate and efficient way to numerically solve the time-dependent Maxwell's equations. In this work, we report on the validation of the proposed methodology by comparison with Mie's solution, a mandatory step before further elaborating the numerical scheme towards the propagation of electromagnetic waves through the human retina.

Reconstructing the Optical Parameters of a Layered Medium with Optical Coherence Elastography

“…Applying the Fourier transform with respect to x 1 and x 2 and solving the resulting ordinary differential equation in x 3 gives us (11).…”

“…Let Ě be a solution of the equation ( 10) on some stripe Ω 0 , written in the form (11). We then call Ě a downwards moving solution if e 2 = 0 and an upwards moving solution if e 1 = 0.…”

“…Only lately, the inverse problems arising in optical coherence tomography have attracted the interest from the mathematical community, see, for example, [2,7,11,13]. For many years, the proposed and commonly used reconstruction method was just the inverse Fourier transform.…”

Inverse problems of combined photoacoustic and optical coherence tomography

“…Clearly, they fulfil the continuity Eqn (12). For the motion of the particles, we assume that they move according to the Lorentz force:…”

“…Even though the mathematical modelling of optical coherence tomography based on Maxwell's equations is well established, most of the literature relies on simplified models of the Helmholtz equation [5][6][7][8][9], where, as a consequence, the frequency dependence of the susceptibility is neglected. It is a recent trend to consider the more general case of Maxwell's equations for the mathematical description of the optical coherence tomography (OCT) system [10][11][12][13].…”