The time-dependent one-dimensional photon transport (radiative transfer) equation is widely used to model light propagation through turbid media with a slab geometry, in a vast number of disciplines. Several numerical and semi-analytical techniques are available to accurately solve this equation. In this work we propose a novel efficient solution technique based on eigen decomposition of the vectorized version of the photon transport equation. Using clever transformations, the four variable integro-differential equation is reduced to a set of first order ordinary differential equations using a combination of a spectral method and the discrete ordinates method. An eigen decomposition approach is then utilized to obtain the closed-form solution of this reduced set of ordinary differential equations.
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