Optimal inference of the scattering cross-section through the phase decoherence

From a random walk model introduced by Jakeman, Field and Tough derived the stochastic dynamics accounting for the scattering of a wavelike field from a random medium, and showed how the scattering cross-section was observable through the fluctuations of the scattered field phase. In the context of K-scattering, we pursue this strategy by deriving an explicit analytical expression of the deviation between the exact (underlying) and the inferred (observed) cross-section. We then deduce a condition to optimize the inference. Simulation results assert the viability of our theoretical formulae. Their consequences are discussed.