Geometrical implications of the compound representation for weakly scattered amplitudes

It is known that a random walk model yields the multiplicative representation of a coherent scattered amplitude in terms of a complex Ornstein–Uhlenbeck process modulated by the square root of the cross-section. A corresponding biased random walk enables the derivation of the dynamics of a weak coherent scattered amplitude as a stochastic process in the complex plane. Strong and weak scattering patterns differ regarding the correlation structure of their radial and angular fluctuations. Investigating these geometric characteristics yields two distinct procedures to infer the scattering cross-section from the phase and intensity fluctuations of the scattered amplitude. These inference techniques generalize an earlier result demonstrated in the strong scattering case. Their significance for experimental applications, where the cross-section enables tracking of anomalies, is discussed.