Shower curtain effect and source imaging

. The shower curtain effect is commonly described as being able to see a person behind a shower curtain better than that person can see us. This asymmetric phenomenon has been observed in numerical simulations in various propagation models and in optics experiments. Here we present an analysis in the paraxial regime to give a novel characterization of the mechanism behind this effect and we discuss applications to imaging. The paraxial regime is for instance appropriate to model the propagation of a laser beam in a turbulent atmosphere. The theory that we present has also applications to tissue imaging. We consider two different measurement and imaging setups (matched field imaging and optical imaging) to clarify the shower curtain mechanism. We give a quantitative description of how the placement of the shower curtain, modeled as a randomly heterogeneous section, affects the optical imaging resolution. We moreover analyze the signal-to-noise ratio of the image. The analysis involves the study of multifrequency fourth-order moments associated with the Ito-Schro center dot dinger equation and reveals that broadband sources are necessary to ensure statistical stability and high signal-to-noise ratio.