Imaging through rough interfaces: The shower curtain effect

Abstract

The quality of an image observed through a scattering layer, such as a shower curtain, depends strongly on the relative position of the scattering layer between the object and the observer. This well-known phenomenon is commonly referred to as the shower curtain effect. When the scattering layer is placed close to the observer, the image is strongly degraded, whereas if it is located close to the object, the object may still be observed with relatively high resolution. Previous analyses of the shower curtain effect have primarily modeled the scattering layer as a section of a random medium. In this work, we present a new analysis in which the scattering layer is modeled instead as a rough interface, a description that arises naturally in many physical configurations. Within this framework, we derive explicit characterizations of both the image resolution and the signal-to-noise ratio, and determine how these quantities depend on the statistical properties of the rough interface and on its relative location between the object and the observer.