Consider a distributed sensor network (DSN) with randomly deployed sensors for binary detection of a phenomenon of interest (PoI). A data fusion center (which may be a sensor itself) monitors the PoI using both the directly acquired PoI data and the wireless communication signals conveying binary decisions about the PoI from other distributed sensors. To address this problem, we look into a PoI with specified statistics and present the modeling paradigm of Chernoff information azimuth spectrum (CIAS) to provide a compact, space-domain representation of asymptotic error exponents in DSNs. This school of thought applies an analogous approach to the description method of directional multipath channels. The above theoretical framework is then elaborated in light of geometrically-based modeling of sensor placement. Finally, we briefly explain the potential applications of the proposed methodology in terms of DSN performance evaluation, simulation and channel measurement.