The most prominent applications of wireless sensors networks are coverage, target detection and field surveillance. This paper investigates detection of a target traversing the region being monitored by some number of sensors using minimum exposure path. The authors derive minimum exposure path formula from Integral geometry. They represent the sensor field as connected grid of points. Then minimum exposure is calculated for different grids of points. They consider the random and deterministic placement of sensors. It illustrates that the target detection can be achieved by choosing the appropriate number of sensors and grid of points.