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We present two algorithms for the efficient placement of sensors in a sensor field. The proposed approach is aimed at optimizing the number of sensors and determining their placement to support distributed sensor networks. The optimization framework is inherently probabilistic due to the uncertainty associated with sensor detections. The proposed algorithms address coverage optimization under the constraints of imprecise detections and terrain properties. These algorithms are targeted at average coverage as well as at maximizing the coverage of the most vulnerable grid points. The issue of preferential coverage of grid points (based on relative measures of security and tactical importance) is also modeled. Experimental results for an example sensor field with obstacles demonstrate the application of our approach.