This thesis examines the general task of active sensing by defining a measure of efficiency for sensing in a particular environment. We focus on fine-scale acoustic mapping from an autonomous underwater vehicle (AUV). The constraints on imaging underwater - vehicle power, vehicle hydrodynamics, computational and telemetry requirements, and typical navigational and attitudinal uncertainties along with the underlying physics of the acoustic sensing modality- are considered in defining an entropic measure of sensor efficiency. 675-kHz pencil-beam sonar data acquired using the JASON remotely operated vehicle in a challenging shallow water environment and 200-kHz echo-sounder data acquired using the ABE A UV are used to demonstrate the utility of the en tropic framework. We show the utility of an entropic framework for the following: (i) Optimizing the speed of the AUV for maximizing the information gathered with a particular sensor. (ii) the rate of convergence and the stability of our mapping efforts in the face of typical uncertainties in navigation and attitude; (iii) as a methodology for actual sensor deployment and use on a real vehicle; and (iv) in tasks such as post-mission analysis for applications such as change detection and path planning for subsequent missions.